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Encyclopedia > Neutron
Neutron
Classification
 Subatomic particle Fermion Hadron Baryon Nucleon Neutron
Properties [1][2]
 Mass: 1.674 927 29(28) × 10−27 kg 939.565 560(81) MeV/c² 1.008665 amu Radius: about 0.8 × 10−15 m Electric charge: 0 C Spin: ½ Magnetic dipole moment: −1.91304273(45) μN Quark composition: 2 Down, 1 Up

In physics, the neutron is a subatomic particle with no net electric charge and a mass of 939.573 MeV/c² (1.6749 × 10−27 kg, slightly more than a proton). Its spin is ½. Its antiparticle is called the antineutron. The neutron, along with the proton, is a nucleon. Neutron, the subatomic particle, may also refer to: Neutron (comics), a Marvel Comics character. ... A free neutron is a neutron that exists outside of an atomic nucleus. ... A subatomic particle is a particle smaller than an atom: it may be elementary or composite. ... In particle physics, fermions are particles with half-integer spin. ... In particle physics, a hadron is a subatomic particle which experiences the strong nuclear force. ... In particle physics, the baryons are a family of subatomic particles including the proton and the neutron (collectively called nucleons), as well as a number of unstable, heavier particles (called hyperons). ... In physics a nucleon is a collective name for two baryons: the neutron and the proton. ... An electronvolt (symbol: eV) is the amount of energy gained by a single unbound electron when it falls through an electrostatic potential difference of one volt. ... A line showing the speed of light on a scale model of Earth and the Moon The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness. It is the speed of all electromagnetic radiation... The unified atomic mass unit (u), or Dalton (Da), is a small unit of mass used to express atomic and molecular masses. ... The coulomb (symbol: C) is the SI unit of electric charge. ... These are the 6 quarks and their most likely decay modes. ... Image File history File links Quark_structure_neutron. ... Physics (Greek: (phÃºsis), nature and (phusikÃ©), knowledge of nature) is the science concerned with the fundamental laws of the universe and their precise formulation in a mathematical framework. ... A subatomic particle is a particle smaller than an atom: it may be elementary or composite. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... Unsolved problems in physics: What causes anything to have mass? The U.S. National Prototype Kilogram, which currently serves as the primary standard for measuring mass in the U.S. Mass is the property of a physical object that quantifies the amount of matter and energy it is equivalent to. ... An electronvolt (symbol: eV) is the amount of energy gained by a single unbound electron when it falls through an electrostatic potential difference of one volt. ... A line showing the speed of light on a scale model of Earth and the Moon The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness. It is the speed of all electromagnetic radiation... // Properties [1][2] In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ... Corresponding to most kinds of particle, there is an associated antiparticle with the same mass and opposite charges. ... The antineutron is the antiparticle of the neutron. ... In physics a nucleon is a collective name for two baryons: the neutron and the proton. ...

The nucleus of most atoms (all stable isotopes except the most common isotope of hydrogen, protium, which consists of a single proton only) consists of protons and neutrons. The number of neutrons determines the isotope of an element. (For example, the carbon-12 isotope has 6 protons and 6 neutrons, while the carbon-14 isotope has 6 protons and 8 neutrons.) Isotopes are atoms of the same element that have the same atomic number but different masses due to a different number of neutrons. A semi-accurate depiction of the helium atom. ... â€œAtomicâ€ redirects here. ... This article needs to be cleaned up to conform to a higher standard of quality. ... Isotopes are any of the several different forms of an element each having different atomic mass (mass number). ... This article is about the chemistry of hydrogen. ... Isotopes are any of the several different forms of an element each having different atomic mass (mass number). ... Carbon 12 is a stable isotope of the element carbon. ... Carbon-14 is the radioactive isotope of carbon discovered February 27, 1940, by Martin Kamen and Sam Ruben. ...

A neutron consists of two down quarks and one up quark, thus classifying it as a baryon. These are the 6 quarks and their most likely decay modes. ... These are the 6 quarks and their most likely decay modes. ... In particle physics, the baryons are a family of subatomic particles including the proton and the neutron (collectively called nucleons), as well as a number of unstable, heavier particles (called hyperons). ...

## Stability

The Feynmann diagram of the neutron beta decay process

Outside the nucleus, free neutrons are unstable and have a mean lifetime of 885.7±0.8 seconds (about 15 minutes), decaying by emitting an electron and antineutrino to become a proton:[1] Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... In this Feynman diagram, an electron and positron annihilate producing a virtual photon that becomes a quark-antiquark pair. ... In nuclear physics, beta decay (sometimes called neutron decay) is a type of radioactive decay in which a beta particle (an electron or a positron) is emitted. ... A free neutron is a neutron that exists outside of an atomic nucleus. ... Given an assembly of elements, the number of which decreases ultimately to zero, the lifetime (also called the mean lifetime) is a certain number that characterizes the rate of reduction (decay) of the assembly. ... e- redirects here. ... Neutrinos are elementary particles. ...

$hbox{n}tohbox{p}+hbox{e}^-+overline{nu}_{mathrm{e}}$

This decay mode, known as beta decay, can also occur within certain unstable nuclei. Protons can also transform into neutrons through the process of electron capture, sometimes called inverse beta decay. Both beta decay and electron capture are types of radioactive decay. In nuclear physics, beta decay (sometimes called neutron decay) is a type of radioactive decay in which a beta particle (an electron or a positron) is emitted. ... Electron capture is a decay mode for isotopes that will occur when there are too many protons in the nucleus of an atom, and there isnt enough energy to emit a positron; however, it continues to be a viable decay mode for radioactive isotopes that can decay by positron... OK : Radioactive and Radioactivity redirect here. ...

Particles inside the nucleus are typically resonances between neutrons and protons, which transform into one another by the emission and absorption of pions. This article is about resonance in physics. ... In particle physics, pion (short for pi meson) is the collective name for three subatomic particles: Ï€0, Ï€+ and Ï€âˆ’. Pions are the lightest mesons and play an important role in explaining low-energy properties of the strong nuclear force. ...

## Interactions

The neutron interacts through all four fundamental interactions: the electromagnetic, weak nuclear, strong nuclear and gravitational interactions. A fundamental interaction is a mechanism by which particles interact with each other, and which cannot be explained by another more fundamental interaction. ... Electromagnetic interaction is a fundamental force of nature and is felt by charged leptons and quarks. ... The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four fundamental interactions of nature. ... The strong interaction or strong force is today understood to represent the interactions between quarks and gluons as detailed by the theory of quantum chromodynamics (QCD). ... â€œGravityâ€ redirects here. ...

Although the neutron has zero net charge, it may interact electromagnetically in two ways: first, the neutron has a magnetic moment of the same order as the proton; second, it is composed of electrically charged quarks. Thus, the electromagnetic interaction is primarily important to the neutron in deep inelastic scattering and in magnetic interactions. A bar magnet. ... // Properties [1][2] In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ... These are the 6 quarks and their most likely decay modes. ... Deep Inelastic Scattering is the name given to a process used to probe the insides of hadrons (particularly the baryons, such as protons and neutrons), using electrons. ... Magnetic lines of force of a bar magnet shown by iron filings on paper In physics, magnetism is one of the phenomena by which materials exert an attractive or repulsive force on other materials. ...

The neutron experiences the weak interaction through beta decay into a proton, electron and electron antineutrino. It experiences the gravitational force as does any energetic body; however, gravity is so weak that it may be neglected in most particle physics experiments. In nuclear physics, beta decay (sometimes called neutron decay) is a type of radioactive decay in which a beta particle (an electron or a positron) is emitted. ... e- redirects here. ... Neutrinos are elementary particles. ... Thousands of particles explode from the collision point of two relativistic (100 GeV per ion) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ...

The most important force to neutrons is the strong interaction. This interaction is responsible for the binding of the neutron's three quarks (one up quark, two down quarks) into a single particle. The residual strong force is also responsible for the binding of nuclei: the nuclear force. The nuclear force plays the leading role when neutrons pass through matter. Unlike charged particles or photons, the neutron cannot lose energy by ionizing atoms. Rather, the neutron goes on its way unchecked until it makes a head-on collision with an atomic nucleus. For this reason, neutron radiation is extremely penetrating and dangerous. These are the 6 quarks and their most likely decay modes. ... The up quark is a first-generation quark with a charge of +(2/3)e. ... The down quark is a first-generation quark with a charge of -(1/3)e. ... This article is about the force sometimes called the strong nuclear force. For the weak nuclear force or weak interaction, see that article. ... A semi-accurate depiction of the helium atom. ... The nuclear force (or nucleon-nucleon interaction or residual strong force) is the force between two or more nucleons. ... Ionization is the physical process of converting an atom or molecule into an ion by changing the difference between the number of protons and electrons. ... Neutron radiation consists of free neutrons. ...

## Detection

Main article: neutron detection

The common means of detecting a charged particle by looking for a track of ionization (such as in a cloud chamber) does not work for neutrons directly. Neutrons that elastically scatter off atoms can create an ionization track that is detectable, but the experiments are not as simple to carry out; other means for detecting neutrons, consisting of allowing them to interact with atomic nuclei, are more commonly used. Neutron detection is the effective detection of neutrons entering a well-positioned laboratory detector. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not made up of smaller particles. ... Discovery of the positron in 1932 by Carl D. Anderson in a cloud chamber The cloud chamber, also known as the Wilson chamber, is used for detecting particles of ionizing radiation. ...

A common method for detecting neutrons involves converting the energy released from such reactions into electrical signals. The nuclides 3He, 6Li, 10B, 233U, 235U, 237Np and 239Pu are useful for this purpose. A good discussion on neutron detection is found in chapter 14 of the book Radiation Detection and Measurement by Glenn F. Knoll (John Wiley & Sons, 1979).

## Uses

The neutron plays an important role in many nuclear reactions. For example, neutron capture often results in neutron activation, inducing radioactivity. In particular, knowledge of neutrons and their behavior has been important in the development of nuclear reactors and nuclear weapons. Neutron activation is the process by which neutron radiation induces radioactivity in materials. ... Radioactivity may mean: Look up radioactivity in Wiktionary, the free dictionary. ... Core of a small nuclear reactor used for research. ... The mushroom cloud of the atomic bombing of Nagasaki, Japan, 1945, rose some 18 kilometers (11 mi) above the hypocenter. ...

Cold, thermal and hot neutron radiation is commonly employed in neutron scattering facilities, where the radiation is used in a similar way one uses X-rays for the analysis of condensed matter. Neutrons are complementary to the latter in terms of atomic contrasts by different scattering cross sections; sensitivity to magnetism; energy range for inelastic neutron spectroscopy; and deep penetration into matter. The neutron temperature indicates a free neutrons energy, usually given in electron volts. ... Neutron radiation consists of free neutrons. ... The term Neutron Scattering encompasses all scientific techniques whereby neutrons are used as a scientific probe. ... In the NATO phonetic alphabet, X-ray represents the letter X. An X-ray picture (radiograph) taken by Röntgen An X-ray is a form of electromagnetic radiation with a wavelength approximately in the range of 5 pm to 10 nanometers (corresponding to frequencies in the range 30 PHz... It has been suggested that Solid state physics be merged into this article or section. ... In nuclear and particle physics, the concept of a cross section is used to express the likelihood of interaction between particles. ...

The development of "neutron lenses" based on total internal reflection within hollow glass capillary tubes or by reflection from dimpled aluminum plates has driven ongoing research into neutron microscopy and neutron/gamma ray tomography.

One use of neutron emitters is the detection of light nuclei, particularly the hydrogen found in water molecules. When a fast neutron collides with a light nucleus, it loses a large fraction of its energy. By measuring the rate at which slow neutrons return to the probe after reflecting off of hydrogen nuclei, a neutron probe may determine the water content in soil. Impact of a drop of water. ... A neutron probe is a device used to measure the quantity of water present in soil. ...

## Sources

Main article: neutron source

Due to the fact that free neutrons are unstable, they (neutron radiation) can be obtained only from nuclear disintegrations, nuclear reactions, and high-energy reactions (such as in cosmic radiation showers or accelerator collisions). Free neutron beams are obtained from neutron sources by neutron transport. For access to intense neutron sources, researchers must go to specialist facilities, such as the ISIS facility in the UK, which is currently the world's most intense pulsed neutron and muon source. A neutron source is a device, used in solid state physics (see neutron diffraction), particle physics and to start nuclear chain reactions, that emits neutrons. ... Neutron radiation consists of free neutrons. ... A neutron source is a device, used in solid state physics (see neutron diffraction), particle physics and to start nuclear chain reactions, that emits neutrons. ... Beams of free neutrons are obtained by extracting neutrons from neutron sources. ... ISIS experimental hall The ISIS facility is a scientific research institution, situated at the Rutherford Appleton Laboratory in Oxfordshire, UK. It contains a pulsed spallation neutron source, the most powerful in the world, which enables muon and neutron scattering science to probe the structure and properties of matter, from the... The muon (from the letter mu (Î¼)--used to represent it) is an elementary particle with negative electric charge and a spin of 1/2. ...

Neutrons' lack of total electric charge prevents engineers or experimentalists from being able to steer or accelerate them. Charged particles can be accelerated, decelerated, or deflected by electric or magnetic fields. However, these methods have almost no effect on neutrons (there is a small effect of a magnetic field on the free neutron because of its magnetic moment). Lightning strikes during a night-time thunderstorm. ... Current (I) flowing through a wire produces a magnetic field () around the wire. ... A bar magnet. ...

## Current developments

The existence of stable clusters of four neutrons, or tetraneutrons, has been hypothesised by a team led by Francisco-Miguel Marqués at the CNRS Laboratory for Nuclear Physics based on observations of the disintegration of beryllium-14 nuclei. This is particularly interesting, because current theory suggests that such clusters should not be stable, and therefore should not exist. A tetraneutron is a hypothesised stable cluster of four neutrons. ... This article needs to be wikified. ... General Name, Symbol, Number beryllium, Be, 4 Chemical series alkaline earth metals Group, Period, Block 2, 2, s Appearance white-gray metallic Atomic mass 9. ...

An experiment at the Institut Laue-Langevin (ILL) has attempted to measure an electric dipole, or separation of charges, within the neutron, and is consistent with an electric dipole moment of zero. These results are important in developing theories that go beyond the Standard Model. See FRONTIERS article, and the experiment's web page. Institut Laue-Langevin The Institut Laue-Langevin is an internationally-financed scientific facility, situated in Grenoble, France. ... This article is about the electromagnetic phenomenon. ... The Standard Model of Fundamental Particles and Interactions For the Standard Model in Cryptography, see Standard Model (cryptography). ...

## Anti-Neutron

Main article: antineutron

The antineutron is the antiparticle of the neutron. It was discovered by Bruce Cork in the year 1956, a year after the antiproton was discovered. The antineutron is the antiparticle of the neutron. ... Corresponding to most kinds of particle, there is an associated antiparticle with the same mass and opposite charges. ... Physicist who discovered the antineutron in 1956. ... Year 1956 (MCMLVI) was a leap year starting on Sunday of the Gregorian calendar. ... The antiproton (aka pbar) is the antiparticle of the proton. ...

CPT-symmetry puts strong constraints on the relative properties of particles and antiparticles and, therefore, is open to stringent tests. The fractional difference in the masses of the neutron and antineutron is (9±5)×10−5. Since the difference is only about 2 standard deviations away from zero, this does not give any convincing evidence of CPT-violation.[1] CPT symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity and time simultaneously. ... For each kind of particle, there is an associated antiparticle with the same mass but opposite electromagnetic, weak, and strong charges, as well as spin. ...

## Protection

### Fields concerning neutrons

Thousands of particles explode from the collision point of two relativistic (100 GeV per ion) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... In physics, the quark model is a classification scheme for hadrons in terms of their valence quarks, ie, the quarks (and antiquarks) which give rise to the quantum numbers of the hadrons. ... Chemistry - the study of atoms, made of nuclei (center particles) and electrons (outer particles), and the structures they form. ... Neutron detection is the effective detection of neutrons entering a well-positioned laboratory detector. ... The term Neutron Scattering encompasses all scientific techniques whereby neutrons are used as a scientific probe. ...

### Types of neutrons

In physics a nucleon is a collective name for two baryons: the neutron and the proton. ... A fast neutron is a free neutron with a kinetic energy level close to 1 MeV (10 TJ/kg, hence a speed of 14,000 km/s. ... A free neutron is a neutron that exists outside of an atomic nucleus. ... This article does not cite its references or sources. ... Neutron radiation consists of free neutrons. ... The sievert (symbol: Sv) is the SI derived unit of dose equivalent. ... The neutron temperature indicates a free neutrons energy, usually given in electron volts. ...

### Objects containing neutrons

A dineutron is a particle consisting of two neutrons that is considered to have a transitory existence in nuclear reactions produced by helions that result in the formation of a proton and a nucleus having the same atomic number as the target nucleus but a mass number two units greater. ... A tetraneutron is a hypothesised stable cluster of four neutrons. ... Neutronium is a term used in science fiction and popular literature to refer to an extremely dense phase of matter composed primarily of neutrons. ... A neutron star is one of the few possible endpoints of stellar evolution. ...

### Neutron sources

A neutron source is a device, used in solid state physics (see neutron diffraction), particle physics and to start nuclear chain reactions, that emits neutrons. ... Neutron generators are devices which contain compact linear accelerators and that produce neutrons by fusing isotopes of hydrogen together. ...

### Processes involving neutrons

Beams of free neutrons are obtained by extracting neutrons from neutron sources. ... Neutron diffraction is a crystallography technique that uses neutrons to determine the atomic structure of a material. ... A neutron bomb is a type of tactical nuclear weapon developed specifically to release a relatively large portion of its energy as energetic neutron radiation. ...

 Particles in physics - composite particles v • d • e Hadrons: Baryons (list) | Mesons (list) Baryons: Nucleons | Hyperons | Exotic baryons | Pentaquarks Mesons: Pions | Kaons | Quarkonium | Exotic mesons Atomic nuclei | Atoms (Periodic table (vertical)) | Molecules Thousands of particles explode from the collision point of two relativistic (100 GeV per ion) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... Elementary particles An elementary particle is a particle with no measurable internal structure, that is, it is not a composite of other particles. ... In particle physics, a hadron is a subatomic particle which experiences the strong nuclear force. ... In particle physics, the baryons are a family of subatomic particles including the proton and the neutron (collectively called nucleons), as well as a number of unstable, heavier particles (called hyperons). ... Baryon decuplet: Spin=3/2 Baryon octet: Spin=1/2 This is a list of baryons. ... Mesons of spin 1 form a nonet In particle physics, a meson is a strongly interacting boson, that is, it is a hadron with integral spin. ... A list of mesons. ... In physics a nucleon is a collective name for two baryons: the neutron and the proton. ... In particle physics, a hyperon is any subatomic particle which is a baryon (and hence a hadron and a fermion) with non-zero strangeness, but with zero charm and zero bottomness. ... Ordinary baryons are bound states of 3 quarks. ... A pentaquark is a subatomic particle consisting of a group of five quarks (compared to three quarks in normal baryons and two in mesons), or more specifically four quarks and one anti-quark. ... In particle physics, pion (short for pi meson) is the collective name for three subatomic particles: Ï€0, Ï€+ and Ï€âˆ’. Pions are the lightest mesons and play an important role in explaining low-energy properties of the strong nuclear force. ... In particle physics, Kaons (also called K-mesons and denoted K) are a group of four mesons distinguished by the fact that they carry a quantum number called strangeness. ... In high energy physics, a quarkonium (pl. ... Identities and classification of possible tetraquark mesons. ... A semi-accurate depiction of the helium atom. ... â€œAtomicâ€ redirects here. ... The alternative table is a standard periodic table rotated counterclockwise and then mirrored across the vertical axis, hence like in many writing systems, the lower groups are to the left and the number increases to the right. ... In science, a molecule is a group of atoms in a definite arrangement held together by chemical bonds. ...

## References

1. ^ a b c Particle Data Group's Review of Particle Physics 2006
2. ^ Povh, Rith, Scholz, Zetche, Particles and Nuclei, 1999, ISBN 3-540-43823-8

Results from FactBites:

 Neutron - Wikipedia, the free encyclopedia (1262 words) Although the neutron has zero net charge, it may interact electromagnetically in two ways: first, the neutron has a magnetic moment of the same order as the proton; second, it is composed of electrically charged quarks. Neutrons that elastically scatter off atoms can create an ionization track that is detectable, but the experiments are not as simple to carry out; other means for detecting neutrons, consisting of allowing them to interact with atomic nuclei, are more commonly used. One use of neutron emitters is the detection of light nuclei, particularly the hydrogen found in water molecules.
 Neutron - MSN Encarta (1492 words) Neutron, electrically neutral elementary particle that is part of the nucleus of the atom. The neutron is also affected by the weak nuclear force, an interaction among the building blocks of the neutron that causes the neutron to decay, or break apart. The neutrons are responsible for the remaining mass of the atom.
More results at FactBites »

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# Bounds for number of coin toss switches

I toss $n$ biased coins and I want to count the number of times you get a H followed by a T or a T followed by a H. I call these switches. So for example if I get HHTTHTHHHT then I have $5$ switches in total. If the coin gives H with prob $p$ and $T$ with prob $1-p$ then how can you find an approximation to the probability of getting at least $k$ switches for large $n$? I would also be interested in a Chernoff style tail bound.

Adjacent switch occurrences are not independent however non adjacent ones appear to be. The probability of having a switch at position $i+1$ given that there is a switch at position $i$ is exactly $1/2$, irrespective of $p$.

The mean number of switches is $\mu= (n-1)2p(1-p)$ and the variance is $2pq(2n−3−2pq(3n−5))$ where $q=(1-p)$.

The exact probability was given at http://math.stackexchange.com/questions/258221/probability-distribution-of-number-of-switches.

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For the total number of switches, the central limit theorem and the large deviation principle are established. The detailed analysis based on two related generating functions is motivated from an analytic argument by the author a few years ago to the following neat fact mentioned by Persi Diaconis (who has a non-analytic argument): For independent random variables $X_i$ with $P(X_i=1)=1/i=1-P(X_i=0)$, $i \ge 1$, one has $\sum_{i=1}^\infty X_iX_{i+1}=^d \hbox{Poisson}(1).$

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# Formula Symbols - C

Written by Jerry Ratzlaff on . Posted in Nomenclature & Symbols for Engineering, Mathematics, and Science

## Formula Symbols

A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z

## C

SymbolGreek SymbolDefinitionUSMetricValue
$$Z$$ - canonical partition function - - -
$$C$$ - capacitance - -  -
$$Q$$, $$\;V$$ - capacity $$in^3$$ $$L$$  -
$$Ca$$ - Capillary number dimensionless dimensionless  -
$$F$$   casing quality factor dimensionless dimensionless -
$$A$$, $$\;L_d$$   characteristic diffusion length - -  -
$$Ca$$ - Cauchy number dimensionless dimensionless  -
$$K$$ - cavitation - -  -
$$K_c$$ - cavitation index - -  -
$$Ca$$, $$\;\sigma$$ sigma Cavitation number dimensionless dimensionless  -
$$c$$ - cement content of concrete $$lb\;/\;yd^3$$ $$kg\;/\;m^3$$ -
$$Q_c$$ - cement quantity - - -
$$r_c$$ - cement ratio - - -
$$Ce$$ - Centrifuge number dimensionless dimensionless  -
$$a_c$$ - centripetal acceleration $$ft\;/\;sec$$ $$m\;/\;s$$  -
$$F_c$$ - centripetal force $$lbf$$ $$N$$  -
$$Q$$ - Chandrasekhar number dimensionless dimensionless  -
$$C$$, $$\;\Delta$$ Delta change - -  -
$$\rho$$ rho change density - -  -
$$\rho$$ rho change density of electrons - -  -
$$\Delta \omega$$ omega change in angular velocity $$ft \;/\; sec$$ $$m \;/\; s$$  -
$$\Delta v$$ - change in fluid velocity $$ft \;/\; sec$$ $$m \;/\; s$$  -
$$l_c$$ - change in length $$ft \;or\; in$$ $$m \;or\; mm$$  -
$$z$$ - change number of an ion - -  -
change / quantum ratio constant constant $$2.417\;989\;348\;x\;10^{14}\;kg^{-1}\;m^{-2}\;s^2\;A$$
$$\Omega$$ Omega characteristic angular velocity - -  -
$$\Delta x$$ Delta characteristic difference of mole fraction - -  -
$$f$$ - characteristic frequency - -  -
$$Z_0$$ mu characteristic impedance of vacuum constant constant $$376.730\;313\;668\;\Omega$$
$$l$$, $$\;l_c$$ - characteristic length $$in \;or\; ft$$ $$mm \;or\; m$$  -
$$v$$ - characteristic speed - -  -
$$\Theta$$ Theta characteristic temperature - -  -
$$\Delta T$$ Delta characteristic temperature difference - -  -
$$\Delta t$$ Delta characteristic time interval - -  -
$$U$$ - characteristic velocity $$ft/sec$$ $$m/s$$  -
$$q$$ - charge of particle - -  -
$$\mu$$ mu chemical potential - -  -
$$C$$ - Chezy coefficient - -  -
$$Ch$$ - Chezy formula - $$m^{1/2}/s$$  -
$$c$$ - chord length $$in \;or\; ft$$ $$mm \;or\; m$$  -
$$\omega$$ omega circular frequency - -  -
$$\Gamma$$ Gamma circulation $$ft^2\;/\;sec$$ $$m^2\;/\;s$$  -
$$C$$ - circumference $$ft$$ $$m$$  -
$$r_e$$ - classical electron radius constant constant $$2.817\;940\;3262\;x\;10^{-15}\;m$$
$$c$$ - clearance $$in$$ $$m$$  -
$$d_3$$ - clearance length $$ft$$ $$m$$ -
$$Q_{co}$$ - coarse quantity (gravel  & rock) - - -
$$r_{co}$$ - coarse ratio (gravel  & rock) - - -
$$C$$ - coefficient - -  -
$$\gamma$$ gamma coefficient of area thermal expansion $$1 \;/\; ^\circ F$$ $$1 \;/\; ^\circ C$$  -
$$K_c$$ - coefficient of constant cavitation dimensionless number dimensionless number  -
$$\mu$$, $$\;C_d$$ mu coefficient of discharge - -  -
$$f$$ - coefficient of friction dimensionless dimensionless  -
$$\alpha_t$$ alpha coefficient of linear thermal expansion $$in$$ $$mm$$  -
$$e$$ - coefficient of restitution - -  -
$$a$$ - coefficient of rolling resistance $$ft$$ $$m$$  -
$$\alpha$$, $$\;\alpha_c$$ alpha coefficient of thermal expansion $$1 \;/\; ^\circ K$$ $$1 \;/\; ^\circ K$$ -
$$C$$ - coefficient of viscous damping $$lbf-sec^2 \;/\; ft^2$$ $$N \cdot s^2 \;/\; m^2$$  -
$$\eta$$ eta coeficient of viscosity $$lbf-sec \;/\; ft^2$$ $$Pa-s$$  -
$$\alpha_v$$ alpha coefficient of volumetric thermal expansion $$ft^3$$ $$m^3$$  -
$$\xi$$ xi coherence depth - -  -
$$Coh$$ - cohesion number dimensionless dimensionless  -
$$v_c$$ - collision frequency - -  -
-  - Colburn J factors dimensionless dimensionless  -
$$k_e$$ - Coulombo's constant constant constant -
$$CCV$$ - combustion chamber volume $$in^3$$ $$cc^3$$  -
$$Psi*$$ Psi complex conjugate - -  -
$$\eta^*$$ eta complex viscosity - -  -
$$k$$, $$\;k_t$$, $$\;\beta$$ beta compressibility $${ft}^2\;/\;lbf$$ $$Pa^{-1}$$  -
$$Z$$ - compressibility factor dimensionless dimensionless  -
$$Z_i$$ - compressibility factor at inlet - -  -
$$Z_o$$ - compressibility factor at outlet - -  -
$$K$$ - compression - -  -
$$CCV$$ - compression chanber volume $$in^3$$ $$cc^3$$  -
$$CR$$ - compression ratio $$in^3$$ $$cc^3$$   -
$$\lambda_c$$ lambda Compton wavelength - -  -
$$CFD$$ - computational fluid dynamics - -  -
$$C$$ - concentration $$ppm$$ $$mg\;/\;L$$  -
$$C$$ - concentration of htdrocarbon in air - - -
$$f_cm$$ - concrete mean compressive cylinder strength $$lb\;/\;in^2 \;or\; psi$$ $$Pa$$ -
$$f_cm28$$ - concrete mean compressive cylinder strength at 28 days $$lb\;/\;in^2 \;or\; psi$$ $$Pa$$ -
$$f_cmt$$ - concrete mean compressive cylinder strength at age t $$lb\;/\;in^2 \;or\; psi$$ $$Pa$$ -
$$f_cmtc$$ - concrete mean compressive cylinder strength when drying starts at age t_c $$lb\;/\;in^2 \;or\; psi$$ $$Pa$$ -
$$f_cmto$$ - concrete mean compressive cylinder strength when loading starts at age t_o $$lb\;/\;in^2 \;or\; psi$$ $$Pa$$ -
$$f_{c}{'}$$ - concrete specific cylinder strength at 28 days $$lb\;/\;in^2 \;or\; psi$$ $$Pa$$ -
$$m_c$$ - condensate load $$lb\;/\;hr$$ $$kg\;/\;h$$  -
$$G$$ - conductance - -  -
$$G_0$$ - conductance quantum constant constant $$7.748\;091\;7346\;x\;10^{-5}\;kg^{-1}\;m^{-2}\;s^3\;A^2$$
$$\gamma$$, $$\;\sigma$$ gamma, sigma conductivity - -  -
$$c$$ - consentration - -  -
$$CP$$ - conservation management and land cover practices - - -
$$k$$ - constant - -  -
$$a_c$$ - constant acceleration $$ft\;/\;sec^2$$ $$m\;/\;s^2$$  -
$$\omega_f$$ omega constant angular acceleration $$ft\;/\;sec$$ $$m\;/\;s$$  -
$$c_p$$, $$\;p$$ - constant pressure $$lb\;/\;in^2 \;or\; psi$$ $$Pa$$  -
$$v$$ - constant volume $$in^3 \;or\; ft^3$$ $$mm^3 \;or\; m^3$$  -
$$\beta$$ beta contact angle $$deg$$ $$deg$$  -
$$C_v$$ - control valve - -  -
$$h$$, $$\;h_c$$ - convective heat transfer coefficient $$Btu \;/\; hr-ft^2-^\circ F$$ $$W \;/\; m^2-K$$  -
$$k$$ - conversion factor of the unit system - -  -
$$k$$ - conveyance $$ft^3\;/\;sec$$ $$m^3\;/\;s$$ -
$$T_c$$ - cooler temperature $$Btu\;/\;lbm$$ $$kJ\;/\;kg$$  -
$$CCD$$ - cooling degree days $$^\circ F-day$$ $$^\circ C-day$$  -
$$CLF$$ - cooling load factor - -  -
$$CLTD$$ - cooling load temperature difference $$^\circ F$$ $$^\circ C$$  -
$$f$$ - Coriolis frequency $$1 \;/\; sec$$ $$1 \;/\; s$$  -
$$C$$, $$\;\alpha$$, $$\;K$$ alpha correction factor - -  -
$$C$$ - corrosion allowance $$in$$ $$cm$$  -
$$C$$ - cost - -  -
$$k$$, $$\;k_e$$ - Coulomb's constant constant constant $$8\;987\;551\;788.7\;N\;m^2\;C^{-2}$$
$$F$$ - Coulomb's law - -  -
$$k$$, $$\;k_e$$ - Coulmbo's wave constant constant constant -
$$k$$ - coupling coefficient - -  -
$$Co$$ - Courant Number dimensionless dimensionless  -
$$Co$$ - Cowling number dimensionless dimensionless  -
$$B$$ - crack coefficient $$ft^3\;/\;ft-hr$$ $$m^2\;/\;m-h$$  -
$$\epsilon$$ epsilon creep $$in\;/\;in$$ $$m\;/\;m$$  -
$$p_c$$ - critical pressure $$lb\;/\;in^2 \;or\; psi$$ $$Pa$$  -
$$F_F$$ - critical pressure ratio factor - -  -
$$T_c$$ - critical temperature $$^\circ F$$ $$^\circ C$$  -
$$\sigma$$ sigma cross-section $$in^2$$ $$mm^2$$  -
$$A_f$$ - cross-section area of flange $$in^2$$ $$mm^2$$  -
$$A_g$$ - cross-section area of grout $$in^2$$ $$mm^2$$  -
$$A_w$$ - cross-section area of web $$in^2$$ $$mm^2$$  -
$$\alpha_v$$, $$\;\gamma$$ alpha, gamma cubic expansion coefficient - -  -
$$CFM$$ - cubic feet per minute $$ft^3 \;/\; min$$ $$m^3 \;/\; m$$  -
$$CID$$ - cubic inch displacement $$in^3$$ $$cc^3$$  -
$$T_c$$ - Curie temperature - -  -
$$I$$ - current $$amp$$ $$amp$$  -
$$j$$ - current density of electrons  - -  -
$$v$$ - cutting speed $$ft\;/\;min$$ $$m\;/\;s$$  -
Symbol Greek Symbol Definition US Metric Value

A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z


text:
# Angular Freq. of small oscillations on a wheel/spring.

1. Dec 2, 2005

### nweibley

I've been busy finishing my online physics homework, and I cannot get this problem for the life of me (which is annoying because I just finished the relativity and lorentz transformation assignments). If you are good at physics and think you know how to do it, please post your line of thoughts on the matter. I've tried obvious variations of the kinematic equations of oscillation that I can think of, but no dice.

The question is below:

A wheel of mass M = 4.5 kg and radius R = 0.90 m is free to rotate about its fixed axle. A spring, with spring constant k = 270 N/m, is attached to one of its spokes, a distance r = 0.33 m from the axle, as shown in the figure. What is the angular frequency of small oscillations of this system (in rad/s)?

http://img225.imageshack.us/img225/1908/prob211yw.gif [Broken]

I was told to think of the disc as a torsional oscillator, but I had no luck doing that. If this is a pend problem I assumed (incorrectly) the axis cannot actually be the axle. It would seem to me there would only be two torques... the rotational inertia of the wheel (MR^2) and the spring. How would I calculate the torques cause by the spring though?

I thought I was to use the formula T = 2 pi * sqrt ( I / Mgd) but that obviously does not work in this case, since the wheel doesnt spin from gravity. I cannot figure out how to determine K the torque constant from the spring and substitute Mgd for K. I know angular freq = 2 pi / (T) but none the less, I only have one attempt to get this right, and I know that the way I was doing it was wrong ("practice" inputs).

Any help?

Thanks,
---Nate

Last edited by a moderator: May 2, 2017
2. Dec 2, 2005

### Staff: Mentor

Yes, it's a torsional oscillator. Why in the world would you think that the axis would be anything but the axle?
Rotational inertia is not a torque!
The only thing exerting a torque on the wheel is the spring. You should know how to find the torque based on the force exerted by the spring for a small displacement.

This is not a physical pendulum, so forget about that formula. Instead, compare this to a mass on a spring. I assume that you could find the angular frequency of an oscillating mass on a spring (the usual simple case). (If not, better read up on that problem first.) Now just figure out the analogous equations for rotational SHM, which deals with torques instead of forces. Here are two big hints:

(1) In the "mass on a spring" case, the force formula is F = kx. For this problem, figure out the corresponding torque formula. (Hint: Write the torque as a function of angular displacement. That way you'll find the torsional spring constant.)

(2) In the "mass on a spring" case, the mass is used to find the period of the SHM. For this problem, what's the rotational analog to mass?

Once you've figured out these two hints, you can translate the answer from the "mass on a spring" to work with this problem.

3. Dec 4, 2005

### nweibley

Thanks, that makes perfect sense.... I completed the problem and everything now makes sense.

I was just taking the wrong approach to the problem.

Thanks for the help!
-----Nate

4. May 4, 2009

### Eagle Eyes

Hello, i have no idea how to do this problem. Can someone PLEASE PLEASE explain me how to do this problem step by step.

I really need to know how to do this.


text:
# Non-degenerate representations preserve approximate identities.

I am currently working through Murphy's book C$^*$-Algebras and Operator Theory, and in the beginning of chapter 5 he mentions the following in passing:

If $(H,\varphi)$ is a non-degenerate representation of a C$^*$-algebra $A$, and $\{u_\lambda\}$ is an approximate identity for $A$, then $\{\varphi(u_\lambda)\}$ is an approximate unit for $\varphi(A)$, so the net $\{\varphi(u_\lambda)\}$ converges strongly to $\text{id}_H$.

Recall that a representation $(H,\varphi)$ of a C$^*$-algebra is non-degenerate if $\overline{\varphi(A)H}=H$, or equivalently for each nonzero $x\in H$ there is some $a\in A$ such that $\varphi(a)x\neq0$.

I'm having trouble seeing why this is true. By virtue of $\varphi$ being a $*$-homomorphism, we know that $\{\varphi(u_\lambda)\}$ is an increasing net (since $\varphi$ is positive) in the closed unit ball of $\varphi(A)$ (since $\varphi$ is norm-decreasing). Furthermore, for all $a\in A$ we have $$\|\varphi(u_\lambda a-a)\|\leq\|u_\lambda a-a\|$$ which should converge to zero. However, this doesn't require $(H,\varphi)$ be non-degenerate, and it seems like it should be necessary.

Could someone please help me see some error in my judgement, or possibly provide a correct proof of the above statement? Any help would be greatly appreciated.

Since the representation is non-degenerate, $\{\varphi(a)x:\ a\in A,\ x\in H\}$ is dense in $H$.
For such $\varphi(a)x\in H$, $$\|\varphi(u_\lambda)\varphi(a)x-\varphi(a)x\|=\|\varphi(u_\lambda a-a)x\| \leq\|\varphi(u_\lambda a -a)\|\leq\|u_\lambda a - a\|\to0.$$ So $\varphi(u_\lambda)\to I$ strongly on a dense subset, and now an approximation argument shows that $\varphi(u_\lambda)\to I$ strongly on $H$.
• Oh ok, so the non-degeneracy is just needed to show that $\{\varphi(u_\lambda)\}$ converges strongly to $I$. Thanks! Apr 28, 2017 at 22:40


text:
# How can two (or more) parties share and agree upon a common random seed?

I really don't know how to call this simple problem: Two (or more) parties need to establish a common (non-secret) value to be used as a seed for a deterministic RNG. The only requirement is that each party can be sure that the seed is really random.

My idea is as follows:

1. Each party generates a random value $x_i$,
2. sends its hash $h(x_i)$ to everyone else,
3. and waits for hashes from all other parties.
4. Then each party sends its original value $x_i$ to everyone else,
5. waits for all the values,
6. and verifies them.
7. Finally, each party computes the seed as $\mathop\oplus\limits_i x_i$

I know that inventing protocols should be left to experts, however, I'm curious if this could work and what's needed for the this. I see that the generated values must be long enough to avoid brute-forcing and that $h$ must be collision-resistant.

-

This is pretty much the schoolbook implementation of a shared random number generation (generate, commit, publish). So yeah, it's secure. But this only works for large random numbers, here's a small adaption that allows for arbitrary size integers:

If you need an $n$-bit random number everyone should generate $n$-bit random numbers - this is independent of the security level of the exchange itself. Then everyone also generates a second random number $m$, which is large (say, 256-bit) to prevent bruteforcing, and publish $H(n || m)$. Then after everyone has commited everyone publishes their $m$ and $n$, but only use $n$ for the XOR-sum.

I'd suggest you to use a 256-bit hash for the commitments.

Beware of all kinds of nastyness with MITM and replay attacks, make sure you do all of this over authenticated channels.

-
Since collision resistance is required, the security level of 64 bits provided by a 128 bit hash is insufficient. –  CodesInChaos Nov 10 '13 at 17:40
@CodesInChaos I think collision resistance is more of an observation on $h$ rather than a protocol requirement, but I might be wrong. –  rath Nov 10 '13 at 19:17
What if instead of generating and hashing $m$ the parties publish their signature on $n$? –  rath Nov 10 '13 at 19:36
@rath Without collision resistance a cheater can pick which of them to reveal and the commitment becomes non binding. So collision resistance if an essential part of the protocol. –  CodesInChaos Nov 10 '13 at 20:44
@nightcracker: I was thinking about generating large random numbers, as cutting them is trivial and they may be useful when the requirements change. And I was thinking about seeding Salsa20 where 256 bits fit perfectly (as the key). –  maaartinus Nov 11 '13 at 11:07


text:
# CFD simulations using Scientific Python

## Introduction

For some simulation topics of my Ph.D., I had to learn/recapitulate some basics about simulations techniques and fluid simulations. The original procedure and code could be found at Archer (UK National Supercomputing Service). This is a simple example for applying the finite difference approach to determine the flow pattern (CFD1) in a cavity. For simplicity, we’re assuming a perfect liquid without viscosity, which also implies that there’re no vortices. The $$z$$-dimension of this setup was defined to be endless. We are interested in the directional velocity of the fluid.

## A bit of math

### Finite Difference Method

#### First order PDE

For solving a first or higher order PDE2 several methods exist. The easiest one is the finite difference method. For that method we’re needing a suitable approximation for the first derivative, for example the left aligned or forward difference:

$$\frac{\partial}{\partial x} F \approx \frac{F(x + \Delta x) - F(x)}{\Delta x} + \mathcal{O(\Delta x)}$$

Also possible, the right aligned or backward difference:

$$\frac{\partial}{\partial x} F \approx \frac{F(x) - F(x - \Delta x)}{\Delta x} + \mathcal{O(\Delta x)}$$

For a better approximation, we could also use the combination of forward and backward difference. This method is called the centered difference and is able to describe the derivative on position $$x$$ only with knowledge about the neighbors left and right.

$$\frac{\partial}{\partial x} F \approx \frac{F(x + \Delta x) - F(x - \Delta x)}{2\Delta x} + \mathcal{O(\Delta x)}$$

#### Second and higher order PDE

\begin{align} \frac{\partial^2 F}{\partial x^2} & = \frac{\partial } {\partial x} \left( \frac{\partial F}{\partial x}\right) \\\\ & \approx \frac{1}{\Delta x}\left(\frac{\partial F(x + \Delta x)}{\partial x} - \frac{\partial F(x - \Delta x)}{\partial x} \right) \\\\ & \approx \frac{1}{ \Delta x} \left( \frac{F(x+\Delta x) - F(x)}{ \Delta x} - \frac{F(x) - F(x - \Delta x)}{ \Delta x} \right)+ \mathcal{O}(\Delta x)^2 \\\\ & \approx \frac{1}{(\Delta x)^2} \Bigg( F(x + \Delta x) - 2F(x) + F(x - \Delta x) \Bigg) + \mathcal{O}(\Delta x)^2 \end{align}

## Cavity problem solving

For the given problem the following second-order PDE exist for the fluid flow $$\Psi$$ which neglecting the existence of viscosity and toroids.

$$\frac{\partial^2 \Psi}{\partial x^2} + \frac{\partial^2 \Psi}{\partial y^2} = 0$$

Using the finite difference approach for second order PDEs we could rewrite the equation, which fully satisfies our problem.

\begin{align} \frac{\partial^2 \Psi}{\partial x^2} + \frac{\partial^2 \Psi}{\partial y^2} & \approx \frac{1}{(\Delta x)^2} \Bigg( \Psi(x + \Delta x, y ) - 2 \Psi (x, y) + \Psi (x - \Delta x, y) \Bigg)\\\\ & + \frac{1}{(\Delta y)^2} \Bigg( \Psi(x, y + \Delta y) - 2 \Psi(x,y) + \Psi(x, y - \Delta y) \Bigg) \end{align}

For discretization we replace the continous terms $$x$$ and $$y$$ by their discrete replacements $$i$$ and $$j$$ and set the spatial resolution in $$x$$- and $$y$$-direction to $$1$$ ($$\Delta x=\Delta y=1$$ ).

$$\frac{\partial^2 \Psi}{\partial x^2} + \frac{\partial^2 \Psi}{\partial y^2} \approx \Psi_{i+1,j} + \Psi_{i-1, j} + \Psi_{i,j-1} + \Psi_{i, j+1} - 4\cdot\Psi_{i,j} = 0$$

With this approximation and the usage of the Dirchlet boundary condition (borders without sources are set to $$0$$) we could solve our problem. For velocity field $$\vec{u}$$ computation, we calculate the partial differentiations.

$$u_x (x,y) = \frac{\partial\Psi}{\partial y} = \frac{1}{2} \left( \Psi_{i,j+1} - \Psi_{i,j-1} \right)$$
$$u_y (x,y) = \frac{\partial\Psi}{\partial x} = \frac{1}{2} \left( \Psi_{i+1,j} - \Psi_{i-1,j} \right)$$

### Implementation

#### Boundary conditions

psi = [[0 for col in range(m+2)] for row in range(n+2)]

# Set the bondary conditions on bottom edge
for i in range(b+1, b+w):
psi[0][i] = float(i-b)
for i in range(b+w, m+1):
psi[0][i] = float(w)
# Set the bondary conditions on right edge
for j in range(1, h+1):
psi[j][m+1] = float(w)
for j in range(h+1, h+w):
psi[j][m+1] = float(w-j+h)

#### Solver implementation

The implementation supports booth convergence criteria: maximum number of iteration steps and minimum achievable tolerance $$\sigma$$. For determining the current tolerance we consider the current and iteration step before. Therefore we calculate the Euclidean distance (magnitude normal) to get the achieved gain between these steps. Was the change less than the given tolerance, we skip further iterations.

$$| \Psi_k - \Psi_{k-1}| \le \sigma$$

def solver ( tol, nMaxIterations, psi, dx, dy ):
M = len(psi) - 2
N = len(psi[0]) - 2
tmp = [[0 for col in range(M+2)] for row in range(N+2)]
cStep = 0;
xs = pow(dx,2)
ys = pow(dy,2)
while ( cStep < nMaxIterations ):
# store old residue
res_old = np.linalg.norm(np.array ( psi ) - np.array ( tmp ) )
# differeniation in booth directions
for i in range(1, M+1):
for j in range(1, N+1):
tmp[i][j] = 0.25 * (psi[i+1][j]+psi[i-1][j]+psi[i][j+1]+psi[i][j-1])

cStep += 1
# update residue
res_new = np.linalg.norm(np.array ( psi ) - np.array ( tmp ) )
# updating flow for next iteration
for i in range(1, M+1):
for j in range(1, N+1):
psi[i][j] = tmp[i][j]

if ( np.linalg.norm( res_new - res_old ) <= tol ):
break
return cStep

### Results

1. Computational fluid dynamics [return]
2. Partial difference equation [return]


text:
## Files in this item

FilesDescriptionFormat

application/pdf

LEONG-DISSERTATION-2018.pdf (6MB)
(no description provided)PDF

## Description

 Title: Power-law liquid in high-temperature superconductors Author(s): Leong, Zhidong Director of Research: Phillips, Philip W Doctoral Committee Chair(s): Fradkin, Eduardo Doctoral Committee Member(s): Abbamonte, Peter; Gadway, Bryce Department / Program: Physics Discipline: Physics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): superconductors cuprates power-law liquid non-Fermi liquid superconducting dome scale-invariance Abstract: Inspired by recent photoemission measurements, we demonstrate that the normal state of cuprate superconductors can be described by a power-law liquid, a state of matter with a power-law self-energy $\Sigma^{\pr\pr}\sim(\omega^{2}+\pi^{2}T^{2})^{\alpha}$. The scaling exponent decreases from $\alpha\sim1$ in the overdoped Fermi-liquid state to $\alpha\lesssim\frac{1}{2}$ in the optimal and underdoped regime. We find that broad scale invariance of a power-law liquid leads to the cuprates' superconducting dome, vanishing Fermi velocity, and diverging effective mass. We propose that a power-law liquid can arise from the presence of a scale-invariant sector known as unparticles. To extend the power-law liquid framework to include the ubiquitous magnetic phases of high-$T_{c}$ superconductors, we study the local-itinerant dichotomy in iron pnictides. We show that an interplay between localized moments and itinerant electrons is needed to reproduce the spin excitations observed in inelastic neutron scattering experiments. These results further our understanding of the degrees of freedom in high-$T_{c}$ superconductors and will help formulate a consistent framework incorporating the physics of the antiferromagnetic, normal, and superconducting states. Issue Date: 2018-07-05 Type: Thesis URI: http://hdl.handle.net/2142/101528 Rights Information: Copyright 2018 Zhidong Leong Date Available in IDEALS: 2018-09-27 Date Deposited: 2018-08


text:
# Export date with specified format

My problem is that I want use PGFplot in $\LaTeX$ to draw my graphs, which x axis is a date. Therefore the output file has to have one column "UTC time" (YYYY-MM-DD hh:mm:ss) and the second one is the corresponding data list.

Would it be possible to specify the date format of Export[] ?

• Use DateString to get the right formatting. – C. E. Jul 30 '14 at 16:11


text:
# Properties of the Category of topological spaces with $n$ basepoints.

I've recently encounted a problem in my reading which would seem to be more naturally phrased if the category we work in shifted from the category $\textbf{Top}^*$ of pointed topological spaces, to the category $\textbf{Top}^{*n}$ of topological spaces with an ordered set of $n$ distinct basepoints and continuous maps between them which preserve the ordered basepoint set.

Let $X$ be a topological space and let $A=\{x_1,\ldots,x_n\}\subseteq X$ be it's baspoint set for some finite natural number $n$.

I'm particularly interested in the homotopy of these spaces and so I feel it is probably natural to consider the relative fundamental groupoid $\pi_1(X,A)$ of these spaces. I don't know too much about the fundamental groupoid of a space though other than basic definitions. I wonder if someone could outline what properties we gain and lose by considering the category $\textbf{Top}^{*n}$ instead of the category $\textbf{Top}^*$. For instance, this category still has an initial object which is just the finite set of $n$ elements with the discrete topology however, I don't believe $\textbf{Top}^{*n}$ has terminal objects. This category still has a coproduct given by identifying the basepoint sets of two objects element-wise with respect to their order (a kind of wedge product at $n$ points) but it's not clear that we still have products. How might these properties change if we loosen our category to include maps which possibly permute the ordering of the basepoint set?

Also how does the fundamental groupoid functor $\pi_1(.,A)$, which takes an object in $\textbf{Top}^{*n}$ to its fundamental groupoid $\textbf{Top}^{*n}$ relative to its basepoint set $A$, differ from the usual fundamental group functor. If there is a functor which takes an object in $\textbf{Top}^{*n}$ to $\textbf{Top}^*$, does this induce a functor $\textbf{Grpd}_n\rightarrow \textbf{Grp}$ from the category of groupoids with $n$ objects to the category of groups (possibly via classifying spaces?)?

Hopefully the questions I've asked are closely related to each other enough that I don't need to break this in to multiple questions. If anyone thinks that would be wise though, please feel free to make a comment and I shall consider doing so.

-
How the $n$ points play role in the fundamental groupoid? –  Berci Mar 11 '13 at 13:57
Most categorical properties are lost because you consider distinct base points. Otherwise it would just be a slice category and limits are created by the forgetful functor (and colimits are a bit more complicated, but also exist). Shall I flesh this out in an answer, or do you really want the base points to be distinct? –  Martin Brandenburg Mar 11 '13 at 14:51
For what I'm studying, the fact that the base points are distinct is fairly crucial (otherwise the functor that I'm thinking of is no longer well-defined) but perhaps there is a way to work around that. If it's not too much trouble, I'd appreciate if you could write your thoughts up as an answer, as I'm sure it will be useful. –  Daniel Rust Mar 11 '13 at 15:52

I will discuss the categorical properties. Let more generally $B$ a topological space (of generic base points) and denote by $\mathsf{Top}_B$ the full subcategory of the slice category $B \downarrow \mathsf{Top}$ whose objects are injective continuous maps $B \to X$. The forgetful functor $B \downarrow \mathsf{Top} \to \mathsf{Top}$ creates all limits, in fact it is monad with corresponding monad $B + (-)$ on $\mathsf{Top}$. This monad also preserves directed colimits, so that the forgetful functor also creates directed colimits.

It is not hard to see that $\mathsf{Top}_B \subseteq B \downarrow \mathsf{Top}$ is stable under non-empty products (i.e. excluding the terminal object), equalizers, as well as under directed colimits: For example, if $(B \to X_i)_{i \in I}$ is a non-empty family of objects in $\mathsf{Top}_B$ and $(B \to \prod_i X_i)_{i \in I}$ is their product in the slice category, then $B \to \prod_i X_i$ is injective since the composition with some projection $\mathrm{pr_i}$ (which exists since $I \neq \emptyset$) gives the injective map $B \to X_i$. Hence this is also the product in $\mathsf{Top}_B$. Equalizers are easy to handle, because they are injective, and for directed colimits just use that two elements are equal iff they are equal at some stage.

The forgetful functor $\mathsf{Top}_B \to \mathsf{Top}$ has a left adjoint, sending $X$ to $B \hookrightarrow B+X$. In particular it preserves all limits. Therefore the underlying space of an terminal object has just one point, which implies that $B$ is just a point, and we get $\mathsf{Top}_*$ which is complete and cocomplete. If $B$ is more than just a point, there is no terminal object.

Coproducts in $B \downarrow \mathsf{Top}$ are pushouts in $\mathsf{Top}$ over $B$. One can check that $\mathsf{Top}_B$ is closed under them, using the explicit construction of pushouts. This also includes the initial object. I am pretty sure that coequalizers don't exist, but I don't have an example right now (of course it is not enough to see that the forgetful functor doesn't create them).

There is a smash product on $B \downarrow \mathsf{Top}$ given by $X \wedge Y = (X \times Y) / (b,y) \sim (x,b')$, where $b$ and $b'$ run through all base points. But $\mathsf{Top}_B$ is not closed under it when $B$ is more than just point, because all the base points become identified.

Summary:

• $\mathsf{Top}_B$ has non-empty limits, directed colimits, coproducts
• $\mathsf{Top}_B$ has no terminal object, coequalizers, smash products
-
Isn't $\textrm{id} : B \to B^\textrm{indisc}$ the terminal object in $\textbf{Top}_B$? –  Zhen Lin Mar 13 '13 at 11:08
No, there is no terminal object (see above). –  Martin Brandenburg Mar 13 '13 at 19:18
@MartinBrandenburg Is B a generic topological space? I mean: any topology? any cardinality? –  magma Mar 14 '13 at 12:17
@magma: Yes. $\phantom{ }$ –  Martin Brandenburg Mar 15 '13 at 13:03
I thought so, thank you @MartinBrandenburg –  magma Mar 16 '13 at 9:16


text:
# Sum of powers of regularized incomplete beta function

Let $$k$$ and $$r$$ be natural numbers, and $$p$$ is a rational number in $$[0,1]$$. Is it possible to compute exactly in closed form the following sum?

$$\sum_{i=1}^{\infty}I_{p}(i,k)^r,$$ where $$I_x(a,b)$$ is the regularized incomplete beta function.

[Update 6 Feb 2019]

Motivation for $$r=1$$

Let $$X$$ be a random variable distributed according to the negative binomial distribution with parameters $$(i-k; k, 1-p)$$, where the probability mass function of the negative binomial distribution with parameters $$(k; r, p)$$ is $$f(k;r,p) = \Pr(X=k) = {r+k-1 \choose k} p^k (1-p)^r$$. It is known that $$\Pr(X \leq i) = 1- I_{1-p}(i+1,k).$$

On the other hand, we know that the variable $$X$$ is the sum of $$k$$ independent geometrically distributed variables with parameter $$p$$. Hence

$$\mathbb{E}[X] = \sum_{i=k}^{\infty} i \Pr(X_{\mathcal{P}} = i) = \sum_{i=0}^{\infty} \Pr(X_{\mathcal{P}} > i) = \sum_{i=0}^{\infty} (1-\Pr(X_{\mathcal{P}} \leq i)) = \sum_{i=0}^{\infty} I_{1-p}(i+1,k) = \frac{k}{p}.$$

Therefore for $$r=1$$ we have $$\sum_{i=1}^{\infty}I_{p}(i,k) = \frac{k}{1-p}.$$

• I doubt it even having a closed form for the simple case of $r=1$. – Ali Feb 1 at 18:12
• @Ali, interestingly, for $r=1$ it can be computed in closed form. See my update. – Victor Feb 6 at 13:39


text:
Emu48 Edit a CSV File
01-10-2022, 04:01 AM
Post: #21
 rprosperi Super Moderator Posts: 5,433 Joined: Dec 2013
RE: Emu48 Edit a CSV File
(01-09-2022 08:39 PM)MNH Wrote:
(01-09-2022 02:34 PM)DavidM Wrote:  SL3: Source string
SL2: Target string to be replaced
SL1: Replacement text that takes the place of target

targ: the text which will end up being replaced in the source string
new: the replacement text for each target encountered
len: the length of the target text (not the length of the source text)

The stack arguments, SL1 through SL3, don't correspond with the local variables targ, new, and len.
I think my problem is that I don't know, or are confused by, what should be on the stack to make REPLS work. I executed REPLS, and the program didn't remove the line feed character from the first extracted string. Also, the program ended up in an infinite loop.

To expand a bit on David's comments:

SL1 means Stack Level 1 - this should be the new text to replace the target string

SL2 means Stack Level 2 - this should be the text which is to be replaced

SL3 means Stack Level 3 - this should be the original string

In order to replace a line feed in the original string, use 10 (the ASCII code for LF) for SL2.

--Bob Prosperi
01-10-2022, 10:50 AM
Post: #22
 DavidM Senior Member Posts: 887 Joined: Dec 2013
RE: Emu48 Edit a CSV File
(01-09-2022 07:16 PM)Giuseppe Donnini Wrote:  Not true, the C method uses all of the remaining characters following "C ", including linefeeds, tabs, spaces, control characters, escape characters, whatever. If you happen to use it while entering a program, it will include everything from that point on, even the closing guillemet. It is therefore only useful for entering a single string object.

Thanks for the correction, Giuseppe! I'm not sure why I was under the wrong impression with that version of C$. I've never had a reason to use the "C$ \$ ..." form of the command. I'm sure I would have seen the error of my ways very quickly if I had. :-)
01-10-2022, 12:41 PM
Post: #23
 DavidM Senior Member Posts: 887 Joined: Dec 2013
RE: Emu48 Edit a CSV File
(01-09-2022 08:39 PM)MNH Wrote:
(01-09-2022 02:34 PM)DavidM Wrote:  SL3: Source string
SL2: Target string to be replaced
SL1: Replacement text that takes the place of target

targ: the text which will end up being replaced in the source string
new: the replacement text for each target encountered
len: the length of the target text (not the length of the source text)

The stack arguments, SL1 through SL3, don't correspond with the local variables targ, new, and len.

You are correct, and it is intentional. There's no reason the stack arguments for REPLS have to be the same as the local variables defined for use within the program.

(01-09-2022 08:39 PM)MNH Wrote:  I think my problem is that I don't know, or are confused by, what should be on the stack to make REPLS work. I executed REPLS, and the program didn't remove the line feed character from the first extracted string. Also, the program ended up in an infinite loop.

Rather than responding with a lengthy line-by-line breakdown of how REPLS works (which I started to do and subsequently closed the window by accident before posting :-) ), I'd recommend that you actually step through the code and watch how it operates. Two possible ways to do this:

1) Place some simple arguments on the stack (I'd suggest "ABCDE" "BCD" "X" as a first attempt)
2) Put 'REPLS' on the stack (single quotes required)
3) Execute DBUG by navigating to PRG -> NXT -> RUN -> DBUG and pressing "DBUG"
4) Step through the code with SST to watch how it loads the stack and proceeds

-or-

1) Place 41 MENU HALT at the beginning of REPLS.
2) Place some simple arguments on the stack (I'd suggest "ABCDE" "BCD" "X" as a first attempt)
3) Execute REPLS
4) Step through the code with SST to watch how it loads the stack and proceeds

Make sure that you are actually passing strings to REPLS, not variables which contain strings. That might be one issue you are running into.

If you have truly found a combination of string arguments passed to REPLS that results in an infinite loop, please post an example so that the code can be fixed to accommodate that situation.
01-14-2022, 04:25 PM
Post: #24
 DavidM Senior Member Posts: 887 Joined: Dec 2013
RE: Emu48 Edit a CSV File
(01-08-2022 07:41 PM)MNH Wrote:  Please note that all substrings will not be of equal lengths, because some coordinate pairs will have point numbers containing 1 to 5 digits. Also, an actual coordinate file will be in the form of P,N,E,Z,D (e.g., 208,1531217.411,520676.455,98.393,IRC 1/2 LB 6300) where:

P is the point number
N is the northing
E is the easting
Z is the elevation
D is the description

Does your final list need to have all of the fields present? Or just some?

One possible way to do this would be to convert every field to a string in a first pass, then extract only the needed fields while converting to numeric objects. It would be easier to show with some real data.

Would you be able to post a complete example of the "FILE" string that contains real data for experimentation?
01-15-2022, 07:34 PM
Post: #25
 MNH Member Posts: 201 Joined: May 2014
RE: Emu48 Edit a CSV File
(01-14-2022 04:25 PM)DavidM Wrote:  Does your final list need to have all of the fields present? Or just some?

My immediate needs require only the first three fields. My future needs will require all five fields.

Quote:Would you be able to post a complete example of the "FILE" string that contains real data for experimentation?

Please see the attached file. It's a contiguous piece of a real CSV file from a project that we're doing. Our data collector, a Topcon FC-5000, stores spatial data as a CSV file. I've been busy, so I haven't kept up with this thread. Again, thank you for your help!

Attached File(s)
09-04-2022, 09:56 PM (This post was last modified: 09-04-2022 09:58 PM by MNH.)
Post: #26
 MNH Member Posts: 201 Joined: May 2014
RE: Emu48 Edit a CSV File
Knowing how many points (point strings, actually) there are in advance and using a definite loop structure eliminates the need to handle a missing line feed character at the end of the last point string. Please note that the PNTS variable is a list of point numbers. The local variable pnezd is called after the definite loop ends so the user can check the output. I renamed the program to CSVO. Kindly test it on your Emu48.

Program: CSVO
Checksum: # D830h
Size: 247 bytes
Purpose: Remove line feed characters from a CSV file.

Code:
 \<< FILE DUP SIZE 10  CHR 1 PNTS SIZE { }  \-> file size lf  start numpnts pnezd   \<< 1 numpnts     START file DUP  DUP lf POS DUP 2 -  ROT start ROT SUB  pnezd SWAP +  'pnezd' STO 1 +  size SUB 'file' STO     NEXT pnezd   \>> \>>

This is the contents of the PNTS variable.

{ 101 102 103 104
105 106 107 108 109
}

Please see the attached file so you can load it in your Emu48 and store it in a variable named FILE.

Attached File(s)