264 research outputs found
Nonequilibrium mesoscopic transport: a genealogy
Models of nonequilibrium quantum transport underpin all modern electronic
devices, from the largest scales to the smallest. Past simplifications such as
coarse graining and bulk self-averaging served well to understand electronic
materials. Such particular notions become inapplicable at mesoscopic
dimensions, edging towards the truly quantum regime. Nevertheless a unifying
thread continues to run through transport physics, animating the design of
small-scale electronic technology: microscopic conservation and nonequilibrium
dissipation. These fundamentals are inherent in quantum transport and gain even
greater and more explicit experimental meaning in the passage to atomic-sized
devices. We review their genesis, their theoretical context, and their
governing role in the electronic response of meso- and nanoscopic systems.Comment: 21p
Stochastic stability research for complex power systems
Bibliography: p. 302-311."November 1980." "Midterm report ... ."U.S. Dept. of Energy Contract ET-76-A-01-2295Tobias A. Trygar
Stochastic hybrid systems in cellular neuroscience
We review recent work on the theory and applications of stochastic hybrid systems in cellular neuroscience. A stochastic hybrid system or piecewise deterministic Markov process involves the coupling between a piecewise deterministic differential equation and a time-homogeneous Markov chain on some discrete space. The latter typically represents some random switching process. We begin by summarizing the basic theory of stochastic hybrid systems, including various approximation schemes in the fast switching (weak noise) limit. In subsequent sections, we consider various applications of stochastic hybrid systems, including stochastic ion channels and membrane voltage fluctuations, stochastic gap junctions and diffusion in randomly switching environments, and intracellular transport in axons and dendrites. Finally, we describe recent work on phase reduction methods for stochastic hybrid limit cycle oscillators
Canards in a bottleneck
In this paper we investigate the stationary profiles of a nonlinear
Fokker-Planck equation with small diffusion and nonlinear in- and outflow
boundary conditions. We consider corridors with a bottleneck whose width has a
global nondegenerate minimum in the interior. In the small diffusion limit the
profiles are obtained constructively by using methods from geometric singular
perturbation theory (GSPT). We identify three main types of profiles
corresponding to: (i) high density in the domain and a boundary layer at the
entrance, (ii) low density in the domain and a boundary layer at the exit, and
(iii) transitions from high density to low density inside the bottleneck with
boundary layers at the entrance and exit. Interestingly, solutions of the last
type involve canard solutions generated at the narrowest point of the
bottleneck. We obtain a detailed bifurcation diagram of these solutions in
terms of the in- and outflow rates. The analytic results based on GSPT are
further corroborated by computational experiments investigating corridors with
bottlenecks of variable width.Comment: arXiv admin note: text overlap with arXiv:2010.1442
Stochastic chaos and thermodynamic phase transitions : theory and Bayesian estimation algorithms
Thesis (M. Eng. and S.B.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 177-200).The chaotic behavior of dynamical systems underlies the foundations of statistical mechanics through ergodic theory. This putative connection is made more concrete in Part I of this thesis, where we show how to quantify certain chaotic properties of a system that are of relevance to statistical mechanics and kinetic theory. We consider the motion of a particle trapped in a double-well potential coupled to a noisy environment. By use of the classic Langevin and Fokker-Planck equations, we investigate Kramers' escape rate problem. We show that there is a deep analogy between kinetic rate theory and stochastic chaos, for which we propose a novel definition. In Part II, we develop techniques based on Volterra series modeling and Bayesian non-linear filtering to distinguish between dynamic noise and measurement noise. We quantify how much of the system's ergodic behavior can be attributed to intrinsic deterministic dynamical properties vis-a-vis inevitable extrinsic noise perturbations.by Zhi-De Deng.M.Eng.and S.B
Differential Equation Models in Applied Mathematics
The present book contains the articles published in the Special Issue “Differential Equation Models in Applied Mathematics: Theoretical and Numerical Challenges” of the MDPI journal Mathematics. The Special Issue aimed to highlight old and new challenges in the formulation, solution, understanding, and interpretation of models of differential equations (DEs) in different real world applications. The technical topics covered in the seven articles published in this book include: asymptotic properties of high order nonlinear DEs, analysis of backward bifurcation, and stability analysis of fractional-order differential systems. Models oriented to real applications consider the chemotactic between cell species, the mechanism of on-off intermittency in food chain models, and the occurrence of hysteresis in marketing. Numerical aspects deal with the preservation of mass and positivity and the efficient solution of Boundary Value Problems (BVPs) for optimal control problems. I hope that this collection will be useful for those working in the area of modelling real-word applications through differential equations and those who care about an accurate numerical approximation of their solutions. The reading is also addressed to those willing to become familiar with differential equations which, due to their predictive abilities, represent the main mathematical tool for applying scenario analysis to our changing world
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