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Differentiating structural evolution from structural development or formation opens many avenues of research. The study particularly advances the chemical and physical sciences, material science, energy science, and chemical engineering. By…
This paper examines the general formalism and applications of isotropic as well as anisotropic polytropic stars in curvature-matter coupled gravity. For this purpose, we consider static spherical and Schwarzschild spacetimes in the interior…
Understanding the contact dynamics of nonspherical particles beyond the microscale is crucial for accurately modeling colloidal and granular systems, where shape anisotropy dictates structural organization and transport properties. In this…
Motivated by the formation of fingerprint patterns we consider a class of interacting particle models with anisotropic, repulsive-attractive interaction forces whose orientations depend on an underlying tensor field. This class of models…
It is frequent for active or living entities to find themselves embedded in a surrounding medium. Resulting composite systems are usually classified as either active fluids or active solids. Yet, in reality, particularly in the biological…
The work analyzes the stability of the quantum eigenstates when they are submitted to fluctuations by using the stochastic generalization of the Madelung quantum hydrodynamic approach. In the limit of sufficiently slow kinetics, the quantum…
In this paper, we initiate the study of global stability for anisotropic systems of quasilinear wave equations. Equations of this kind arise naturally in the study of crystal optics, and they exhibit birefringence. We introduce a physical…
We study the two-dimensional structural stability of shock waves in a compressible isentropic inviscid elastic fluid in the sense of the local-in-time existence and uniqueness of discontinuous shock front solutions of the equations of…
We propose a sharp interface model for simulating solid-state dewetting where the surface energy is (weakly) anisotropic. The morphology evolution of thin films is governed by surface diffusion and contact line migration. The mathematical…
A continuum model for the dynamics of a single step with the strongly anisotropic line energy is formulated and analyzed. The step grows by attachment of adatoms from the lower terrace, onto which atoms adsorb from a vapor phase or from a…
The evolution of closed gravitational systems is studied by means of $N$-body simulations. This, as well as being interesting in its own right, provides insight into the dynamical and statistical mechanical properties of gravitational…
The generalized hydrodynamic (GHD) approach has been extremely successful in describing the out-of-equilibrium properties of a great variety of integrable many-body quantum systems. It naturally extracts the large-scale dynamical degrees of…
We present a new analytic study of the equilibrium and stability properties of close binary systems containing polytropic components. Our method is based on the use of ellipsoidal trial functions in an energy variational principle. We…
In this work, we aim to develop energy-stable parametric finite element approximations for a sharp-interface model with strong surface energy anisotropy, which is derived from the first variation of an energy functional composed of…
The equilibrium properties of polymer droplets on a soft deformable surface are investigated by molecular dynamics simulations of a bead-spring model. The surface consists of a polymer brush with irreversibly end-tethered linear homopolymer…
Nonequilibrium steady states in an open system connecting two reservoirs of platelike colloidal particles are investigated by means of a recently proposed phenomenological dynamic density functional theory [M. Bier and R. van Roij, Phys.…
A classical model of fluid dynamics is considered which describes the shape evolution of a viscous liquid droplet on a homogeneous substrate. All equilibria are characterized and their stability is analyzed by a geometric reduction…
Geometrical constructions, such as the tangent construction on the molar free energy for determining whether a particular composition of a solution, is stable, are related to similar tangent constructions on the orientation-dependent…
A model predicting the structure of repulsive, spherically symmetric, monodisperse particles confined between two walls is presented. We study the buckling transition of a single flat layer as the double layer state develops. Experimental…
Our recent quasi-two-dimensional thermodynamic description of thin-liquid films stabilized by colloidal particles is generalized to describe nonuniform equilibrium states of films in external potentials and nonequilibrium transport…