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Holland Tunnel

The Holland Tunnel is a vehicular tunnel under the Hudson River that connects Hudson Square and Lower Manhattan in New York City in the east to Jersey City, New Jersey in the west. The tunnel is operated by the Port Authority of New York and New Jersey and carries Interstate 78. The New Jersey side of the tunnel is the eastern terminus of New Jersey Route 139. The Holland Tunnel is one of three vehicular crossings between Manhattan and New Jersey; the two others are the Lincoln Tunnel and George Washington Bridge.

Plans for a fixed vehicular crossing over the Hudson River were first devised in 1906. However, disagreements prolonged the planning process until 1919, when it was decided to build a tunnel under the river. Construction of the Holland Tunnel started in 1920, and it opened in 1927. At the time of its opening, it was the longest continuous underwater tunnel for vehicular traffic in the world.

The Holland Tunnel was the world's first mechanically ventilated tunnel. Its ventilation system was designed by Ole Singstad, who oversaw the tunnel's completion. Original names considered for the tunnel included Hudson River Vehicular Tunnel and Canal Street Tunnel, but it was ultimately named the Holland Tunnel in memory of Clifford Milburn Holland, its initial chief engineer who died suddenly in 1924 prior to the tunnel's opening.

Description
The Holland Tunnel is operated by the Port Authority of New York and New Jersey. It consists of a pair of parallel tubes underneath the Hudson River. The tunnel was designed by Clifford Milburn Holland, the project's chief engineer, who died in October 1924, before it was completed. He was succeeded by Milton Harvey Freeman, who died less than a year after Holland did. Ole Singstad then oversaw the completion of the tunnel. The tunnel was designated a National Historic Civil and Mechanical Engineering Landmark in 1982 and a National Historic Landmark in 1993. Emergency services at the Holland Tunnel are provided by the Port Authority Police Department, who are stationed at the Port Authority's crossings.

Materials and dimensions
Each tube has a 29.5 ft diameter, and the two tubes run 15 ft apart under the Hudson River. The exteriors of each tube are composed of a series of cast iron rings, each of which comprises 14 curved steel pieces that are each 6 ft long. The steel rings are covered by a 19 in layer of concrete. Each tube provides a 20 ft roadway with two lanes and 12 ft of vertical clearance. The north tube is 8558 ft between portals, while the south tube is slightly shorter, at 8371 ft. If each tube's immediate approach roads are included, the north tube is 9,210 ft long and the south tube 9,275 ft long. Most vehicles carrying hazmats, trucks with more than three axles, and vehicles towing trailers cannot use the tunnel. There is a width limit of 8 ft for vehicles entering the tunnel.

Both tubes' underwater sections are 5410 ft long and are situated in the silt beneath the river. The lowest point of the roadways is about 93 ft below mean high water. The lowest point of the tunnel ceiling is about 72 ft below mean high water. The tubes descend at a maximum grade of 4.06% and ascend at a grade of up to 3.8%. The tubes stretch an additional 1000 ft from the eastern shoreline to the New York portals, and 500 ft from the western shoreline to the New Jersey portals. These sections of the tunnel are more rectangular in shape, since they were built as open cuts that were later covered over. The walls and ceiling are furnished with glazed ceramic tiles, which were originally engineered to minimize staining. The majority of the tiles are white, but there is a two-tile-high band of yellow-orange tiles at the bottom of each tube's walls, as well as two-tile-high band of blue tiles on the top.

The northern tube, which carries westbound traffic, originates at Broome Street in Lower Manhattan between Varick and Hudson Streets. It continues to 14th Street east of Marin Boulevard in Jersey City. The southern tube, designed for eastbound traffic, originates at 12th Street east of Marin Boulevard, and surfaces at the Holland Tunnel Rotary in Manhattan. The entrance and exit ramps to and from each portal are lined with granite and are 30 ft wide. Although the two tubes' underwater sections are parallel and adjacent to each other, the tubes' portals on either side are located two blocks apart in order to reduce congestion on each side.

The Holland Tunnel's tubes initially contained a road surface made of Belgian blocks and concrete. This was replaced with asphalt in 1955. Each tube contains a catwalk on its left (inner) side, raised 4 ft above the roadway. Five emergency-exit cross-passages connect the two tubes' inner catwalks. When the Holland Tunnel opened, the catwalk was equipped with police booths and a telephone system, stationed at intervals of 250 ft.

Traffic
The volume of traffic going through the Holland Tunnel has remained steady despite tight restrictions on eastbound traffic in response to the September 11 attacks, including a ban on commercial traffic entering New York City put in place after an August 2004 threat. Aside from a sharp decline immediately following the September 11 attacks, the number of vehicles using the Holland Tunnel in either direction daily steadily declined from a peak of 103,020 daily vehicles in 1999 to 89,792 vehicles in 2016. , the eastbound direction of the Holland Tunnel was used by 14,871,543 vehicles annually.

Ventilation
The Holland Tunnel was the first mechanically ventilated underwater vehicular tunnel in the world. It contains a system of vents that run transverse, or perpendicular, to the tubes. Each side of the Hudson River has two ventilation shaft buildings: one on land, and one in the river approximately 1000 ft from the respective shoreline. All of the ventilation buildings have buff brick facades with steel and reinforced-concrete frames.

The shafts within the river rise 107 ft above mean high water. Their supporting piers descend 45 ft, of which 40 ft are underwater and 5 ft are embedded in the riverbed. The river shafts double as emergency exits by way of shipping piers that connected each ventilation shaft to the shoreline. The New York Land Ventilation Tower, a five-story building with a trapezoidal footprint, is 122 ft tall. The New Jersey Land Ventilation Tower is a four-story, 84 ft building with a rectangular perimeter.

The four ventilation towers contain a combined 84 fans. Of these, 42 are intake fans with varying capacities from 84000 to 218000 ft3 per minute. The other 42 are exhaust fans, which can blow between 87500 and 227000 ft3 per minute. At the time of the tunnel's construction, two-thirds of the 84 fans were being used regularly, while the other fans were reserved for emergency use. The fans blow fresh air into ducts, which provide air intake to the tunnel via openings at the tubes' curbside. The ceiling contains slits, which are used to exhaust air. The fans can replace all of the air inside the tunnel every 90 seconds. A forced ventilation system is essential because of the poisonous carbon monoxide component of automobile exhaust, which constituted a far greater percentage of exhaust gases before catalytic converters became prevalent.

Boyle Plaza
The approach to the Holland Tunnel in Jersey City begins where the lower level of NJ Route 139 and the Newark Bay Extension merge. On May 6, 1936, the section of what became Route 139/I-78 between Jersey Avenue and Marin Boulevard was named in memory of John F. Boyle, the former interstate tunnel commissioner. Despite being part of the Interstate Highway System, I-78 and Route 139 run concurrently along 12th and 14th Street Streets to reach the Holland Tunnel. Westbound traffic uses 14th Street while eastbound traffic uses 12th Street. The plaza was restored and landscaped by the Jersey City government in 1982.

There is a nine-lane toll plaza for eastbound traffic only at the eastern end of 12th Street, just west of the tunnel portal. The original toll plaza had eight lanes; it was renovated in 1953–1954, and the current nine-lane tollbooth was constructed in 1988.

Holland Tunnel Rotary
Soon after construction of the tunnel, and amid rising vehicular traffic in the area, a railroad freight depot, St. John's Park Terminal, was abandoned and later demolished. The depot was located on the city block bounded by Laight, Varick, Beach, and Hudson Streets. The depot's site was used as a storage yard until the 1960s when it became a circular roadway for traffic exiting the eastbound tube in Manhattan.

The original structure had four exits, but the plaza was renovated in the early 2000s with landscaping by Studio V Architecture and Ives Architecture Studio. A fifth exit was added in 2004.

Freeman Plaza
Originally used as the toll plazas for New Jersey-bound traffic, the small triangular patches of land at the mouth of the westbound tube entrance are referred to as Freeman Plaza or Freeman Square. The plaza is named after Milton Freeman, the engineer who took over the Holland Tunnel project after the death of Clifford Milburn Holland. The Freeman Plaza received its name just before the tunnel opened in 1927. The toll plaza was removed circa 1971 when the Port Authority stopped collecting tolls for New Jersey-bound drivers, and the square was later fenced off by the Port Authority. The small maintenance buildings for toll collectors were removed around 1982 or 1983. A bust of Holland sits outside the entrance to the westbound tube in Freeman Plaza.

A business improvement district for the area, the Hudson Square Connection, was founded in 2009 with the goal of repurposing the square for pedestrian use. Hudson Square Connection and the Port Authority collaborated to create a five-year, $27 million master plan for Freeman Plaza. In 2013, Freeman Plaza West was opened to the public. Bounded by Hudson, Broome, and Watts Streets, it features umbrellas, bistro tables and chairs, and tree plantings.

In 2014, Freeman Plaza East and Freeman Plaza North were opened on Varick and Broome Streets, respectively. The plazas contained chaise longues, bistro tables, and umbrellas. In 2016, the Hudson Square Connection added solar powered charging stations to both plazas, and introduced a summer lunchtime music series, called live@lunch. A statue by the artist Isamu Noguchi was also installed within the plaza. To the south of Freeman Plaza, between Varick, Watts, and Canal Streets is One Hudson Square, a New York City designated landmark in 2013.

Need for vehicular tunnel
Until the first decade of the 20th century, passage across the lower Hudson River was possible only by ferry. The first tunnels to be bored below the Hudson River were for railroad use. The Hudson & Manhattan Railroad, now PATH, constructed two pairs of tubes to link the major railroad terminals in New Jersey with Manhattan Island: the Uptown Hudson Tubes, which opened in 1908, and the Downtown Hudson Tubes, which opened in 1909. The Pennsylvania Railroad's twin North River Tunnels, constructed to serve the new Pennsylvania Station, opened in 1910. The construction of these three tunnels proved that tunneling under the Hudson River was feasible. However, although train traffic was allowed to use the tunnel crossings, automotive traffic still had to be transported via ferry.

At the same time, freight traffic in the Port of New York and New Jersey was mostly carried on boats, but traffic had grown to such a point that the boats were at full capacity, and some freight started going to other ports in the United States. To alleviate this, officials proposed building a freight railroad tunnel, but this was blocked by the organized syndicates that held influence over much of the port's freight operations. The public learned of the excessive traffic loads on existing boat routes, as well as the limited capacity of the H&M and North River Tunnels, when the surface of the Hudson River froze in winter 1917, and again when Pennsylvania Railroad workers went on strike in winter 1918. One engineer suggested that three freight railroad tunnels would be cheaper to construct than one bridge.

Initial plans
In 1906, the New York and New Jersey Interstate Bridge Commission, a consortium of three groups, was formed to consider the need for a crossing across the Hudson River between New York City and New Jersey. That year, three railroads asked the commission to consider building a railroad bridge over the river. In 1908, the commission considered building three bridges across the Hudson River at 57th, 110th, and 179th Streets in Manhattan. The reasoning was that bridges would be cheaper than tunnels. These three locations were considered to be the only suitable locations for suspension bridges; other sites were rejected on the grounds of aesthetics, geography, or traffic flows. John Vipond Davies, one of the partners for the consulting firm Jacobs and Davies (which had constructed the Uptown Hudson Tubes), wanted to build a vehicular tunnel between Canal Street, Manhattan, and 13th Street, Jersey City. This proposal would compete with the six-lane suspension bridge at 57th Street. Some plans provided for the construction of both the bridge and the tunnel. The ferries could not accommodate all of the 19,600 vehicles per day, as of 1913, that traveled between New York and New Jersey. The Bridge Commission hosted several meetings to tell truck drivers about the details of both the 57th Street Bridge and Canal Street Tunnel plans.

The United States Department of War brought up concerns about the 57th Street bridge plans: the span would need to be at least 200 ft above the mean high water to avoid interfering with shipping. By comparison, the tunnel would be 95 ft below mean water level. The Interstate Bridge Commission, which had been renamed the New York State Bridge and Tunnel Commission in April 1913, published a report that same month, stating that the Canal Street tunnel would cost $11 million while the 57th Street bridge would cost $42 million. In October 1913, Jacobs and Davies stated that a pair of tunnels, with each tube carrying traffic in one direction, would cost only $11 million, while a bridge might cost over $50 million. The low elevation and deep bedrock of Lower Manhattan was more conducive to a tunnel than to a bridge. By the end of that year, the consulting engineers for both the 57th Street Bridge and the Canal Street Tunnel had submitted their plans to the Bridge and Tunnel Commission. New York City merchants mainly advocated for the tunnel plan, while New Jerseyans and New York automobile drivers mostly supported the bridge plan. Meanwhile, the New York State Bridge and Tunnel Commission indicated that it favored the Canal Street tunnel plan. On the other hand, the 57th Street bridge plan remained largely forgotten.

The Public Service Commission of New Jersey published a report in April 1917, stating that the construction of a Hudson River vehicle tunnel from Lower Manhattan to Jersey City was feasible. That June, following this report, Walter Evans Edge, then Governor of New Jersey, convened the Hudson River Bridge and Tunnel Commission of New Jersey, which would work with the New York Bridge and Tunnel Commission to construct the new tunnel. In March 1918, a report was sent to the New York State Legislature, advocating for the construction of the tunnel as soon as possible. That year, six million dollars in funding for the Hudson River Tunnel was proposed in two bills presented to subcommittees of the United States Senate and House of Representatives. The bill was voted down by the Interstate Commerce Committee before it could be presented to the full Senate.

Plans approved
The original plans for the Hudson River tunnel were for twin two-lane tubes, with each tube carrying traffic in a single direction. A request for proposals for the tunnel was announced in 1918, and eleven such requests were considered. One of these proposals, authored by engineer George Goethals, was for a bi-level tube. A modification of Jacobs and Davies' 1913 plan, the Goethals proposal specified that each level would carry three lanes of traffic, and that traffic on each level would run in a different direction. Goethals stated that his plan would cost $12 million and could be completed in three years. Subsequently, John F. O'Rourke offered to build the tunnel for $11.5 million. Goethals cited the area's freight traffic as one of the reasons for constructing the tube. His proposal would use a 42 ft diameter shield to dig the tunnel. This large tunnel size was seen as a potential problem, since there were differences in the air pressure at the top and the bottom of each tunnel, and that air pressure difference increased with a larger tunnel diameter. Five engineers were assigned to examine the feasibility of Goethals's design. In July 1919, President Woodrow Wilson ratified a Congressional joint resolution for a trans-Hudson tunnel, and Clifford Milburn Holland was named the project's chief engineer. Holland stated that, based on the construction methods used for both pair of tubes, including the downtown pair, it should be relatively easy to dig through the mud on the bottom of the Hudson River, and that construction should be completed within two years.

The federal government refused to finance the project, even in part, and so it fell to the states to raise the funds. In June 1919, U.S. Senator and former New Jersey governor Edge presented another iteration of the Hudson River Tunnel bill to the U.S. Senate, where it was approved. The New York and New Jersey governments signed a contract in September 1919, in which the states agreed to build, operate, and maintain the tunnel in partnership. The contract was signed by the states' respective tunnel commissions in January 1920.

Under Holland's plan, each of the two tubes would have an outside diameter of 29 ft including exterior linings, and the tubes would contain two-lane roadways with a total width of 20 ft. One lane would be for slower traffic, and the other would be for faster traffic. This contrasted with Goethals's plan, wherein the three roadways would have had a total width of 24.5 ft, only a few feet wider than Holland's two-lane roadways. Additionally, according to Holland, the 42-foot-wide tube would require the excavation of more dirt than both 29-foot tubes combined: two circles with 29-foot diameters would have a combined area of 5282.2 sqft, while a circle with a 42-foot diameter would have an area of 5541.8 sqft. The more northerly westbound tube would begin at Broome and Varick Streets on the Manhattan side and end at the now-demolished intersection of 14th and Provost Streets on the New Jersey side. The more southerly eastbound tube would begin at the still-intact intersection of 12th and Provost Streets in Jersey City, and end at the south side of Canal Street near Varick Street. By way of comparison, Goethals's plan would have combined the entrance and exit plazas on each side. The Motor Truck Association of America unsuccessfully advocated for three lanes in each tube.

Even though Goethals's method of digging had not been tested, he refused to concede to Holland's proposal, and demanded to see evidence that Holland's proposal would work. The New York and New Jersey Tunnel Commission subsequently rejected Goethals's plan in favor of a twin-tube proposal that Holland had devised, which was valued at around $28.7 million. When Goethals asked why, the commission responded that Goethals's proposal had never been tested; that it was too expensive; and that the tunnel plans had many engineering weaknesses that could cause the tube to flood. Additionally, while a tube with three lanes in each direction would be able to handle more traffic than a tube with two lanes, projections showed that traffic on the tunnel's approach roads could barely handle the amount of traffic going to and from the two-lane tubes, and that widening the approach roads on each side would cost millions of dollars more. The commission then voted to forbid any further consideration of Goethals's plan. Holland defended his own plan by pointing out that the roadways in Goethals's plan would not only feature narrower road lanes, but also would have ventilation ducts that were too small to ventilate the tube efficiently.

In May 1920, the New Jersey Legislature voted to approve the start of construction, overriding a veto from the New Jersey governor. The same month, the New York governor signed a similar bill that had been passed in the New York legislature. The legislature of New Jersey approved a $5 million bond issue for the tunnel in December 1920.

Construction
The first bid for constructing the Hudson River Tunnel, a contract for digging two of the tunnel's eight planned shafts, was advertised in September 1920. A groundbreaking for the Hudson River Tunnel's ventilation shaft, which marked the official start of construction on the tunnel, occurred on October 12, 1920, at Canal and Washington Streets on the Manhattan side. However, further construction of the Hudson River Tunnel was soon held up due to concerns over its ventilation system. There was also a dispute over whether the New York City government should pay for street-widening projects on the New Jersey side. Further delays arose when the New York and New Jersey tunnel commissions could not agree over which agency would award the contract to build the construction and ventilation shafts.

Ventilation system
The most significant design aspect of the Holland Tunnel is its ventilation system; it is served by four ventilation towers designed by Norwegian architect Erling Owre. At the time of its construction, underwater tunnels were a well-established part of civil engineering, but no long vehicular tunnels had been built, as all of the existing tunnels under New York City waterways carried only railroads and subways. These tubes did not have as much of a need for ventilation, since the trains that used the tubes were required to be electrically powered, and thus emitted very little pollution. On the other hand, the traffic in the Holland Tunnel consisted mostly of gasoline-driven vehicles, and ventilation was required to evacuate the carbon monoxide emissions, which would otherwise asphyxiate the drivers. There were very few tunnels at that time that were not used by rail traffic; the most notable of these non-rail tunnels, the Blackwall Tunnel and Rotherhithe Tunnel in London, did not need mechanical ventilation. However, a tunnel of the Hudson River Tunnel's length required an efficient method of ventilation, so Chief Engineer Singstad pioneered a system of ventilating the tunnel transversely (perpendicular to the tubes).

In October 1920, General George R. Dyer, the chairman of the New York Tunnel Commission, published a report in which he wrote that Singstad had devised a feasible ventilation system for the Hudson River Tunnel. Working with Yale University, the University of Illinois, and the United States Bureau of Mines, Singstad built a test tunnel in the bureau's experimental mine at Bruceton, Pennsylvania, measuring over 400 ft long, where cars were lined up with engines running. Volunteer students were supervised as they breathed the exhaust in order to confirm air flows and tolerable carbon monoxide levels by simulating different traffic conditions, including backups. The University of Illinois, which had hired the only professors of ventilation in the United States, built an experimental 300 ft ventilation duct at its Urbana campus to test air flows. In October 1921, Singstad concluded that a conventional, longitudinal ventilation system would have to be pressurized to an air flow rate of 27 m3/s along the tunnel. On the other hand, the tunnel could be adequately ventilated transversely if the compartment carrying the tube's roadway was placed in between two plenums. A lower plenum below the roadway floor could supply fresh air, and an upper plenum above the ceiling could exhaust fumes at regular intervals.

Two thousand tests were performed with the ventilation system prototype. The system was determined to be of sufficiently low cost, relative to the safety benefits, that it was ultimately integrated into the tunnel's design. By the time the tunnel was in service, the average carbon monoxide content in both tunnels was 0.69 parts per 10,000 parts of air. The highest recorded carbon monoxide level in the Holland Tunnel was 1.60 parts per 10,000, well below the permissible maximum of 4 parts per 10,000. The public and the press proclaimed air conditions were better in the tubes than in some streets of New York City; after the tunnel opened, Singstad stated that the carbon monoxide content in the tubes were half of those recorded on the streets.

Tunnel boring
The ventilation system and other potential issues had been resolved by December 1921, and officials announced that the tunnel would break ground the following spring. Builders initially considered building a trench at the bottom of the Hudson River and then covering it up, but this was deemed infeasible because of the soft soil that comprised the riverbed, as well as the heavy maritime traffic that used the river. Officials started purchasing the properties in the path of the tunnel's approaches, evicting and compensating the tenants "without delay" so that construction could commence promptly. A bid to construct the tubes was advertised, and three firms responded. On March 29, 1922, the contract to dig the tubes was awarded to the lowest bidder, Booth & Flinn Ltd., for $19.3 million. The materials that were necessary to furnish the Hudson River Tunnel had already been purchased, so it was decided to start work immediately. Construction on the bores began two days later as workers broke ground for an air compressor to drive the tubes. The ceremony for the air compressor was held at the corner of Canal Street and West Side Highway on the Manhattan side. The workers who were performing the excavations, who were referred to as "sandhogs", were to dig each pair of tubes from either bank of the Hudson River, so that the two sides would eventually connect somewhere underneath the riverbed. The tunnel was to be 9250 ft long between portals, and the roadway was to descend to a maximum depth of 93 ft below mean high water level.

The start of construction for the tubes from the New Jersey side was delayed because the Hudson River Vehicular Tunnel Commission had not yet acquired some of the land for the project. Although Jersey City officials had insisted that the Tunnel Commission widen 12th and 14th Streets in Jersey City, these officials were involved in a disagreement over sale prices with the Erie Railroad, which owned some of the land that was to be acquired for the street widening. As a result, work on the Hudson River Tunnel was delayed by one year and could not be completed before 1926 at the earliest. Work on the New Jersey side finally started on May 30, 1922, after Jersey City officials continued to refuse to cede public land for the construction of the tunnel's plazas. The Jersey City Chamber of Commerce wrote a letter that denounced this action, since the New Jersey Tunnel Commission's members on the Hudson River Tunnel Commission had not been notified of the groundbreaking until they read about it in the following day's newspapers. In mid-June, a state chancellor made permanent an injunction that banned Jersey City officials from trying to preclude construction on the Hudson River Tunnel. The Hudson River Tunnel Commission ultimately decided that Jersey City would not have its own groundbreaking celebration due to the city's various efforts at blocking the tunnel's construction. However, although Jersey City officials had been primarily accused of delaying construction, officials from both states had wanted the Tunnel Commission to widen the approach streets to the Hudson River Tunnel as part of the construction process.

For the project, six tunnel digging shields were to be delivered. These shields comprised cylinders whose diameters were wider than the tunnel bores, and these cylinders contained steel plates of various thicknesses on the face that was to be driven under the riverbed. Four of the shields would dig the Hudson River Tunnel under the river, while the remaining two shields would dig from the Hudson River west bank to the Jersey City portals. They could dig through rock at a rate of 2.5 ft per day, or through mud at a daily rate of 5 to 6 ft. The air compressors would provide an air pressure of 20 to 45 psi. The shovels used to dig the tunnel were provided by the Marion Power Shovel Company, while the six digging shields were built by the Merchants Shipbuilding Corporation. The air compressor was completed in September 1922, and the first shield was fitted into place in the Manhattan side's construction shaft. By this point, the shafts on the New Jersey side were being excavated, and two watertight caissons were being constructed.

The shield started boring in late October of that year after the steel plates that were necessary for the shield's operation had been delivered. The first permanent steel-rings lining the tubes were laid a short time afterward. The caissons were completed and launched into the river in December, and after the caissons were outfitted with the requisite equipment such as airlocks, tugboats dropped the caissons into place in January 1923. Officials projected that at this rate of progress, the tunnel would be finished within 36 months, by late 1926 or early 1927.

Tunnel construction required the sandhogs to spend large amounts of time in the caisson under high pressure of up to 47.5 psi, which was thought to be necessary to prevent river water from entering prior to completion of the tubes. The caissons were massive metal boxes with varying dimensions, but each contained 6 ft walls. Sandhogs entered the tunnel through a series of airlocks, and could only remain inside of the tunnel for a designated time period. On exiting the tunnel, sandhogs had to undergo controlled decompression to avoid decompression sickness or "the bends", a condition in which nitrogen bubbles form in the blood from rapid decompression. The rate of decompression for sandhogs working on the Hudson River Tunnel was described as being "so small as to be negligible". Sandhogs underwent such decompressions 756,000 times throughout the course of construction, which resulted in 528 cases of the bends, though none were fatal. The tunnel's pressurization caused other problems, including a pressure blowout in April 1924 that flooded the tube.

Due to the geology of the Hudson River, the shields digging from the New Jersey side were mostly being driven through mud, and so could be driven at a faster rate than the shields from the New York side, which were being dug through large rock formations. When workers tried to dig through the Manhattan shoreline, they had encountered several weeks of delay due to the existence of an as-yet-unrecorded granite bulkhead on the shoreline. In September 1923, after having proceeded about 1100 ft from the Manhattan shoreline, workers encountered a sheet of Manhattan schist under the riverbed, forcing them to slow shield digging operations from 12.5 ft/day to less than 1 ft/day. This outcropping was fed from a stream in Manhattan that emptied into the Hudson River. The sandhogs planned to use small explosive charges to dig through the rock shelf without damaging the shield. By December 1923, about 4400 ft of each tube's total length had been excavated, and the first of the shields had passed through the underwater shafts that had been sunk during construction. Due to these unexpected issues, the cost estimate for the tunnel was increased from $28 million to $42 million in January 1924. By March 1924, all seven of the ventilation shafts had been dug, and three of the four shields that were digging underwater had passed through their respective underwater construction shafts, with the fourth shield nearing its respective shaft.

Workers also performed tests to determine whether they could receive radio transmissions while inside the tunnel. They found that they were able to receive transmissions within much of the Hudson River Tunnel. However, a New Jersey radio station later found that there was a spot in the middle of the tunnel that had no reception.

The cost of the project increased as work progressed. In July 1923, the New York and New Jersey Vehicular Tunnel Commission had revised plans for the entrance and exit plazas on each side to accommodate an increase in traffic along Canal Street on the Manhattan side. The commission had spent $2.1 million to acquire land. Further redesigns were made in January 1924 due to a change of major components in the tunnel plan, including tunnel diameters and ventilation systems, which had increased the cost by another $14 million.

Nearing completion
The two ends of both tubes were scheduled to be connected to each other at a ceremony on October 29, 1924, in which President Calvin Coolidge would have remotely set off an explosion to connect the tunnel's two sides. However, two days before the ceremony, Holland died of a heart attack at the sanatorium in Battle Creek, Michigan, aged 41. Individuals cited in The New York Times attributed his death to the stress associated with overseeing the tunnel's construction. The ceremony was postponed out of respect for Holland's death.

The tunnel was ultimately holed through on October 29, but it was a nondescript event without any ceremony. On November 12, 1924, the Hudson River Vehicular Tunnel was renamed the Holland Tunnel by the two states' respective tunnel commissions. Holland was succeeded by Milton Harvey Freeman, who died of pneumonia in March 1925, after several months of overseeing the project. After Freeman's death, the position was occupied by Ole Singstad, who oversaw the tunnel's completion.

As part of the tunnel project, one block of Watts Street in Manhattan was widened to accommodate traffic heading toward the westbound tube. Sixth Avenue was also widened and extended between Greenwich Village and Church Street. Ten thousand people were evicted to make way for the Sixth Avenue extension. The north-south Church Street was widened and extended southward to Church Street and Trinity Place; West Side Highway was expanded and supplemented with an elevated highway; and the west-east Vestry and Laight Streets were also widened. On the New Jersey side, the Holland Tunnel was to connect a new highway (formerly the Route 1 Extension; now New Jersey Route 139), which extended westward to Newark. This included a 2100 ft viaduct, rising 80 ft from 12th and 14th Streets, at the bottom of the Palisades, to the new highway, at the top of the Palisades. The New Jersey highway approach was opened in stages beginning in 1927, and most of that highway was finished in 1930.

The construction of the tunnel approach roads on the New Jersey side was delayed for months by Erie Railroad, whose Bergen Arches right-of-way ran parallel to and directly south of Route 139, in the right of way of the proposed approach roads. Although the Erie had promised to find another site for its railroad yards, it had refused to respond to the plans that the New Jersey State Highway Commission had sent them. In March 1925, the Highway Commission decided that construction on the approach roads would begin regardless of Erie's response, and so the land would be taken using eminent domain. This led to a legal disagreement between the Erie and the Highway Commission. The Erie maintained that it absolutely needed 30 feet of land along 12th Street, while the Highway Commission stated that the most direct approach to the eastbound Holland Tunnel's 12th Street portal should be made using 12th Street. The commission rejected a suggestion that it should use 13th Street, one block north, because it would cost $500,000 more and involve two perpendicular turns. In October 1926, one million dollars was allocated to the completion of the Route 139 approach.

The contracts for constructing the Holland Tunnel's ventilation systems were awarded in December 1925. Two months later, the New York-New Jersey Vehicular Tunnel Commission asked for $3.2 million more in funding. The tunnel was now expected to cost $46 million, an increase of $17 million over what was originally budgeted. The Holland Tunnel was nearly complete: in March 1926, Singstad stated that the tunnel was expected to be opened by the following February. By May 1926, the tubes had been almost completely furnished: the polished-white tile walls were in place, as were the bright lighting systems and the Belgian-block-and-concrete road surfaces. The north tube's tiles were sourced locally by the Sonzogni Brothers of Union City, New Jersey, while the south tube's tiles were sourced in equal amounts from Czechoslovakia and Germany. The tiles' surfaces were specially engineered so that they could maintain their coloring even after years of use. The lighting systems used in the Holland Tunnel were designed to allow motorists to adjust to a gradual change in lighting levels just before leaving the tubes.

The ventilation towers were the only major component of the Holland Tunnel that was not completed, but major progress had been made by the end of 1926. Ole Singstad and the two states' tunnel commissions tested the tunnel's ventilation system by releasing gas clouds in one of the tubes in February 1927. Singstad subsequently declared that the ventilation system was well equipped to ventilate the tunnel air. However, the New York Board of Trade and Transportation disagreed, stating that the system would be inadequate if there was a genuine incident within the tunnel. In April 1927, the board had conducted their own tests with two lighted candles, and a cloud of smoke had filled the entire tube before the ventilation system was able to perform a full exhaust. The Chief Surgeon of the U.S. Board of Mines supported Singstad's position that the ventilation system could sufficiently filter the tubes' air. To affirm the ventilation system's efficacy, in November 1927, the New York and New Jersey tunnel commissions burned a car within the tunnel; the ventilation system dissipated the fire within three and a half minutes.

The governors of New York and New Jersey took ceremonial rides through the tunnel in August 1926, meeting at the tunnel's midpoint. The first unofficial drive through the entirety of the Holland Tunnel was undertaken by a group of British businessmen a year later, in August 1927. The next month, a group from the Buffalo and Niagara Frontier Port Authority Survey Commission also visited the tunnel. In October, a delegation of representatives from Detroit, Michigan, and Windsor, Ontario, toured the nearly complete Holland Tunnel to get ideas for the then-proposed Detroit–Windsor Tunnel. A reporter for The New York Times was able to make a test drive through the tunnel, noting that "there is no sudden pressure of wind upon the ear-drums" and that it would reduce the duration of crossing the Hudson River by between 15 and 22 minutes. Three hundred police officers were trained in advance of the Holland Tunnel's opening, and bus companies started receiving franchises to operate buses through the tunnel.

Opening
The Holland Tunnel was officially opened at 4:55 p.m. EST on November 12, 1927. President Coolidge ceremonially opened the tunnel from his yacht by turning the same key that had opened the Panama Canal in 1915. Time magazine reported that Coolidge had used "the golden lever of the Presidential telegraphic instrument." It rang a giant brass bell at the tunnel's entrances that triggered American flags on both sides of the tunnel to separate. The tunnel's opening ceremony was broadcast on local radio stations. Approximately 20,000 people walked the entire length of the Holland Tunnel before it was closed to pedestrians at 7 p.m. The Holland Tunnel officially opened to vehicular traffic at 12:01 a.m. on November 13, the next day; over a thousand vehicles had gathered on the New Jersey side, ready to pay a toll. The first car to pay a toll was driven by the daughter of the chairman of New Jersey's Bridge and Tunnel Commission. The widows of chief engineers Holland and Freeman rode in the second vehicle that paid a toll. At the time, the Holland Tunnel was the world's longest continuous underwater vehicular tunnel, as well as the world's first tunnel designed specifically for vehicular traffic.

Each passenger car paid a 50-cent toll (worth about $ in ). Tolls for other vehicular classes ranged from 25 cents for a motorcycle to two dollars for large trucks. Commuter bus routes, which paid a 50-cent-per-vehicle toll, began operating through the tunnel in December 1927. Truckers subsequently objected that these rates were too high, as the Holland Tunnel truck tolls were double the tolls that were charged on the trans-Hudson ferries; by contrast, the tunnel's passenger vehicle, motorcycle, and bus tolls were on par with those charged by the ferries. The toll revenues would be used to pay off the tunnel's cost (which was estimated at $48 million in 1927 dollars, $ in  dollars). Within ten years of opening, it was expected that all construction costs would be paid off. Horsedrawn vehicles were banned from the tunnel from the start, since it was believed that horses' slow speeds would cause traffic congestion in the tubes. Pedestrian and bicycle traffic was also banned. A few months before the tunnel's opening, there were suggestions that pedestrians would be allowed to cross the tunnel if they paid a toll described as "not encouraging," but the idea was never seriously considered.

The Holland Tunnel was expected to relieve congestion on the vehicular ferries across the Hudson River, since the capacity of the tunnel was similar to that of the vehicular ferries. Upon opening, it had been estimated that up to 15 million vehicles per year could use the tunnel in both directions, equating to a maximum daily capacity of 46,000 vehicles or an hourly capacity of 3,800 vehicles. Singstad stated that increasing freight traffic across the river would result in a corresponding increase in truck traffic, which would then cause the tunnel to reach its maximum traffic capacity shortly after its opening.

The Holland Tunnel was immediately popular. On November 13, a Sunday, 52,285 vehicles passed through the tunnel on its first day of operation, more than its projected maximum capacity. The lines to enter the tunnel stretched for miles on either end, although many of these vehicles were passenger cars who were making a round trip to tour the tunnel. On November 14, the Holland Tunnel's first weekday of operation, the tunnel carried 17,726 cars. Traffic counts in the Holland Tunnel remained relatively steady until the following weekend, when over 40,000 vehicles went through the tunnel. The first holiday rush period for the Holland Tunnel occurred two weeks after the tunnel's opening, when around 30,000 motorists used the tunnel over the Thanksgiving holiday; there were no major traffic disruptions. A half-million vehicles had passed through the Holland Tunnel within three weeks, and a million had used the tubes by New Year's Day. Within the tunnel's first year, 8.5 million vehicles had used it, and the toll revenue had grossed $4.7 million in profit; it was estimated that at this rate, the Holland Tunnel's construction costs might be paid off sooner than expected.

Trans-Hudson ferries reported that their traffic counts had been halved in the two weeks since the tunnel opened, and at least one ferry route reduced service within one month of the opening. Another ferry cut its toll rates to half those of the Holland Tunnel in an effort to recover business. The Hudson & Manhattan Railroad (later PATH), which operated rapid transit services across the Hudson River through its Uptown and Downtown Hudson Tubes, also saw a decline in ridership after the Holland Tunnel opened. Even after the start of the Great Depression in 1929, when most transit in New York City saw declines, the Holland Tunnel saw an increase in traffic, as did ferry lines.

Early years
In 1930, there was a disagreement between the Hudson River Tunnel Commission and the Port of New York Authority over who would construct the Lincoln Tunnel. The tunnel was to be located further north along the Hudson River, connecting nearby Weehawken to Manhattan. The two agencies merged that April, and the expanded Port Authority of New York and New Jersey took over operations of the Holland Tunnel, a role that it maintains to this day. Real property title was not passed however. A second vehicular link between New Jersey and Manhattan, the George Washington Bridge, opened in October 1931. The Lincoln Tunnel, the third and final vehicular connection between New Jersey and Manhattan, first opened in December 1937. Within the first 25 years of the Holland Tunnel's opening, it had carried 330 million vehicles in total, but a significant portion of Holland Tunnel traffic was diverted to the Lincoln Tunnel and George Washington Bridge after the opening of the latter two crossings.

In 1945, the Port Authority approved the extension of a tunnel approach on the New Jersey side. A new viaduct for westbound traffic would connect the intersection of 14th Street and Jersey Avenue, outside the Holland Tunnel's exit portal, to Hoboken Avenue and NJ Route 139, on top of The Palisades. This would supplement an existing bidirectional viaduct, which connected Hoboken Avenue with 12th Street and currently only carries eastbound traffic. The 14th Street viaduct was first opened for vehicular use in January 1951, although the road was not complete; it was officially completed that February. The 12th and 14th Street viaducts were later also connected to the New Jersey Turnpike Extension. The first part of the extension, Newark Bay Bridge, opened between Bayonne and Newark Liberty International Airport in April 1956; the connection between Bayonne and the 12th/14th Street viaducts was completed that September, providing direct highway connection between the Holland Tunnel and Newark Airport. The NJ Turnpike Extension, as well as the Holland Tunnel and the 12th/14th Street approaches, was designated as part of I-78 in 1958.

Starting in the 1940s, New York City officials developed plans to connect the Holland Tunnel's Manhattan end to the Lower Manhattan Expressway, a proposed elevated highway connecting to both the Williamsburg Bridge and the Manhattan Bridge to Brooklyn. This connection would be part of I-78. In 1956, Robert Moses suggested adding a third tube to the Holland Tunnel, similar to the Lincoln Tunnel's third tube, so there would be sufficient capacity for the proposed expressway traffic. The route of the Lower Manhattan Expressway was approved in 1960, but quickly became controversial due to the large number of tenants who would have to be relocated. The Lower Manhattan Expressway project was ultimately canceled in March 1971.

The Port Authority voted in 1953 to replace the original tollbooths on the New Jersey side, which did not contain canopies, with an updated plaza that contained a canopy. The next year, the Port Authority also voted to refurbish the Holland Tunnel's administration building on the New Jersey side, as well as construct a new service building. The development of a 2 ft one-man miniature electric car for tunnel police, to be installed on the tubes' catwalks, was announced in August 1954. The Port Authority tested the "catwalk car" along a 2200 ft stretch of the Holland Tunnel. After the car had passed its test, policemen could patrol the full length of the tubes using the catwalk car instead of having to walk the tubes' entire length. By use of a swivel seat the policemen could drive the car in either direction.

Late 20th century
In 1970, the Port Authority stopped collecting tolls for New Jersey-bound drivers through the Holland Tunnel, who used the westbound tube, while doubling tolls to $1 for New York City-bound drivers, who used the eastbound tube. This was done in an effort to speed up traffic, and it was the first toll increase in the tunnel's history. Although westbound drivers initially saved time by not paying tolls, the removal of westbound tolls ultimately had an adverse effect on traffic in the Holland Tunnel. In 1986, the Verrazzano-Narrows Bridge, between the New York City boroughs of Brooklyn and Staten Island, stopped collecting tolls for Brooklyn-bound drivers (who were generally headed eastbound) and doubled its tolls for Staten Island-bound drivers (who were generally headed westbound). This had the effect of increasing congestion along the New Jersey-bound tube of the Holland Tunnel, which drivers could use for free. Drivers would go through New Jersey and use the Bayonne Bridge, paying a lower toll to enter Staten Island. The amount of westbound traffic in the Holland Tunnel increased compared to eastbound traffic: by 1998, there were 50,110 daily westbound trips and 46,688 daily eastbound trips through the tunnel. Simultaneously, there was a decrease in westbound trips on the Verrazzano-Narrows Bridge compared to eastbound trips on the bridge. The Verrazzano-Narrows Bridge toll pattern also caused traffic gridlock around the Holland Tunnel, and Canal Street saw the most severe congestion because it served as the main entrance to the tunnel. Fatal accidents involving pedestrians in Lower Manhattan also increased greatly as a result. Rush-hour congestion within the Holland Tunnel has persisted for more than thirty years due to the Verrazzano-Narrows Bridge's one-way westbound toll.

A renovation of the Holland Tunnel's tiled ceilings, which were deteriorating due to water damage, started in 1983. The ceilings were replaced at a total cost of $78 million, and the south tube's ceiling was renovated first. Since the Holland Tunnel had to remain open during the renovation, 4,000 modular concrete ceiling panels were made offsite, and narrow lift trucks parked in one of the tube's two lanes installed the panels while traffic continued to move through the tube's other lane. The panels were each designed to the specifications of a certain section of tube, such that none of the ceiling panels were identical; the Port Authority stated that the ceiling-replacement project was the first one of its kind in the world. In 1988, after the ceiling renovations had been completed, work started on replacing the 8-lane tollbooth, which consisted of six lanes built in the 1950s and two additional lanes built in the 1980s. The new $54 million tollbooth contained 9 lanes and a central control center.

The Holland Tunnel was listed as a National Historic Landmark on June 27, 1993, becoming part of the National Register of Historic Places. With this designation, it became the 92nd National Historic Landmark in New York City and the sixth such landmark nationally that was a tunnel. According to M. Ann Belkov, the National Park Service superintendent for Ellis Island, the tunnel had been granted landmark status because it had been the first "mechanically ventilated underwater vehicular tunnel" in the world.

21st century
Between 2003 and 2006, the fire protection system in both tunnels was modernized. Fire extinguishers were placed in alcoves along the tunnel walls. Although the water supply was turned off, it remained in place during the renovation.

The Holland Tunnel was closed on October 29, 2012, as Hurricane Sandy approached. The tunnel, like many other New York City tunnels, was flooded by the high storm surge. It remained closed for several days, opening for buses only on November 2 and to all traffic on November 7. In February 2018, the PANYNJ approved a $364 million project to repair flood damage from the hurricane. The agency closed the Holland Tunnel's eastbound tube during late nights, except on Saturday nights, beginning in April 2020. Though the work was initially supposed to be completed in early 2022, the work was delayed by nearly a year. The PANYNJ then announced that the westbound tube would be closed during late nights, except on Saturdays, between February 2023 and late 2025.

Accidents and terrorism
The first fatal vehicular crash in the Holland Tunnel happened in March 1932, four and a half years after it opened. One person died and two others were injured.

The 1949 Holland Tunnel fire, which started aboard a chemical truck, caused severe damage to the south tube of the tunnel. The fire resulted in 69 injuries and nearly $600,000 worth of damage to the structure. In addition, two first responders, a FDNY battalion chief and a Port Authority patrolman, died as a result of injuries sustained in fighting the fire.

Due to its status as one of the few connections between Manhattan and New Jersey, the Holland Tunnel is considered to be one of the most high-risk terrorist target sites in the United States. Other such sites in New Jersey include the Lincoln Tunnel in Weehawken, New Jersey, the PATH station at Exchange Place in Jersey City, and the Port of Newark in Elizabeth.

In 1995, Sheik Omar Abdel Rahman and nine other men were convicted of a bombing plot in which a radical Islamic group plotted to blow up five or six sites in New York City, including the Holland and Lincoln Tunnels and the George Washington Bridge.

In 2006, a plot to detonate explosives in a Hudson River tunnel was uncovered by the Federal Bureau of Investigation. It was originally reported that the Holland Tunnel was the target, but in a later update of the source, the plot was clarified to be aimed at the PATH's tubes instead of the Holland Tunnel.

September 11 attacks
Following the September 11 attacks on the World Trade Center, the Holland Tunnel remained closed to all but emergency traffic for over a month, due to its proximity to the World Trade Center site. When the tunnel reopened on October 15, 2001, strict new regulations were enacted, and single-occupancy vehicles and trucks were banned from entering the tunnel. In March 2002, before all of the post-9/11 restrictions were lifted, a warehouse fire near the eastbound tube's New Jersey portal caused the tunnel to be closed entirely for five days; the fire continued for over a week. That April, all trucks were banned from the westbound tube, and trucks with more than three axles were also banned from the eastbound tube. Single-occupant vehicles were prohibited in the tunnel on weekday mornings between 6:00 am and 10:00 am until November 17, 2003, when the restrictions were lifted.

Tolls
, the tolls-by-mail rate going from New Jersey to New York City are $17.63 for cars and motorcycles; there is no toll for passenger vehicles going from New York City to New Jersey. New Jersey and New York–issued E-ZPass users are charged $13.38 for cars and $12.38 for motorcycles during off-peak hours, and $15.38 for cars and $14.38 for motorcycles during peak hours. Users with E-ZPass issued from agencies outside of New Jersey and New York are charged the tolls-by-mail rate.

Tolls are collected at a tollbooth on the New Jersey side. Originally, tolls were collected in both directions. In August 1970, the toll was abolished for westbound drivers, and at the same time, eastbound drivers saw their tolls doubled. The tolls of eleven other New York City to New Jersey and Hudson River crossings along a 130 mi stretch, from the Outerbridge Crossing in the south to the Rip Van Winkle Bridge in the north, were also changed to south- or eastbound-only at that time. E-ZPass was first made available at the Holland Tunnel in October 1997.

In March 2020, due to the COVID-19 pandemic, all-electronic tolling was temporarily placed in effect for all Port Authority crossings, including the Holland Tunnel. Open road tolling began on December 23, 2020. The tollbooths were dismantled, and drivers were no longer able to pay cash at the tunnel. Instead, there will be cameras mounted onto new overhead gantries at the New Jersey side going to New York City. A vehicle without E-ZPass will have a picture taken of its license plate and a bill for the toll will be mailed to its owner. For E-ZPass users, sensors will detect their transponders wirelessly. The carpool discount plan was eliminated because the discount required a manual count of passengers.

Congestion toll
Congestion pricing in New York City is indefinitely postponed ; if congestion pricing is implemented, drivers who enter Manhattan via the tunnel would pay a second toll. The congestion charges are planned to be collected via E-ZPass and tolls-by-mail. The charges are planned to vary based on time of day and vehicle class, but the congestion toll is expected to be charged once per day. Drivers who use the Holland Tunnel to enter the congestion zone will receive a credit toward the congestion charge during the day, and they would pay a discounted toll at night.

title: Holland Tunnel


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Simulated annealing

Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. For large numbers of local optima, SA can find the global optima. It is often used when the search space is discrete (for example the traveling salesman problem, the boolean satisfiability problem, protein structure prediction, and job-shop scheduling). For problems where finding an approximate global optimum is more important than finding a precise local optimum in a fixed amount of time, simulated annealing may be preferable to exact algorithms such as gradient descent or branch and bound.

The name of the algorithm comes from annealing in metallurgy, a technique involving heating and controlled cooling of a material to alter its physical properties. Both are attributes of the material that depend on their thermodynamic free energy. Heating and cooling the material affects both the temperature and the thermodynamic free energy or Gibbs energy. Simulated annealing can be used for very hard computational optimization problems where exact algorithms fail; even though it usually achieves an approximate solution to the global minimum, it could be enough for many practical problems.

The problems solved by SA are currently formulated by an objective function of many variables, subject to several mathematical constraints. In practice, the constraint can be penalized as part of the objective function.

Similar techniques have been independently introduced on several occasions, including Pincus (1970), Khachaturyan et al (1979, 1981 ), Kirkpatrick, Gelatt and Vecchi (1983), and Cerny (1985). In 1983, this approach was used by Kirkpatrick, Gelatt Jr., Vecchi, for a solution of the traveling salesman problem. They also proposed its current name, simulated annealing.

This notion of slow cooling implemented in the simulated annealing algorithm is interpreted as a slow decrease in the probability of accepting worse solutions as the solution space is explored. Accepting worse solutions allows for a more extensive search for the global optimal solution. In general, simulated annealing algorithms work as follows. The temperature progressively decreases from an initial positive value to zero. At each time step, the algorithm randomly selects a solution close to the current one, measures its quality, and moves to it according to the temperature-dependent probabilities of selecting better or worse solutions, which during the search respectively remain at 1 (or positive) and decrease toward zero.

The simulation can be performed either by a solution of kinetic equations for probability density functions, or by using a stochastic sampling method. The method is an adaptation of the Metropolis–Hastings algorithm, a Monte Carlo method to generate sample states of a thermodynamic system, published by N. Metropolis et al. in 1953.

Overview
The state s of some physical systems, and the function E(s) to be minimized, is analogous to the internal energy of the system in that state. The goal is to bring the system, from an arbitrary initial state, to a state with the minimum possible energy.

The basic iteration
At each step, the simulated annealing heuristic considers some neighboring state s* of the current state s, and probabilistically decides between moving the system to state s* or staying in state s. These probabilities ultimately lead the system to move to states of lower energy. Typically this step is repeated until the system reaches a state that is good enough for the application, or until a given computation budget has been exhausted.

The neighbors of a state
Optimization of a solution involves evaluating the neighbors of a state of the problem, which are new states produced through conservatively altering a given state. For example, in the traveling salesman problem each state is typically defined as a permutation of the cities to be visited, and the neighbors of any state are the set of permutations produced by swapping any two of these cities. The well-defined way in which the states are altered to produce neighboring states is called a "move", and different moves give different sets of neighboring states. These moves usually result in minimal alterations of the last state, in an attempt to progressively improve the solution through iteratively improving its parts (such as the city connections in the traveling salesman problem).

Simple heuristics like hill climbing, which move by finding better neighbor after better neighbor and stop when they have reached a solution which has no neighbors that are better solutions, cannot guarantee to lead to any of the existing better solutions – their outcome may easily be just a local optimum, while the actual best solution would be a global optimum that could be different. Metaheuristics use the neighbors of a solution as a way to explore the solution space, and although they prefer better neighbors, they also accept worse neighbors in order to avoid getting stuck in local optima; they can find the global optimum if run for a long enough amount of time.

Acceptance probabilities
The probability of making the transition from the current state $$s$$ to a candidate new state $$s_\mathrm{new}$$ is specified by an acceptance probability function $$P(e, e_\mathrm{new}, T)$$, that depends on the energies $$e = E(s)$$ and $$e_\mathrm{new}= E(s_\mathrm{new})$$ of the two states, and on a global time-varying parameter $$T$$ called the temperature. States with a smaller energy are better than those with a greater energy. The probability function $$P$$ must be positive even when $$e_\mathrm{new}$$ is greater than $$e$$. This feature prevents the method from becoming stuck at a local minimum that is worse than the global one.

When $$T$$ tends to zero, the probability $$P(e, e_\mathrm{new}, T)$$ must tend to zero if $$e_\mathrm{new} > e$$ and to a positive value otherwise. For sufficiently small values of $$T$$, the system will then increasingly favor moves that go "downhill" (i.e., to lower energy values), and avoid those that go "uphill." With $$T=0$$ the procedure reduces to the greedy algorithm, which makes only the downhill transitions.

In the original description of simulated annealing, the probability $$P(e, e_\mathrm{new}, T)$$ was equal to 1 when $$e_\mathrm{new} < e$$—i.e., the procedure always moved downhill when it found a way to do so, irrespective of the temperature. Many descriptions and implementations of simulated annealing still take this condition as part of the method's definition. However, this condition is not essential for the method to work.

The $$P$$ function is usually chosen so that the probability of accepting a move decreases when the difference $$e_\mathrm{new}-e$$ increases—that is, small uphill moves are more likely than large ones. However, this requirement is not strictly necessary, provided that the above requirements are met.

Given these properties, the temperature $$T$$ plays a crucial role in controlling the evolution of the state $$s$$ of the system with regard to its sensitivity to the variations of system energies. To be precise, for a large $$T$$, the evolution of $$s$$ is sensitive to coarser energy variations, while it is sensitive to finer energy variations when $$T$$ is small.

The annealing schedule
The name and inspiration of the algorithm demand an interesting feature related to the temperature variation to be embedded in the operational characteristics of the algorithm. This necessitates a gradual reduction of the temperature as the simulation proceeds. The algorithm starts initially with $$T$$ set to a high value (or infinity), and then it is decreased at each step following some annealing schedule—which may be specified by the user but must end with $$T=0$$ towards the end of the allotted time budget. In this way, the system is expected to wander initially towards a broad region of the search space containing good solutions, ignoring small features of the energy function; then drift towards low-energy regions that become narrower and narrower, and finally move downhill according to the steepest descent heuristic.

For any given finite problem, the probability that the simulated annealing algorithm terminates with a global optimal solution approaches 1 as the annealing schedule is extended. This theoretical result, however, is not particularly helpful, since the time required to ensure a significant probability of success will usually exceed the time required for a complete search of the solution space.

Pseudocode
The following pseudocode presents the simulated annealing heuristic as described above. It starts from a state $s_{0}$ and continues until a maximum of $k_{max}$ steps have been taken. In the process, the call $neighbour(s)$ should generate a randomly chosen neighbour of a given state $s$; the call $random(0, 1)$ should pick and return a value in the range $[0, 1]$, uniformly at random. The annealing schedule is defined by the call $temperature(r)$, which should yield the temperature to use, given the fraction $r$ of the time budget that has been expended so far.

 * Let $s = s_{0}$
 * For $k = 0$ through $k_{max}$ (exclusive):
 * Pick a random neighbour, $T ← temperature( 1 - (k+1)/k_{max} )$
 * If $s_{new} ← neighbour(s)$:
 * Output: the final state $s$
 * Output: the final state ⇭⇭⇭
 * Output: the final state ⇭⇭⇭

Selecting the parameters
In order to apply the simulated annealing method to a specific problem, one must specify the following parameters: the state space, the energy (goal) function E, the candidate generator procedure neighbor, the acceptance probability function P, and the annealing schedule temperature AND initial temperature init_temp. These choices can have a significant impact on the method's effectiveness. Unfortunately, there are no choices of these parameters that will be good for all problems, and there is no general way to find the best choices for a given problem. The following sections give some general guidelines.

Sufficiently near neighbour
Simulated annealing may be modeled as a random walk on a search graph, whose vertices are all possible states, and whose edges are the candidate moves. An essential requirement for the neighbor function is that it must provide a sufficiently short path on this graph from the initial state to any state which may be the global optimum – the diameter of the search graph must be small. In the traveling salesman example above, for instance, the search space for n = 20 cities has n! = 2,432,902,008,176,640,000 (2.4 quintillion) states; yet the number of neighbors of each vertex is $$\sum_{k=1}^{n-1} k=\frac{n(n-1)}{2}=190$$ edges (coming from n choose 20), and the diameter of the graph is $$n-1$$.

Transition probabilities
To investigate the behavior of simulated annealing on a particular problem, it can be useful to consider the transition probabilities that result from the various design choices made in the implementation of the algorithm. For each edge $$(s,s')$$ of the search graph, the transition probability is defined as the probability that the simulated annealing algorithm will move to state $$s'$$ when its current state is $$s$$. This probability depends on the current temperature as specified by temperature, on the order in which the candidate moves are generated by the neighbor function, and on the acceptance probability function P. (Note that the transition probability is not simply $$P(e, e', T)$$, because the candidates are tested serially.)

Acceptance probabilities
The specification of neighbour, P, and temperature is partially redundant. In practice, it's common to use the same acceptance function P for many problems and adjust the other two functions according to the specific problem.

In the formulation of the method by Kirkpatrick et al., the acceptance probability function $$P(e, e', T)$$ was defined as 1 if $$e' < e$$, and $$\exp(-(e'-e)/T)$$ otherwise. This formula was superficially justified by analogy with the transitions of a physical system; it corresponds to the Metropolis–Hastings algorithm, in the case where T=1 and the proposal distribution of Metropolis–Hastings is symmetric. However, this acceptance probability is often used for simulated annealing even when the neighbor function, which is analogous to the proposal distribution in Metropolis–Hastings, is not symmetric, or not probabilistic at all. As a result, the transition probabilities of the simulated annealing algorithm do not correspond to the transitions of the analogous physical system, and the long-term distribution of states at a constant temperature $$T$$ need not bear any resemblance to the thermodynamic equilibrium distribution over states of that physical system, at any temperature. Nevertheless, most descriptions of simulated annealing assume the original acceptance function, which is probably hard-coded in many implementations of SA.

In 1990, Moscato and Fontanari, and independently Dueck and Scheuer, proposed that a deterministic update (i.e. one that is not based on the probabilistic acceptance rule) could speed-up the optimization process without impacting on the final quality. Moscato and Fontanari conclude from observing the analogous of the "specific heat" curve of the "threshold updating" annealing originating from their study that "the stochasticity of the Metropolis updating in the simulated annealing algorithm does not play a major role in the search of near-optimal minima". Instead, they proposed that "the smoothening of the cost function landscape at high temperature and the gradual definition of the minima during the cooling process are the fundamental ingredients for the success of simulated annealing." The method subsequently popularized under the denomination of "threshold accepting" due to Dueck and Scheuer's denomination. In 2001, Franz, Hoffmann and Salamon showed that the deterministic update strategy is indeed the optimal one within the large class of algorithms that simulate a random walk on the cost/energy landscape.

Efficient candidate generation
When choosing the candidate generator neighbor, one must consider that after a few iterations of the simulated annealing algorithm, the current state is expected to have much lower energy than a random state. Therefore, as a general rule, one should skew the generator towards candidate moves where the energy of the destination state $$s'$$ is likely to be similar to that of the current state. This heuristic (which is the main principle of the Metropolis–Hastings algorithm) tends to exclude very good candidate moves as well as very bad ones; however, the former are usually much less common than the latter, so the heuristic is generally quite effective.

In the traveling salesman problem above, for example, swapping two consecutive cities in a low-energy tour is expected to have a modest effect on its energy (length); whereas swapping two arbitrary cities is far more likely to increase its length than to decrease it. Thus, the consecutive-swap neighbor generator is expected to perform better than the arbitrary-swap one, even though the latter could provide a somewhat shorter path to the optimum (with $$n-1$$ swaps, instead of $$n(n-1)/2$$).

A more precise statement of the heuristic is that one should try the first candidate states $$s'$$ for which $$P(E(s), E(s'), T)$$ is large. For the "standard" acceptance function $$P$$ above, it means that $$E(s') - E(s)$$ is on the order of $$T$$ or less. Thus, in the traveling salesman example above, one could use a neighbor function that swaps two random cities, where the probability of choosing a city-pair vanishes as their distance increases beyond $$T$$.

Barrier avoidance
When choosing the candidate generator neighbor one must also try to reduce the number of "deep" local minima—states (or sets of connected states) that have much lower energy than all its neighboring states. Such "closed catchment basins" of the energy function may trap the simulated annealing algorithm with high probability (roughly proportional to the number of states in the basin) and for a very long time (roughly exponential on the energy difference between the surrounding states and the bottom of the basin).

As a rule, it is impossible to design a candidate generator that will satisfy this goal and also prioritize candidates with similar energy. On the other hand, one can often vastly improve the efficiency of simulated annealing by relatively simple changes to the generator. In the traveling salesman problem, for instance, it is not hard to exhibit two tours $$A$$, $$B$$, with nearly equal lengths, such that (1) $$A$$ is optimal, (2) every sequence of city-pair swaps that converts $$A$$ to $$B$$ goes through tours that are much longer than both, and (3) $$A$$ can be transformed into $$B$$ by flipping (reversing the order of) a set of consecutive cities. In this example, $$A$$ and $$B$$ lie in different "deep basins" if the generator performs only random pair-swaps; but they will be in the same basin if the generator performs random segment-flips.

Cooling schedule
The physical analogy that is used to justify simulated annealing assumes that the cooling rate is low enough for the probability distribution of the current state to be near thermodynamic equilibrium at all times. Unfortunately, the relaxation time—the time one must wait for the equilibrium to be restored after a change in temperature—strongly depends on the "topography" of the energy function and on the current temperature. In the simulated annealing algorithm, the relaxation time also depends on the candidate generator, in a very complicated way. Note that all these parameters are usually provided as black box functions to the simulated annealing algorithm. Therefore, the ideal cooling rate cannot be determined beforehand and should be empirically adjusted for each problem. Adaptive simulated annealing algorithms address this problem by connecting the cooling schedule to the search progress. Other adaptive approaches such as Thermodynamic Simulated Annealing, automatically adjusts the temperature at each step based on the energy difference between the two states, according to the laws of thermodynamics.

Restarts
Sometimes it is better to move back to a solution that was significantly better rather than always moving from the current state. This process is called restarting of simulated annealing. To do this we set  and   to   and   and perhaps restart the annealing schedule. The decision to restart could be based on several criteria. Notable among these include restarting based on a fixed number of steps, based on whether the current energy is too high compared to the best energy obtained so far, restarting randomly, etc.

Related methods

 * Interacting Metropolis–Hasting algorithms (a.k.a. sequential Monte Carlo ) combines simulated annealing moves with an acceptance-rejection of the best-fitted individuals equipped with an interacting recycling mechanism.
 * Quantum annealing uses "quantum fluctuations" instead of thermal fluctuations to get through high but thin barriers in the target function.
 * Stochastic tunneling attempts to overcome the increasing difficulty simulated annealing runs have in escaping from local minima as the temperature decreases, by 'tunneling' through barriers.
 * Tabu search normally moves to neighbouring states of lower energy, but will take uphill moves when it finds itself stuck in a local minimum; and avoids cycles by keeping a "taboo list" of solutions already seen.
 * Dual-phase evolution is a family of algorithms and processes (to which simulated annealing belongs) that mediate between local and global search by exploiting phase changes in the search space.
 * Reactive search optimization focuses on combining machine learning with optimization, by adding an internal feedback loop to self-tune the free parameters of an algorithm to the characteristics of the problem, of the instance, and of the local situation around the current solution.
 * Genetic algorithms maintain a pool of solutions rather than just one. New candidate solutions are generated not only by "mutation" (as in SA), but also by "recombination" of two solutions from the pool. Probabilistic criteria, similar to those used in SA, are used to select the candidates for mutation or combination, and for discarding excess solutions from the pool.
 * Memetic algorithms search for solutions by employing a set of agents that both cooperate and compete in the process; sometimes the agents' strategies involve simulated annealing procedures for obtaining high-quality solutions before recombining them. Annealing has also been suggested as a mechanism for increasing the diversity of the search.
 * Graduated optimization digressively "smooths" the target function while optimizing.
 * Ant colony optimization (ACO) uses many ants (or agents) to traverse the solution space and find locally productive areas.
 * The cross-entropy method (CE) generates candidate solutions via a parameterized probability distribution. The parameters are updated via cross-entropy minimization, so as to generate better samples in the next iteration.
 * Harmony search mimics musicians in improvisation where each musician plays a note to find the best harmony together.
 * Stochastic optimization is an umbrella set of methods that includes simulated annealing and numerous other approaches.
 * Particle swarm optimization is an algorithm modeled on swarm intelligence that finds a solution to an optimization problem in a search space, or models and predicts social behavior in the presence of objectives.
 * The runner-root algorithm (RRA) is a meta-heuristic optimization algorithm for solving unimodal and multimodal problems inspired by the runners and roots of plants in nature.
 * Intelligent water drops algorithm (IWD) which mimics the behavior of natural water drops to solve optimization problems
 * Parallel tempering is a simulation of model copies at different temperatures (or Hamiltonians) to overcome the potential barriers.
 * Multi-objective simulated annealing algorithms have been used in multi-objective optimization.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Simulated annealing


text:
University of Münster

The University of Münster (Universität Münster, until 2023 Westfälische Wilhelms-Universität Münster, WWU) is a public research university located in the city of Münster, North Rhine-Westphalia in Germany.

With more than 43,000 students and over 120 fields of study in 15 departments, it is Germany's fifth largest university and one of the foremost centers of German intellectual life. The university offers a wide range of subjects across the sciences, social sciences and the humanities. Several courses are also taught in English, including PhD programmes as well as postgraduate courses in geoinformatics, geospational technologies or information systems.

Professors and former students have won ten Leibniz Prizes, the most prestigious as well as the best-funded prize in Europe, one Fields Medal and two Nobel Prizes. The University of Münster has also been successful in the German government's Excellence Initiative.

History
The university has its roots in the Münster's Jesuit College (Jesuiten-Kolleg Münster), founded in 1588, and the convent of lay sisters Liebfrauen-Überwasser, founded in 1040, of which it took its seal. The convent was dissolved in 1773, so that its funds could be used to found the University of Münster on 16 April 1780.

In 1631, Pope Urban VIII and Emperor Ferdinand II issued privileges, allowing the establishment of a university in Münster. However, due to a lack of funding, they were only put to use in 1780, when the modern University of Münster was founded with four faculties: Law, Medicine, Philosophy and Theology.

In 1843, it was renamed to Royal Theological and Philosophical Academy (Königliche Theologische und Philosophische Akademie), informally Münster Academy (Akademie Münster).

The ceremony of constitution was performed by Franz Freiherr von Fürstenberg. The university received the name Westphalian Wilhelm University (Westfälische Wilhelms-Universität Münster), from Emperor Wilhelm II on 22 August 1907. In 2023 the university was renamed as the University of Münster (Universität Münster).

European degrees
1999 saw the beginning of the Bologna Process, which aimed to ensure comparability in the standards and quality of higher education qualifications. The Münster School of Business Administration and Economics was the first one to establish bachelor's and master's degrees.

In the winter semester 2006/2007 nearly all studies have been changed according to Bachelor/Master system. Exceptions are made in studies leading to the Staatsexamen in medicine, dentistry, pharmacy and law.

Academics

 * Faculty of Protestant Theology
 * Faculty of Catholic Theology
 * Faculty of Law
 * Faculty of Economics (Muenster School of Business Administration and Economics)
 * Faculty of Health Science (Medicine and Dental Medicine)
 * Faculty of Educational and Social Science
 * Institute of Communication Science (IfK) (PR, Journalism, Media Science)
 * Faculty of Psychology and Sport Science
 * Faculty of History/Philosophy
 * Faculty of Philology
 * Faculty of Mathematics and Computer Science
 * Faculty of Physics
 * Faculty of Chemistry and Pharmacy
 * Faculty of Biology
 * Faculty of Earth Science
 * Faculty of Music (Musikhochschule Münster)

Campus
The central library of the university is the Universitäts- und Landesbibliothek Münster (ULB), which is also the regional library of Westphalia. As of 2011, the library owns more than 6.2 million volumes of which 2.68 million volumes are held in the ULB, while 3.53 million volumes are held by the 146 faculty and department libraries. Of those, 47,350 are electronical articles and newspapers.

Points of interest

 * Botanischer Garten Münster, the university's historic botanical garden

Student life

The university offers a very active student life. The university's sports club ("Hochschulsport") offers more than 100 sport courses, sport tours, further education and international tournaments. The university's IT organization ("Zentrum für Informationsverarbeitung" (ZIV)) provides central services for information processing and communication technology. It offers IT facilities for the students with standard and special software. Foreign languages can be learned at the university's language center ("Sprachenzentrum"). It offers traditional language courses, tandem courses (two persons with different native languages meet in order to learn from each other) and language certificates (for example UNIcert). The cultural programme also includes various museums, music (choirs, ensembles, orchestra), theatres and cinemas. Student organisations such as AIESEC, AEGEE, move, MTP e.V. and many more are well represented with high membership. The city of Münster itself has a very active night life with more than 1,000 bars and clubs. As the city of the Peace of Westphalia, Münster also has a very rich cultural life.

Rankings
As per the QS World 2024 edition, the university was ranked 384th globally and 21st nationally. In the THE World 2023 rankings, the institution placed 193rd on a global scale and between 19th and 21st within its home country. The university was also evaluated in the ARWU World 2023, where it fell within the 201-300 range worldwide and within the top 10-19 nationally.

The University of Münster is member of the association German U15 e.V. which is a coalition of fifteen major research-intensive and leading medical universities in Germany with a full disciplinary spectrum, excluding any defining engineering sciences.

The Leiden university ranking, ranks Münster as the third best German university in the size-independent ranking. Strong faculties include mathematics, chemistry, medicine and business studies. According to the Shanghai university ranking, the University of Münster is the fourth best German university for chemistry (46th best university for chemistry worldwide).

Two Max-Planck-Prize and five Gottfried-Wilhelm-Leibniz-Winner are currently professors at the faculty of mathematics.

Münster has been successful with three excellence clusters "Cells in Motion" (discontinued), "Religion and Politics" and "Mathematics Münster: Dynamics - Geometry - Structure" in the German excellence initiative.

title: University of Münster


text:
Göppingen

Göppingen (Swabian: Geppenge or Gebbenga) is a town in southern Germany, part of the Stuttgart Region of Baden-Württemberg. It is the capital of the district Göppingen. Göppingen is home to the toy company Märklin, and it is the birthplace of football player Jürgen Klinsmann. It also hosts the headquarters of TeamViewer AG.

Geography
Göppingen is situated at the bottom of the Hohenstaufen mountain, in the valley of the river Fils. The districts of Göppingen are Bartenbach, Bezgenriet, Faurndau, Göppingen, Hohenstaufen, Holzheim, Jebenhausen and Maitis.

History
Tradition holds that the city was founded by an Alemannic leader called Geppo sometime in the 3rd or 4th century. A disastrous fire on August 25, 1782 destroyed most of the town, but it was immediately rebuilt. Industrialisation during the 19th century made the area into a centre of industry. The importance of such industry is still seen in the town in the present day in companies such as Märklin and Schuler.

Jewish community
Göppingen and the nearby village of Jebenhausen were home to a thriving Jewish community from 1777 until the Second World War. In 1777, the Baron von Liebenstein issued a "Letter of Protection" granting Elias Gutmann and other Jews permission to settle in Jebenhausen. The community grew and peaked in the mid-1800s, with the population center shifting from Jebenhausen to Göppingen and a substantial emigration of Jewish families to America by the late 19th Century. The Göppingen synagogue, constructed in 1881, was destroyed during the Kristallnacht from 9–10 November 1938. Detailed records of the communities were collected by Rabbi Dr. Aron Tänzer, who served the community from 1907-1937, and who was also a driving force behind the establishment of the secular city library in Göppingen. A comprehensive Jewish community history, Die Geschichte der Juden in Jebenhausen und Göppingen, was first produced by Tänzer in 1927, on the 150th anniversary of the settlement of Jebenhausen, and re-released in 1988 by the city of Göppingen with updated material added by Karl-Heinz Ruess. The Jewish Museum in Jebenhausen, opened in 1992, documents and preserves the history of the Jewish community of Jebenhausen and Göppingen.

Cooke Barracks
In 1930, a civilian air field was built north of Göppingen. This was acquired by the Luftwaffe (German Air Force) in 1935 and expanded into Fliegerhorst Kaserne. From 1945 through 1949, displaced persons and refugees were housed in the kaserne. In 1949, it was renamed Cooke Barracks in honor of Charles H. Cooke, Jr. who had been posthumously awarded the Silver Star and Soldier's Medal for gallantry in action. In late 1950, the VII Corps (US) had been reactivated in Stuttgart and U.S. Army units began to be stationed at Cooke Barracks. The barracks began to be expanded and was used as the 28th Infantry Division headquarters. The 28th Infantry was redesignated as the 9th Infantry Division (United States) in 1954 and was replaced by the 8th Infantry Division in 1956. They were then replaced by the 4th Armored Division in 1957, which was redesignated as the 1st Armored Division in 1971 and moved to Hindenburg Kaserne in Ansbach in 1972. The 1st Infantry Division (Forward) moved from Augsburg in 1972 until they were deactivated in 1991. Cooke Barracks was returned to the German government in 1992. The barracks were again used to house refugees for some time, then returned to civilian use.

Mayors

 * 1819–1824: Viktor David Keller
 * 1824–1858: Ludwig Heinrich Widmann
 * 1858–1881: Georg Christian Philipp Friedrich Seefried (1814-1881)
 * 1881–1908: Gottlob Friedrich Allinger
 * 1908–1919: Julius Keck (1869-1924)
 * 1919–1933: Otto Hartmann
 * 1933–1945: Erich Pack
 * 1945–1954: Christian Eberhard (1886–1973)
 * 1954–1980: Herbert König
 * 1981–1996: Hans Haller
 * 1997–2004: Reinhard Frank (born 1955), (CDU)
 * 2005–2021: Guido Till (born 1955), (SPD/independent/CDU)
 * since 2021: Alexander Maier (born 1991), (Greens)

Sports
Local sports club Frisch Auf Göppingen currently play in the German first team handball men's top division Handball-Bundesliga.

Media
Göppingen has its own daily newspaper called "Neue Württembergische Zeitung". The "Stuttgarter Zeitung" also has a local editorial office in Göppingen. In addition, Göppingen has its own local TV station, the "Filstalwelle". It can be received in the local cable network and via the web. Göppingen also has "Radio Fips" which is a radio station operated by a non-profit association.

Twin towns – sister cities

Göppingen is twinned with:
 * 🇮🇹 Foggia, Italy (1971)
 * 🇦🇹 Klosterneuburg, Austria (1971)
 * 🇫🇷 Pessac, France (2000)
 * 🇩🇪 Sonneberg, Germany (1990)

Notable people

 * Michael Maestlin (1550–1631), mathematician and astronomer
 * Friedrich Christoph Oetinger (1702–1782), theologian, leading pietist
 * August Ludwig Schott (1751–1787), lawyer and university professor
 * Eduard Fuchs (1870–1940), scholar, writer, political activist
 * Hugo Borst (1881–1967), private art collector and patron of the arts
 * Adolf Kurz (1888–1959), wrestler
 * Karl Aberle (1901–1963), publisher and politician (SPD), member of Parliament, co-editor of the Neue Württembergische Zeitung
 * Hans Robert Jauss (1921–1997), literary scholar and linguist
 * Peter Häberle (born 1934), constitutional lawyer
 * F. W. Bernstein (born 1938), poet, artist and satirist
 * Frieder Birzele (born 1940), politician (SPD), former member of Landtag
 * Otto Hauser (born 1952), politician (CDU), Member of the Bundestag, parliamentary secretary and government spokesman
 * Brigitte Russ-Scherer (born 1956), jurist, 1999-2007 mayor of Tübingen (SPD)
 * Charles Pelkey (born 1958), journalist, lawyer and Democratic Whip of the Wyoming House of Representatives from 2015 to 2021.
 * Jürgen Klinsmann (born 1964), footballer, national coach of German football team (2004-2006)
 * Michael Kraus (born 1983), handball player
 * Ann-Katrin Berger (born 1990), footballer

title: Göppingen


text:
Talk:New Yorker

This page should be a redirect to The New Yorker. All but one page that links here should be going to The New Yorker. I fixed a few, but there will be more in the future. The only thing that links here that shouldn't be to the magazine is the article New York City which delivers us to the wonderful definition that a New Yorker is someone from New York. Ortolan88 17:16 Jan 21, 2003 (UTC)

I'm checking on the "what links here" and further fixing ones that link to here rather than THE New Yorker. Does Wikipedia have a consensus on the status of orphaned pages? --zandperl 00:31, 13 Feb 2004 (UTC)

Why did you revert this? All the information was moved to the New York article and nwe the same information is in two places. It is against wikipedia practice to have articles like this. Canadian redirects to Canada, Belgian redirects to Belgium etc. Why not turn it back into the redirect it was before? - SimonP 00:57, Feb 13, 2004 (UTC)

When this page was redirected to The New Yorker, I didn't see anything saying the info in this page was added to New York, New York, and thought that the information had just been eliminated. Thank you for pointing out to me that it has been put into the other page. I'd like to change this page (New Yorker) into a disambig, with links to The New Yorker and New York, New York, rather than only a redirect to the magazine, and change all that links here to the appriate one of the two. How does that sound to you? --zandperl 17:38, 14 Feb 2004 (UTC)

title: Talk:New Yorker


text:
Woldemar Voigt

Woldemar Voigt (2 September 1850 – 13 December 1919) was a German physicist.

Biography
Voigt was born in Leipzig, and died in Göttingen. He was a student of Franz Ernst Neumann. Voigt taught at the Georg August University of Göttingen and eventually went on to head the Mathematical Physics Department there. He was succeeded in 1914 by Peter Debye, who took charge of the theoretical department of the Physical Institute.

Voigt worked on crystal physics, thermodynamics and electro-optics. His main work was the Lehrbuch der Kristallphysik (Textbook on crystal physics), first published in 1910. He discovered what is now called the Voigt effect in 1898. The word tensor in its current meaning was introduced by him in 1898. Voigt profile and Voigt notation are named after him. He was also an amateur musician and became known as a Bach expert (see External links). He was the first to suggest, in 1886, that Bach's Concerto for two harpsichords in C minor, BWV 1060 was originally scored for violin and oboe.

In 1887 Voigt formulated a form of the Lorentz transformation between a rest frame of reference and a frame moving with speed $$v$$ in the $$x$$ direction. However, as Voigt himself said, the transformation was aimed at a specific problem and did not carry with it the idea of a general coordinate transformation, as is the case in relativity theory.

Voigt transformation
In modern notation Voigt's transformation was
 * $$x' = x - vt,$$
 * $$y' = y/\gamma,$$
 * $$z' = z/\gamma,$$
 * $$t' = t - vx/c^2,$$

where $$\gamma = 1/\sqrt{1 - v^2/c^2}$$. If the right-hand sides of his equations are multiplied by $$\gamma$$, they become the modern Lorentz transformation. Hermann Minkowski said in 1908 that the transformations which play the main role in the principle of relativity were first examined by Voigt in 1887. Also Hendrik Lorentz (1909) is on record as saying that he could have taken these transformations into his theory of electrodynamics, if only he had known of them, rather than developing his own. It is interesting then to examine the consequences of these transformations from this point of view. Lorentz might then have seen that the transformation introduced relativity of simultaneity, and also time dilation. However, the magnitude of the dilation was greater than the now accepted value in the Lorentz transformations. Moving clocks, obeying Voigt's time transformation, indicate an elapsed time $$\Delta t_\text{Voigt} = \gamma^{-2} \Delta t = \gamma^{-1} \Delta t_\text{Lorentz}$$, while stationary clocks indicate an elapsed time $$\Delta t$$.

Since Voigt's transformation preserves the speed of light in all frames, the Michelson–Morley experiment and the Kennedy–Thorndike experiment can not distinguish between the two transformations. The crucial question is the issue of time dilation. The experimental measurement of time dilation by Ives and Stillwell (1938) and others settled the issue in favor of the Lorentz transformation.

title: Woldemar Voigt


text:
Stoewer

Stoewer was a German automobile manufacturer before World War II whose headquarters were in Stettin (now Szczecin, Poland).

History
The first company was founded by the Stoewer brothers, Emil (lived 1873 – 1942) and Bernhard (1875 – 1937) in 1896 for manufacturing sewing machines in Stettin.

In 1899, the Stoewer brothers founded the firm Gebrüder Stoewer, Fabrik für Motorfahrzeugen and started to produce automobiles. Their first automobile was the Großer Stoewer Motorwagen, with 6.5 hp (4.8 kW) and 17 km/h maximum speed.

In 1908 Stoewers constructed the Stoewer G4. This model was successful for them at the time – 1070 cars were built. In 1910, Stoewer cars were built under licence by Mathis of Strassburg. In 1916, the family-owned company was transformed into a limited company under the name of Stoewer-Werke AG, vormals Gebrüder Stoewer.

In the mid-20s a new class of cars was introduced: the D-Types included D3, D9 and D10 with four-cylinder engines, as well as D5, D6 and D12 with six cylinders. Something special was the 1921 D7 with a proprietary six-cylinder aero engine with 120 hp. Of the fifty "D10" made, the only survivor was in Melbourne, Australia in original condition. It was on display at the 2014 MotorClassica. It is now in Germany.

In 1928 the company started to build S8 and G14 models with eight-cylinder engines. At the beginning of the 1930s Stoewers delivered their highlights: G15 Gigant, M12 Marschall and P20 Repräsentant, each with eight-cylinder engines, with 60 to 120 hp (45 to 90 kW) and 130 km/h maximum speed. The production of these cars had to be cancelled after 2,500 vehicles being produced due to worldwide economic troubles. In 1931 Stoewer constructed one of the first cars with front-wheel drive at all, class V5 25 hp (19 kW), 80 km/h maximum speed. The model named Greif Junior was built under the licence of Tatra. Its successor V8 Greif was the last car constructed by Stoewer himself; class Arkona and Sedina were the last civilian cars produced by the company.

In 1936 the Stoewer factory developed the 'uniform light off-road car' (le.E.Pkw, leichter geländegängiger Einheits-PKW) for the German army, a versatile four-wheel drive car, the Stoewer R200 initially (until 1940) equipped with four-wheel steering. Due to capacity-limitations, the cars also had to be produced by BMW-Factory Eisenach, as BMW 325, and by Hanomag in Hanover as the Type 20B. Together the three manufacturers made a total of ca. 13,000 units. Stoewer was one of many German companies that exploited slave labour during World War II and had its own camp for prisoners. After World War II, the Red Army seized the remaining production facilities, dismantled the factory and sent the equipment to the Soviet Union. The company subsequently ceased to exist.

title: Stoewer