Stochastic Processes in Physics and Chemistry

By C. Cercignani. 2005

1,510 citations recorded by the source corpus.

Subfields: Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6877d11f801a1a65addfc1790bb5f6422b1ae19b

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In Statistical and Nonlinear Physics

Citations in the corpus

WKB theory of large deviations in stochastic populations (2016, background): “E 93 032109 [53] Gardiner C W 2004 Handbook of Stochastic Methods (Berlin: Springer) [54] van Kampen N G 2001 Stochastic Processes in Physics and Chemistry (Amsterdam: North- Holland) [55] Elgart V and Kamenev A 2004 Phys.”
Constructive methods of invariant manifolds for kinetic problems (2003, background): “The Fokker-Planck equation (FPE) is a familiar model in various problems of nonequilibrium statistical physics [84, 85].”
Fixation times in evolutionary games under weak selection (2008, background): “Equivalently, the average fixation times for such onedimensional random walks can also be interpreted as mean first passage times or mean exit times [27]–[29].”
Relativistic Brownian Motion (2008, methodology): “Once the Fokker–Planck equation has been found, it is straightforward to write down a corresponding Langevin dynamics [75,76].”
Thermodynamic prediction of protein neutrality. (2004, neutral): “Under this additivity assumption, we can therefore directly calculate the distribution pm( Gm) for Gm by performing an m-fold convolution (27) of p1( G).”
Voter model on heterogeneous graphs. (2004, background): “This consensus time satisfies the recursion formula [17, 18]:”
Active Brownian particles (2012, methodology): “Thus our general modelling approach will be based on the concept of stochastic differential equations (Langevin equation, SDE) and the corresponding Fokker-Planck equations for the evolution of the probability densities of the involved (stochastic) variables [136,292,357].”
Network Inference and Biological Dynamics (2011, methodology): “However, it is usually possible to construct a ﬁnite memory approximation of the form (2) using a so-called “system size expansion” [Van Kampen (2007)].”
A Diffusion Theory for Deep Learning Dynamics: Stochastic Gradient Descent Escapes From Sharp Minima Exponentially Fast (2020, methodology): “Mean escape time, also called ﬁrst exit time, means the mean time required for a particle to escape a loss valley, a widely used concept in statistical physics and stochastic process (Kramers, 1940; Van Kampen, 1992; Nguyen et al., 2019).”
Irreversibility in Active Matter Systems: Fluctuation Theorem and Mutual Information (2018, methodology): “[45] Nicolaas Godfried Van Kampen, Stochastic processes in physics and chemistry, Vol.”
On the validity of the 0–1 test for chaos (2009, neutral): “Indeed, S(c) = ∑∞k=−∞ eikcρ(|k|) on (0, 2π) by the Wiener–Khintchine theorem [9].”
Stochastic switching in biology: from genotype to phenotype (2017, background): “The most common is the diffusion approximation obtained by carrying out an expansion in the system size Ω [83, 105, 242].”
A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties (2006, background): “…alternative formalism is the Fokker–Planck equation, which describes the time evolution of the probability density P(v, t) of the membrane potential (van Kampen 1992; Risken 1996) ∂ ∂t P(v, t) = [ − ∂ ∂v A(v, t) + 1 2 ∂2 ∂v2 B(v, t) ] P(v, t) , (30) where A(v, t) is the drift function and B(v, t)…”