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The stability of the hard-sphere icosahedral quasilattice is analyzed using the differential formulation of the generalized effective liquid approximation. We find that the icosahedral quasilattice is metastable with respect to the…
The description of the early stage of microfracture growth in a quasibrittle solid with thermodynamic positions is considered. From the most general thermodynamic performances the "principle" of minimization of free energy is received. The…
The accuracy of quasilinear theory applied to the electron bump-on-tail instability, a classic model problem, is explored with conservative high-order discontinuous Galerkin methods applied to both the quasilinear equations and to a direct…
We give a strong evidence that noncrystalline materials such as quasicrystals or incommensurate solids are not exceptions but rather are generic in some regions of a phase space. We show this by constructing classical lattice-gas models…
The two-phase horizontally periodic quasistationary Stokes flow in $\mathbb{R}^2$, describing the motion of two immiscible fluids with equal viscosities that are separated by a sharp interface, which is parameterized as the graph of a…
Highlights: \begin{itemize} \item Relativistic effect of crystal dynamics "freezing". \item Non-statistical model of thermodynamic equilibration. \end{itemize} The dynamics of oscillations of a one-dimensional atomic chain is investigated…
For low to moderate supersaturations, crystals grow by lateral build-up of new layers. The edges of the layers are known as "steps". We consider the rate of step advance on a flat crystal face under the influence of bulk diffusion in the…
We continue our investigation of viscoelasticity by extending the Holzapfel-Simo approach discussed in Part I to the fully nonlinear regime. By scrutinizing the relaxation property for the non-equilibrium stresses, it is revealed that a…
We study the dynamical behavior of a one dimensional interface interacting with a sticky unpenetrable substrate or wall. The interface is subject to two effects going in opposite directions. Contact between the interface and the substrate…
A solid-on-solid model of epitaxial growth in 1+1 dimensions is investigated in which slope dependent upward and downward particle currents compete on the surface. The microscopic mechanisms which give rise to these currents are the…
We study the quantitative stability of Serrin's symmetry problem and it's connection with a dynamic model for contact angle motion of quasi-static capillary drops. We prove a new stability result which is both linear and depends only on a…
The interrelation of dynamic processes active on separated time-scales in glasses and viscous liquids is investigated using a model displaying two time-scale bifurcations both between fast and secondary relaxation and between secondary and…
The theory and simulations of quasi-perpendicular and strictly perpendicular collisionless shocks are reviewed. The text is structured into the following sections and subsections: 1. Setting the frame, where the quasi-perpendicular shock…
We study experimentally the impact on rigid surfaces of different soft porous solids saturated with liquid: hydrogel balls and liquid-saturated foam balls. The static con tact of such soft solids with the substrate is well described by…
The glass transition can simply be viewed as the point at which the viscosity of a structurally disordered liquid reaches 10^{13} Poise [1]. This definition is operational but it sidesteps fundamental controversies about the glass: Is the…
We establish the connection between the standard ADM 3+1 treatment of matter with its characteristic equivalent, in the context of spherical symmetry. The flux-conservative rendition of the fluid equations are obtained. Considering…
We study crystal nucleation under the influence of sedimentation in a model of colloidal hard spheres via Brownian Dynamics simulations. We introduce two external fields acting on the colloidal fluid: a uniform gravitational field (body…
Under steady shear, a foam relaxes stress through intermittent rearrangements of bubbles accompanied by sudden drops in the stored elastic energy. We use a simple model of foam that incorporates both elasticity and dissipation to study the…
Rate-effects in sheared disordered solids are studied using molecular dynamics simulations of binary Lennard-Jones glasses in two and three dimensions. In the quasistatic (QS) regime, systems exhibit critical behavior: the magnitudes of…
The paper addresses stability and finite element analysis of the stationary two-phase Stokes problem with a piecewise constant viscosity coefficient experiencing a jump across the interface between two fluid phases. We first prove a priori…