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Planck

Gibbs free energy or Gibbs molar free energy molar flow of gas phase acceleration of gravity enthalpy, molar enthalpy, weight enthalpy Henry s constant Planck s constant height horsepower radiation intensity molar flux... [Pg.494]

The miderstanding of the quantum mechanics of atoms was pioneered by Bohr, in his theory of the hydrogen atom. This combined the classical ideas on planetary motion—applicable to the atom because of the fomial similarity of tlie gravitational potential to tlie Coulomb potential between an electron and nucleus—with the quantum ideas that had recently been introduced by Planck and Einstein. This led eventually to the fomial theory of quaiitum mechanics, first discovered by Heisenberg, and most conveniently expressed by Schrodinger in the wave equation that bears his name. [Pg.54]

Mn is the mass of the nucleon, jis Planck s constant divided by 2ti, m. is the mass of the electron. This expression omits some temis such as those involving relativistic interactions, but captures the essential features for most condensed matter phases. [Pg.87]

In the previous section we discussed light and matter at equilibrium in a two-level quantum system. For the remainder of this section we will be interested in light and matter which are not at equilibrium. In particular, laser light is completely different from the thennal radiation described at the end of the previous section. In the first place, only one, or a small number of states of the field are occupied, in contrast with the Planck distribution of occupation numbers in thennal radiation. Second, the field state can have a precise phase-, in thennal radiation this phase is assumed to be random. If multiple field states are occupied in a laser they can have a precise phase relationship, something which is achieved in lasers by a teclmique called mode-locking Multiple frequencies with a precise phase relation give rise to laser pulses in time. Nanosecond experiments... [Pg.225]

This is the Planck distribution function. The themial average energy in theyth mode is (including the zero point energy)... [Pg.409]

This is known as the Planck radiation law. Figure A2.2.3 shows this spectral density fiinction. The surface temperature of a hot body such as a star can be estimated by approximating it by a black body and measuring the frequency at which the maximum emission of radiant energy occurs. It can be shown that the maximum of the Planck spectral density occurs at 2.82. So a measurement of yields an estimate of the... [Pg.411]

Figure A2.2.3. Planck spectral density fimction as a fimction of the dimensionless frequency /)oi/(/rj 7). A2.2.4.7 APPLICATION TO IDEAL SYSTEMS ELASTIC WAVES IN A SOLID... Figure A2.2.3. Planck spectral density fimction as a fimction of the dimensionless frequency /)oi/(/rj 7). A2.2.4.7 APPLICATION TO IDEAL SYSTEMS ELASTIC WAVES IN A SOLID...
A fiill theory of micleation requires a dynamical description. In the late 1960s, the early theories of homogeneous micleation were generalized and made rigorous by Langer [47]. Here one starts with an appropriate Fokker-Planck... [Pg.755]

Here h(x) is the Heaviside step function with h(x > 0) = 1 and h(x > 0) = 0 (not to be confused with Planck s constant). The limit a(J.. . ) indicates that the sunnnation is restricted to channel potentials witir a given set of good quantum numbers (J.. . ). [Pg.783]

From these equations one also finds the rate coefficient matrix for themial radiative transitions including absorption, induced and spontaneous emission in a themial radiation field following Planck s law [35] ... [Pg.1048]

The transition occurs with significant probability only if the frequency of the light is very close to the familiar resonance condition, namely hv = AE, where h is Planck s constant and AE is the difference in energy of the... [Pg.1125]

Finally, exchange is a kinetic process and governed by absolute rate theory. Therefore, study of the rate as a fiinction of temperature can provide thennodynamic data on the transition state, according to equation (B2.4.1)). This equation, in which Ids Boltzmaim s constant and h is Planck s constant, relates tlie observed rate to the Gibbs free energy of activation, AG. ... [Pg.2090]

Planck M 1897 Vorlesungen uber Thermodynamik (Leipzig von Veit)... [Pg.2848]

A linear dependence approximately describes the results in a range of extraction times between 1 ps and 50 ps, and this extrapolates to a value of Ws not far from that observed for the 100 ps extractions. However, for the simulations with extraction times, tg > 50 ps, the work decreases more rapidly with l/tg, which indicates that the 100 ps extractions still have a significant frictional contribution. As additional evidence for this, we cite the statistical error in the set of extractions from different starting points (Fig. 2). As was shown by one of us in the context of free energy calculations[12], and more recently again by others specifically for the extraction process [1], the statistical error in the work and the frictional component of the work, Wp are related. For a simple system obeying the Fokker-Planck equation, both friction and mean square deviation are proportional to the rate, and... [Pg.144]


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A Differential Geometry-Based Poisson-Nernst-Planck Model

Augmented Fokker-Planck equation

Bivariate Fokker-Planck equation

Blackbody, Planck

Boltzmann Planck entropy equation

Boundary conditions Fokker-Planck equation

Brownian motion Fokker-Planck equation, solutions

Brownian motion fractional Fokker-Planck equation

Characteristics Planck spectrum

Complex Fokker-Planck equation

Diffusion Fokker-Planck equation

Diffusion coefficient Fokker-Planck equation

Einstein-Planck quantum theory

Einstein-Planck quantum theory radiation

Einstein-Planck relation

Elementary Quantum Theory of Max Planck

Energy Planck’s constant

Equations Planck-Henderson

Equilibrium Planck function

Extended Nernst Planck Equation

Ferromagnetic particle relaxation Fokker-Planck

Fick-Nernst-Planck equation

Fokker Planck equation anomalous diffusion

Fokker Planck equation ferrofluids

Fokker Planck equation fractions

Fokker Planck multivariate

Fokker-Planck

Fokker-Planck Equation for Systems of SDEs

Fokker-Planck Kinetic Equation for Determination of EEDF

Fokker-Planck Modeling of the Electronic Localization

Fokker-Planck and Langevin Equations

Fokker-Planck approach, molecular

Fokker-Planck differential equation

Fokker-Planck equation

Fokker-Planck equation Brownian motion

Fokker-Planck equation Levy flight processes

Fokker-Planck equation background

Fokker-Planck equation behavior

Fokker-Planck equation calculations

Fokker-Planck equation dielectric relaxation

Fokker-Planck equation differential equations

Fokker-Planck equation equations

Fokker-Planck equation evolution times

Fokker-Planck equation expansion coefficients

Fokker-Planck equation ferromagnetic particles

Fokker-Planck equation fractional rotational diffusion

Fokker-Planck equation generalized

Fokker-Planck equation inertial effects

Fokker-Planck equation moment

Fokker-Planck equation moment equations

Fokker-Planck equation multiplicative noise

Fokker-Planck equation nonlinear problems

Fokker-Planck equation operator

Fokker-Planck equation particles

Fokker-Planck equation related equations

Fokker-Planck equation relaxation

Fokker-Planck equation reliability

Fokker-Planck equation representation

Fokker-Planck equation solution methods

Fokker-Planck equation solutions

Fokker-Planck equation stationary solution

Fokker-Planck equation stochastic processes

Fokker-Planck equation time-dependent distribution function

Fokker-Planck kinetic equation

Fokker-Planck model

Fokker-Planck operator

Fokker-Planck quantum equation

Fokker-Planck theory

Fokker-Planck to Schrodinger Equation Transformation

Fokker-Planck transport

Fokker-Planck-Kolmogorov

Fokker-Planck-Kramers equation

Fokker-Planck-Langevin model

Fokker-Planck-Smoluchowski Equation

Fractional Fokker-Planck equation

Fractional Fokker-Planck equation Levy flight processes

Fractional Fokker-Planck equation model

Fritz Haber Institute of the Max Planck Society, Faradayweg

Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg

Gaussian distribution, Fokker-Planck

Gaussian distribution, Fokker-Planck equation

H Planck s constant

H, the Planck constant

Karl Ernst Ludwig Planck

Kelvin-Planck statement

Kelvin-Planck statement of the second law

Linear Fokker-Planck equation

MAX-PLANCK-INSTITUT FUER

MAX-PLANCK-INSTITUT FUER KOLLOID

MAX-PLANCK-INSTITUT FUER POLYMERFORSCHUNG

Many-body Fokker-Planck-Kramers

Many-body Fokker-Planck-Kramers equation

Markovian-Fokker-Planck equation

Massieu-Planck function

Max Planck Gesellschaft

Max Planck Institute

Max Planck Institute for

Max Planck Institute for Evolutionary

Max Planck Institute for Marine Microbiology

Max Planck Institute for Medical Research

Max Planck Institute for Molecular Genetics

Max Planck Medal

Max-Planck Institute for Chemistry

Max-Planck-Institut fiir medizinische

Max-Planck-Institut fiir medizinische Forschung

Max-Planck-Institut fur Kohlenforschung

Max-Planck-Institut fur Plasmaphysik

Max-Planck-Institut fur Polymerforschung

Max-Planck-Institute for Solid State

Max-Planck-Institute for Solid State Research, Stuttgart

Membranes Nernst-Planck model)

Micromagnetic Fokker-Planck equation

Micromagnetic Fokker-Planck equation moment

Molecular modeling Fokker-Planck equation

Multiplicative noise, Fokker-Planck

Multivariate Fokker-Planck equation

Nemst-Planck

Nemst-Planck diffusion equations, applied

Nemst-Planck diffusion equations, applied membranes

Nemst-Planck effect

Nemst-Planck equation

Nemst-Planck equation diffusive term

Nemst-Planck theory

Nernst-Planck

Nernst-Planck approximation

Nernst-Planck equation

Nernst-Planck equation, membrane potential

Nernst-Planck equations, problems with

Nernst-Planck expression

Nernst-Planck flux equation

Nernst-Planck postulate

Nernst-Planck relation

Nernst-Planck theorem

Nernst-Planck’s equation

Nonlinear Fokker-Planck equation

PLANCK satellite

Physical chemist Planck

Planck Einstein relationship

Planck Max

Planck Scale Physics in Our Low-Energy World

Planck Theory of Black Body Radiation

Planck action constant

Planck black body equation

Planck blackbody distribution

Planck constant

Planck constant numerical values

Planck constant quantum theory

Planck constant theory

Planck curves

Planck distribution

Planck distribution function

Planck distribution law

Planck equation

Planck expression

Planck formula

Planck frequency distribution

Planck function

Planck function change

Planck function defined

Planck function properties

Planck function temperature

Planck intensity function

Planck length

Planck mean absorption coefficient

Planck natural unit system

Planck oscillator

Planck postulate

Planck quanta

Planck quantization

Planck quantization development

Planck radiation formula

Planck radiation law

Planck radiation model

Planck radiator

Planck relation

Planck relationship

Planck s Law of Radiation

Planck s constant

Planck s law

Planck s quantum theory

Planck scale

Planck spectrum

Planck statement

Planck statement of the second law

Planck tension

Planck time

Planck units

Planck, Max Karl Ernst Ludwig

Planck, black-body radiation

Planck, radiation oscillators

Planck-Einstein equation

Planck-Einstein function

Planck-Einstein quantization

Planck-Henderson

Planck-Henderson expression

Planck-mean absorption length

Plancks Approach

Plancks Discovery

Plancks Formulation

Plancks law

Planck’s distribution

Planck’s distribution law

Planck’s equation

Planck’s formula

Planck’s hypothesis

Planck’s quantum

Planck’s quantum theory of radiation

Planck’s radiation distribution

Planck’s radiation distribution formula

Planck’s radiation formula

Planck’s radiation law

Planck’s relationship

Planck’s rule

Planck’s theory

Poisson-Nemst- Planck

Poisson-Nemst- Planck theory

Poisson-Nemst-Planck model

Poisson-Nernst-Planck equation

Poisson-Nernst-Planck method

Poisson-Nernst-Planck model

Probability distribution Fokker-Planck equation

Quantum electrodynamics Planck constant

Quasilinear Fokker-Planck equation

Radiation Planck

Radiation distribution formula Planck

Relaxation equations fractional Fokker-Planck equation

Second law of thermodynamics Kelvin-Planck statement

Space-fractional Fokker-Planck equation, Levy

Space-fractional Fokker-Planck equation, Levy flight processes

Stochastic Liouville equation Fokker-Planck equations

Stochastic differential equations Fokker-Planck equation

Stochastic simulation Fokker-Planck equation

System Planck

The Fokker - Planck Equation for Stochastic Motion

The Fokker-Planck Approach to Thermalization

The Fokker-Planck Equation for P ( t)

The Fokker-Planck approach Numerical solutions

The Fokker—Planck equation

The Max Planck Society

The Nernst-Planck Equation

The Nernst-Planck-Poisson Problem

The Photon Stream and Planck s Equation

The Planck Radiation Law

The Planck function

The multidimensional Fokker-Planck equation

Thermal Radiation and Plancks Law

Thermal radiation Planck

Thermodynamics Kelvin-Planck statement

Three-body Fokker-Planck-Kramers

Two-body Fokker-Planck-Kramers model

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