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Let be a principal fiber bundle and an associated fiber bundle. Our interest is to study the harmonic sections of the projection of into . Our first purpose is give a characterization of harmonic sections of into regarding its equivariant lift. The second purpose is to show a version of a Liouville theorem for harmonic sections of .
We analyze the equation coming from the Eulerian-Lagrangian description of fluids. We discuss a couple of ways to extend this notion to viscous fluids. The main focus of this paper is to discuss the first way, due to Constantin. We show that this description can only work for short times, after which the ``back to coordinates map'' may have no smooth inverse. Then we briefly discuss a second way that uses Brownian motion. We use this to provide a plausibility argument for the global regularity for...
We present a Monte Carlo technique for sampling from the
canonical distribution in molecular dynamics. The method is built upon
the Nosé-Hoover constant temperature formulation and the generalized
hybrid Monte Carlo method. In contrast to standard hybrid Monte Carlo methods
only the thermostat degree of freedom is stochastically resampled
during a Monte Carlo step.
We study a model of motion of a passive tracer particle in a turbulent flow that is strongly mixing in time variable. In [8] we have shown that there exists a probability measure equivalent to the underlying physical probability under which the quasi-Lagrangian velocity process, i.e. the velocity of the flow observed from the vintage point of the moving particle, is stationary and ergodic. As a consequence, we proved the existence of the mean of the quasi-Lagrangian velocity, the so-called Stokes...
The paper concerns a model of influence in which agents make their decisions on a certain
issue. We assume that each agent is inclined to make a particular decision, but due to a
possible influence of the others, his final decision may be different from his initial
inclination. Since in reality the influence does not necessarily stop after one step, but
may iterate, we present a model which allows us to study the dynamic of influence. An
innovative...
The paper concerns a model of influence in which agents make their decisions on a certain
issue. We assume that each agent is inclined to make a particular decision, but due to a
possible influence of the others, his final decision may be different from his initial
inclination. Since in reality the influence does not necessarily stop after one step, but
may iterate, we present a model which allows us to study the dynamic of influence. An
innovative...
In this paper, we prove the existence and uniqueness of the solution of the initial boundary value problem for a stochastic mass conserved Allen-Cahn equation with nonlinear diffusion together with a homogeneous Neumann boundary condition in an open bounded domain of with a smooth boundary. We suppose that the additive noise is induced by a Q-Brownian motion.
This paper is dedicated to the analysis of backward stochastic differential equations (BSDEs) with jumps, subject to an additional global constraint involving all the components of the solution. We study the existence and uniqueness of a minimal solution for these so-called constrained BSDEs with jumps via a penalization procedure. This new type of BSDE offers a nice and practical unifying framework to the notions of constrained BSDEs presented in [S. Peng and M. Xu, Preprint. (2007)] and BSDEs...
We consider multiscale systems for which only a fine-scale model describing the evolution of individuals (atoms, molecules, bacteria, agents) is given, while we are interested in the evolution of the population density on coarse space and time scales. Typically, this evolution is described by a coarse Fokker-Planck equation. In this paper, we consider a numerical procedure to compute the solution of this Fokker-Planck equation directly on the coarse level, based on the estimation of the unknown...
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