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Amorphous solids are known to fail catastrophically and in some situations, nano-scaled cavities are believed to play a significant role in the failure. In a recent work, using numerical simulations, we have shown the correspondence between…
We consider the systematic force on a heavy probe induced by interaction with an overdamped diffusive medium where particles undergo a rotating force around a fixed center. The stiffness matrix summarizes the stability of the probe around…
We use event driven simulations to analyze glassy dynamics as a function of density and energy dissipation in a two-dimensional bidisperse granular fluid under stationary conditions. Clear signatures of a glass transition are identified,…
The interplay of electronic interactions and frustration in crystalline systems leads to a panoply of correlated phases, including exotic Mott insulators with non-trivial patterns of entanglement. Disorder introduces additional quantum…
The Stefan problem with surface tension is well known to exhibit discontinuities in the associated moving aggregate (i.e., in the domain occupied by the solid), whose structure has only been understood under translational or radial symmetry…
Substrate disorder effects on the scaling properties of growing crystalline surfaces in solidification or epitaxial deposition processes are investigated. Within the harmonic approach there is a phase transition into a low-temperature…
Much of standard galaxy dynamics rests on the implicit assumption that the corresponding N-body problem is (near) integrable. This notion although leading to great simplification is by no means a fact. It is therefore important to develop…
We studied the shock propagation and its stability with the causal dissipative hydrodynamics in 1+1 dimensional systems. We show that the presence of the usual viscosity is not enough to stabilize the solution. This problem is solved by…
We perform stability analysis of a kinetic bacterial chemotaxis model of bacterial self-organization, assuming that bacteria respond sharply to chemical signals. The resulting discontinuous tumbling kernel represents the key challenge for…
We study various dynamical aspects of systems possessing a first order phase transition in their phase diagram. We isolate three qualitatively distinct types of theories depending on the structure of instabilities and the nature of the low…
Classical density-functional theory is employed to study finite-temperature trends in the relative stabilities of one-component quasicrystals interacting via effective metallic pair potentials derived from pseudopotential theory. Comparing…
In this paper we focus on crystal surfaces led out of equilibrium by a growth or erosion process. As a consequence of that the surface may undergo morphological instabilities and develop a distinct structure: ondulations, mounds or…
Dynamic buckling is addressed for complete elastic spherical shells subject to a rapidly applied step in external pressure. Insights from the perspective of nonlinear dynamics reveal essential mathematical features of the buckling…
This letter presents a study on the stability of the 12-fold symmetry soft-matter quasicrystals from the angle of thermodynamics combining dynamics of the matter. The results are quantitative, which depend upon only the material constants…
Periodic approximations of quasicrystals are a powerful tool in analyzing spectra of Schr\"odinger operators arising from quasicrystals, given the known theory for periodic crystals. Namely, we seek periodic operators whose spectra…
We study the evolution from a liquid to a crystal phase in two-dimensional curved space. At early times, while crystal seeds grow preferentially in regions of low curvature, the lattice frustration produced in regions with high curvature is…
In this paper we contribute to studying the issue of quasistatic limit in the context of Griffith's theory by investigating a one-dimensional debonding model. It describes the evolution of a thin film partially glued to a rigid substrate…
Sedimentation of a dispersed solid phase is widely encountered in applications and environmental flows, yet little is known about the behavior of finite-size particles in homogeneous isotropic turbulence. To fill this gap, we perform Direct…
The hydrodynamic equations for a crystals with interstitials, taking into account the dissipative processes of the viscosity, heat conduction and the interstitial diffusion are derived. To achieve that we use the phenomenological approach…
The structure, thermodynamics and slow activated dynamics of the equilibrated metastable regime of glass-forming fluids remains a poorly understood problem of high theoretical and experimental interest. We apply a highly accurate…