相关论文: Matter evolution in Burgulence

In this work, we study convection-diffusion equations in the cases of bounded drifts and drifts induced by the gradient of a potential. We define a new notion of solution and prove its existence and uniqueness. Furthermore, we show the…

The adhesive dynamics of a one-dimensional aggregating gas of point particles is rigorously described. The infinite hierarchy of kinetic equations for the distributions of clusters of nearest neighbours is shown to be equivalent to a system…

We establish the general conditions under which evolution in the laws of physics and matter creation or destruction are closely intertwined. They make use of global time variables canonically dual to the constants of Nature. Such times flow…

Invasion fronts in ecology are well studied but very few mathematical results concern the case with variable motility (possibly due to mutations). Based on an apparently simple reaction-diffusion equation, we explain the observed phenomena…

Dynamics of viscous shocks is considered in the modular Burgers equation, where the time evolution becomes complicated due to singularities produced by the modular nonlinearity. We prove that the viscous shocks are asymptotically stable…

The decay of Burgers turbulence with compactly supported Gaussian "white noise" initial conditions is studied in the limit of vanishing viscosity and large time. Probability distribution functions and moments for both velocities and…

Cosmological perturbation theory for the late Universe dominated by dark matter is extended beyond the perfect fluid approximation by taking the dark matter velocity dispersion tensor as an additional field into account. A proper tensor…

This paper is concerned with the uniqueness, existence, comparison principle and long-time behavior of solutions to the initial-boundary value problem for a unidirectional diffusion equation. The unidirectional evolution often appears in…

We develop a theory of Brownian motion of a massive particle, including the effects of inertia (Kramers' problem), in spaces with curvature and torsion. This is done by invoking the recently discovered generalized equivalence principle,…

We analyze the field theory of fully developed Burgers turbulence. Its key elements are shock fields, which characterize the singularity statistics of the velocity field. The shock fields enter an operator product expansion describing…

We introduce a modified divergence law for the energy-momentum tensor in the theory of unimodular relativity. Consequently, an additional equation for the measure field follows from the divergence of the field equations. The equations of…

The evolution of an inhomogeneous universe composed entirely of matter is followed from an early, nearly uniform state until the time when the inhomogeneities have begun to grow large. The particular distribution of matter studied in this…

The motion of a particle is studied in a random space-time. It is assumed that the velocity is small enough for the non-relativistic approximation to be valid. The randomness of the metric induces a diffusion in coordinate space. Hence it…

The inviscid Burgers equation with random and spatially smooth forcing is considered in the limit when the size of the system tends to infinity. For the one-dimensional problem, it is shown both theoretically and numerically that many of…

The dynamics of the multi-dimensional randomly forced Burgers equation is studied in the limit of vanishing viscosity. It is shown both theoretically and numerically that the shocks have a universal global structure which is determined by…

It is well known that the solutions to the non-viscous Burgers equation develop a gradient catastrophe at a critical time provided the initial data have a negative derivative in certain points. We consider this equation assuming that the…

We analyse the evolution of cosmological perturbations which leads to the formation of large isolated voids in the Universe. We assume that initial perturbations are spherical and all components of the Universe (radiation, matter and dark…

Moments are expectation values of products of powers of position and momentum, taken over quantum states (or averages over a set of classical particles). For free particles, the evolution in the quantum case is closely related to that of a…

Within the class of nonlinear hyperbolic balance laws posed on a curved spacetime (endowed with a volume form), we identify a hyperbolic balance law that enjoys the same Lorentz invariance property as the one satisfied by the Euler…

We perform the discrete-to-continuum limit passage for a microscopic model describing the time evolution of dislocations in a one dimensional setting. This answers the related open question raised by Geers et al. in [GPPS13]. The proof of…