text:
Talk:Interferometry

Advice on re-organization
helpme Like others on this talk page, I found this article to be surprisingly lame considering the importance of the subject matter. The original article was written by people who were mainly interested in astronomical interferometry, and other applications of interferometry were sort of neglected. Most of the edits over the last few years have been timid additions and corrections compared with what the article really needed in terms of a rewrite. So I decided to try my hand at reorganization.

What I need is another set of eyeballs critiquing what I've done so far. Am I headed on the right path, or no? And what in tarnation should I do with the awful Interferometry section? I shoved it to the rear, but should I really be splitting it out to its own separate article? Or should I merge it into Astronomical interferometer and let those guys deal with the mess? (not a very nice thing to do ...) Maybe I should just (shudder) delete it?

Also, I removed the "radio-astronomy" template at the bottom. This contributed to the article imbalance. Agree?

Thanks for the extra eyes, Stigmatella aurantiaca (talk) 18:29, 1 April 2012 (UTC)

Figure 10 is missing
173.243.179.223 (talk) 13:52, 21 June 2016 (UTC)

Needs History section
Considering the broad impact that this subject has had on many areas of science, there should be a short section on the history of the development of this idea. This is actually the information I hoped to find on this page. 67.222.236.65 (talk) 19:23, 1 February 2014 (UTC)
 * I'll look into adding a history section. Thanks for the suggestion! Stigmatella aurantiaca (talk) 23:45, 1 February 2014 (UTC)

Delete reference to White–Juday warp-field interferometer
Providing a link to the White–Juday warp-field interferometer in the "See Also" section implies that this is a type of interferometer that is different than those already listed. It is not. It is a Michelson interferometer being used to detect optical pathlength changes that might be caused by changes in "warp fields." I have therefore deleted the reference. CQ123 (talk) 01:42, 12 June 2014 (UTC)

Surveillance, and warfare applications missing :)
This article is missing the beef on NSA and other agencies use of interferometry for surveillance and electronic warfare. Interferometry involves directing frequencies for active scans of homes, people, brains, effects and the like or even passive scans as energy emits from alternative sources such as electronic devices, over the horizon radar, cell towers, and even human beings (bioelectromagnetic emanations). Interferometry is used to create holographic 3D scans and 3D fields of energy remote from the transmitter. Interferometry has weapons applications, using the energy from transmitters to assault people, do weather modification, house haunting simulations, projections of holograms in the sky and environment, sound creation such as the frey effect and microwave auditory hearing effect, and even alteration of brainwaves based on Robert Malech's 1974 patent, apparatus and method for remotely reading and altering brainwaves (the patent describes using military radar/satellites and interferometry to read and alter brainwaves).

Numerous scientists including Dr. Judy Wood, Dr. Fred Bell, and Dr. Robert Duncan describe interferometry being used from space, land and sea based platforms for these purposes yet the articles are devoid of information on the matter. Military documents and patents and numerous articles also describe such.

NSA whistleblower Russell Tice described in numerous interviews including Russia Today's Breaking the Set with Abby Martin using space capability to spy domestically on Americans, including lawyers, journalists, congressmen, senators judges, banks, and civillians - under classified special access programs, exceptionally controlled information programs, very restricted knowledge programs, and the like.

Based on a review of wikipedia articles it seems as if military applications are being censored and this common knowledge, often even taught at universities, is being kept from public knowledge bases such as wikipedia. ObamasWeapon.com DrRobertDuncan.com 66.87.112.204 (talk) 01:22, 17 July 2015 (UTC)

Superpose vs Superimpose
The Basic Principles section claims that interferometry uses the principle of superposition, yet the lead links to superimposed. Shouldn't this link be changed to superposed? Mysticdan (talk) 17:42, 26 August 2015 (UTC)
 * Good catch! Stigmatella aurantiaca (talk) 00:24, 3 September 2015 (UTC)

Error in optical flat interferometry diagram
Just corrected a serious booboo of mine in the optical flat diagram in the Engineering and applied science section. Due to 180° phase reversal of the ray reflecting from the bottom surface, while the ray undergoing internal reflection from the top surface undergoes no phase change, constructive interference occurs with path length difference of odd multiples of λ/2, not even. Sorry. -- Chetvorno TALK 01:01, 16 December 2016 (UTC)

What is a "linear interferometer"?
The qualification linear is often used (e.g. in Boson sampling, second sentence, or in List of types of interferometers), but I cannot find an explanation for it. Could that be added somewhere, please? --H.Marxen (talk) 17:33, 8 May 2017 (UTC)

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title: Talk:Interferometry


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Prosopagnosia

Prosopagnosia (from Greek prósōpon, meaning "face", and agnōsía, meaning "non-knowledge"), also known as face blindness, is a cognitive disorder of face perception in which the ability to recognize familiar faces, including one's own face (self-recognition), is impaired, while other aspects of visual processing (e.g. object discrimination) and intellectual functioning (e.g., decision-making) remain intact. The term originally referred to a condition following acute brain damage (acquired prosopagnosia), but a congenital or developmental form of the disorder also exists, with a prevalence of 2.5%. The brain area usually associated with prosopagnosia is the fusiform gyrus, which activates specifically in response to faces. The functionality of the fusiform gyrus allows most people to recognize faces in more detail than they do similarly complex inanimate objects. For those with prosopagnosia, the method for recognizing faces depends on the less sensitive object-recognition system. The right hemisphere fusiform gyrus is more often involved in familiar face recognition than the left. It remains unclear whether the fusiform gyrus is specific for the recognition of human faces or if it is also involved in highly trained visual stimuli. Prosopagnosic patients are under normal conditions able to recognize facial expressions and emotions.

Acquired prosopagnosia results from occipito-temporal lobe damage and is most often found in adults. It is subdivided into apperceptive and associative prosopagnosia. In congenital prosopagnosia, the individual never adequately develops the ability to recognize faces.

Though there have been several attempts at remediation, no therapies have demonstrated lasting improvements across a group of prosopagnosics. Prosopagnosics often learn to use "piecemeal" or "feature-by-feature" recognition strategies. This may involve secondary clues such as clothing, gait, hair color, skin color, body shape, and voice. Because the face seems to function as an important identifying feature in memory, it can also be difficult for people with this condition to keep track of information about people, and socialize normally with others. Prosopagnosia has also been associated with other disorders that are associated with nearby brain areas: left hemianopsia (loss of vision from left side of space, associated with damage to the right occipital lobe), achromatopsia (a deficit in color perception often associated with unilateral or bilateral lesions in the temporo-occipital junction) and topographical disorientation (a loss of environmental familiarity and difficulties in using landmarks, associated with lesions in the posterior part of the parahippocampal gyrus and anterior part of the lingual gyrus of the right hemisphere).

The opposite of prosopagnosia is the skill of superior face recognition ability. People with this ability are called "super recognizers".

Apperceptive
Apperceptive prosopagnosia has typically been used to describe cases of acquired prosopagnosia with some of the earliest processes in the face perception system. The brain areas thought to play a critical role in apperceptive prosopagnosia are right occipital temporal regions. People with this disorder cannot make any sense of faces and are unable to make same–different judgments when they are presented with pictures of different faces. They are unable to recognize both familiar and unfamiliar faces. In addition, apperceptive sub-types of prosopagnosia struggle recognizing facial emotion. However, they may be able to recognize people based on non-face clues such as their clothing, hairstyle, skin color, or voice. Apperceptive prosopagnosia is believed to be associated with impaired fusiform gyrus. Experiments on the formation of new face detectors in adults on face-like stimuli (learning to distinguish the faces of cats) indicate that such new detectors are formed not in the fusiform, but in the lingual gyrus.

Associative
Associative prosopagnosia has typically been used to describe cases of acquired prosopagnosia with spared perceptual processes but impaired links between early face perception processes and the semantic information humans hold about people in our memories. Right anterior temporal regions may also play a critical role in associative prosopagnosia. People with this form of the disorder may be able to tell whether photos of people's faces are the same or different and derive the age and sex from a face (suggesting they can make sense of some face information) but may not be able to subsequently identify the person or provide any information about them such as their name, occupation, or when they were last encountered. Associative prosopagnosia is thought to be due to impaired functioning of the parahippocampal gyrus.

Developmental
Developmental prosopagnosia (DP), also called congenital prosopagnosia (CP), is a face-recognition deficit that is lifelong, manifesting in early childhood, and that cannot be attributed to acquired brain damage. While developmental prosopagnosia begins early in life, many people do not realize that they have DP until later in their adult lives. A number of studies have found functional deficits in DP both on the basis of EEG measures and fMRI. It has been suggested that a genetic factor is responsible for the condition. The term "hereditary prosopagnosia" was introduced if DP affected more than one family member, essentially accenting the possible genetic contribution of this condition. To examine this possible genetic factor, 689 randomly selected students were administered a survey in which seventeen developmental prosopagnosics were quantifiably identified. Family members of fourteen of the DP individuals were interviewed to determine prosopagnosia-like characteristics, and in all fourteen families, at least one other affected family member was found. Individuals with congenital prosopoagnosia have no mental images of faces, including of close relatives, but they may be able to recognize emotions. Under optimal conditions, recognition of facial expressions and emotions is normally preserved, though under more challenging conditions, it may exhibit subtle deficits.

In 2005, a study led by Ingo Kennerknecht showed support for the proposed congenital disorder form of prosopagnosia. This study provides epidemiological evidence that congenital prosopagnosia is a frequently occurring cognitive disorder that often runs in families. The analysis of pedigree trees formed within the study also indicates that the segregation pattern of hereditary prosopagnosia (HPA) is fully compatible with autosomal dominant inheritance. This mode of inheritance explains why HPA is so common among certain families (Kennerknecht et al. 2006).

Cause
Prosopagnosia can be caused by lesions in various parts of the inferior occipital areas (occipital face area), fusiform gyrus (fusiform face area), and the anterior temporal cortex. Positron emission tomography (PET) and fMRI scans have shown that, in individuals without prosopagnosia, these areas are activated specifically in response to face stimuli. The inferior occipital areas are mainly involved in the early stages of face perception and the anterior temporal structures integrate specific information about the face, voice, and name of a familiar person.

Acquired prosopagnosia can develop as the result of several neurologically damaging causes. Vascular causes of prosopagnosia include posterior cerebral artery infarcts (PCAIs) and hemorrhages in the infero-medial part of the temporo-occipital area. These can be either bilateral or unilateral, but if they are unilateral, they are almost always in the right hemisphere. Recent studies have confirmed that right hemisphere damage to the specific temporo-occipital areas mentioned above is sufficient to induce prosopagnosia. MRI scans of patients with prosopagnosia showed lesions isolated to the right hemisphere, while fMRI scans showed that the left hemisphere was functioning normally. Unilateral left temporo-occipital lesions result in object agnosia, but spare face recognition processes, although a few cases have been documented where left unilateral damage resulted in prosopagnosia. It has been suggested that these face recognition impairments caused by left hemisphere damage are due to a semantic defect blocking retrieval processes that are involved in obtaining person-specific semantic information from the visual modality.

Other less common etiologies include carbon monoxide poisoning, temporal lobectomy, encephalitis, neoplasm, right temporal lobe atrophy, injury, Parkinson's disease, and Alzheimer's disease.

Diagnosis
There are few neuropsychological assessments that can definitively diagnose prosopagnosia. One commonly used test is the famous faces tests, where individuals are asked to recognize the faces of famous persons. However, this test is difficult to standardize. The Benton Facial Recognition Test (BFRT) is another test used by neuropsychologists to assess face recognition skills. Individuals are presented with a target face above six test faces and are asked to identify which test face matches the target face. The images are cropped to eliminate hair and clothes, as many people with prosopagnosia use hair and clothing cues to recognize faces. Both male and female faces are used during the test. For the first six items only one test face matches the target face; during the next seven items, three of the test faces match the target faces and the poses are different. The reliability of the BFRT was questioned when a study conducted by Duchaine and Nakayama showed that the average score for 11 self-reported prosopagnosics was within the normal range. One reason for this may be the way the test is designed. People with developmental prosopagnosia often use piecemeal strategies, which this test encourages by providing the target face to compare with possible matching faces. As the test increases in difficulty more and more facial features become obscured due to position and lighting, leading normal control subjects to rely on the exact same strategy of looking for individual features to match with the target face.

The test may be useful for identifying patients with apperceptive prosopagnosia, since this is mainly a matching test and they are unable to recognize both familiar and unfamiliar faces. They would be unable to pass the test. It would not be useful in diagnosing patients with associative prosopagnosia since they are able to match faces.

The Cambridge Face Memory Test (CFMT) was developed by Duchaine and Nakayama to better diagnose people with prosopagnosia. This test initially presents individuals with three images each of six different target faces. They are then presented with many three-image series, which contain one image of a target face and two distracters. Duchaine and Nakayama showed that the CFMT is more accurate and efficient than previous tests in diagnosing patients with prosopagnosia. Their study compared the two tests and 75% of patients were diagnosed by the CFMT, while only 25% of patients were diagnosed by the BFRT. However, similar to the BFRT, patients are being asked to essentially match unfamiliar faces, as they are seen only briefly at the start of the test. The test is not widely used and will need further testing before it can be considered reliable.

The 20-item Prosopagnosia Index (PI20) is a freely available and validated self-report questionnaire that can be used alongside computer-based face recognition tests to help  identify individuals with prosopagnosia. It has been validated using objective measures of face perception ability including famous face recognition tests and the Cambridge Face Memory Test. Less than 1.5% of the general population score above 65 on the PI20 and less than 65% on the CFMT.

Treatment
There are no widely accepted treatments.

Prognosis
Management strategies for acquired prosopagnosia, such as a person who has difficulty recognizing people's faces after a stroke, generally have a low rate of success. Acquired prosopagnosia sometimes spontaneously resolves.

History
Selective inabilities to recognize faces were documented as early as the 19th century, and included case studies by Hughlings Jackson and Jean-Martin Charcot. However, it was not named until the term prosopagnosia was first used in 1947 by Joachim Bodamer, a German neurologist. He described three cases, including a 24-year-old man who sustained a bullet wound to the head and lost his ability to recognize his friends, family, and even his own face. However, he was able to recognize and identify them through other sensory modalities such as auditory, tactile, and even other visual stimuli patterns (such as gait and other physical mannerisms). Bodamer gave his paper the title Die Prosop-Agnosie, derived from Classical Greek πρόσωπον (prósōpon) meaning "face" and αγνωσία (agnōsía) meaning "non-knowledge". In October 1996, Bill Choisser began popularizing the term face blindness for this condition; the earliest-known use of the term is in an 1899 medical paper.

A case of a prosopagnosia is "Dr P." in Oliver Sacks' 1985 book The Man Who Mistook His Wife for a Hat, though this is more properly considered to be one of a more general visual agnosia. Although Dr P. could not recognize his wife from her face, he was able to recognize her by her voice. His recognition of pictures of his family and friends appeared to be based on highly specific features, such as his brother's square jaw and big teeth. Oliver Sacks himself had prosopagnosia, but did not know it for much of his life.

The study of prosopagnosia has been crucial in the development of theories of face perception. Because prosopagnosia is not a unitary disorder (i.e., different people may show different types and levels of impairment), it has been argued that face perception involves a number of stages, each of which can cause qualitative differences in impairment that different persons with prosopagnosia may exhibit.

This sort of evidence has been crucial in supporting the theory that there may be a specific face perception system in the brain. Most researchers agree that the facial perception process is holistic rather than featural, as it is for perception of most objects. A holistic perception of the face does not involve any explicit representation of local features (i.e., eyes, nose, mouth, etc.), but rather considers the face as a whole.

As the prototypical face has a specific spatial layout (eyes are always located above nose, and nose located above mouth), it is beneficial to use a holistic approach to recognize individual/specific faces from a group of similar layouts. This holistic processing of the face is exactly what is damaged in prosopagnosics. They are able to recognize the specific spatial layout and characteristics of facial features, but they are unable to process them as one entire face. This is counterintuitive to many people, as not everyone believes faces are "special" or perceived in a different way from other objects in the rest of the world. Though evidence suggests that other visual objects are processed in a holistic manner (e.g., dogs in dog experts), the size of these effects are smaller and are less consistently demonstrated than with faces. In a study conducted by Diamond and Carey, they showed this to be true by performing tests on dog-show judges. They showed pictures of dogs to the judges and to a control group and they then inverted those same pictures and showed them again. The dog-show judges had greater difficulty in recognizing the dogs once inverted compared to the control group; the inversion effect, the increased difficulty in recognizing a picture once inverted, was shown to be in effect. It was previously believed that the inversion effect was associated only with faces, but this study shows that it may apply to any category of expertise.

It has also been argued that prosopagnosia may be a general impairment in understanding how individual perceptual components make up the structure or gestalt of an object. Psychologist Martha Farah has been particularly associated with this view.

Children
Developmental prosopagnosia can be a difficult thing for a child to both understand and cope with. Many adults with developmental prosopagnosia report that for a long time they had no idea that they had a deficit in face processing, unaware that others could distinguish people solely on facial differences. Individuals with congenital prosopoagnosia have no mental images of faces, even though they may be able to normally distinguish emotions.

Prosopagnosia in children may be overlooked; they may just appear to be very shy or slightly odd due to their inability to recognize faces. They may also have a hard time making friends, as they may not recognize their classmates. They often make friends with children who have very clear, distinguishing features. Children with prosopagnosia can have a particularly difficult time at school, as many school professionals are not well versed in prosopagnosia, if they are aware of the disorder at all. Recently, a database of children's faces and test for child face perception has been developed, which may offer professionals a way to evaluate if a child has prosopagnosia.

Children with prosopagnosia may also have difficulties following the plots of television shows and movies, as they have trouble recognizing the different characters. They tend to gravitate towards cartoons, in which characters have simple but well-defined characteristics, and tend to wear the same clothes, may be strikingly different colours or even different species. Prosopagnosiac children even have a hard time telling family members apart, or recognizing people out of context (e.g., the teacher in a grocery store). Some have difficulty recognising themselves in group photographs.

Prosopoagnosia particularly in children poses a special risk of danger, as the inability to accurately recognize familiar faces or the misidentification of strangers can put the child in an unsafe situation.

Notable people
The following is a list of public figures and other notable people with prosopagnosia.

 * Alan Alda (born 1936), American actor
 * Duncan Bannatyne (born 1949), Scottish entrepreneur
 * Sara Benincasa (born 1980) American comedian and author
 * Dave Chalk (born 1963), Canadian entrepreneur
 * Chuck Close (1940–2021), American painter
 * Paul Foot (born 1973), English comedian
 * Stephen Fry (born 1957), English actor
 * Robert Gascoyne-Cecil, 3rd Marquess of Salisbury (1830–1903)
 * Jane Goodall (born 1934), English primatologist
 * John Hickenlooper (born 1952), US Senator and former Governor of Colorado
 * Margaret Kerry (born 1929), American actress and reference model for Tinker Bell
 * Karl Kruszelnicki (born 1948), Australian science communicator
 * Joanna Lumley (born 1946), Indian-born British actress, presenter, former model, author, television producer, and activist
 * Markos Moulitsas (born 1971), American blogger and founder of DailyKos.com
 * Brad Pitt (born 1963), American actor and film producer
 * Oliver Sacks (1933–2015), British neurologist
 * Mary Ann Sieghart (born 1961), English journalist and radio presenter
 * Victoria, Crown Princess of Sweden (born 1977)
 * Jim Woodring (born 1952), American cartoonist
 * Steve Wozniak (born 1950), American computer engineer and co-founder of Apple Inc.

Pop Culture
The respective protagonists in the films Faces in the Crowd and Prasanna Vadanam are afflicted with this disorder due to brain injury.

The fictional character Marky Bark from the TV show Arrested Development suffers from the disorder

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

title: Prosopagnosia


text:
Versus de scachis

Versus de scachis (Latin: "Verses on Chess"), also known as the Einsiedeln Poem in some literature, is the title given to a 10th-century Medieval Latin poem about chess. It is the first known European text to provide a technical description of chess for didactic purposes and it is considered a fundamental document to understand the development of chess in Europe.

Background
It was found on two manuscripts (Codex Einsidlensis 365 and 319) from Einsiedeln Abbey Library (where they are also currently preserved) located in Einsiedeln, Canton of Schwyz, Switzerland and it was dated to about AD 1000. The dating of the document makes the poem the earliest known reference to chess in a European text, as well as the earliest known document to mention the chess queen (called regina in Latin), and the first reference to a bicolor board with dark and light colors (a pattern that was absent from boards in precursors such as Indian chaturanga and Perso-Arabic shatranj, both of which were single-color and were divided only by horizontal and vertical lines).

The poem occupies both written sides of a sheet, and was only extracted in 1839 by the then abbey archivist Gall Morel (1803–1872) who combined it together with other loose sheets to form a composite volume, catalogued in the abbey archives as "Einsiedeln 365". In 1877, professor and classical philologist Hermann Hagen (1844–1898) made the verses accessible to the general public in his medieval poetry compilation Carmina Medii Aevi Maximam Partem Inedita: Ex Bibliothecis Helveticis Collecta. In 1913, the English chess historian H. J. R. Murray (1868–1955) translated, printed, and interpreted the verses. However, it was not until 1954 that historian H.M. Gamer drew attention to their extraordinary historical importance. There exists, in addition, an early medieval copy (though not of the Codex Einsidlensis 365) of lines 65 to 98 with a somewhat more classical orthography, which is dated to 997 AD and is also preserved in the Einsiedeln Abbey Library.

The title of Versus de scachis is from Codex Einsidlensis 365. The poem most likely dates to the 10th century. Gamer (1954) argues that the text in Codex Einsidlensis 365 might date to shortly before AD 1000, and the one in Codex Einsidlensis 319 dates to about the same time, or possibly to a few years after AD 1000. The text in Codex Einsidlensis 319 is incomplete, and entitled De aleae ratione.

Content
The poem itself consists of 98 lines in elegiac couplets and written in Medieval Latin. The first ten verses justify the game as mental recreation, in which there is no malice (ne dollus ullus inest), no perjurious fraud, and no physical risk (non laceras corpus membra vel ulla tui), underlining also the advantage of playing without dice. Thus, the poem begins by expressing praise for the game of chess as a unique game that did not require gambling or dice. According to some chess historians, this initial statement was made in order to oppose common religious disapproval of games of chance that involved gambling.

In the next ten verses the alternative coloring of the squares on the board is mentioned for the first time, not yet in general use but used by some players (Sunt quibus has placuit duplici fucare colore) as a simple yet advantageous invention to better calculate the moves, besides giving players the ability to discover, more easily, mistakes or false moves. Between verses 21-44 the two sides, red and white (Pars hæc si candet, illa rubore nitet), are described, together with the pieces. The movement of the pieces as well as the main regulatory conditions of the game are near identical to shatranj (Perso-Arabic chess), except for the pawn-promotion rule. From the poetic descriptions of the pieces and their movements, it can be interpreted that the movements differ from modern chess and can be summarized as follows:

 * Rex (king): It can move to any adjacent square. Unlike other pieces, it can never be captured, but when it's under attack and surrounded so that it can no longer move, the game comes to an end.
 * Regina (queen): It can move only to a diagonal adjacent square, making it the second weakest piece.
 * Comes or curvus (meaning "count" or "aged one", today’s bishop): It can move diagonally to the third square of its original color.
 * Æques (knight): It can move to the third square of a different color, two steps straight ahead, then one step on the diagonal.
 * Rochus or marchio ("rook" or "marquis", respectively): It can move in a straight direction as far as the player wishes.
 * Pedes or pedites ("soldier", today's pawn): It can only move to the square in front of it and captures another piece diagonally on an adjacent square of the same color, making it the weakest piece. If it reaches the eighth row then it's allowed to move like the queen but only if the original queen is out of the board.

According to chess historian H. J. R. Murray:

"The most striking feature of this rather tedious poem is its freedom from Arabic terminology. The words check and mate are not used, and it is only the name of the game, scachi, in the title, and the word rochus that show that the writer is dealing with a game that is not of European invention. The nomenclature of the game is drawn from that of the state, and not from that of the army."

title: Versus de scachis


text:
Processor register

A processor register is a quickly accessible location available to a computer's processor. Registers usually consist of a small amount of fast storage, although some registers have specific hardware functions, and may be read-only or write-only. In computer architecture, registers are typically addressed by mechanisms other than main memory, but may in some cases be assigned a memory address e.g. DEC PDP-10, ICT 1900.

Almost all computers, whether load/store architecture or not, load items of data from a larger memory into registers where they are used for arithmetic operations, bitwise operations, and other operations, and are manipulated or tested by machine instructions. Manipulated items are then often stored back to main memory, either by the same instruction or by a subsequent one. Modern processors use either static or dynamic RAM as main memory, with the latter usually accessed via one or more cache levels.

Processor registers are normally at the top of the memory hierarchy, and provide the fastest way to access data. The term normally refers only to the group of registers that are directly encoded as part of an instruction, as defined by the instruction set. However, modern high-performance CPUs often have duplicates of these "architectural registers" in order to improve performance via register renaming, allowing parallel and speculative execution. Modern x86 design acquired these techniques around 1995 with the releases of Pentium Pro, Cyrix 6x86, Nx586, and AMD K5.

When a computer program accesses the same data repeatedly, this is called locality of reference. Holding frequently used values in registers can be critical to a program's performance. Register allocation is performed either by a compiler in the code generation phase, or manually by an assembly language programmer.

Size
Registers are normally measured by the number of bits they can hold, for example, an "8-bit register", "32-bit register", "64-bit register", or even more. In some instruction sets, the registers can operate in various modes, breaking down their storage memory into smaller parts (32-bit into four 8-bit ones, for instance) to which multiple data (vector, or one-dimensional array of data) can be loaded and operated upon at the same time. Typically it is implemented by adding extra registers that map their memory into a larger register. Processors that have the ability to execute single instructions on multiple data are called vector processors.

Types
A processor often contains several kinds of registers, which can be classified according to the types of values they can store or the instructions that operate on them:

 * User-accessible registers can be read or written by machine instructions. The most common division of user-accessible registers is a division into data registers and address registers.
 * Data registers can hold numeric data values such as integers and, in some architectures, floating-point numbers, as well as characters, small bit arrays and other data. In some older architectures, such as the IBM 704, the IBM 709 and successors, the PDP-1, the PDP-4/PDP-7/PDP-9/PDP-15, the PDP-5/PDP-8, and the HP 2100, a special data register known as the accumulator is used implicitly for many operations.
 * Address registers hold addresses and are used by instructions that indirectly access primary memory.
 * Some processors contain registers that may only be used to hold an address or only to hold numeric values (in some cases used as an index register whose value is added as an offset from some address); others allow registers to hold either kind of quantity. A wide variety of possible addressing modes, used to specify the effective address of an operand, exist.
 * The stack pointer is used to manage the run-time stack. Rarely, other data stacks are addressed by dedicated address registers (see stack machine).
 * General-purpose registers (GPRs) can store both data and addresses, i.e., they are combined data/address registers; in some architectures, the register file is unified so that the GPRs can store floating-point numbers as well.
 * Status registers hold truth values often used to determine whether some instruction should or should not be executed.
 * Floating-point registers (FPRs) store floating-point numbers in many architectures.
 * Constant registers hold read-only values such as zero, one, or pi.
 *  hold data for vector processing done by SIMD instructions (Single Instruction, Multiple Data).
 * Special-purpose registers (SPRs) hold some elements of the program state; they usually include the program counter, also called the instruction pointer, and the status register; the program counter and status register might be combined in a program status word (PSW) register. The aforementioned stack pointer is sometimes also included in this group. Embedded microprocessors can also have registers corresponding to specialized hardware elements.
 * Model-specific registers (also called machine-specific registers) store data and settings related to the processor itself. Because their meanings are attached to the design of a specific processor, they are not expected to remain standard between processor generations.
 * Memory type range registers (MTRRs)
 * Internal registers are not accessible by instructions and are used internally for processor operations.
 * The instruction register holds the instruction currently being executed.
 * Registers related to fetching information from RAM, a collection of storage registers located on separate chips from the CPU:
 * Memory buffer register (MBR), also known as memory data register (MDR)
 * Memory address register (MAR)
 * Architectural registers are the registers visible to software and are defined by an architecture. They may not correspond to the physical hardware if register renaming is being performed by the underlying hardware.

Hardware registers are similar, but occur outside CPUs.

In some architectures (such as SPARC and MIPS), the first or last register in the integer register file is a pseudo-register in that it is hardwired to always return zero when read (mostly to simplify indexing modes), and it cannot be overwritten. In Alpha, this is also done for the floating-point register file. As a result of this, register files are commonly quoted as having one register more than how many of them are actually usable; for example, 32 registers are quoted when only 31 of them fit within the above definition of a register.

Examples
The following table shows the number of registers in several mainstream CPU architectures. Note that in x86-compatible processors, the stack pointer is counted as an integer register, even though there are a limited number of instructions that may be used to operate on its contents. Similar caveats apply to most architectures.

Although all of the below-listed architectures are different, almost all are in a basic arrangement known as the von Neumann architecture, first proposed by the Hungarian-American mathematician John von Neumann. It is also noteworthy that the number of registers on GPUs is much higher than that on CPUs.

Usage
The number of registers available on a processor and the operations that can be performed using those registers has a significant impact on the efficiency of code generated by optimizing compilers. The Strahler number of an expression tree gives the minimum number of registers required to evaluate that expression tree.

title: Processor register


text:
Talk:SU(3) × SU(2) × U(1)

this model no predicts monopoles...

Just curious: should that be now or not? Great article, by the way. —Herbee 13:40, 2004 Feb 24 (UTC)

This is a terrible name for an article. I'd move it to a different name, but the article text is completely impenetrable to me... Surely there is a better name for this. -- Wapcaplet 01:13, 18 Sep 2004 (UTC)

 * I'd have renamed it SU(3) × SU(2) × U(1) by now, but software changes in June make it impossible for such symbols to appear in article titles. (Of course, I realize that's not what Wapcaplet had in mind.) Michael Hardy 19:26, 18 Sep 2004 (UTC)

Well, what I'm saying is that it seems wrong for the article to be named after a formula (or whatever it is). I don't know whether this is an apt comparison, but for instance we have Quadratic equation, not ax² plus bx plus c (though, by contrast, we do have E=mc², but I suspect that is because it's the most widely recognized "name" for the equation). Is there a name, in normal English, for what this article is talking about? Among those in this field of study, how is this subject referred to? Do they say "Yeah, the other day I was reading about ess you three times ess you two times you, when I realized something..." If it is a formulation of the Standard Model, then perhaps a name like "XXX model" or "XXX formulation" would be better. -- Wapcaplet 23:25, 18 Sep 2004 (UTC)

 * Physicists, or at least those I know call it 3-2-1 but that's an even worse name for the article, isn't it? Phys 06:06, 28 Dec 2004 (UTC)

title: Talk:SU(3) × SU(2) × U(1)


text:
Rotational–vibrational spectroscopy

Rotational–vibrational spectroscopy is a branch of molecular spectroscopy that is concerned with infrared and Raman spectra of molecules in the gas phase. Transitions involving changes in both vibrational and rotational states can be abbreviated as rovibrational (or ro-vibrational) transitions. When such transitions emit or absorb photons (electromagnetic radiation), the frequency is proportional to the difference in energy levels and can be detected by certain kinds of spectroscopy. Since changes in rotational energy levels are typically much smaller than changes in vibrational energy levels, changes in rotational state are said to give fine structure to the vibrational spectrum. For a given vibrational transition, the same theoretical treatment as for pure rotational spectroscopy gives the rotational quantum numbers, energy levels, and selection rules. In linear and spherical top molecules, rotational lines are found as simple progressions at both higher and lower frequencies relative to the pure vibration frequency. In symmetric top molecules the transitions are classified as parallel when the dipole moment change is parallel to the principal axis of rotation, and perpendicular when the change is perpendicular to that axis. The ro-vibrational spectrum of the asymmetric rotor water is important because of the presence of water vapor in the atmosphere.

Overview
Ro-vibrational spectroscopy concerns molecules in the gas phase. There are sequences of quantized rotational levels associated with both the ground and excited vibrational states. The spectra are often resolved into lines due to transitions from one rotational level in the ground vibrational state to one rotational level in the vibrationally excited state. The lines corresponding to a given vibrational transition form a band.

In the simplest cases the part of the infrared spectrum involving vibrational transitions with the same rotational quantum number (ΔJ = 0) in ground and excited states is called the Q-branch. On the high frequency side of the Q-branch the energy of rotational transitions is added to the energy of the vibrational transition. This is known as the R-branch of the spectrum for ΔJ = +1. The P-branch for ΔJ = −1 lies on the low wavenumber side of the Q branch. The appearance of the R-branch is very similar to the appearance of the pure rotation spectrum (but shifted to much higher wavenumbers), and the P-branch appears as a nearly mirror image of the R-branch. The Q branch is sometimes missing because of transitions with no change in J being forbidden.

The appearance of rotational fine structure is determined by the symmetry of the molecular rotors which are classified, in the same way as for pure rotational spectroscopy, into linear molecules, spherical-, symmetric- and asymmetric- rotor classes. The quantum mechanical treatment of rotational fine structure is the same as for pure rotation.

The strength of an absorption line is related to the number of molecules with the initial values of the vibrational quantum number ν and the rotational quantum number $$J$$, and depends on temperature. Since there are actually $$2J+1$$ states with rotational quantum number $$J$$, the population with value $$J$$ increases with $$J$$ initially, and then decays at higher $$J$$. This gives the characteristic shape of the P and R branches.

A general convention is to label quantities that refer to the vibrational ground and excited states of a transition with double prime and single prime, respectively. For example, the rotational constant for the ground state is written as $$B^{\prime\prime} ,$$ and that of the excited state as $$B^\prime .$$ Also, these constants are expressed in the molecular spectroscopist's units of cm−1. so that $$B$$ in this article corresponds to $$\bar B = B/hc$$ in the definition of rotational constant at Rigid rotor.

Method of combination differences
Numerical analysis of ro-vibrational spectral data would appear to be complicated by the fact that the wavenumber for each transition depends on two rotational constants, $$B^{\prime\prime}$$ and $$B^\prime$$. However combinations which depend on only one rotational constant are found by subtracting wavenumbers of pairs of lines (one in the P-branch and one in the R-branch) which have either the same lower level or the same upper level. For example, in a diatomic molecule the line denoted P(J + 1) is due to the transition (v = 0, J + 1) → (v = 1, J) (meaning a transition from the state with vibrational quantum number ν going from 0 to 1 and the rotational quantum number going from some value J + 1 to J, with J > 0), and the line R(J − 1) is due to the transition (v = 0, J − 1) → (v = 1, J). The difference between the two wavenumbers corresponds to the energy difference between the (J + 1) and (J − 1) levels of the lower vibrational state and is denoted by $$\Delta_2$$ since it is the difference between levels differing by two units of J. If centrifugal distortion is included, it is given by

 * $$\Delta_2^{\prime\prime}F(J) = \bar \nu (R(J-1)) - \bar \nu(P(J+1)) = (2B^{\prime\prime}-3D^{\prime\prime}) \left(2J+1\right)-D^{\prime\prime}\left(2J+1\right)^3$$

where $$\bar \nu $$ means the frequency (or wavenumber) of the given line. The main term, $$2B(2J+1),$$ comes from the difference in the energy of the $$J+1$$ rotational state, $$B((J+1)(J+2)),$$ and that of the $$J-1$$ state, $$B''((J-1)J).$$

The rotational constant of the ground vibrational state B′′ and centrifugal distortion constant, D′′ can be found by least-squares fitting this difference as a function of J. The constant B′′ is used to determine the internuclear distance in the ground state as in pure rotational spectroscopy. (See Appendix)

Similarly the difference R(J) − P(J) depends only on the constants B′ and D′ for the excited vibrational state (v = 1), and B′ can be used to determine the internuclear distance in that state (which is inaccessible to pure rotational spectroscopy).

 * $$\Delta_2^{\prime}F(J) = \bar \nu(R(J)) - \bar \nu(P(J)) = (2B^{\prime}-3D^{\prime}) \left(2J+1\right)-D^{\prime}\left(2J+1\right)^3$$

Heteronuclear diatomic molecules

Diatomic molecules with the general formula AB have one normal mode of vibration involving stretching of the A-B bond. The vibrational term values $$ G(v)$$, for an anharmonic oscillator are given, to a first approximation, by
 * $$ G(v) = \omega_e \left(v+{1 \over 2}\right) - \omega_e\chi_e \left(v+{1 \over 2}\right)^2\,$$

where v is a vibrational quantum number, ωe is the harmonic wavenumber and χe is an anharmonicity constant.

When the molecule is in the gas phase, it can rotate about an axis, perpendicular to the molecular axis, passing through the centre of mass of the molecule. The rotational energy is also quantized, with term values to a first approximation given by
 * $$ F_v(J) = B_v J \left( J+1 \right) - D J^2 \left( J+1 \right)^2 $$

where J is a rotational quantum number and D is a centrifugal distortion constant. The rotational constant, Bv depends on the moment of inertia of the molecule, Iv, which varies with the vibrational quantum number, v
 * $$ B_v = {h \over{8\pi^2cI_v}}; \quad I_v=\frac{m_A m_B}{m_A+m_B}d_v^2$$

where mA and mB are the masses of the atoms A and B, and d represents the distance between the atoms. The term values of the ro-vibrational states are found (in the Born–Oppenheimer approximation) by combining the expressions for vibration and rotation.
 * $$ G(v)+F_v(J) = \left[ \omega_e \left(v+{1 \over 2}\right) + B_v J (J+1) \right]- \left[ \omega_e\chi_e \left(v+{1 \over 2}\right)^2 + D J^2 (J+1)^2 \right]$$

The first two terms in this expression correspond to a harmonic oscillator and a rigid rotor, the second pair of terms make a correction for anharmonicity and centrifugal distortion. A more general expression was given by Dunham.

The selection rule for electric dipole allowed ro-vibrational transitions, in the case of a diamagnetic diatomic molecule is
 * $$ \Delta v = \pm 1 \ (\pm 2, \pm 3, \textit{ etc.}$$ $$),\Delta J = \pm 1 $$

The transition with Δv=±1 is known as the fundamental transition. The selection rule has two consequences. The calculation of the transition wavenumbers is more complicated than for pure rotation because the rotational constant Bν is different in the ground and excited vibrational states. A simplified expression for the wavenumbers is obtained when the centrifugal distortion constants $$D^\prime$$ and $$D^{\prime\prime}$$ are approximately equal to each other.
 * 1) Both the vibrational and rotational quantum numbers must change. The transition :$$ \Delta v = \pm 1, \Delta J = 0 $$ (Q-branch) is forbidden
 * 2) The energy change of rotation can be either subtracted from or added to the energy change of vibration, giving the P- and R- branches of the spectrum, respectively.

 * $$ \bar \nu = \omega_0 +(B ^\prime+B^{\prime\prime})m +(B^\prime-B^{\prime\prime})m^2-2(D^\prime+D^{\prime\prime})m^3,

\quad \omega_0=\omega_e(1-2\chi_e)\quad m=\pm 1, \pm 2 \ etc. $$ where positive m values refer to the R-branch and negative values refer to the P-branch. The term ω0 gives the position of the (missing) Q-branch, the term $$(B ^\prime+B^{\prime\prime})m$$ implies an progression of equally spaced lines in the P- and R- branches, but the third term, $$(B^\prime-B^{\prime\prime})m^2$$shows that the separation between adjacent lines changes with changing rotational quantum number. When $$B^{\prime\prime}$$ is greater than $$B^\prime$$, as is usually the case, as J increases the separation between lines decreases in the R-branch and increases in the P-branch. Analysis of data from the infrared spectrum of carbon monoxide, gives value of $$B^{\prime\prime}$$ of 1.915 cm−1 and $$B^{\prime}$$ of 1.898 cm−1. The bond lengths are easily obtained from these constants as r0 = 113.3 pm, r1 = 113.6 pm. These bond lengths are slightly different from the equilibrium bond length. This is because there is zero-point energy in the vibrational ground state, whereas the equilibrium bond length is at the minimum in the potential energy curve. The relation between the rotational constants is given by
 * $$B_v=B_{eq}-\alpha \left(v+{1\over 2}\right)$$

where ν is a vibrational quantum number and α is a vibration-rotation interaction constant which can be calculated when the B values for two different vibrational states can be found. For carbon monoxide ''req = 113.0 pm.

Nitric oxide, NO, is a special case as the molecule is paramagnetic, with one unpaired electron. Coupling of the electron spin angular momentum with the molecular vibration causes lambda-doubling with calculated harmonic frequencies of 1904.03 and 1903.68 cm−1. Rotational levels are also split.

Homonuclear diatomic molecules
The quantum mechanics for homonuclear diatomic molecules such as dinitrogen, N2, and fluorine, F2, is qualitatively the same as for heteronuclear diatomic molecules, but the selection rules governing transitions are different. Since the electric dipole moment of the homonuclear diatomics is zero, the fundamental vibrational transition is electric-dipole-forbidden and the molecules are infrared inactive. However, a weak quadrupole-allowed spectrum of N2 can be observed when using long path-lengths both in the laboratory and in the atmosphere. The spectra of these molecules can be observed by Raman spectroscopy because the molecular vibration is Raman-allowed.

Dioxygen is a special case as the molecule is paramagnetic so magnetic-dipole-allowed transitions can be observed in the infrared. The unit electron spin has three spatial orientations with respect to the molecular rotational angular momentum vector, N, so that each rotational level is split into three states with total angular momentum (molecular rotation plus electron spin) $$\mathrm {J\hbar} \,$$, J = N + 1, N, and N - 1, each J state of this so-called p-type triplet arising from a different orientation of the spin with respect to the rotational motion of the molecule. Selection rules for magnetic dipole transitions allow transitions between successive members of the triplet (ΔJ = ±1) so that for each value of the rotational angular momentum quantum number N there are two allowed transitions. The 16O nucleus has zero nuclear spins angular momentum, so that symmetry considerations demand that N may only have odd values.

Raman spectra of diatomic molecules
The selection rule is
 * $$\Delta J = 0, \pm 2$$

so that the spectrum has an O-branch (∆J = −2), a Q-branch (∆J = 0) and an S-branch (∆J=+2). In the approximation that B′′ = B′ = B the wavenumbers are given by
 * $$\bar \nu (S(J))= \omega_0 +4BJ+6B = \omega_0 + 6B, \quad\omega_0 + 10B, \quad\omega_0 + 14B, \quad ...$$
 * $$\bar \nu (O(J))= \omega_0 -4BJ+2B = \omega_0 - 6B, \quad\omega_0 - 10B, \quad\omega_0 - 14B, \quad ...$$

since the S-branch starts at J=0 and the O-branch at J=2. So, to a first approximation, the separation between S(0) and O(2) is 12B and the separation between adjacent lines in both O- and S- branches is 4B. The most obvious effect of the fact that B′′ ≠ B′ is that the Q-branch has a series of closely spaced side lines on the low-frequency side due to transitions in which ΔJ=0 for J=1,2 etc. Useful difference formulae, neglecting centrifugal distortion are as follows.
 * $$\Delta_4^{\prime\prime}F(J) = \bar \nu [S(J-2)] - \bar \nu [O(J+2) ] = 4B^{\prime\prime}(2J+1)$$
 * $$\Delta_4^{\prime}F(J) = \bar \nu [S(J)] - \bar \nu [O(J)] = 4B^{\prime}(2J+1)$$

Molecular oxygen is a special case as the molecule is paramagnetic, with two unpaired electrons.

For homonuclear diatomics, nuclear spin statistical weights lead to alternating line intensities between even-$$J^{\prime\prime}$$ and odd-$$J^{\prime\prime}$$ levels. For nuclear spin I = 1/2 as in 1H2 and 19F2 the intensity alternation is 1:3. For 2H2 and 14N2, I=1 and the statistical weights are 6 and 3 so that the even-$$J^{\prime\prime}$$ levels are twice as intense. For 16O2 (I=0) all transitions with even values of $$J^{\prime\prime}$$ are forbidden.

Polyatomic linear molecules
These molecules fall into two classes, according to symmetry: centrosymmetric molecules with point group D∞h, such as carbon dioxide, CO2, and ethyne or acetylene, HCCH; and non-centrosymmetric molecules with point group C∞v such as hydrogen cyanide, HCN, and nitrous oxide, NNO. Centrosymmetric linear molecules have a dipole moment of zero, so do not show a pure rotation spectrum in the infrared or microwave regions. On the other hand, in certain vibrational excited states the molecules do have a dipole moment so that a ro-vibrational spectrum can be observed in the infrared.

The spectra of these molecules are classified according to the direction of the dipole moment change vector. When the vibration induces a dipole moment change pointing along the molecular axis the term parallel is applied, with the symbol $$\parallel$$. When the vibration induces a dipole moment pointing perpendicular to the molecular axis the term perpendicular is applied, with the symbol $$\perp$$. In both cases the P- and R- branch wavenumbers follow the same trend as in diatomic molecules. The two classes differ in the selection rules that apply to ro-vibrational transitions. For parallel transitions the selection rule is the same as for diatomic molecules, namely, the transition corresponding to the Q-branch is forbidden. An example is the C-H stretching mode of hydrogen cyanide.

For a perpendicular vibration the transition ΔJ=0 is allowed. This means that the transition is allowed for the molecule with the same rotational quantum number in the ground and excited vibrational state, for all the populated rotational states. This makes for an intense, relatively broad, Q-branch consisting of overlapping lines due to each rotational state. The N-N-O bending mode of nitrous oxide, at ca. 590 cm−1 is an example.

The spectra of centrosymmetric molecules exhibit alternating line intensities due to quantum state symmetry effects, since rotation of the molecule by 180° about a 2-fold rotation axis is equivalent to exchanging identical nuclei. In carbon dioxide, the oxygen atoms of the predominant isotopic species 12C16O2 have spin zero and are bosons, so that the total wavefunction must be symmetric when the two 16O nuclei are exchanged. The nuclear spin factor is always symmetric for two spin-zero nuclei, so that the rotational factor must also be symmetric which is true only for even-J levels. The odd-J rotational levels cannot exist and the allowed vibrational bands consist of only absorption lines from even-J initial levels. The separation between adjacent lines in the P- and R- branches is close to 4B rather than 2B as alternate lines are missing. For acetylene the hydrogens of 1H12C12C1H have spin-1/2 and are fermions, so the total wavefunction is antisymmetric when two 1H nuclei are exchanged. As is true for ortho and para hydrogen the nuclear spin function of the two hydrogens has three symmetric ortho states and one antisymmetric para states. For the three ortho states, the rotational wave function must be antisymmetric corresponding to odd J, and for the one para state it is symmetric corresponding to even J. The population of the odd J levels are therefore three times higher than the even J levels, and alternate line intensities are in the ratio 3:1.

Spherical top molecules
These molecules have equal moments of inertia about any axis, and belong to the point groups Td (tetrahedral AX4) and Oh (octahedral AX6). Molecules with these symmetries have a dipole moment of zero, so do not have a pure rotation spectrum in the infrared or microwave regions.

Tetrahedral molecules such as methane, CH4, have infrared-active stretching and bending vibrations, belonging to the T2 (sometimes written as F2) representation. These vibrations are triply degenerate and the rotational energy levels have three components separated by the Coriolis interaction. The rotational term values are given, to a first order approximation, by
 * $$F^+=B_\nu J(J+1) +2B_\nu\zeta_r (J+1)$$
 * $$F^0=B_\nu J(J+1) $$
 * $$F^-=B_\nu J(J+1) -2B_\nu\zeta_r J$$

where $$\zeta_r$$ is a constant for Coriolis coupling. The selection rule for a fundamental vibration is
 * $$\Delta J = 0, \pm 1$$

Thus, the spectrum is very much like the spectrum from a perpendicular vibration of a linear molecule, with a strong Q-branch composed of many transitions in which the rotational quantum number is the same in the vibrational ground and excited states, $$J^\prime =J^{\prime\prime} = 1, 2 ...$$ The effect of Coriolis coupling is clearly visible in the C-H stretching vibration of methane, though detailed study has shown that the first-order formula for Coriolis coupling, given above, is not adequate for methane.

Symmetric top molecules
These molecules have a unique principal rotation axis of order 3 or higher. There are two distinct moments of inertia and therefore two rotational constants. For rotation about any axis perpendicular to the unique axis, the moment of inertia is $$I_{\perp}$$ and the rotational constant is $$B = {h \over{8\pi^2cI_{\perp}}}$$, as for linear molecules. For rotation about the unique axis, however, the moment of inertia is $$I_{\parallel}$$ and the rotational constant is $$A = {h \over{8\pi^2cI_{\parallel}}}$$. Examples include ammonia, NH3 and methyl chloride, CH3Cl (both of molecular symmetry described by point group C3v), boron trifluoride, BF3 and phosphorus pentachloride, PCl5 (both of point group D3h), and benzene, C6H6 (point group D6h).

For symmetric rotors a quantum number J is associated with the total angular momentum of the molecule. For a given value of J, there is a 2J+1- fold degeneracy with the quantum number, M taking the values +J ...0 ... -J. The third quantum number, K is associated with rotation about the principal rotation axis of the molecule. As with linear molecules, transitions are classified as parallel, $$\parallel$$ or perpendicular,$$\perp$$, in this case according to the direction of the dipole moment change with respect to the principal rotation axis. A third category involves certain overtones and combination bands which share the properties of both parallel and perpendicular transitions. The selection rules are
 * $$\parallel$$ If K ≠ 0, then ΔJ = 0, ±1 and ΔK = 0
 * If K = 0, then ΔJ = ±1 and ΔK = 0
 * $$\perp$$ ΔJ = 0, ±1 and ΔK = ±1

The fact that the selection rules are different is the justification for the classification and it means that the spectra have a different appearance which can often be immediately recognized. An expression for the calculated wavenumbers of the P- and R- branches may be given as

 * $$\bar \nu = \bar \nu_0 +(B^\prime+B^{\prime\prime})m+(B^\prime-B^{\prime\prime} -D_J^\prime+D_J^{\prime\prime})m^2$$
 * $$-2(D_J^\prime+D_J^{\prime\prime})m^3-(D_J^\prime-D_J^{\prime\prime})m^4$$
 * $$+\left\{

\left[ (A^\prime-B^\prime)- (A^{\prime\prime}-B^{\prime\prime}) \right]-\left[ D_{JK}^\prime+D_{JK}^{\prime\prime} \right]m -\left[ D_{JK}^\prime - D_{JK}^{\prime\prime} \right] m^2 \right \} K^2 -(D_K^\prime - D_K^{\prime \prime} ) K^4$$ in which m = J+1 for the R-branch and -J for the P-branch. The three centrifugal distortion constants $$D_J, D_{JK}$$, and $$D_K$$ are needed to fit the term values of each level. The wavenumbers of the sub-structure corresponding to each band are given by
 * $$\bar \nu = \bar\nu_{sub} + (B^\prime-B^{\prime\prime})J(J+1) - (D_J^\prime -D_J^{\prime\prime})J^2(J+1)^2 -(D_{JK}^\prime -D_{JK}^{\prime\prime})J(J+1)K^2

$$ $$\bar \nu_{sub}$$ represents the Q-branch of the sub-structure, whose position is given by
 * $$\bar\nu_{sub}= \bar\nu_0+ \left[ (A^\prime - B^\prime) - (A^{\prime\prime}-B^{\prime\prime}) \right]K^2 -(D_K^\prime-D_K^{\prime\prime})K^4

$$.

Parallel bands
The C-Cl stretching vibration of methyl chloride, CH3Cl, gives a parallel band since the dipole moment change is aligned with the 3-fold rotation axis. The line spectrum shows the sub-structure of this band rather clearly; in reality, very high resolution spectroscopy would be needed to resolve the fine structure fully. Allen and Cross show parts of the spectrum of CH3D and give a detailed description of the numerical analysis of the experimental data.

Perpendicular bands
The selection rule for perpendicular bands give rise to more transitions than with parallel bands. A band can be viewed as a series of sub-structures, each with P, Q and R branches. The Q-branches are separated by approximately 2(A′-B′). The asymmetric HCH bending vibration of methyl chloride is typical. It shows a series of intense Q-branches with weak rotational fine structure. Analysis of the spectra is made more complicated by the fact that the ground-state vibration is bound, by symmetry, to be a degenerate vibration, which means that Coriolis coupling also affects the spectrum.

Hybrid bands
Overtones of a degenerate fundamental vibration have components of more than one symmetry type. For example, the first overtone of a vibration belonging to the E representation in a molecule like ammonia, NH3, will have components belonging to A1 and E representations. A transition to the A1 component will give a parallel band and a transition to the E component will give perpendicular bands; the result is a hybrid band.

Inversion in ammonia
For ammonia, NH3, the symmetric bending vibration is observed as two branches near 930 cm−1 and 965 cm−1. This so-called inversion doubling arises because the symmetric bending vibration is actually a large-amplitude motion known as inversion, in which the nitrogen atom passes through the plane of the three hydrogen atoms, similar to the inversion of an umbrella. The potential energy curve for such a vibration has a double minimum for the two pyramidal geometries, so that the vibrational energy levels occur in pairs which correspond to combinations of the vibrational states in the two potential minima. The two v = 1 states combine to form a symmetric state (1+) at 932.5 cm−1 above the ground (0+) state and an antisymmetric state (1−) at 968.3 cm−1.

The vibrational ground state (v = 0) is also doubled although the energy difference is much smaller, and the transition between the two levels can be measured directly in the microwave region, at ca. 24 GHz (0.8 cm−1). This transition is historically significant and was used in the ammonia maser, the fore-runner of the laser.

Asymmetric top molecules

Asymmetric top molecules have at most one or more 2-fold rotation axes. There are three unequal moments of inertia about three mutually perpendicular principal axes. The spectra are very complex. The transition wavenumbers cannot be expressed in terms of an analytical formula but can be calculated using numerical methods.

The water molecule is an important example of this class of molecule, particularly because of the presence of water vapor in the atmosphere. The low-resolution spectrum shown in green illustrates the complexity of the spectrum. At wavelengths greater than 10 μm (or wavenumbers less than 1000 cm−1) the absorption is due to pure rotation. The band around 6.3 μm (1590 cm−1) is due to the HOH bending vibration; the considerable breadth of this band is due to the presence of extensive rotational fine structure. High-resolution spectra of this band are shown in Allen and Cross, p 221. The symmetric and asymmetric stretching vibrations are close to each other, so the rotational fine structures of these bands overlap. The bands at shorter wavelength are overtones and combination bands, all of which show rotational fine structure. Medium resolution spectra of the bands around 1600 cm−1 and 3700 cm−1 are shown in Banwell and McCash, p91.

Ro-vibrational bands of asymmetric top molecules are classed as A-, B- or C- type for transitions in which the dipole moment change is along the axis of smallest moment of inertia to the highest.

Experimental methods
Ro-vibrational spectra are usually measured at high spectral resolution. In the past, this was achieved by using an echelle grating as the spectral dispersion element in a grating spectrometer. This is a type of diffraction grating optimized to use higher diffraction orders. Today at all resolutions the preferred method is FTIR. The primary reason for this is that infrared detectors are inherently noisy, and FTIR detects summed signals at multiple wavelengths simultaneously achieving a higher signal to noise by virtue of Fellgett's advantage for multiplexed methods. The resolving power of an FTIR spectrometer depends on the maximum retardation of the moving mirror. For example, to achieve a resolution of 0.1 cm−1, the moving mirror must have a maximum displacement of 10 cm from its position at zero path difference. Connes measured the vibration-rotation spectrum of Venusian CO2 at this resolution. A spectrometer with 0.001 cm−1 resolution is now available commercially. The throughput advantage of FTIR is important for high-resolution spectroscopy as the monochromator in a dispersive instrument with the same resolution would have very narrow entrance and exit slits.

When measuring the spectra of gases it is relatively easy to obtain very long path-lengths by using a multiple reflection cell. This is important because it allows the pressure to be reduced so as to minimize pressure broadening of the spectral lines, which may degrade resolution. Path lengths up to 20m are commercially available.

Appendix
The method of combination differences uses differences of wavenumbers in the P- and R- branches to obtain data that depend only on rotational constants in the vibrational ground or excited state. For the excited state
 * $$\Delta_2^{\prime}F(J)^{observed} = \bar \nu [R(J) ] - \bar \nu [P(J) ] $$

This function can be fitted, using the method of least-squares to data for carbon monoxide, from Harris and Bertolucci. The data calculated with the formula
 * $$\Delta_2^{\prime}F(J)^{calculated} = 2B^{\prime\prime} \left(2J+1\right)$$

in which centrifugal distortion is ignored, are shown in the columns labelled with (1). This formula implies that the data should lie on a straight line with slope 2B′′ and intercept zero. At first sight the data appear to conform to this model, with a root mean square residual of 0.21 cm−1. However, when centrifugal distortion is included, using the formula
 * $$\Delta_2^{\prime}F(J)^{calculated} = (2B^{\prime\prime}-3D^{\prime\prime}) \left(2J+1\right)-D^{\prime\prime}\left(2J+1\right)^3$$

the least-squares fit is improved markedly, with ms residual decreasing to 0.000086 cm−1. The calculated data are shown in the columns labelled with (2).

title: Rotational–vibrational spectroscopy


text:
Tunnels underneath the River Thames

The table below lists many of the tunnels under the River Thames in and near London, which, thanks largely to its underlying bed of clay, is one of the most tunnelled cities in the world. The tunnels are used for road vehicles, pedestrians, Underground and railway lines and utilities. Several tunnels are over a century old: the original Thames Tunnel was the world's first underwater tunnel.

Other tunnels
The figure and list above leaves out a tunnel to the site of the old Ferranti power station on the east side of the mouth of Deptford Creek.

There is also a tunnel between Cottons centre and the old Billingsgate Fish Market near to London Bridge. Citibank used it for cabling at one point; it was large enough for a person to walk through.

The Silvertown Tunnel is a new Thames river crossing proposed to supplement the existing Blackwall Tunnel, which will join the Greenwich Peninsula with West Silvertown.

The Thames Tideway Tunnel, due for completion in 2025, will be a 25 km long tunnel running mostly under the tidal section of the River Thames through central London to capture, store and convey almost all the raw sewage and rainwater that currently overflows into the river.

Background
London's abundance of river tunnels has resulted from a number of factors. For historical reasons, the city centre has relatively few railway bridges. Only three railway bridges exist in central London, only one of which provides through services across the capital. Consequently, railway builders have had to tunnel under the river in the city centre rather than bridge it. By contrast, railway bridges are relatively common to the west of the inner city.

Another historical factor has been the presence of the Port of London, which until the 1980s required large ships to be able to access the river as far upstream as the City of London. Until the construction of the Queen Elizabeth II Bridge at Dartford in 1991, the easternmost bridge on the Thames was Tower Bridge in central London. Even now, the Dartford Crossing provides the only way to cross the Thames by road between London and the sea. The width of the river downstream meant that tunnels were the only options for crossings before improvements in technology allowed the construction of high bridges such as the Queen Elizabeth II Bridge.

title: Tunnels underneath the River Thames