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Generalized Langevin Equations
2013We now turn to problems in statistical mechanics where the assumption of thermal equilibrium does not apply. In nonequilibrium problems, one should in principle solve the full Liouville equation, at least approximately. There are many situations in which one attempts to do that under different assumptions and conditions, giving rise to the Euler and ...
Alexandre J. Chorin, Ole H. Hald
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2014
Abstract In this chapter, Langevin field equations (or Ito stochastic field equations, SFEs) are derived that are equivalent to functional Fokker–Planck equations (FFPEs) for bosons and fermions. Phase space fields are replaced by stochastic phase space fields satisfying Ito SFEs containing c-number Wiener increments, together with ...
Bryan J. Dalton +2 more
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Abstract In this chapter, Langevin field equations (or Ito stochastic field equations, SFEs) are derived that are equivalent to functional Fokker–Planck equations (FFPEs) for bosons and fermions. Phase space fields are replaced by stochastic phase space fields satisfying Ito SFEs containing c-number Wiener increments, together with ...
Bryan J. Dalton +2 more
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Physics Letters A, 1977
Abstract Two known extensions of the Langevin equation are shown to contain “random” forces of equal power but different colour. An extended equation which contains both the previous ones is proposed and briefly discussed.
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Abstract Two known extensions of the Langevin equation are shown to contain “random” forces of equal power but different colour. An extended equation which contains both the previous ones is proposed and briefly discussed.
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2021
While you are reading this thesis, at every instant of time countless particles of the surrounding air hit your skin due to their irregular thermal motion. There are of the order of \({\sim } 10^{23}\) molecules in every liter of air [1, 2].
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While you are reading this thesis, at every instant of time countless particles of the surrounding air hit your skin due to their irregular thermal motion. There are of the order of \({\sim } 10^{23}\) molecules in every liter of air [1, 2].
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Langevin equations for fluctuating surfaces
Physical Review E, 2005Exact Langevin equations are derived for the height fluctuations of surfaces driven by the deposition of material from a molecular beam. We consider two types of model: deposition models, where growth proceeds by the deposition and instantaneous local relaxation of particles, with no subsequent movement, and models with concurrent random deposition and
Alvin L-S, Chua +3 more
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Langevin equations from time series
Physical Review E, 2005We discuss the link between the approach to obtain the drift and diffusion of one-dimensional Langevin equations from time series, and Pope and Ching's relationship for stationary signals. The two approaches are based on different interpretations of conditional averages of the time derivatives of the time series at given levels. The analysis provides a
E, Racca, A, Porporato
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The langevin equation of weak turbulence
Annals of Physics, 1971Abstract The hieraichy equations describing weakly interacting waves in a fluid are solved by the method of characteristic functionals, combined with the time asymptotic method of Bogoliubov and Mitropolski. The result to lowest nontrivial order allows one to characterize the stochastic state of the fluid in close analogy to the Brownian motion of a ...
Elsässer, K., Gräff, P.
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2000
The objective of this Lecture is to present the Langevin equation, which is a physically deduced equation of motion for particles in a fluid. The starting point is not the canonical ensemble; rather, this Lecture presents a rationale for postulating that the correct equation of motion has a particular mathematical form.
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The objective of this Lecture is to present the Langevin equation, which is a physically deduced equation of motion for particles in a fluid. The starting point is not the canonical ensemble; rather, this Lecture presents a rationale for postulating that the correct equation of motion has a particular mathematical form.
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2020
As a prelude, some of the important properties of the Maxwellian distribution of velocities in thermal equilibrium are highlighted. The basic equation of motion of a particle in a fluid incorporating the effects of random molecular collisions, the Langevin equation, is introduced.
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As a prelude, some of the important properties of the Maxwellian distribution of velocities in thermal equilibrium are highlighted. The basic equation of motion of a particle in a fluid incorporating the effects of random molecular collisions, the Langevin equation, is introduced.
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2014
In this chapter, we study the Langevin equation and the associated Fokker –Planck equation. In Sect. 6.1, we introduce the equation and study some of the main properties of the corresponding Fokker–Planck equation. In Sect. 6.2 we give an elementary introduction to the theories of hypoellipticity and hypocoercivity. In Sect.
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In this chapter, we study the Langevin equation and the associated Fokker –Planck equation. In Sect. 6.1, we introduce the equation and study some of the main properties of the corresponding Fokker–Planck equation. In Sect. 6.2 we give an elementary introduction to the theories of hypoellipticity and hypocoercivity. In Sect.
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