Femtosecond quantum fluid dynamics of helium atom under an

... step and therefore can probe both excitation and ionization of the atom under the external TD perturbation. A stability analysis of our numerical scheme is also presented here. The scheme is quite general and applicable to other TD EOMs, including generalized nonlinear SEs. The present overall appro ...

... step and therefore can probe both excitation and ionization of the atom under the external TD perturbation. A stability analysis of our numerical scheme is also presented here. The scheme is quite general and applicable to other TD EOMs, including generalized nonlinear SEs. The present overall appro ...

Doped Semiconductors: Role of Disorder

... and call the sites resonant if their energy falls into the band. Then let us look for connected resonant states which share a site. Non-resonant sites can be disregarded as I A. It is clear that it must be a threshold in the quantity A/I where the transition takes place. If one assumes that the co ...

... and call the sites resonant if their energy falls into the band. Then let us look for connected resonant states which share a site. Non-resonant sites can be disregarded as I A. It is clear that it must be a threshold in the quantity A/I where the transition takes place. If one assumes that the co ...

Efficient Magnetization Reversal with Noisy Currents

... hhi thj t0 i ij ij t t0 for i; j 2 f; ; rg. Such a model befits an electromagnetic environment with a large number of degrees of freedom that generates Gaussian noise with correlation times much shorter than the magnetization response time. At room temperature, shot noise does not hav ...

... hhi thj t0 i ij ij t t0 for i; j 2 f; ; rg. Such a model befits an electromagnetic environment with a large number of degrees of freedom that generates Gaussian noise with correlation times much shorter than the magnetization response time. At room temperature, shot noise does not hav ...

On the consequences of bi-Maxwellian distributions on parallel electric fields.

... show that the density profile is a maximum at the equator and the equatorially trapped plasma is confined closer to the equator for higher anisotropy ratios. The modeled density profiles are in agreement with some observations. The electric fields that result are on the order of 0.1 uV/m pointing aw ...

... show that the density profile is a maximum at the equator and the equatorially trapped plasma is confined closer to the equator for higher anisotropy ratios. The modeled density profiles are in agreement with some observations. The electric fields that result are on the order of 0.1 uV/m pointing aw ...

Effects of topological defects and local curvature on the electronic

... theoretical point of view, graphene has received a lot of attention in the past because it constitutes a beautiful and simple model of correlated electrons in two dimensions with unexpected physical properties[3]. A tight-binding method applied to the honeycomb lattice allows to describe the low ene ...

... theoretical point of view, graphene has received a lot of attention in the past because it constitutes a beautiful and simple model of correlated electrons in two dimensions with unexpected physical properties[3]. A tight-binding method applied to the honeycomb lattice allows to describe the low ene ...

V720 -Testing of Geiger Mode APDs (GmAPs)

... state with a complex energy (the imaginary component means the wave function evolves with time and ‘leaks’ out of the trap potential). Numerical techniques are required to solve for the tunnel lifetime, which is highly dependent upon the trap depth and applied electric field.2 This is because these ...

... state with a complex energy (the imaginary component means the wave function evolves with time and ‘leaks’ out of the trap potential). Numerical techniques are required to solve for the tunnel lifetime, which is highly dependent upon the trap depth and applied electric field.2 This is because these ...

Casimir effects in systems containing 2D gases B E Sernelius

... replaced by a summation over discrete frequencies, the socalled Matsubara frequencies [1, 2]. The prime on the summation sign indicates that the n = 0 term should be divided by two. Note that the temperature enters in the discrete frequencies ξn and in the temperature dependence of the dielectric fu ...

... replaced by a summation over discrete frequencies, the socalled Matsubara frequencies [1, 2]. The prime on the summation sign indicates that the n = 0 term should be divided by two. Note that the temperature enters in the discrete frequencies ξn and in the temperature dependence of the dielectric fu ...

Theory of ferromagnetism in planar heterostructures of Mn,III

... interdependence of the two magnetizations. Each is governed by the effective magnetic field generated by the other. They have to be determined selfconsistently. We report here only the work on the transition temperature. Theoretical finite magnetization studies are being carried out. Close to the Cu ...

... interdependence of the two magnetizations. Each is governed by the effective magnetic field generated by the other. They have to be determined selfconsistently. We report here only the work on the transition temperature. Theoretical finite magnetization studies are being carried out. Close to the Cu ...

Line of Sight Column Densities of Polars Student: Scott Swindell

... The program that uses these formulas takes three coordinates for a single point or an array of coordinates as input and gives the rotated coordinates or coordinate system as ...

... The program that uses these formulas takes three coordinates for a single point or an array of coordinates as input and gives the rotated coordinates or coordinate system as ...

introduction to information theory

... spaces, we shall sometimes make use of continuous random variables taking values in Rd or in some smooth finite-dimensional manifold. The probability measure for an ‘infinitesimal element’ dx will be denoted by dpX (x). Each time pX admits a density (with respect to the Lebesgue measure), we shall u ...

... spaces, we shall sometimes make use of continuous random variables taking values in Rd or in some smooth finite-dimensional manifold. The probability measure for an ‘infinitesimal element’ dx will be denoted by dpX (x). Each time pX admits a density (with respect to the Lebesgue measure), we shall u ...

Linear Response in Classical Physics

... The quantity hvx (t0 )vx (t00 )i is an example of a time correlation function - in this case, the “velocity auto-correlation function” (VACF). This quantity measures the degree of correlation between the velocity of a particle at two different times t0 and t00 . When t0 = t00 , the value of the of t ...

... The quantity hvx (t0 )vx (t00 )i is an example of a time correlation function - in this case, the “velocity auto-correlation function” (VACF). This quantity measures the degree of correlation between the velocity of a particle at two different times t0 and t00 . When t0 = t00 , the value of the of t ...

Lecture Notes on Linear Response Theory

... walk problem for a single particle. Despite the seeming simplicity, this constitutes a rich example that will help to illustrate many of the principles of fluctuation about equilibrium generally. Examples of such random walks include the Brownian motion of a particle in a fluid, as well as the rando ...

... walk problem for a single particle. Despite the seeming simplicity, this constitutes a rich example that will help to illustrate many of the principles of fluctuation about equilibrium generally. Examples of such random walks include the Brownian motion of a particle in a fluid, as well as the rando ...

15. The Simplest Integrals

... the simplest integrals in the form of a table. When one of these integrals is needed for a calculation, we can simply look it up in the table. Appendix F provides a short table of indefinite integrals (i.e., antiderivatives). Please verify that the entries in the table follow simply from the basic d ...

... the simplest integrals in the form of a table. When one of these integrals is needed for a calculation, we can simply look it up in the table. Appendix F provides a short table of indefinite integrals (i.e., antiderivatives). Please verify that the entries in the table follow simply from the basic d ...

Document

... hi = wij Sj + hext where wij is exchange interaction strength and wij = wji At low temperature Sj = sgn(hi) ...

... hi = wij Sj + hext where wij is exchange interaction strength and wij = wji At low temperature Sj = sgn(hi) ...

transparencies

... Isobutane-based one the efficiency knee is expected to be at the same gain value: 7 x 103 Vtot = 1250 V; ...

... Isobutane-based one the efficiency knee is expected to be at the same gain value: 7 x 103 Vtot = 1250 V; ...

Harmonic functions, Green`s functions, potentials

... Example 1. Consider the Poisson problem in a bounded domain D ⊂ Rn , with non-homogeneous Neumann boundary conditions: ∆u = f in D; ∂n u = h on ∂D. This problem has physical meaning: we seek the electrostatic potential in a region with given charge density (represented by f ), and given normal compo ...

... Example 1. Consider the Poisson problem in a bounded domain D ⊂ Rn , with non-homogeneous Neumann boundary conditions: ∆u = f in D; ∂n u = h on ∂D. This problem has physical meaning: we seek the electrostatic potential in a region with given charge density (represented by f ), and given normal compo ...

Computing Quark and Gluon Distribution Functions for Very Large

... where µ is a parameter which we shall compute which behaves as A1/3 . In this theory, the dimensionful scale factor µ will set the scale of the coupling constant. All perturbation theory can be done in terms of α(µ), and if α(µ) << 1 a weak coupling expansion is valid. This is equivalent to ρ ∼ µ2 ...

... where µ is a parameter which we shall compute which behaves as A1/3 . In this theory, the dimensionful scale factor µ will set the scale of the coupling constant. All perturbation theory can be done in terms of α(µ), and if α(µ) << 1 a weak coupling expansion is valid. This is equivalent to ρ ∼ µ2 ...

Experimental Spectroscopy II - IAEA Atomic and Molecular Data Unit

... This allows an estimate of Te from the mere existence of an ion! ...

... This allows an estimate of Te from the mere existence of an ion! ...

Statistical modeling of pulse height spectrum of gamma

... age increases the electron and hole drift lengths increase, the resolution improves and the charge collection efficiency increases. In summary, the pulse height spectrum of gamma-ray spectrometers is calculated as a function of photon energy, electron and hole mobility-lifetime products, and applied ...

... age increases the electron and hole drift lengths increase, the resolution improves and the charge collection efficiency increases. In summary, the pulse height spectrum of gamma-ray spectrometers is calculated as a function of photon energy, electron and hole mobility-lifetime products, and applied ...

F. Skiff, H. Gunell, A. Bhattacharjee, C. S. Ng, and W. A. Noonan

... Equations 共5兲 and 共8兲 can be thought of as an integral transform pair or as a variable transformation and were introduced by Morrison 共thus we refer to it as Morrison’s G-transform兲.3 Despite the singular functions, these integrals can be conveniently performed on experimental data. Especially for p ...

... Equations 共5兲 and 共8兲 can be thought of as an integral transform pair or as a variable transformation and were introduced by Morrison 共thus we refer to it as Morrison’s G-transform兲.3 Despite the singular functions, these integrals can be conveniently performed on experimental data. Especially for p ...

On the definition of a kinetic equilibrium in global gyrokinetic

... of ion charge and mass). Fig. 2 shows ψ and ψ0 on an unperturbed trajectory as function of time. ψ oscillates around a mean value, ψ0 is constant but its value is far away from the mean value of ψ. This means that the effective temperature and density profiles (evaluated from the particle distributi ...

... of ion charge and mass). Fig. 2 shows ψ and ψ0 on an unperturbed trajectory as function of time. ψ oscillates around a mean value, ψ0 is constant but its value is far away from the mean value of ψ. This means that the effective temperature and density profiles (evaluated from the particle distributi ...

Long-range forces and the Ewald sum

... which the lattice images are summed. It is necessary to order the terms in a concentric fashion, so that terms with larger l lx2 l y2 lz2 are added only after all terms with smaller values of |l| have been included. The charge density is a periodic function and, just like the square-wave examp ...

... which the lattice images are summed. It is necessary to order the terms in a concentric fashion, so that terms with larger l lx2 l y2 lz2 are added only after all terms with smaller values of |l| have been included. The charge density is a periodic function and, just like the square-wave examp ...

Electric Field of a Uniform Charge Density

... A solution for which the interior electric ﬁeld has the cylindrical form (4) exists for any value of V0 , since this only contributes to the uniform component of the surface charge distribution, which does not aﬀect the interior electric ﬁeld. In particular, there exists a solution (V0 = 2π a2 /3) ...

... A solution for which the interior electric ﬁeld has the cylindrical form (4) exists for any value of V0 , since this only contributes to the uniform component of the surface charge distribution, which does not aﬀect the interior electric ﬁeld. In particular, there exists a solution (V0 = 2π a2 /3) ...

Test Code: CS (Short answer type) 2011 M.Tech. in Computer Science

... General properties of matter - elasticity, surface tension, viscosity. Classical dynamics - Lagrangian and Hamiltonian formulation, symmetries and conservation laws, motion in central field of force, planetary motion, collision and scattering, mechanics of system of particles, small oscillation and ...

... General properties of matter - elasticity, surface tension, viscosity. Classical dynamics - Lagrangian and Hamiltonian formulation, symmetries and conservation laws, motion in central field of force, planetary motion, collision and scattering, mechanics of system of particles, small oscillation and ...

# Probability density function

In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function that describes the relative likelihood for this random variable to take on a given value. The probability of the random variable falling within a particular range of values is given by the integral of this variable’s density over that range—that is, it is given by the area under the density function but above the horizontal axis and between the lowest and greatest values of the range. The probability density function is nonnegative everywhere, and its integral over the entire space is equal to one.The terms ""probability distribution function"" and ""probability function"" have also sometimes been used to denote the probability density function. However, this use is not standard among probabilists and statisticians. In other sources, ""probability distribution function"" may be used when the probability distribution is defined as a function over general sets of values, or it may refer to the cumulative distribution function, or it may be a probability mass function rather than the density. Further confusion of terminology exists because density function has also been used for what is here called the ""probability mass function"".