text:
Douglas Trumbull

Douglas Hunt Trumbull (April 8, 1942 – February 7, 2022) was an American film director and visual effects supervisor, who pioneered innovative methods in special effects. He created scenes for 2001: A Space Odyssey, Close Encounters of the Third Kind, Star Trek: The Motion Picture, Blade Runner and The Tree of Life, and directed the movies Silent Running and Brainstorm.

Early life
Trumbull was born in Los Angeles. His father was an aerospace engineer who had briefly worked in Hollywood creating visual effects for the 1939 movie The Wizard of Oz.; his mother, who died when Trumbull was 7, was an artist. As a child, he liked to construct mechanical and electrical devices such as crystal-set radios, and enjoyed watching alien invasion movies. He initially wanted to be an architect, leading him to take classes in illustration. He studied technical drawing at El Camino Junior College and joined the Screen Cartoonists Guild upon graduating. However, Hollywood initially rejected his portfolio of spaceships and planetary drawings. Though his abilities in creating photorealistic art led to a job at Graphic Films, which produced short films for NASA and the Air Force.

1960s
Douglas Trumbull's early work was at Graphic Films in Los Angeles. The small animation and graphic arts studio produced a film called To the Moon and Beyond about spaceflight for the 1964 New York World's Fair. Trumbull, the son of a mechanical engineer and an artist, worked at Graphic Films as an illustrator and airbrush artist. He painted a rotating spiral galaxy, and using a fish eye lens, projected the film onto a custom-built dome. The effect was ground-breaking for its time and the film caught the attention of director Stanley Kubrick, who was beginning work on the project that would become 2001: A Space Odyssey. Kubrick hired director Con Pederson from Graphic Films and the company was to work on visual effects for the film. When Kubrick decided to move all production to England, he cancelled the contract with Graphic Films. Trumbull wanted to keep working on the film as he had already done considerable pre-production work, so he cold-called Kubrick after obtaining the director's home phone number from Pederson. Kubrick hired Trumbull and flew him to London for the production of 2001. Trumbull's first task was to create the dozens of animations seen in the data display screens in the Aries moon shuttle and the Discovery. They looked like computer graphics, but they were created by photographing and animating reproductions of charts and graphs from technical publications. Trumbull initially created the shots using a number of Rube Goldberg-like contraptions he built with gears and motors ordered from a scientific equipment supply house. Kubrick gave the young effects technician creative freedom and encouragement: "He would say ... 'What do you need to do it?' and I would have complete carte blanche, which was wild as a young guy", Trumbull recalled. "I was 23–24 when I started the movie, and was 25 by the time I was doing the Star Gate. He would say, 'What do you need?' and I'd say, 'Well, I need to go into town and buy some weird bearings and some stuff' and he would send me off to town in his Bentley, with a driver, into London. It was great!"

Trumbull's responsibilities and talents grew as the production continued, and he became one of four special effects supervisors on the film (the others were fellow Graphic Films alumnus Con Pederson, along with Tom Howard and Wally Veevers.) Trumbull's most memorable contribution was the development of the slit-scan photography process, used in the "Stargate" sequence. "... I just happened to be in the right place at the right time ... We were struggling with the Star Gate. Nobody knew what a Star Gate was; but, I came up with some ideas that I didn't even know at the time were based on some things I was learning as a young guy about street photography and weird photographic techniques ...". He created the Stargate by building a 6ft-tall sheet of rotatable metal and cut a narrow slit in it. The sheet was placed in front of a 12ft-long backlit glass panel, through which lighting patterns were shone. With a long camera exposure, the kaleidoscope of lights appeared to be darting towards the camera from a single point.

Trumbull and Kubrick wanted the audience to feel like they were on the adventure themselves, and immersed in the film by participating. This approach eventually led to the Imax system of high resolution projection, which Trumbull helped to develop. Working on 2001 hooked Trumbull on the concept of producing immersive film experiences on huge screens — ironically, at a time when the industry was moving towards the multiplexing of theatres with smaller screens.

Although Trumbull's association with Kubrick was a huge boost for his career, he swore afterwards that he would "never work for someone else again", in part because Kubrick "was a hell of a taskmaster ... his level of quality-control bordered on perfectionism."

The film earned an Oscar for best special effects, but the award went solely to Kubrick, with Trumbull receiving none of the accolade for his work. This led to threats of legal action and the two men did not speak for a decade. Trumbull said after Kubrick's death that Kubrick "was a genius", someone whom Trumbull missed terribly.

In 1969 Trumbull was filming the annual Flying Saucer Convention in Giant Rock California. This evolved into a full-length project initially called Giant Rock, Rutabaga Deluxe, and then Saturation 70: An Ecological Horror Fantasy. The star of the film was a five-year-old Julian Jones, who was the son of Brian Jones, of Rolling Stones fame. The story involved Jones losing his mother in a giant garbage dump and wandering a desolate planet looking for her, while being menaced by gas-masked garbage men and helped by a fairy godmother in a sequined cowgirl creation by Nudie. Some footage includes a battle with a Green Beret and a Viet Cong in a supermarket. Trumbull's partner on the film was Anthony Foutz. A company called Dimension V took over backing of the film.

1970–1974
Having returned to Hollywood, Trumbull set up his own company and subsequently bid on the job to produce special effects for the science-fiction film The Andromeda Strain. ("I was a young guy and very naive", he later recalled, "And I seriously underbid the job – I had no idea what these things were supposed to cost. I nearly went bankrupt as a result!") Trumbull and associate James Shourt produced dozens of shots, including the "electron microscope" pictures of the Andromeda organism and various on-screen readouts. Though many of these looked like computer graphics, they were created using techniques Trumbull had used for 2001. Author Michael Crichton and director Robert Wise were much impressed by Trumbull's work.

Trumbull's participation and success on Andromeda set him up to direct the 1971 film Silent Running, with a script based on his original treatment: America's last great forests are preserved and sent into space inside huge geodesic domes, in the hope that one day they can be returned to an earth that can once again sustain them. When orders are issued by faceless bureaucrats to abandon and destroy the domes, the ship's botanist (Bruce Dern) rebels and takes over the ship, aided by three anthropomorphic "drone" robots. He steers the ship away from the fleet and hides among the rings of Saturn, out of contact (silent running), attempting to keep the forest in good health, alone except for the drones who follow him around like pets.

Silent Running was produced by Universal on a shoestring budget of one million dollars, one-tenth the budget of 2001. The film used a number of special effects techniques that Trumbull had helped develop. The spacecraft interiors were shot aboard a mothballed aircraft carrier, which lent its name to the movie spacecraft Valley Forge. Trumbull was not originally slated to direct, but as the start of production loomed he became the obvious choice. (Other newcomers included the script writing team of Deric Washburn and Michael Cimino, who would later collaborate on The Deer Hunter, along with writer Steven Bochco of Hill Street Blues and L.A. Law fame.)

When Silent Running was released, insiders were astonished that the finished film had been produced for so little money. Lead actor Bruce Dern compared Trumbull's creative vision to that of Alfred Hitchcock, with whom Dern had also worked. Trumbull was seen as one of Hollywood's up and coming young directors.

Although a critical success, Silent Running was a flop at the box office. Trumbull recalled that "It was just a great experience for me as a film maker, but I didn't know that I was part of an experiment by Universal Studios . . . to see if it was possible to have a movie survive on word of mouth alone without an advertising campaign." It was not, but Silent Running's environmental message struck a chord, and the movie has since become a cult classic.

After Silent Running, Trumbull developed a number of movie projects, but a series of misfortunes and bad luck kept them from getting beyond the initial development stage. One project nearly did get into production, and was already being cast when it was abruptly scuttled – the investor had decided to abandon the movie business and build a Las Vegas casino instead. Trumbull described this period of his career as "development hell". Unable to live on development fees alone and needing money, Trumbull returned to creating special effects, including some uncredited work using blue screen techniques on the 1974 film The Towering Inferno, a huge commercial hit.

1975–1980
In 1975, Trumbull turned down an offer to provide the effects for George Lucas' Star Wars due to other commitments, but in 1977 he contributed effects to Close Encounters of the Third Kind. In late 1978, Trumbull's Future General Corporation, a research/special effects house that was funded by Gulf + Western and Paramount Pictures, was offered the job to produce the special effects for Star Trek: The Motion Picture. Trumbull, already deeply involved in Close Encounters, refused, wanting instead to focus his efforts on his patented Showscan process, a high-speed, large-format movie process that provided unprecedented visual clarity. Paramount awarded the contract to effects house Robert Abel and Associates, and in a move seen by some as payback for Trumbull's refusal to take on the project, all but shuttered Future General.

Robert Abel had produced many high-end, visually advanced commercials for clients such as 7-Up, but it soon became apparent that their choice of technology, which featured software-controlled camera rigs and graphics imaging systems very advanced for the day, simply couldn't scale up to the volume of material required. In August 1978, with rumors of an impending meltdown at Abel swirling, Trumbull approached Paramount offering to step in and do the effects with partner Richard Yuricich. Paramount declined, hoping that Abel could still work a miracle.

Early in 1979, and with principal photography nearly finished and a December release date looming, Abel was fired after failing to produce even a few seconds of usable footage. Paramount approached Trumbull to take over effects production, which Trumbull did after securing an agreement to be released from his contract at Paramount upon completion of the film. "At the time", he recalled, "I think they would have entertained anyone who could have pulled them out of the jam." Trumbull reassembled his Future General team, rebuilt his facility which Paramount had nearly gutted, and with a mere six months to create the hundreds of effects shots needed, worked virtually around the clock for months. His team made the date, but their in-house battle cry became "... crop it, flop it, or drop it!" (That is, re-use part of an existing scene, take an existing scene and "flop" it over so that a right-to-left shot of the ship now plays the other way, or "drop" the shot from the script altogether.)

The model of the Enterprise, already built by the time Trumbull's team took over, proved especially tricky. While the model of Discovery in "2001" was over 50 feet (15 m.) long and featured a wealth of detail (from parts gleaned from, among other things, hundreds of plastic model tank kits), the model of the Enterprise was only seven feet (2 m.) in length, which severely limited the photographic possibilities. Other compromises had to be overcome. Trumbull had several ideas for unconventional effects – such as a modified slitscan technique to produce fantastic streaks when the Enterprise went into warp drive, but many had to be shelved due to time constraints. Trumbull also made several contributions to the story line, in collaboration once again with his Andromeda Strain director Robert Wise.

As Trumbull told Wolfram Hannemann of in70mm.com, "There were as many shots [in the movie] as "Close Encounters" and "Star Wars" combined ... There were 650 shots, which had to be completed in six months ... and we all worked 24 hours a day for six months. Seven days a week, around the clock, to get that movie done ... I ended up in the hospital – it was a major recovery. I had ulcers, all kinds of exhaustion because I was working seven days a week, almost living in the studio, not getting enough sleep."

1980–1990s
In 1981 Trumbull directed the special effects for the Ridley Scott film Blade Runner. By this time Trumbull had sworn off doing special effects for other directors, but was lured to the project by the opportunity to work with Scott, and a chance to create something other than sterile, grey and white spacecraft. "One of the things that appealed to me about the project", Trumbull recalled in an interview in Cinefex magazine, "was that it was NOT a space movie. I'm just real tired of doing spaceships against star backgrounds." Indeed, the iconic images of a polluted, dystopian Los Angeles, looking more like an oil refinery than a metropolis, and complete with building-sized electronic billboards and a bulbous blimp circling overhead advertising "Off World" job opportunities became the film's visual trademarks.

Trumbull did not complete Blade Runner, (David Dryer took over as special effects supervisor) leaving the film as agreed about halfway through to concentrate on pre-production for his next directing effort, Brainstorm, a story of two brilliant scientists who develop a revolutionary device to record and vicariously experience other people's feelings and perceptions, a device the military tries to steal for its own purposes.

Brainstorm was to be a showcase for Trumbull's "Showscan" process, which used special cameras and projectors to capture and project 70 mm film at 60 frames per second. At the last minute the Showscan process was not used, because theatre owners balked at the idea of installing expensive new projection equipment. The film was shot conventionally at 24 frames per second on 35 mm film, though Trumbull continued his process of shooting effects work in 70 mm. "In movies people often do flashbacks and point-of-view shots as a gauzy, mysterious, distant kind of image", Trumbull recalled, "And I wanted to do just the opposite, which was to make the material of the mind even more real and high-impact than 'reality'".

The film was nearly scuttled by the mysterious drowning death of Natalie Wood during a break in production. MGM immediately shut down production and initially wanted to dump Brainstorm (and collect the insurance on the unfinished film). Trumbull, though perhaps bereft by the death of Natalie, reasoned that the film would be finished after filming just a few more scenes. Lawyers and insurance companies battled over whether to even complete the film. The movie was finally finished two years later when the insurance company supplied the money to finish production. Trumbull had pushed all the while for the studio to finish and release his movie. "I can do this", Trumbull recalled in an interview with GreenCine, "I've got all the coverage ... All you need to do is let me in the editing room and I'll show you. They said, 'No, you can't come back, we don't want you in the cutting room, you can't finish this movie.'" Because of his determination to finish his film, Trumbull became persona non grata at MGM in the process. Eventually released on a small number of screens and with little publicity (though Trumbull recalled in the Greencine interview that the film became "Quote, Natalie Wood's last film, unquote") Brainstorm was well received critically but a commercial failure at the box office.

Exhausted from his battles with the Hollywood system ("The movie business is so totally screwed up that I just don't have the energy to invest three or four years in a feature film"), Trumbull retreated to the Berkshire Hills of western Massachusetts, to escape "the lawyers, the insurance agents, the creeps", redirecting his career away from traditional Hollywood projects and concentrating instead on developing new technology for movie production, and for the exhibition industry and theme-park rides, such as the very first flight-simulator ride, Tour of the Universe, and the Back to the Future Ride at Universal Studios Theme Park. Until recently, Trumbull's Showscan technology could be seen on a theme-park type ride at the Luxor Hotel in Las Vegas.

In 1994 Trumbull was briefly a Vice Chairman of IMAX Corporation and President of its Ridefilm division through his involvement in the simultaneous combination and takeover of the Canadian-based private company Imax Corp. and Trumbull Co.

2000–2018
Trumbull spent nearly two decades in the Berkshire hills of western Massachusetts, starting and running a series of companies involved in effects production and innovation.

In 2010, Trumbull used social media to publicize a video on Vimeo and YouTube demonstrating an invention intended to cap the BP oil spill with a strong vacuum seal. Although the video "went viral" almost immediately, Trumbull never heard from BP or any of the US government agencies struggling to contain the spill, which left him bemused and mildly annoyed. "I didn't do it with the hope of compensation", he later said, "I did it because I thought it was the moral thing to do."

After nearly thirty years away from Hollywood, Trumbull contributed to special effects work on Terrence Malick's 2011 film The Tree of Life. Malick, reportedly a Trumbull fan, approached him about the effects work and mentioned that he did not like the look of computer-generated effects. Reportedly Trumbull asked, "Why not do it the way we did it on 2001?" Recent compositing programs such as Nuke allow practical scenes shot on film to be combined with fewer of the head-aches of "traditional" effects work, such as shooting multiple camera passes on a single piece of film, matte passes, and the like. Trumbull eventually signed on as special effects consultant, working with the film's effects supervisor, Dan Glass. Many of the "organic" effects processes used in 2001 and Close Encounters were resurrected, such as photographing chemical interactions in petri dishes and releasing paints into water tanks. "It was a working environment that's almost impossible to come by these days", Trumbull told The Guardian newspaper in July 2011. "Terry wanted to create the opportunity for the unexpected to occur before the camera, then make something of that. He didn't want to use a very stringent design process, he wanted the unexpected phenomenon to occur – and use that."

In March 2011, director James Cameron announced plans to film his next Avatar-type 3D feature in a digital version of Showscan. Cameron has been pushing for movie theatres to adopt higher frame-rates to maintain the 3D effect during scenes involving high-speed motion (such as explosions). At twenty-four frames per second the 3D effect breaks down, while at forty-eight or sixty frames per second it is maintained. Sixty frames per second is difficult to achieve with conventional film because of the stress on the medium itself; recording sixty frames per second using a digital camera is commonplace.

In 2012 Trumbull said he was working on a new science-fiction project that he claimed is "way beyond anything that Peter Jackson and James Cameron have been doing", which will probably be shot with a camera capable of recording 120 frames per second, twice the speed of its ancestor, Showscan.

Trumbull was a guest speaker at the Massachusetts Production Coalition in February 2013.

Since 2013 Trumbull maintained a workshop and studio on his property in the Berkshire hills of Massachusetts where he continued to develop new tools for film-makers. He often traveled to film screenings and seminars and was enjoying a resurgence of his celebrity among film and visual effects enthusiasts. Trumbull seemed grateful for the recognition and reverence accorded by his followers. "They really keep me going", he told The Australian newspaper in February 2011. "They reinforce some enthusiasm about my work. It's very hard to keep me going, because the setbacks [were] really tragic and difficult." When asked by a reporter how he had managed to persevere in the face of setbacks, Trumbull laughed and replied that he didn't know, and "Maybe I'm just out of my mind!"

In 2014 Trumbull announced that he had developed a new digital capture and projection system called Magi. It shoots and projects native 3D in 4K at 120 fps, using an innovative technique he called "cadence", which had never been used in previous 3D systems: "We were shooting 60 [frames] per eye, projector was going 120—left eye, right eye, left eye, right eye. You’re shooting the same way you’re going to project it. And that's when this magic happens. It's only one flash per frame, and the sequence is actually temporally correct. There are in fact 120 different positions. Anything that moves in front of the camera is going to have 120 different positions." That year he also produced a short dramatic film, UFOTOG, to highlight the capabilities of the Magi system. The story deals with a man who has developed a sophisticated 3D photographic system to track UFOs and prove their existence, despite interference from a shadowy government agency. The film has been shown at film festivals and industry conferences and to filmmakers and studio executives.

In 2016, he told Science & Film, "I am planning on making a feature-length movie that will be almost entirely miniatures, but it will be photorealistic, full-scale, epic in quality, and have the kind of things that I like about Blade Runner and 2001."

In 2018, Trumbull provided the visual effects for and executive produced the movie The Man Who Killed Hitler and Then the Bigfoot. The same year, he participated in the documentary Trumbull Land (Grégory Wallet, 2018) devoted to him and his universe.

Honors
Trumbull was twice honored by the Society of Motion Picture and Television Engineers (SMPTE). Most recently, he received the Progress Medal in recognition of his numerous contributions to photographic processes and technologies in visual effects (VFX) and HFR cinematography. Trumbull conducted pioneering biometric research on audience response to HFR imaging and developed a novel cinematic process using 65mm film at 60 frames per second that resulted in a "Giant Screen" 70mm image with extraordinarily high definition along with smoother and more realistic motion rendering. His work continues to advance stereoscopic 3D and digital HFR imaging including his 120FPS Magi single-camera/single projector "lens-to-lens" system that harnesses existing cameras, post-production tools, and projectors to deliver images and sound that are almost indistinguishable from reality. The Progress Medal is the most prestigious SMPTE award, and it recognizes outstanding technical contributions to the progress of engineering phases of the motion picture, television, or motion-imaging industries. The honor was conferred upon Trumbull at the SMPTE Centennial Gala on October 28, 2016, at the Ray Dolby Ballroom in Hollywood. In 2011, he received the SMPTE Presidential Proclamation, which recognizes individuals of established and outstanding status and reputation in the motion-picture, television, and motion-imaging industries worldwide. Trumbull was honored for his more than 45 years of pioneering work in visual effects photography and groundbreaking innovation in motion picture technologies.

Trumbull was inducted by the Science Fiction Hall of Fame in 2010, citing first his stature as "innovative master of special effects". He has been nominated for Academy Awards on three occasions and has received the American Society of Cinematographer's Lifetime Achievement Award.

Trumbull received the International Press Academy's Tesla award in December 2011, named in honor of Nikola Tesla, an inventor, scientist and engineer, who, Trumbull noted dryly in a runway interview, "Died penniless, after lots of people took credit for his work." He went on to say that he hopes it doesn't turn out that way for him. Trumbull also received the Gordon E. Sawyer Award in February 2012, an honorary Academy Award given to an "individual in the motion picture industry whose technological contributions have brought credit to the industry", as well as the Georges Méliès award from the Visual Effects Society in the same month.

Personal life and death
Trumbull was married three times and had two children. He was in poor health for the last two years of his life, due to complications from a stroke and cancer. He died from mesothelioma at a hospital in Albany, New York, on February 7, 2022, at the age of 79. His ashes are due to be sent into space with those of Majel Barrett and Nichelle Nichols.

title: Douglas Trumbull


text:
Magnetic helicity

In plasma physics, magnetic helicity is a measure of the linkage, twist, and writhe of a magnetic field.

Magnetic helicity is a significant concept in the analysis of astrophysical systems, where the resistivity may be very low, so that magnetic helicity is conserved to a good approximation. In practice, magnetic helicity dynamics are important in analyzing solar flares and coronal mass ejections. Magnetic helicity is present in the solar wind. Its conservation is significant in dynamo processes, and it also plays a role in fusion research, such as reversed field pinch experiments.

When a magnetic field contains magnetic helicity, it tends to form large-scale structures from small-scale ones. This process can be referred to as an inverse transfer in Fourier space. This property of increasing the scale of structures makes magnetic helicity special in three dimensions, as other three-dimensional flows in ordinary fluid mechanics are the opposite, being turbulent and having the tendency to "destroy" structure, in the sense that large-scale vortices break up into smaller ones, until dissipating through viscous effects into heat. Through a parallel but inverted process, the opposite happens for magnetic vortices, where small helical structures with non-zero magnetic helicity combine and form large-scale magnetic fields. This is visible in the dynamics of the heliospheric current sheet, a large magnetic structure in the Solar System.

Mathematical definition
Generally, the helicity $$H^{\mathbf f}$$ of a smooth vector field $$\mathbf f$$ confined to a volume $$V$$ is the standard measure of the extent to which the field lines wrap and coil around one another. It is defined as the volume integral over $$V$$ of the scalar product of $$\mathbf f$$ and its curl, $$\nabla\times{\mathbf f}$$:
 * $$ H^{\mathbf f} = \int_V {\mathbf f} \cdot \left(\nabla\times{\mathbf f}\right)\ dV . $$

Magnetic helicity
Magnetic helicity $$H^{\mathbf M}$$ is the helicity of a magnetic vector potential $${\mathbf A}$$ where $$\nabla \times {\mathbf A}={\mathbf B}$$ is the associated magnetic field confined to a volume $$V$$. Magnetic helicity can then be expressed as
 * $$ H^{\mathbf M} = \int_V {\mathbf A}\cdot{\mathbf B}\ dV . $$

Since the magnetic vector potential is not gauge invariant, the magnetic helicity is also not gauge invariant in general. As a consequence, the magnetic helicity of a physical system cannot be measured directly. In certain conditions and under certain assumptions, one can however measure the current helicity of a system and from it, when further conditions are fulfilled and under further assumptions, deduce the magnetic helicity.

Magnetic helicity has units of magnetic flux squared: Wb2 (webers squared) in SI units and Mx2 (maxwells squared) in Gaussian Units.

Current helicity
The current helicity, or helicity $$M^{\mathbf{J}}$$ of the magnetic field $$\mathbf{B}$$ confined to a volume $$V$$, can be expressed as
 * $$ H^{\mathbf J} = \int_V {\mathbf B}\cdot{\mathbf J}\ dV $$

where $$ {\mathbf J} = \nabla \times {\mathbf B} $$ is the current density. Unlike magnetic helicity, current helicity is not an ideal invariant (it is not conserved even when the electrical resistivity is zero).

Gauge considerations
Magnetic helicity is a gauge-dependent quantity, because $$\mathbf A$$ can be redefined by adding a gradient to it (gauge choosing). However, for perfectly conducting boundaries or periodic systems without a net magnetic flux, the magnetic helicity contained in the whole domain is gauge invariant, that is, independent of the gauge choice. A gauge-invariant relative helicity has been defined for volumes with non-zero magnetic flux on their boundary surfaces.

Topological interpretation
The name "helicity" is because the trajectory of a fluid particle in a fluid with velocity $$\boldsymbol v$$ and vorticity $$\boldsymbol{\omega}=\nabla \times \boldsymbol{v}$$ forms a helix in regions where the kinetic helicity $$\textstyle H^K=\int \mathbf v \cdot \boldsymbol{\omega} \neq 0$$. When $$\textstyle H^K > 0$$, the resulting helix is right-handed and when $$\textstyle H^K < 0$$ it is left-handed. This behavior is very similar to that found concerning magnetic field lines.

Regions where magnetic helicity is not zero can also contain other sorts of magnetic structures, such as helical magnetic field lines. Magnetic helicity is a continuous generalization of the topological concept of linking number to the differential quantities required to describe the magnetic field. Where linking numbers describe how many times curves are interlinked, magnetic helicity describes how many magnetic field lines are interlinked.

Magnetic helicity is proportional to the sum of the topological quantities twist and writhe for magnetic field lines. The twist is the rotation of the flux tube around its axis, and writhe is the rotation of the flux tube axis itself. Topological transformations can change twist and writhe numbers, but conserve their sum. As magnetic flux tubes (collections of closed magnetic field line loops) tend to resist crossing each other in magnetohydrodynamic fluids, magnetic helicity is very well-conserved.

As with many quantities in electromagnetism, magnetic helicity is closely related to fluid mechanical helicity, the corresponding quantity for fluid flow lines, and their dynamics are interlinked.

Ideal quadratic invariance
In the late 1950s, Lodewijk Woltjer and Walter M. Elsässer discovered independently the ideal invariance of magnetic helicity, that is, its conservation when resistivity is zero. Woltjer's proof, valid for a closed system, is repeated in the following:

In ideal magnetohydrodynamics, the time evolution of a magnetic field and magnetic vector potential can be expressed using the induction equation as
 * $$ \frac{\partial {\mathbf B}}{\partial t} = \nabla \times ({\mathbf v} \times {\mathbf B}),\quad \frac{\partial {\mathbf A}}{\partial t} = {\mathbf v} \times {\mathbf B} + \nabla\Phi, $$

respectively, where $$ \nabla\Phi $$ is a scalar potential given by the gauge condition (see ). Choosing the gauge so that the scalar potential vanishes, $$\nabla \Phi = \mathbf{0}$$, the time evolution of magnetic helicity in a volume $$V$$ is given by:
 * $$\begin{align}

\frac{\partial H^{\mathbf M}}{\partial t} &= \int_V \left( \frac{\partial {\mathbf A}}{\partial t} \cdot {\mathbf B} + {\mathbf A} \cdot \frac{\partial {\mathbf B}}{\partial t} \right) dV \\ &= \int_V ({\mathbf v} \times {\mathbf B}) \cdot{\mathbf B}\ dV + \int_V {\mathbf A} \cdot \left(\nabla \times \frac{\partial {\mathbf A}}{\partial t}\right) dV. \end{align}$$ The dot product in the integrand of the first term is zero since $${\mathbf B}$$ is orthogonal to the cross product $${\mathbf v} \times {\mathbf B}$$, and the second term can be integrated by parts to give
 * $$ \frac{\partial H^{\mathbf M}}{\partial t} = \int_V \left(\nabla \times {\mathbf A}\right) \cdot \frac{\partial {\mathbf A}}{\partial t}\ dV + \int_{\partial V} \left({\mathbf A} \times \frac{\partial {\mathbf A}}{\partial t}\right) \cdot d\mathbf{S} $$

where the second term is a surface integral over the boundary surface $$\partial V$$ of the closed system. The dot product in the integrand of the first term is zero because $$ \nabla \times {\mathbf A} = {\mathbf B} $$ is orthogonal to $$ \partial {\mathbf A}/\partial t .$$ The second term also vanishes because motions inside the closed system cannot affect the vector potential outside, so that at the boundary surface $$ \partial {\mathbf A}/\partial t = \mathbf{0} $$ since the magnetic vector potential is a continuous function. Therefore,
 * $$ \frac{\partial H^{\mathbf M}}{\partial t} = 0, $$

and magnetic helicity is ideally conserved. In all situations where magnetic helicity is gauge invariant, magnetic helicity is ideally conserved without the need for the specific gauge choice $$ \nabla \Phi = \mathbf{0}. $$

Magnetic helicity remains conserved in a good approximation even with a small but finite resistivity, in which case magnetic reconnection dissipates energy.

Inverse transfer
Small-scale helical structures tend to form larger and larger magnetic structures. This can be called an inverse transfer in Fourier space, as opposed to the (direct) energy cascade in three-dimensional turbulent hydrodynamical flows. The possibility of such an inverse transfer was first proposed by Uriel Frisch and collaborators and has been verified through many numerical experiments. As a consequence, the presence of magnetic helicity is a possibility to explain the existence and sustainment of large-scale magnetic structures in the Universe.

An argument for this inverse transfer taken from is repeated here, which is based on the so-called "realizability condition" on the magnetic helicity Fourier spectrum $$ \hat{H}^M_{\mathbf k} = \hat{\mathbf A}^*_{\mathbf k} \cdot \hat{\mathbf B}_{\mathbf k} $$ (where $$ \hat{\mathbf B}_{\mathbf k} $$ is the Fourier coefficient at the wavevector $$ {\mathbf k} $$ of the magnetic field $$ {\mathbf B} $$, and similarly for $$ \hat{\mathbf A} $$, the star denoting the complex conjugate). The "realizability condition" corresponds to an application of Cauchy-Schwarz inequality, which yields: $$ \left|\hat{H}^M_{\mathbf k}\right| \leq \frac{2E^M_{\mathbf k}}{|{\mathbf k}|} ,$$ with $ E^M_{\mathbf k} = \frac{1}{2} \hat{\mathbf B}^*_{\mathbf k}\cdot\hat{\mathbf B}_{\mathbf k} $  the magnetic energy spectrum. To obtain this inequality, the fact that $$ |\hat{\mathbf B}_{\mathbf k}|=|{\mathbf k}||\hat{\mathbf A}^\perp_{\mathbf k}| $$ (with $$  \hat{\mathbf A}^\perp_{\mathbf k} $$ the solenoidal part of the Fourier transformed magnetic vector potential, orthogonal to the wavevector in Fourier space) has been used, since $$  \hat{\mathbf{B}}_{\mathbf k} = i {\mathbf k} \times \hat{\mathbf{A}}_{\mathbf k} $$. The factor 2 is not present in the paper since the magnetic helicity is defined there alternatively as $$ \frac{1}{2} \int_V {\mathbf A} \cdot {\mathbf B}\ dV $$.

One can then imagine an initial situation with no velocity field and a magnetic field only present at two wavevectors $$ \mathbf p $$ and $$ \mathbf q $$. We assume a fully helical magnetic field, which means that it saturates the realizability condition: $$ \left|\hat{H}^M_{\mathbf p}\right| = \frac{2E^M_{\mathbf p}}{|{\mathbf p}|} $$ and $$ \left|\hat{H}^M_{\mathbf q}\right| = \frac{2E^M_{\mathbf q}}{|{\mathbf q}|} $$. Assuming that all the energy and magnetic helicity transfers are done to another wavevector $$ \mathbf k $$, the conservation of magnetic helicity on the one hand and of the total energy $$ E^T = E^M + E^K $$ (the sum of magnetic and kinetic energy) on the other hand gives:

$$ H^M_{\mathbf k} = H^M_{\mathbf p} + H^M_{\mathbf q}, $$

$$ E^T_{\mathbf k} = E^T_{\mathbf p}+E^T_{\mathbf q} = E^M_{\mathbf p}+E^M_{\mathbf q}. $$

The second equality for energy comes from the fact that we consider an initial state with no kinetic energy. Then we have the necessarily $$ |\mathbf k| \leq \max(|\mathbf p|, |\mathbf q| ) $$. Indeed, if we would have $$ |\mathbf k| > \max(|\mathbf p|,|\mathbf q| ) $$, then:

$$ H^M_{\mathbf k} = H^M_{\mathbf p} + H^M_{\mathbf q} = \frac{2E^M_{\mathbf p}}{|\mathbf p|} + \frac{2E^M_{\mathbf q}}{|\mathbf q|} > \frac{2\left(E^M_{\mathbf p} + E^M_{\mathbf q}\right)}{|\mathbf k|} = \frac{2E^T_{\mathbf k}}{|\mathbf k|} \geq \frac{2E^M_{\mathbf k}}{|\mathbf k|}, $$

which would break the realizability condition. This means that $$  |\mathbf k| \leq \max(|\mathbf p|,|\mathbf q| ) $$. In particular, for $$  |{\mathbf p}| = |{\mathbf q}| $$, the magnetic helicity is transferred to a smaller wavevector, which means to larger scales.

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

title: Magnetic helicity


text:
Jennie Elias

Jennie Elias is a politician in the United Kingdom. Having been appointed by David Cameron in December 2005 she currently serves as one of the Treasurers of the Conservative Party. Previously she served as Vice-Chairman of the Party during the period of Michael Howard's leadership (2003 to 2005). Prior to this Jennie Elias has had various other political roles including being a London Area Officer, Vice-Chairman of Kensington and Chelsea Conservative Association and serving several times on the London mayoral selection committee. She remains a member of the Executive Committee of the Thatcherite pressure group Conservative Way Forward and is President of the Ronald Reagan Memorial Fund Trust.

Outside politics Jennie Elias is also a well-known interior designer authoring the Percy Bass Book of Traditional Decoration (ISBN 1859385389) and co-authoring the Decorator's Guide to Fabrics, Wallpapers, Rugs and Trimmings (ISBN 0955200709). She also serves on the governing body of Sussex House School.

title: Jennie Elias


text: Category:Lampasas County, Texas

title: Category:Lampasas County, Texas


text:
ANZ

ANZ may refer to:

 Countries:

 * Australia and New Zealand

People

 * Anz (musician), a British DJ and electronic musician

Banks

 * ANZ (bank), Australia and New Zealand Banking Group Limited, the fourth-largest bank in Australia
 * ANZ Bank New Zealand, the largest bank in New Zealand
 * ANZ (Fiji), one of the largest banks in Fiji
 * ANZ Royal Bank, a bank in Cambodia
 * ANZ Amerika Samoa Bank, a bank in American Samoa
 * ANZ Bank Building (Fremantle)
 * ANZ Bank Centre, the tenth tallest building in Sydney
 * Trustees Chambers, a heritage-listed bank building in Brisbane, Queensland, Australia, once known as an ANZ Bank building

Sports

 * AFL New Zealand, the governing body of Australian rules football in New Zealand
 * ANZ Championship (golf)
 * ANZ Tasmanian International (tennis)
 * Archery New Zealand, the national governing body for the sport of Archery in New Zealand
 * Athletics New Zealand, the national organisation for athletics in New Zealand
 * Australasia at the Olympics, the combined team of Australia and New Zealand in 1908 and 1912
 * Queensland Sport and Athletics Centre, known as ANZ Stadium from 1993 to 2003
 * Stadium Australia, known as ANZ Stadium from 2008 to 2020

Transportation

 * Air New Zealand, airline's ICAO code
 * Airways New Zealand, the sole Air Traffic Service provider in New Zealand
 * Anerley railway station (London), from its UK National Rail code

Other uses

 * Academic ranks (Australia and New Zealand)
 * Animal Planet (Australia and New Zealand)
 * Antarctica New Zealand, an Institute that manages New Zealand's interests in Antarctica and the Ross Sea
 * ANZ Centre, a skyscraper in Auckland, New Zealand

title: ANZ


text:
Haptotaxis

Haptotaxis (from Greek ἅπτω (hapto, "touch, fasten") and τάξις (taxis, "arrangement, order")) is the directional motility or outgrowth of cells, e.g. in the case of axonal outgrowth, usually up a gradient of cellular adhesion sites or substrate-bound chemoattractants (the gradient of the chemoattractant being expressed or bound on a surface, in contrast to the classical model of chemotaxis, in which the gradient develops in a soluble fluid.). These gradients are naturally present in the extracellular matrix (ECM) of the body during processes such as angiogenesis or artificially present in biomaterials where gradients are established by altering the concentration of adhesion sites on a polymer substrate.

Clinical Significance
Haptotaxis plays a major role in the efficient healing of wounds. For example, when corneal integrity is compromised, epithelial cells quickly cover the damaged area by proliferation and migration (haptotaxis). In the corneal stroma, keratocytes within the wounded area undergo apoptosis, leaving the stroma devoid of cells that must be replaced. Keratocytes surrounding the wounded area proliferate and become fibroblasts that migrate to fill the wounded area. This creates a healthy environment with myofibroblasts and extracellular matrix. This is known as light backscattering or subepithial haze. When there is injury to an epithelial cell heptotaxis occurs, which is highly influenced by the cell's velocity, which is in turn influenced by direction of cell motility. Cells migrate easily and quickly in packs, so when one cell moves the rest follow in response to the gradient and initial cell movement. Mechanical effects like the buildup of tensile forces may play an important role for both division as well as motility of cells in tissue.

Methods of Study
As defined above, haptotaxis is the motility of cells up a gradient of substrate bound molecules. There is a wide variety of procedures to set up this gradient in vitro for the study of haptotaxis. The two main categories can be classified into either continuous or digital. Both types are relatively easy to produce, but digital gradients give more accurate concentration calculations. Overall, the methods in use currently can be improved to mirror the in vivo environment more, as the resolution of the gradients is not as sharp in vitro as they are in vivo. Also, biological gradients have the ability to change geometry, which current models in vitro cannot mimic. These gradients are useful in gaining understanding of the basics of haptotaxis, but because of the complex and fluid nature of these gradients, a deeper understanding of the in vivo condition is difficult to ascertain.

Tumor Cells and Haptotaxis
A characteristic of many cancers is the ability to move throughout the body. These are malignant cells, and pose a serious threat to the health of an individual. It has been indicated that haptotaxis plays a role in the ability of malignant cells to metastasize. One factor that was initially found to influence haptotaxis is serum spreading factor, which is present in blood serum and interstitial tissues. The presence of serum spreading factor was shown to influence directed migration along a gradient of substrate molecules in a few types of cancer cells. Another component important in the haptotaxis of tumor cells is MenaINV, which is an actin regulatory protein that becomes increasingly expressed in tumor cells. This actin regulatory protein binds to fibronectin receptors and aids in the haptotactic and chemotactic processes of tumor cells.

Pathology
Haptotaxis plays a role in several kinds of diseases where the movement or aggregation of cells causes the symptoms. As mentioned before, cancers that are metastatic have the ability to perform haptotaxis in order to spread throughout the body. This ability is not limited to tumor cells. Idiopathic pulmonary fibrosis (IPF) is a disease marked by fibrosis in lung mesothelial cells. TGF-β1 is a cytokine found in higher concentrations of lungs from patients who have IPF, and induces haptotaxis of pleural mesothelial cells. At the same time, TGF-β1 causes the mesothelial cells to develop into myofibroblasts, which contribute to the symptoms in IPF. The result is that there becomes an aggregation of myofibroblasts in the lungs, which leads to fibrosis of the mesothelial cells. During nephritis, VCAM-1 is expressed in higher levels on the tubules of nephrons, which leads to increased leukocyte migration via the gradient established by VCAM-1. It is important to note that this increased expression was not found on the capillary endothelial cells. This migration of leukocytes leads to inflammation and tissue destruction characteristic of an inflammatory response.

Immune System
Movement of cells is vital for the function of the immune system, and especially for antigen presenting cells. Dendritic cells (one of the main antigen presenting cells in the immune system), move towards the lymph nodes after phagocytizing an antigen in order to present the antigen to T cells. Chemokines influence these movements, especially CCL21, which is bound to lymphatic endothelial cell membranes. The influence is short range, but causes movement of the dendritic cells up a fixed chemical gradient. Other leukocytes also exhibit haptotactic movement: neutrophils undergo IL-8 mediated migration, while monocytes, basophils, eosinophils and some T cells are influenced by RANTES chemokines. In the autoimmune disorder rheumatoid arthritis and in osteoarthritis, the associated swelling and migration of neutrophils to the affected site has been shown to be linked to membrane bound midkine cytokine. This cytokine operates in a haptotactic fashion, attracting local neutrophils to the site of expression.

Tissue Development
Haptotaxis plays a role in organizing cells to form tissues and specific regions of those tissues. Fibronectin and laminin both play a role in adrenocyte mutation into distinctive distribution in the adrenal gland. The adrenocytes migrate centripetally as they mature towards the medulla of the adrenal gland, and this movement may be a result of haptotactic forces mediated by fibronectin and laminin. In nerve cells, axonal growth is mediated by nerve growth factor in a haptotactic manner, where the axon of nerve cells grows along the gradient. This information could be used to possibly develop methods to promote nerve regeneration in patients that have nerve damage. Another regenerative strategy is the use of mesenchymal stem cells, which can differentiate into different kinds of connective tissue in the wound healing process. The haptotaxis is mediated by fibronectin, vitronectin, and type I collagen. A recent study has tentatively proposed the idea that the structures on cells responsible for sensing the membrane protein gradients are attenuated filopodia. Also, the more amount of filopodia present on the leading edge of the migrating cell, the more responsive the cell is to the haptotactic gradient. This is important because there is the possibility that all motile cells that display filopodia may be responding to haptotactic gradients. Further research is required in the subject, but it is clear that more and more kinds of cell undergo haptotaxis than originally believed.

Therapeutic Uses
The placement of haptotactic molecules would benefit most in situations where increased numbers of cells are required to move to a desired location to help the healing process either directly or by their cell products. The introduction of haptotactic peptides may help in healing several diseases such as diabetes mellitus, hemophilia A and B deficiencies, and Parkinson's disease. The haptoctatic molecules would play a role in healing by restricting other bioengineered cells that have the ability to produce the needed cell products to the desired area of the body where therapy is needed. This application can also be used in wound healing, where increased numbers of fibroblasts and keratinocytes aid in wound re-granularization, thus decreasing overall healing time. In regard to prosthetics, making the prosthetic device incorporate successfully with the tissue is a challenge. When the prosthetic's surface is coated with haptotactic materials, the prosthetic is aided in forming covalent bonds with the cells and becomes securely attached to the cell layer. While haptotaxis may not be occurring in this process, it demonstrates the diversity with which this knowledge about haptotaxis can be used.

title: Haptotaxis


text:
Ligue 1

Ligue 1, officially known as Ligue 1 McDonald's for sponsorship reasons, is a French professional league for men's association football clubs. Being the top of the French football league system, it is the country's primary football competition. Administered by the Ligue de Football Professionnel, Ligue 1 is contested by 18 clubs (as of the 2023–24 season) and operates on a system of promotion and relegation from and to Ligue 2.

Seasons run from August to May. Clubs play two matches against each of the other teams in the league – one home and one away – totalling to 34 matches over the course of the season. Most games are played on Saturdays and Sundays, with a few games played during weekday evenings. Play is regularly suspended the last weekend before Christmas for two weeks before returning in the second week of January. As of 2024, Ligue 1 is considered one of the top national leagues, ranked fifth in Europe, behind England's Premier League, Spain's La Liga, Italy's Serie A and Germany's Bundesliga.

Ligue 1 was inaugurated on 11 September 1932 under the name National before switching to Division 1 after a year of existence. It continued to operate under that name until 2002, when it adopted its current name. Paris Saint-Germain are the most successful club with twelve league titles, while Lyon is the club that has won the most consecutive titles (seven between 2002 and 2008). Saint-Étienne was the first club with ten titles. With the presence of 73 seasons in Ligue 1, Marseille holds the record for most seasons among the elite, while Paris Saint-Germain hold the league record for longevity with 50 consecutive seasons (from 1974 to present). Nantes is the team with the longest consecutive unbeaten streak (32 matches) and the fewest number of defeats (one match) in a single season, doing so in the 1994–95 campaign. In addition, Nantes also holds the record for the longest time without losing at home with a run of 92 matches from May 1976 to April 1981.

The current champions are Paris Saint-Germain, who won a record twelfth title in the 2023–24 season. The league has been won on multiple occasions by foreign-based club Monaco, the presence of which within the league makes it a cross-border competition.

Ahead of the 2023–24 season, the number of teams in the league was reduced to 18; four teams in the 2022–23 Ligue 1 were relegated to Ligue 2 and only two teams in Ligue 2 were promoted to Ligue 1.

Foundation
Professionalism in French football did not exist until July 1930, when the National Council of the French Football Federation voted 128–20 in favour of its adoption. The founders of professionalism in French football are Georges Bayrou, Emmanuel Gambardella, and Gabriel Hanot. Professionalism was officially implemented in 1932.

In order to successfully create a professional football league in the country, the Federation limited the league to twenty clubs. In order to participate in the competition, clubs were subjected to three important criteria:

 * The incoming club must have had positive results in the past.
 * The incoming club must be able to pull in enough revenue to balance its finances.
 * The incoming club must be able to successfully recruit at least eight professional players.

Many clubs disagreed with the subjective criteria, most notably Strasbourg, RC Roubaix, Amiens and Stade Français, while others like Rennes, due to fear of bankruptcy, and Lille, due to a conflict of interest, were reluctant to become professional. Lille's president, Henri Jooris, also chairman of the Ligue du Nord, feared his league would fold and proposed it become the second division of the new league. Eventually, many clubs earned professional status, though it became more difficult to convince clubs in the northern half of the country; Strasbourg, Roubaix and Amiens refused to accept the new league, while conversely Mulhouse, Excelsior AC Roubaix, Metz and Fives accepted professionalism. In southern France, clubs such as Marseille, Hyères, Montpellier, Nîmes, Cannes, Antibes and Nice were extremely supportive of the new league and accepted their professional status without argument.

Establishment
The league's inaugural season of the all-professional league, called National, was held in 1932–1933. The 20 inaugural members of National were Antibes, CA Paris, Cannes, Club Français, Excelsior AC Roubaix, Fives, Hyères, Marseille, Metz, Mulhouse, Nice, Nîmes, Alès, Lille, Racing Club de France, Red Star Olympique, Rennes, Sochaux, Sète and Montpellier. The 20 clubs were inserted into two groups of 10 with the bottom three of each group suffering relegation to Division 2. The two winners of each group would then face each other in a final held at a neutral venue, which later turned out to the Stade Olympique Yves-du-Manoir. The first final was held on 14 May 1933 and it matched the winner of Group A, Olympique Lillois, against the runner-up of Group B, Cannes. Antibes, the winner of Group B, was supposed to take part in the final but was suspected of bribery by the French Football Federation and was disqualified. In the first final, Lillois were crowned the inaugural champions following the club's 4–3 victory. After the season, the league decided to retain the 14 clubs and not promote any sides from the second division. The league also agreed to change its name from National to simply Division 1. For the 1934–35 season, the league organised a legitimate promotion and relegation system bringing the total tally of clubs in the first division to 16. The number remained until the 1938–39 season.

Because of World War II, football was suspended by the French government and the Ligue de Football Professionnel, although its member clubs continued playing in regional competitions. During the "war championships", as they are called, professionalism was abolished by the Vichy regime and clubs were forced to participate in regional leagues, designated as Zone Sud and Zone Nord. Due to its non-association with the two leagues, the LFP and FFF do not recognise the championships won by the clubs and thus 1939–1945 is non-existent in the two organisations' view. Following the conclusion of the war and the liberation of France, professional football returned to France. The first division increased its allotment of clubs to 18. This number remained until the 1965–66 season when the number was increased to 20. In 2002, the league changed its name from Division 1 to Ligue 1.

Format

 * 20 clubs: 1932–1933
 * 14 clubs: 1933–1934
 * 16 clubs: 1934–1939
 * 18 clubs: 1945–1946
 * 20 clubs: 1946–1947
 * 18 clubs: 1947–1958
 * 20 clubs: 1958–1963
 * 18 clubs: 1963–1965
 * 20 clubs: 1965–1968
 * 18 clubs: 1968–1970
 * 20 clubs: 1970–1997
 * 18 clubs: 1997–2002
 * 20 clubs: 2002–2023
 * 18 clubs: 2023–present

Competition format
There are 18 clubs in Ligue 1. During the course of a season, usually from August to May, each club plays the others twice, once at their home stadium and once at that of their opponents, for a total of 34 games, though special circumstances may allow a club to host matches at other venues such as when Lille hosted Lyon at the Stade de France in 2007 and 2008. Teams receive three points for a win and one point for a draw. No points are awarded for a loss. Teams are ranked by total points, then goal difference, and then goals scored. At the end of each season, the club with the most points is crowned champion. If points are equal, the goal difference and then goals scored determine the winner. If still equal, teams are deemed to occupy the same position. If there is a tie for the championship, for relegation, or for qualification to other competitions, a play-off match at a neutral venue decides rank. For the 2015–16 season only, two teams were to be relegated and only two teams from Ligue 2 were to be promoted, but this decision was overturned and three teams were relegated and three teams promoted. Thus, it was the 2016–17 season which saw the return of a relegation play-off between the 18th-placed Ligue 1 team and the third-placed team in the Ligue 2 on a two-legged confrontation, with the Ligue 2 team hosting the first game.

Previously, the league utilised a different promotion and relegation format. Prior to 1995, the league's format was direct relegation of the bottom two teams and a play-off between the third-last first-division team and the winner of the second-division play-offs, similar to the Dutch Eredivisie, and the German Bundesliga. The league has also experimented with a "bonus" rule. From 1973 to 1976, a rule rewarded teams scoring three or more goals in a game with one extra point, regardless of outcome, with the objective of encouraging offensive play. The experience was ultimately inconclusive. At the start of the 2006–07 season, the league introduced an Attacking Play Table to encourage the scoring of more goals in Ligue 1 and Ligue 2. The LFP, with the help of the former manager Michel Hidalgo introduced the idea to reward those teams who score the most goals. The table was similar to the previous idea, but was independent from the official league table and clubs were only rewarded with monetary bonuses.

In June 2021, the LFP voted overwhelmingly at its general assembly to contract Ligue 1 back to 18 clubs for the 2023–24 season by relegating four to, and promoting two from, Ligue 2 after 2022–23.

European qualification
As of the 2023–24 season, as determined by the UEFA coefficient, the top four teams in Ligue 1 qualify for the Champions League, with the top three proceeding directly to the group phase. The fourth-placed team enters in the third qualifying round. The fifth-placed team qualifies for the UEFA Europa League, the sixth for UEFA Conference League. The last Europa League place is determined through the country's domestic cup competition, the Coupe de France. If the cup winner qualifies for Europe through their league position, the seventh-placed team in Ligue 1 will qualify for the Conference League. If France is among the top two nations that earned the most coefficient points from a single season, an additional Champions League group phase spot will be awarded to the team in fourth place; as such the Champions League third qualifying round spot and all spots below will be pushed back one position.

Clubs
A total of 74 clubs have played in Ligue 1 from its foundation in the 1932–33 season to the start of the 2024–25 season. Currently, Marseille, Montpellier, Nice and Rennes are the only founding members of the league to be playing in Ligue 1. Paris Saint-Germain is the only club to have not suffered points relegation. They earned promotion to the first division for the 1974–75 season and have not faltered down since. Paris Saint-Germain was administratively relegated by the league following its split from Paris FC in 1972, but returned to the top flight two seasons later.

Internationally, the most well-known Ligue 1 clubs include Marseille, Lyon, Monaco and Lille.

Members for 2024–25
The following 18 clubs are competing in the 2024–25 Ligue 1 season.

Finances
Ligue 1 clubs' finances and budgets are managed by the DNCG (Direction Nationale du Contrôle de Gestion), an organisation responsible for monitoring the accounts of professional association football clubs in France. It was founded in 1984 and is an administrative directorate of the Ligue de Football Professionnel (LFP). The mission of the DNCG is to oversee all financial operations of the 44 member clubs of the LFP, develop the resources of professional clubs, apply sanctions to those clubs breaking the rules of operation, defend the morals and interests of French football in general.

Following a report by the DNCG, it was determined that the combined budget of Ligue 1 clubs was €910 million for the 2005–06 season, a 39% increase from the 2002–03 season. The prominent reason for the rise was mainly associated with the television rights deal the league regularly signs. Excluding Paris Saint-Germain, many of the top division clubs are extremely healthy with clubs such as Auxerre, Bordeaux, Lille and Lyon being referred to as "managed to perfection". However, recently the DNCG has encouraged clubs to concentrate on limiting their "skyrocketing wage bills and the magnitude of their debts" after it was discovered that the LFP clubs accounts as a whole were in the red for the third consecutive season (2008–2011) with an estimated deficit of €130 million. In 2012, the LFP announced that the clubs deficit had been cut in half from €130 million to €65 million. Ligue 1 ranks fifth in terms of revenue brought in by clubs with the league bringing in £0.6 billion for the 2006–07 season trailing England, Italy, Spain and Germany.

In terms of world football, clubs Lyon and Marseille are among the richest football clubs in the world and regularly feature in the Deloitte Football Money League ranking of football clubs by revenue generated from football operations. In the list compiled in the 2008–09 season, Lyon ranked 13th among clubs generating approximately €139.6 million, while Marseille were right behind them in 14th position generating €133.2 million.

In 2016, just Paris Saint-Germain was in the top 30 of the Deloitte Football Money League (ranked 4). From 2017 to 2020, Paris Saint-Germain (ranked between five and seven) and Lyon (ranked between 17 and 28) were part of the top 30.

Performance by club
Bold indicates clubs playing in 2024–25 Ligue 1.

 * Notes

Appearances

 * Notes

Italics denotes players still playing professional football, Bold denotes players still playing in Ligue 1.

Goalscorers

 * Notes

Italics denotes players still playing professional football, Bold denotes players still playing in Ligue 1.

Media coverage
The LFP formerly had rights agreements with the premium channels Canal+ and beIN Sports. The agreement with beIN Media Group, reached on 23 June 2011, paid the LFP €510 million over four seasons. Following the announcement of the agreement, it was revealed that Canal+ had acquired four television packages, while beIN Sports acquired two packages.

In 2018, Mediapro acquired three of the four major packages of LFP media rights for 2020-21 through 2024, largely replacing Canal+ in a deal valued at a record €1.15 billion. beIN Sports maintained "lot 3", which contained two matches per-week on Saturday nights and Sunday afternoons. Mediapro was expected to establish a new channel to house these rights. beIN Sports later sub-licensed its package to Canal+. In June 2020, Mediapro announced a partnership with TF1, under which the new channel would leverage the network's talent and resources, and be branded as Téléfoot—an extension of TF1's long-running football programme. Téléfoot presenters Grégoire Margotton and Bixente Lizarazu would serve as the lead broadcast team for at least 20 matches per-season.

Seeking to renegotiate its contract due to the financial impact of COVID-19, Mediapro began withholding its rights payments to the LFP in October 2020. LFP CEO Arnaud Rouger stated in October 2020 that they may have to pursue a new broadcaster if they are unable to resolve the dispute with Mediapro. In December 2020, it was reported that Mediapro were preparing to wind down Téléfoot, after it agreed to compensate the LFP for the two missed rights payments. In February 2021, Canal+ reached an interim agreement to acquire the rights packages held by Mediapro for the remainder of the season, and later sub-licensed Ligue 2 to beIN; Téléfoot shut down on 8 February 2021.

In June 2021, the LFP resold the broadcast rights packages for Ligue 1 to Canal+ and Amazon Prime Video through 2024, with the two broadcasters paying a total of €663 million in total. Canal+ holds rights to two matches per-week. In August 2023, it announced a sub-licensing agreement with DAZN to stream its matches on a branded channel within the service as part of DAZN's local launch. Canal+ does not plan to renew its rights after the conclusion of the 2024 season.

Trophy
The current Ligue 1 trophy, L'Hexagoal, was developed by the Ligue de Football Professionnel and designed and created by Pablo Reinoso. The trophy has been awarded to the champion of France since the end of the 2006–07 season, replacing the previous Ligue 1 trophy that had existed for only five years. The name Hexagoal was derived from an official competition created by the LFP and French TV channel TF1 to determine a name for the new trophy. Over 9,000 proposals were sent in and, on 20 May 2007, French Football Federation member Frédéric Thiriez announced that, following an online vote, the term Hexagoal had received half of the votes. The first club to hoist the new trophy was Olympique Lyonnais who earned the honour after winning the 2007–08 season.

Monthly and annual
In addition to the winner's trophy and the individual winner's medal players receive, Ligue 1 also awards the monthly Player of the Month award. Following the season, the UNFP Awards are held and awards such as the Player of the Year, Manager of the Year, and Young Player of the Year from both Ligue 1 and Ligue 2 are handed out.

Sponsorship names

 * Ligue 1 Orange (2002–2008)
 * Ligue 1 Conforama (2017–2020)
 * Ligue 1 Uber Eats (2020–2024)
 * Ligue 1 McDonald's (2024–)

title: Ligue 1


text:
Long-jawed orb weaver

Long-jawed orb weavers or long jawed spiders (Tetragnathidae) are a family of araneomorph spiders first described by Anton Menge in 1866. They have elongated bodies, legs, and chelicerae, and build small orb webs with an open hub with few, wide-set radii and spirals with no signal line or retreat. Some species are often found in long vegetation near water.

Systematics

, the World Spider Catalog accepts the following extant genera:

 * Allende Álvarez-Padilla, 2007 — Chile, Argentina
 * Antillognatha Bryant, 1945 — Hispaniola
 * Atelidea Simon, 1895 — Sri Lanka
 * Azilia Keyserling, 1881 — United States, Panama, South America, Caribbean
 * Chrysometa Simon, 1894 — South America, Central America, Mexico, Caribbean
 * Cyrtognatha Keyserling, 1881 — South America, Central America, Caribbean, Mexico
 * Dianleucauge Song & Zhu, 1994 — China
 * Diphya Nicolet, 1849 — Asia, South America, Africa
 * Dolichognatha O. Pickard-Cambridge, 1869 — Asia, Africa, South America, Oceania, United States, Panama
 * Doryonychus Simon, 1900 — Hawaii
 * Dyschiriognatha Simon, 1893 — Indonesia, Brazil, Samoa
 * Glenognatha Simon, 1887 — Africa, South America, Asia, North America, Central America, Caribbean
 * Harlanethis Álvarez-Padilla, Kallal & Hormiga, 2020 — Australia (Queensland)
 * Hispanognatha Bryant, 1945 — Hispaniola
 * Homalometa Simon, 1898 — Central America, Cuba, Mexico, Brazil
 * Iamarra Álvarez-Padilla, Kallal & Hormiga, 2020 — Australia (Queensland)
 * Leucauge White, 1841 (including Opas) — Africa, North America, Asia, Oceania, South America, Central America, Caribbean
 * Leucognatha Wunderlich, 1992 — Azores, Kenya, Tanzania
 * Mesida Kulczyński, 1911 — Oceania, Asia, Africa
 * Meta C. L. Koch, 1836 — Asia, North America, Tanzania, Oceania, Cuba
 * Metabus O. Pickard-Cambridge, 1899 — Mexico, Guatemala, Ecuador, Dominican Republic
 * Metellina Chamberlin & Ivie, 1941 — Africa, Asia, Canada
 * Metleucauge Levi, 1980 — Asia, United States
 * Mitoscelis Thorell, 1890 — Indonesia
 * Mollemeta Álvarez-Padilla, 2007 — Chile
 * Nanningia Zhu, Kim & Song, 1997
 * Nanometa Simon, 1908 — Australia
 * Neoprolochus Reimoser, 1927 — Indonesia
 * Okileucauge Tanikawa, 2001 — China, Japan
 * Orsinome Thorell, 1890 — Asia, Oceania, Madagascar
 * Pachygnatha Sundevall, 1823 — Africa, Asia, North America, Cuba, Europe
 * Parameta Simon, 1895 — Ethiopia, Somalia, Sierra Leone
 * Parazilia Lessert, 1938 — Congo
 * Pholcipes Schmidt & Krause, 1993 — Comoros
 * Pickardinella Archer, 1951 — Mexico
 * Pinkfloydia Dimitrov & Hormiga, 2011 — Australia
 * Sancus Tullgren, 1910 — Kenya, Tanzania
 * Schenkeliella Strand, 1934 — Sri Lanka
 * Taraire Álvarez-Padilla, Kallal & Hormiga, 2020 — New Zealand
 * Tawhai Álvarez-Padilla, Kallal & Hormiga, 2020 — New Zealand
 * Tetragnatha Latreille, 1804 — Asia, South America, Oceania, Africa, North America, Caribbean, Central America, Europe
 * Timonoe Thorell, 1898 — Myanmar
 * Tylorida Simon, 1894 — Asia, Africa, Oceania
 * Wolongia Zhu, Kim & Song, 1997 — China
 * Zhinu Kallal & Hormiga, 2018 — Taiwan, Korea, Japan
 * Zygiometella Wunderlich, 1995 — Israel

Fossil genera
Several extinct, fossil genera have been described:

 * †Anameta Wunderlich, 2004 (Palaeogene, Bitterfield and Baltic amber)
 * †Balticgnatha Wunderlich, 2004 (Palaeogene, Baltic amber)
 * †Corneometa Wunderlich, 2004 (Palaeogene, Baltic amber)
 * †Eometa Petrunkevitch, 1958 (Palaeogene, Baltic amber)
 * †Huergnina Selden & Penney, 2003 (Cretaceous, Las Hoyas, Spain)
 * †Macryphantes Selden, 1990 (Cretaceous)
 * †Palaeometa Petrunkevitch, 1922 (Palaeogene, Florissant)
 * †Palaeopachygnatha Petrunkevitch, 1922 (Palaeogene, Florissant)
 * †Priscometa Petrunkevitch, 1958 (Palaeogene, Baltic amber)
 * †Samlandicmeta Wunderlich, 2012 (Palaeogene, Baltic amber)

Formerly placed here

 * Deliochus Simon, 1894 – now in Araneidae
 * Eryciniolia Strand, 1912 – now a synonym of Nanometa
 * Menosira Chikuni, 1955 – now a synonym of Metellina
 * Nediphya Marusik & Omelko, 2017 – now a synonym of Nanometa
 * Phonognatha Simon, 1894 – now in Araneidae
 * Prolochus Thorell, 1895 – see Dolichognatha

title: Long-jawed orb weaver


text: Category:History of Catholicism in Spain


text:
List of racing cyclists and pacemakers with a cycling-related death

Vélodrome Parc des Princes.jpg,

site of Breton's 1902 death

(c. 1900 postcard)]]

The first documented deaths of competitive cyclists during competition or training date to the 1890s and early 1900s when the recently-invented safety bicycle made cycling more popular, both as a sport and as a mode of transport. The athletes listed here were either professional cyclists, professional pacemakers or well-known competitive amateurs who had a cycling-related death, mostly during a race or during training. Pacemakers are motorcyclists utilized in motor-paced racing, riding motorcycles in front of their cycling teammates to provide additional speed to those cyclists via the resulting slipstream.

Safety has been a concern since cycling's early days. By 1929, at least 47 people had died while racing at velodromes – 33 cyclists and 14 pacemakers. Motor-paced cycling still exists in the modern era as keirin racing and derny racing. A number of professionals and competitive amateurs have been killed in crashes with motorized vehicles while training on public roads plus there is a growing number of cyclists who have died of heart attacks while cycling in a race or while training. Some of these deaths affect cycle racing afterwards – the death of Andrey Kivilev in a crash during the 2003 Paris–Nice race caused the Union Cycliste Internationale to institute a mandatory helmet rule.

The dangers of the various sporting forms of cycling continue to be an issue, including training on public roadways. A survey of 2008 Olympics teams, however, indicated that cycling was not even in the top six most injury-prone sports during competition that year. Racing cyclists who have died during a race or during training are remembered by cycling aficionados and the cycling press. Their personal effects are exhibited in museums, their cemetery markers and tombstones are visited by fans, and as one commentator wrote: "Plaques, statues and shrines to cycling's fallen heroes are scattered all over Europe's mountain roads, turning any ride into a pilgrimage."

Cyclists who died during training
The following athletes died while individually training for competitions or during scheduled breaks while participating in a professional race. The only incident of multiple deaths from a team involved Néstor Mora, Augusto Triana, and Hernán Patiño from Team Postobón in 1995. The death rates for cyclists, in general, differ from country to country depending on how popular cycling is. A 2015 study of European Union cyclists' deaths, for instance, showed that in the Netherlands almost 25% of road deaths were cyclists while Greece had less than 5%.


text:
User:Brudberg~enwiki

Started as a member October 19, 2004.

title: User:Brudberg~enwiki


text:
Mechanotaxis

Mechanotaxis refers to the directed movement of cell motility via mechanical cues (e.g., fluidic shear stress, substrate stiffness gradients, etc.). In response to fluidic shear stress, for example, cells have been shown to migrate in the direction of the fluid flow. Mechanotaxis is critical in many normal biological processes in animals, such as gastrulation, inflammation, and repair in response to a wound, as well as in mechanisms of diseases such as tumor metastasis.

A subset of mechanotaxis - termed durotaxis - refers specifically to cell migration guided by gradients in substrate rigidity (i.e. stiffness). The observation that certain cell types seeded on a substrate rigidity gradient migrate up the gradient (i.e. in the direction of increasing substrate stiffness) was first reported by Lo et al. The primary method for creating rigidity gradients for cells (e.g., in biomaterials) consists of altering the degree of cross-linking in polymers to adjust substrate stiffness. Alternative substrate rigidity gradients include micropost array gradients, where the stiffness of individual microposts is increased in a single, designed direction.

History/background
There are multiple ways in which a cell's migration pattern can be influenced, including mechanotaxis, chemotaxis, which is cell movement following a molecular gradient, and haptotaxis, which is cell movement following an adhesion gradient. The first subset of mechanotaxis to be experimentally observed was durotaxis, detailing how contact with a substrate could cause a change in a cell's migration pattern, but more recently researchers have also examined how contact with a neighboring cell could cause changes in a cell's migration pattern. Researchers began investigating mechanotaxis of endothelial cells in blood vessels and wound repair in the 1990s and early 2000s. The early 2000s and 2010s also saw more interest in mechanotaxis in the biomedical engineering community as a potential method of cell manipulation.

Factors/pathways
Cells can detect and react to mechanical stimuli in a variety of ways. One method is through the interaction of E-cadherin presented on the cell membrane. As these receptors interact and are pulled or pushed, tension can be created, leading to a change in the conformation of alpha-catenin bound to B-catenin on the intracellular portion of E-cadherin. This causes the recruitment of vinculin and leads to a change in actin conformation and in the orientation of the cell. Another signaling pathway important in a cell's response to mechanical stimuli is the Wnt planar cell polarity (PCP) pathway. This noncanonical pathway involves the activation of Rho and Rac families of GTPases, which are essential in reorganizing the cytoskeleton in preparation for cell migration. When cells collide, localized signaling of the PCP pathway leads to a change in the polarity of the cell, redirecting the cell in a different direction.

Different cellular receptors are important in cellular mechanotransduction involved in contact with a substrate such as the extracellular matrix (ECM). For example, many cell types express a5b1 integrin on their membranes, which can bind to a major ECM component called fibronectin. This leads to an accumulation of integrins in the area of contact with the ECM, attaching the ECM to the cytoskeleton of the cell and allowing for migration to occur along the ECM through tension at the points of attachment (called focal adhesions, FA) and subsequently the dismantling of FAs as the cell moves along. For this reason, the elasticity of the ECM or another binding substrate is very important. The tension created by a cell pulling against a stiff substrate needs to reach a certain threshold to allow for mechanotaxis to occur.

Mechanotaxis in development
Cell migration is essential in early embryonic development, as a defining characteristic of this phase is the folding and reorganization of the embryo that occurs during and after gastrulation. Without cell migration, complex structures involving multiple cell types that make up complex organisms – like tissues, organs, limbs, etc. – would not develop correctly. There are multiple factors that influence cells to move during development –– but the factors that influence mechanotaxis in development often involve interactions between cells or between a cell and a substrate such as a yolk or membrane.

Contact inhibition of locomotion is involved in the migration of many cell types, including neural crest (NC) cells in vertebrates which give rise to cells of the peripheral nervous system (PNS), facial cartilage, and other non-neural cells throughout the body. NC cells are very mobile, with actin-rich protrusions at the leading edge of each cell in the direction of travel. When an NC cell collides with another NC cell, activation of the Wnt planar cell polarity (PCP) signaling pathway occurs at the point of cell contact, causing localized activation of the downstream effector RhoA. This activation is likely caused by interactions between cadherins on the cell surfaces, and leads to the retraction of the cell protrusions and a change in the cell's polarity, causing the NC cell to change direction. Interestingly, this contact inhibition of locomotion among NC cells is coupled with chemical coattraction between NC cells, which allows the cells to keep in motion for efficient migration as well as to stay together, respectively, leading to collective migration. Cells are most often influenced by surrounding cells towards collective migration in development,  such as polster cells which are the first to internalize at the start of gastrulation in zebrafish. Unlike neural crest cells, these cells don't exhibit contact inhibition of locomotion or coattraction, but instead migrate collectively due to E-cadherin interactions between leading cells and following cells. The following polster cells are polarized and migrate towards the animal pole of the embryo for unknown reasons, reaching their actin-rich protrusions towards the leading cells and inducing interactions between E-cadherin proteins located on following cell protrusion membranes and leading cell membranes. The interactions between E-cadherins create tension, which causes internal a-catenin (bridging extracellular E-cadherin with intracellular actin) to be stretched into an open configuration, leading to the recruitment of vinculin and eventually the orientation of actin towards the same direction of migration as the following cells. Without these E-cadherin interactions, leading cells will exhibit non-directional migration.

Mechanotaxis in wound healing
In wound healing, fluid shear stress plays a large role in the mechanotaxis of endothelial cells to the wound site. The inner lining of blood vessels is composed of these endothelial cells, which means that these cells are continuously experiencing fluid shear stress from blood rushing through the vessels. This mechanical stress on the apical side of the endothelial cells leads to integrin signaling, which involves the recruitment of focal adhesion kinase (FAK), Shc, and Crk, and will lead to changes in cell-cell and cell-ECM adhesion. These changes involve lamellipodial protrusions and focal adhesion (FA) formation at the front of the cell, as well as the dismantling of FAs at the rear of the cell, and cause endothelial cells to move in the direction of the flow. Constant laminar flow has been found to improve cell migration in wounds and increases the rate of wound closure.

title: Mechanotaxis