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The full non-linear evolution of the tidal instability is studied numerically in an ellipsoidal fluid domain relevant for planetary cores applications. Our numerical model, based on a finite element method, is first validated by reproducing…
This paper uses dynamical invariants to describe the evolution of collisionless systems subject to time-dependent gravitational forces without resorting to maximum-entropy probabilities. We show that collisionless relaxation can be viewed…
We investigate free hydromagnetic eigenmodes of an incompressible, inviscid and ideal electrically conducting fluid in rotating triaxial ellipsoids. The container rotates with an angular velocity tilted from its figure. The magnetic base…
Dynamics of inelastic gases are studied within the framework of random collision processes. The corresponding Boltzmann equation with uniform collision rates is solved analytically for gases, impurities, and mixtures. Generally, the energy…
We study the statistical properties of the eigenvalues of the primordial tidal and deformation tensor for random Gaussian cosmic density fields. With the tidal and deformation tensors, Hessians of the gravitational and velocity potential,…
The results of our study of the motion of a three particle, self-gravitating system in general relativistic lineal gravity is presented for an arbitrary ratio of the particle masses. We derive a canonical expression for the Hamiltonian of…
We present a study of dynamical scaling and front motion in a one dimensional system that describes Rayleigh-Benard convection in a rotating cell. We use a model of three competing modes proposed by Busse and Heikes to which spatial…
We study freely evolving and forced inelastic gases using the Boltzmann equation. We consider uniform collision rates and obtain analytical results valid for arbitrary spatial dimension d and arbitrary dissipation coefficient epsilon. In…
This paper studies the scale and redshift variation of density and velocity distributions in self-gravitating collisionless dark matter flow by a halo-based non-projection approach. All particles are divided into halo and out-of-halo…
This article examines the dynamics of gravitational collapse in $f(\mathcal{R},\mathcal{T},\mathcal{Q})$ gravity, where $\mathcal{Q}=\mathcal{R}_{\mathrm{ab}}\mathcal{T}^{\mathrm{ab}}$. We consider self-gravitating anisotropic cylindrical…
This study leverages the basic insight that the gradient-flow equation associated with the relative Boltzmann entropy, in relation to a Gaussian reference measure within the Hellinger-Kantorovich (HK) geometry, preserves the class of…
We performed molecular dynamics simulations to study relaxation phenomena during vapor-liquid transitions in a single component Lennard-Jones system. Results from two different overall densities are presented; one in the neighborhood of the…
A three-dimensional round liquid jet within a low-speed coaxial gas flow is numerically simulated and explained via vortex dynamics ($\lambda_2$ method). The instabilities on the liquid-gas interface reflect well the vortex interactions…
We study the non-linear evolution of a dust ellipsoid,embedded in a Friedmann flat background universe, in order to determine the evolution of the density of the ellipsoid as the perturbation to it related detaches from general expansion…
The purpose of this article is to show that when dynamically cold, dissipationless self-gravitating systems collapse, their evolution is a strong function of the symmetry in the initial distribution. We explore with a set of pressure-less…
We present a new method based on functional tensor decomposition and dynamic tensor approximation to compute the solution of a high-dimensional time-dependent nonlinear partial differential equation (PDE). The idea of dynamic approximation…
We discuss the gravitational collapse of spherical compact objects in the background of $f(R,T,Q)$ theory, where $R$ represent the Ricci scalar, $T$ is the trace of energy momentum tensor while $Q\equiv R_{\mu\nu}T^{\mu\nu}$, and…
Proper knowledge of velocity is required in accurately determining enormous destructive energy of a landslide. We present the first physics-based general analytical landslide velocity model that incorporates internal deformation and…
A phenomenological model of the evolution of an ensemble of interacting dislocations in an isotropic elastic medium is formulated. The line-defect microstructure is described in terms of a spatially coarse-grained order parameter, the…
Recently, Jiang--Jiang (J. Differential Equations 282, 2021) showed the existence of unique strong solutions in spatial periodic domain (denoted by $\mathbb{T}^3$), whenever the elasticity coefficient is larger than the initial velocity…