1,720,985 research outputs found
Computing a Class of Blow-up Solutions for the Navier-Stokes Equations
No full textThe three-dimensional incompressible Navier-Stokes equations play a fundamental role in a large number of applications to fluid motions, and a large amount of theoretical and experimental studies were devoted to it. Our work is in the context of the Global Regularity Problem, i.e., whether smooth solutions in the whole space R^3 can become singular (“blow-up”) in a finite time. The problem is still open and also has practical importance, as the singular solutions would describe new phenomena. Our work is mainly inspired by a paper of Li and Sinai, who proved the existence of a blow-up for a class of smooth complex initial data. We present a study by computer simulations of a larger class of complex solutions and also of a related class of real solutions, which is a natural candidate for evidence of a blow-up. The numerical results show interesting features of the solutions near the blow-up time. They also show some remarkable properties for the real flows, such as a sharp increase of the total enstrophy and a concentration of high values of velocities and vorticity in small regions
The dynamics of a particle interacting with a semi-infinite ideal gas is a Bernoulli flow
No full text
An Antisymmetric Solution of the 3D Incompressible Navier-Stokes Equations with "Tornado-Like" Behavior
No full textWe consider a solution of the incompressible Navier–Stokes equations in R3, related to the singular
complex solutions of Li and Sinai [1], and such that a growth of the enstrophy S(t) is expected. The computer
simulations show that S(t) increases up to a time TE (singularities are excluded by axial symmetry). They also
reveal an interesting “tornado-like” behavior, with a sharp increase of speed and vorticity in an annular region,
as for some “extreme” weather phenomena
Computer simulations for some one-dimensional models of random walks in fluctuating random environment
No full textSummary: "We report some results of computer simulations for two models of random walks in random environment (rwre) on the one-dimensional lattice Z for fixed space-time configuration of the environment (`quenched rwre'): a `Markov model' with Markov dependence in time, and a `quasi-stationary' model with long range space-time correlations. We compare the corresponding results for a model with an i.i.d. (in space-time) environment. In the range of times available to us the quenched distributions of the random walk displacement are far from Gaussian, but as the behavior is similar for all three models one cannot exclude asymptotic Gaussianity, which is proved for the model with i.i.d. environment. We also report results on the random drift and on some time correlations which show a clear power decay.'
Almost-sure Central Limit Theorem for a Model of Random Walk in Fluctuating Random Environment
No full textDiscrete time random motion in a continuous random medium
No full textWe propose a discrete-time random walk on R(d), d = 1, 2,..., as a variant of recent models of random walk on Z(d) in a random environment which is i.i.d. in space-time. We allow space correlations of the environment and develop an analytic method to deal with them. We prove, under some general assumptions, that if the random term is small, a "quenched" (i.e., for a fixed "history" of the environment) Central Limit Theorem for the displacement of the random walk holds almost-surely. Proofs are based on L(2) estimates. We consider for brevity only the case of odd dimension d, as even dimension requires somewhat different estimates. (C) 2009 Elsevier B.V. All rights reserved
On the blow-up of some complex solutions of the 3D Navier–Stokes equations: theoretical predictions and computer simulations
Full text linkWe consider some complex-valued solutions of the Navier–Stokes equations in R^3 for which Li and Sinai proved a finite time blow-up. We show that there are two types of solutions, with different divergence rates, and report results of computer simulations, which give a detailed picture of the blow-up for both types. They reveal in particular important features not, as yet, predicted by the theory, such as a concentration of the energy and the enstrophy around a few singular points, while elsewhere the ‘fluid’ remains quiet
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