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Topic: Coulomb logarithm

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	Coulomb, Charles Augustin de - Hutchinson encyclopedia article about Coulomb, Charles Augustin de
		Coulomb's law of 1787 states that the force between two electric charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.
		Coulomb took full advantage of his various postings to pursue a variety of studies, including structural mechanics, friction in machinery, and the elasticity of metal and silk fibres.
		The torsion balance Coulomb invented is described in a paper of 1777, and in a paper of 1785 he discussed its adaptation for electrical studies.
	encyclopedia.farlex.com /Coulomb%2c+Charles+Augustin+de (305 words)

	Progressive failure on the North Anatolian fault
		The Coulomb stress is seen to drop by 50-100 bars along most of the 1939 rupture, with increases of several bars along the west end, beyond the east end, and along most of the succeeding 1942 fault rupture zone.
		Note that a right-lateral Coulomb stress of 100 bars is not equivalent to a left-lateral Coulomb stress of -100 bars on the same fault unless m'=0, because unlike the shear stress change, the sign of the normal stress change is the same for right- or left-lateral slip (e.g., fault-normal tension always favors failure).
		Coulomb stress changes on optimally oriented planes are also plotted for a decade of secular stress buildup in Fig.
	atlas.cc.itu.edu.tr /~barka/pubs/anatolia/anatolia.html (8964 words)

	Coulomb collision (Site not responding. Last check: 2007-10-15)
		A Coulomb collision is a collision between two particles when the force between them is given by Coulomb's Law.
		The cumulative effect of the many small angle collisions, however, is often larger than the effect of the few large angle collisions, so it is instructive to consider the collision dynamics in the limit of small deflections.
		The integral of 1/b thus yields the logarithm of the ratio of the upper and lower cut-offs.
	www.tocatch.info /en/Coulomb_logarithm.htm (592 words)

	Physics Myths and physics facts
		Coulomb Logarithm: In all corresponding treatments in the literature, the total cross section for Coulomb Scattering, as derived over the differential cross section, is obtained as a logarithmically divergent expression unless an arbitrary cut off value for the impact parameter (or scattering angle) is introduced.
		However, a correct consideration of the scattering geometry shows that this result is erroneous: it is the consequence of neglecting a cos- factor which describes the density of particles hitting the surface of the spherical target and provides the geometrical connection between the monodirectional incident particle beam and the spherical scattering surface.
		The notion of 'infinite range' potentials in general and the 'Coulomb Logarithm' in particular must therefore be abandoned, as the total effective cross section has always a finite value independent of the macroscopic parameters of the plasma.
	www.physicsmyths.org.uk (7966 words)

	exponential function
		The inverse of the exponential function is the logarithmic function or logarithm.
		For 2 as the base of the logarithm the binary logarithm lb(x) is the case.
		In the time of the logarithmic tables the cologarithm was used to prevent negative results.
	www.2dcurves.com /exponential/exponentiale.html (869 words)

	Personnel : Department of Mathematics and Statistics : University of Melbourne
		The logarithmic potential is intimately related to topological charge -- for example vortices in a fluid carry a topological charge determined by the circulation, and the energy between two vortices is proportional to the logarithm of the separation.
		The logarithmic potential is also the potential between two-dimensional electric charges, so properties of the two-dimensional Coulomb gas can be directly related to properties of systems with topological charges.
		In my studies of the two-dimensional Coulomb gas I have exploited the fact that at a special value of the coupling the system is equivalent to the Dirac field and so is exactly solvable.
	www.ms.unimelb.edu.au /Personnel/index.php?person_id=22 (724 words)

	Electric Log Splitter (Site not responding. Last check: 2007-10-15)
		The magnitude of the force of attractionor repulsion is given by Coulomb's law.
		The SI unit of electricity is the coulomb, whichhas the abbreviation "C".
		The symbol Q is used in equations to represent the quantity of electricity or charge.
	www.cabaret-54.com /dust17896-electric%20log%20splitter.html (491 words)

	Electromagnetic Waves (Site not responding. Last check: 2007-10-15)
		The logarithmic potential is infinite not only at the line charge, r → 0, but also at infinity, so we cannot make it vanish there, as we can with the potential of a point charge, that only has a pole at r = 0.
		The logarithmic potential is zero at r = 1, but its absolute value has no significance, and we could add any constant to it that we like without changing the field.
		They resemble the Coulomb dipole fields, but are a quarter-wavelength out of phase and are still considerable at a greater distance than the Coulomb fields.
	www.du.edu /~jcalvert/phys/emwaves.htm (9513 words)

	[No title] (Site not responding. Last check: 2007-10-15)
		Coulomb: standard unit of electric charge representing one mole of electrons.
		Coulomb barrier: no entry yet, but see reference 8.
		Coulomb Collision: An interparticle collision where the Coulomb Force (electrical attraction and repulsion) is the governing force.
	www.pppl.gov /~rfheeter/fusion-faq/glossary/c.html (4444 words)

	Encyclopedia: Plasma physics (Site not responding. Last check: 2007-10-15)
		; Z is charge state; k is Boltzmann's constant; K is wavelength; Î³ is the adiabatic index; ln Î is the Coulomb logarithm.
		Temperature is the physical property of a system which underlies the common notions of hot and cold; the material with the higher temperature is said to be hotter.
		The adiabatic index of a gas, is the ratio of its specific heat capacity at constant pressure (CP) to its specific heat capacity at constant volume (CV).
	www.nationmaster.com /encyclopedia/Plasma-physics (4750 words)

	THE MODIFICATION FOR PLASMA TRANSPORT DUE TO A NEW COULOMB LOGARITHM (Site not responding. Last check: 2007-10-15)
		It is shown [1] that we should use momentum transfer instead of scattering angle to describe the Coulomb collisions since relative velocities is not constant in plasma.
		The Coulomb logarithm should be reduced to half the value of conventional plasma kinetic theory.
		It is extending the normal approach to the Fokker-Plank equation for the Coulomb collisions by expanding distribution function.
	flux.aps.org /meetings/YR01/DPP01/abs/S2540012.html (232 words)

	Boris Skoric: Quantum Hall Effect (Site not responding. Last check: 2007-10-15)
		The Coulomb interactions prevent you from using the single-particle wave functions with which you can attack the disorder, while the disorder breaks the symmetry that would help you tackle the interaction problem.
		Due to the presence of localised bulk states and the Coulomb interactions between all states, the many body eigenfunctions are not restricted to the edge.
		We have done a calculation that shows that the Coulomb interactions can be effectively taken care of by writing down a theory that lives only on the edge but has modified constants.
	www.xs4all.nl /~skoric/quantum (3046 words)

	Coherent effects during electron-ion collisions (Site not responding. Last check: 2007-10-15)
		The effects caused by the focusing properties of Coulomb potential are demonstrated numerically and analytically.
		One of the important effects is that a quiver electron has time to change sufficiently its impact parameter due to multiple oscillations close to an ion and collides much more efficiently.
		It is shown that the effect of "Coulomb logarithm" is absent in super strong fields.
	www.vimi.ru /applphys/appl-00/00-3/00-3-18e.htm (146 words)

	Coulomb Collision Cross Section and Coulomb Logarithm
		In all corresponding treatments in the literature, the total cross section for Coulomb scattering, as derived over the differential cross section, is obtained as a divergent expression unless an arbitrary cut-off value for the impact parameter (or scattering angle) is introduced (this leads to the well known Coulomb Logarithm factor).
		This is however not the case when considering the energy transfer function, and the neglection of this aspect is the reason for the well known logarithmic divergence of the total cross section for Coulomb scattering (Coulomb Logarithm) in other treatments of this problem.
		Despite the restrictions used in this derivation, it is clear that this is a general result relevant for Coulomb collisions of particles with arbitrary masses and velocities.
	www.plasmaphysics.org.uk /coulomb.htm (929 words)

	Special Functions
		There are some computations, particularly in number theory, where the logarithm of the gamma function often appears.
		Coulomb wave functions give solutions to the radial Schrödinger equation in the Coulomb potential of a point nucleus.
		The function can be viewed as a generalization of a logarithm.
	documents.wolfram.com /v4/MainBook/3.2.10.html (1396 words)

	~!~=(@)=(@)=Physics of Phone Lines !!! (Site not responding. Last check: 2007-10-15)
		Since we can compute the logarithm in many other ways, it is ridiculous to attach to k any intrinsic meaning.
		For example, the Coulomb interaction between two electrons is mediated by virtual photons faster than the speed of light, with imaginary masses.
		Examples are: - relating the Coulomb interaction and corrections to scattering amplitudes and then using the nonrelativistic Schroedinger equation, - computing Lamb shift contributions (now usually done in what is called the NRQED expansion), - Bethe-Salpeter and Schwinger-Dyson equations obtained by resumming infinitely many diagrams.
	www.talkaboutcollege.com /group/alt.radio.college/messages/9388.html (17432 words)

	Physics Today November 2001
		Now because the coupling strength changes only logarithmically with the energy scale, a big factor in this scale is required to make a significant change in the effective coupling strength.
		And, beyond the bare observation that the logarithm of a very large number need not be very large, it lacks sharp quantitative focus.
		Because the running depends only weakly (logarithmically) on the masses of the virtual particles involved, we can't use the success of our calculation to discriminate finely among detailed models of unified gauge symmetry, or supersymmetry, or the way in which these symmetries are broken.
	www.physicstoday.org /pt/vol-54/iss-11/p12.html (1747 words)

	New Coulomb logarithm
		It is important to restudy Coulomb collisions since they are fundamental for plasma transport.
		The conventional theory uses the scattering angle instead of momentum transfer to describe the Coulomb collisions in a plasma.
		In both cases, it is found that the Coulomb logarithm should be reduced to half the value of the conventional plasma kinetic theory.
	epub.iaea.org /fusion/subscribe/41/may/ms7024LiD/7024.html (1764 words)

	Bibliography
		Cody and K. Hillstrom, Chebyshev approximations for the natural logarithm of the gamma function, Math.
		Cody and K. Hillstrom, Chebyshev approximations for the Coulomb phase shift, Math.
		A robust and reliable algorithm for the logarithm of the gamma function, Appl.
	math.nist.gov /mcsd/Reports/2001/nesf/node38.html (8398 words)

	Nuclear Force equations. - Physics Help and Math Help - Physics Forums
		Newton's law of gravitation and Coulomb's law for electrostatics are classical (not quantum) relations, and they are applicable for sufficiently strong field intensities and sufficiently large distances.
		I'm at a loss as to how a logarithm would enter into the analysis at all.
		Last, the whole colective of nucleons in a nucleus add to form a kind of well potential; this is approached with saxon-wood potential, or even with a square well.
	www.physicsforums.com /showthread.php?t=12670&goto=nextoldest (1336 words)

	Welcome to the Cannibal JavaLab (Site not responding. Last check: 2007-10-15)
		Dynamical Friction: We use a Chandrasekhar-like frictional formula, where the braking due to dynamical friction is determined by the local galaxy density, and the mass and velocity of the companion.
		We use a factor for the Coulomb logarithm of Lamda=3.
		Tidal Stripping: To calculate the tidal radius, we simply calculate the radius inside the satellite at which the satellite density is equal to the local mass density of the satellite.
	burro.astr.cwru.edu /JavaLab/cannibal/CannibalPhysics.html (285 words)

	New Coulomb logarithm (Site not responding. Last check: 2007-10-15)
		New Coulomb logarithm and its effects on the Fokker-Planck equation, relaxation times and cross-field transport in fusion plasmas
		It is shown that a new cut-off at small scattering angle should be introduced for the case of constant relative velocity.
		It is found that the Coulomb logarithm should be reduced to half the value of conventional plasma kinetic theory.
	epub.iaea.org /fusion/public/41/may/ms7024LiD/7024.abstract.html (214 words)

	Advection-dominated Accretion Flows
		In § 3 we treat a model for the radial variation of electron and ion temperatures assuming that a fraction g of the dissipated energy goes into heating the electrons and a fraction (1 - g) goes into heating the ions.
		In this limit, the Coulomb energy exchange between ions and electrons is negligible.
		In contrast with Narayan and Yi (1995), we do not assume that a constant fraction f of the dissipated energy is advected inward by the flow.
	ecf.hq.eso.org /~ralbrech/sepdec97apjl/5160.html (2572 words)

	Electron Conductivity of Stellar Plasmas
		Recent progress in the treatment of electrical and thermal conductivities of strongly coupled Coulomb plasmas is connected with improvements of ion structure factors relevant to calculation of electron relaxation times.
		In the Coulomb liquid, an approximate treatment has been proposed to describe reduction of the effective electron-ion collision rate due to incipient ordering of the ions in the regime of strong ion coupling.
		Both modifications (in the solid and liquid phases) change the kinetic coefficients near the melting point and drastically reduce their discontinuities at the solid/liquid phase interface.
	www.ioffe.rssi.ru /astro/conduct/conduct.html (1285 words)

	Galaxy Collisions: 5. Coming Back (Ixx)
		The ratio of these impact parameters appears in the so-called Coulomb logarithm term (from plasma physics) in the formula.
		Specifically, TW applied the analysis to the case where the perturbing potential was a weak bar component, and derived the "LBK torque formula" (after Lynden-Bell and Kalnajs 1972) for the "frictional" torque exerted on the bar.
		Though this formula and the procedure from which it is derived are very complex, no logarithmic divergences result from this approach.
	www.public.iastate.edu /~curt/cg/section5.html (8612 words)

	Physics & Astronomy Department
		Usually, the Standard Coulomb Logarithm Approximation is used to analytically calculate the cross section.
		This is an approximation, however, and physicists are unsure as to how correct it is in plasmas that haven't been tested.
		The simulation calculates the actual values for the cross section and can be used to check to see if the Coulomb Logarithm Approximation is close to correct or not for unfamiliar plasmas.
	www.depauw.edu /acad/physics/studentresearch.asp (1443 words)

	Patent 4000036
		maintaining said gas in said well to ionize the gas and to raise the temperature of ions by coulomb interaction to a nuclear fusion level.
		501-505, were used to eliminate the restrictions of the Born approximation in computing the matrix elements of the Coulomb potential.
		exp is the base of the natural logarithm.
	www.freepatentsonline.com /4000036.html (11799 words)

	Astron. Astrophys. 322, 242-255 (1997)
		Whilst they are accelerating, electrons can also lose energy by synchrotron losses, Coulomb losses or plasma instabilities of the loss-cone type.
		The synchrotron and Coulomb losses for electrons are given by (e.g.
		Depending on factors such as the particle energy, pitch-angle and position in the magnetosphere, a particle will either precipitate onto the poles (due to synchrotron losses and Coulomb collisions) or be kept in the atmosphere by the magnetic mirror force (due to the converging magnetic field).
	aa.springer.de /papers/7322001/2300242/sc5.htm (782 words)

	[No title] (Site not responding. Last check: 2007-10-15)
		The capacity of this memory unit is equal to the number of significant binary digits to which the angle can be measured.
		As the universe expands and the stars recede, the number of significant digits in the angle will increase logarithmically with time.
		Measurements of atomic frequencies and energy levels can also in principle be measured with a number of significant figures proportional to (log t).
	www.aleph.se /Trans/Global/Omega/dyson.txt (4015 words)

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