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Encoding physics to learn reaction–diffusion processes
Nature Machine Intelligence, 2021Modelling complex spatiotemporal dynamical systems, such as reaction–diffusion processes, which can be found in many fundamental dynamical effects in various disciplines, has largely relied on finding the underlying partial differential equations (PDEs).
Chengping Rao +5 more
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Increasing Understanding of Public Problems and Policies, 1956 This paper is a summary of the flannel board presentation on how farm people accept new ideas. It is based on the findings of 35 research studies conducted during the past twenty years in various parts of the United States, including Illinois, Iowa, Missouri, Wisconsin, New Hampshire, New York, West Virginia, Kentucky, and Tennessee.1 The findings of ...
Beal, George M. +3 more
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Generalisation of the Eyring–Kramers Transition Rate Formula to Irreversible Diffusion Processes
Annales de l'Institute Henri Poincare. Physique theorique, 2015In the small noise regime, the average transition time between metastable states of a reversible diffusion process is described at the logarithmic scale by Arrhenius’ law. The Eyring–Kramers formula classically provides a subexponential prefactor to this
F. Bouchet, J. Reygner
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Siberian Mathematical Journal, 2003
The author studies the elliptic system of first-order strongly nonlinear differential equations of one complex variable \[ u_{\bar z} = \mu^1u_z + \mu^2\bar u_{\bar z} + f \equiv A(z,u,v),\quad v = u_{z} \] which is commonly used to describe diffusion and convective processes of heat and mass transfer in a fluid.
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The author studies the elliptic system of first-order strongly nonlinear differential equations of one complex variable \[ u_{\bar z} = \mu^1u_z + \mu^2\bar u_{\bar z} + f \equiv A(z,u,v),\quad v = u_{z} \] which is commonly used to describe diffusion and convective processes of heat and mass transfer in a fluid.
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On coupling of diffusion processes
Journal of Applied Probability, 1983The coupling method is well fitted to be used in the study of the asymptotics of one-dimensional diffusion processes. We give an elementary proof of Orey's theorem in the recurrent case, and establish rate results for tendency towards equilibrium under moment conditions on the speed measure and the initial distributions.
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On the transformation of diffusion processes into the Feller process
Mathematical Biosciences, 1976Abstract Due to the recently revived interest toward the diffusion process proposed by Feller in the population dynamics context, the class of Kolmogorov equations that can be transformed into a similar equation possessing linear infinitesimal variance and affine drift is determined.
R. M. CAPOCELLI, RICCIARDI, LUIGI MARIA
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Diffusion reproduction processes
Journal of Statistical Physics, 1990Interesting physics emerges from studying a population of reproducing individuals. Each can be regarded as a random walker, but it can either duplicate or die. Novel features of the collective behavior are quite surprising: if individuals reproduce or die freely, the life expectation is proportional to the size of the population, and if it is kept ...
Zhang Y. C +2 more
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2001
Abstract Write down Bartlett’s equation in the case of the Wiener process D having drift m and instantaneous variance 1, and solve it subject to the boundary condition D(0) = 0.
Geoffrey R Grimmett, David R Stirzaker
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Abstract Write down Bartlett’s equation in the case of the Wiener process D having drift m and instantaneous variance 1, and solve it subject to the boundary condition D(0) = 0.
Geoffrey R Grimmett, David R Stirzaker
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, 2015
We study generalized anomalous diffusion processes whose diffusion coefficient D(x, t) ∼ D0|x|αtβ depends on both the position x of the test particle and the process time t.
Andrey G. Cherstvy, R. Metzler
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We study generalized anomalous diffusion processes whose diffusion coefficient D(x, t) ∼ D0|x|αtβ depends on both the position x of the test particle and the process time t.
Andrey G. Cherstvy, R. Metzler
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