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In this paper we study two models for crowd motion and herding. Each of the models is of Keller-Segel type and involves two parabolic equations, one for the evolution of the density and one for the evolution of a mean field potential. We…
We study static, spherically symmetric neutron stars in a class of scalar-tensor theories with non-canonical kinetic terms (K-essence) obeying all causality and hyperbolicity conditions. These models have non-trivial dynamics that lead to a…
We consider a class of $L^2$-supercritical inhomogeneous nonlinear Schr\"odinger equations with potential in three dimensions \[ i\partial_t u + \Delta u - V u = \pm |x|^{-b} |u|^\alpha u, \quad (t,x) \in \mathbb{R} \times \mathbb{R}^3, \]…
Simulation and experimental studies have demonstrated non-equilibrium ordering in driven colloidal suspensions: with increasing driving force, a uniform colloidal mixture transforms into a locally demixed state characterized by the lane…
In this paper, we propose a novel approach to modeling nonstationary spatial fields. The proposed method works by expanding the geographic plane over which these processes evolve into higher dimensional spaces, transforming and clarifying…
Galaxy formation and evolution involves a variety of effectively stochastic processes that operate over different timescales. The Extended Regulator model provides an analytic framework for the resulting variability (or `burstiness') in…
We study FRW cosmology for scalar tensor theory where two scalar functions nonminimally coupled to the geometry and matter Lagrangian. In a framework to study stability and attractor solutions of the model in the phase space, we…
Dynamic density functionals (DDFs) are popular tools for studying the dynamical evolution of inhomogeneous polymer systems. Here, we present a systematic evaluation of a set of diffusive DDF theories by comparing their predictions with data…
The Jeans equations give the second moments or stresses required to support a stellar population against the gravity field. A general solution of the Jeans equations for arbitrary axisymmetric scale-free densities in flattened scale-free…
We present analytic radiative transfer solutions for the spectra of unresolved, spherically symmetric, centrally heated, dusty sources. We find that the dust thermal spectrum possesses scaling relations that provide a natural classification…
Energy functionals of the Green's function can simultaneously provide spectral and thermodynamic properties of interacting electrons' systems. Though powerful in principle, these formulations need to deal with dynamical…
In this paper we examine the stability of stellar configurations in which the interior solution is described by a closed FLRW geometry sourced with a charged pressureless fluid and radiation. An interacting vacuum component and a…
The pointwise space-time behaviors of the Green's function and the global solution to the Vlasov-Poisson-Fokker-Planck (VPFP) system in spatial three dimension are studied in this paper. It is shown that the Green's function consists of the…
When studying massive stars and their life cycles, rotation plays a key role. Hence, understanding the rotation of these stars is crucial when determining their properties, or for constraining evolutionary models. We examine the reliability…
We use $N$-body simulations to compare the evolution of spatial distributions of stars and brown dwarfs in young star-forming regions. We use three different diagnostics; the ratio of stars to brown dwarfs as a function of distance from the…
Stationary solutions to the equations of non-linear diffusive shock acceleration play a fundamental role in the theory of cosmic-ray acceleration. Their existence usually requires that a fraction of the accelerated particles be allowed to…
A particle method for reproducing the phase space of collisionless stellar systems is described. The key idea originates in Liouville's theorem which states that the distribution function (DF) at time t can be derived from tracing necessary…
The main concern of this paper is to mathematically investigate the formation of a plasma sheath near the surface of nonplanar walls. We study the existence and asymptotic stability of stationary solutions for the nonisentropic…
We study a Newtonian model which allows us to describe some extremely flat objects in galactic dynamics. This model is described by a partial differential equation system called Vlasov-Poisson, whose solutions describe the temporal…
In this paper, we investigated a density-dependent reaction-diffusion equation, $u_t = (u^{m})_{xx} + u - u^{m}$. This equation is known as the extension of the Fisher or Kolmogoroff-Petrovsky-Piscounoff equation which is widely used in the…