Related papers: Morphological attractors in natural convective dis…
In the scalar-tensor theory of gravitation it seems nontrivial to establish if solutions of the cosmological equations in the presence of a cosmological constant behave as attractors independently of the initial values. We develop a general…
Oscillating shape motion of a freely falling water droplet has long fascinated and inspired scientists. We propose dynamic non-linear equations for closed, two dimensional surfaces in gravity and apply it to analyze shape dynamics of freely…
This paper refined and introduced some notations (namely attractors, physical attractors, proper attractors, topologically exact and topologically mixing) within the context of relations. We establish necessary and sufficient conditions,…
We show that unconstrained asymmetric dissolving solids floating in a fluid can move rectilinearly as a result of attached density currents which occur along their inclined surfaces. Solids in the form of boats composed of centimeter-scale…
A fundamental open problem in the theory of the multidimensional compressible Navier-Stokes equations is whether smooth solutions can develop singularities in finite time. For constant viscosity coefficients, recent remarkable results show…
We modeled the change in the temperature of maximum density (TMD) of a water-like solvent when small amounts of solute are added to the mixture. The solvent is modeled as a two length scales potential, which is known to exhibit water-like…
In this paper we study the fractal dimension of global attractors for a class of wave equations with (single-point) degenerate nonlocal damping. Both the equation and its linearization degenerate into linear wave equations at the degenerate…
In the presence of a minimal length physical objects cannot collapse to an infinite density, singular, matter point. In this note we consider the possible final stage of the gravitational collapse of "thick" matter layers. The energy…
Morphological instability of the solid-liquid interface occuring in a crystal growing from an undercooled thin liquid being bounded on one side by a free surface and flowing down inclined plane is investigated by a linear stability analysis…
We consider a thermodynamically consistent model for the evolution of thermally conducting two-phase incompressible fluids. Complementing previous results, we prove additional regularity properties of solutions in the case when the…
The state of a classical point-particle system may often be specified by giving the position and momentum for each constituent particle. For non-pointlike particles, the center-of-mass position may be augmented by an additional coordinate…
Surface nanobubbles are stable gaseous phases in liquids that form on solid substrates. While their existence has been confirmed, there are many open questions related to their formation and dissolution processes along with their structures…
We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation in $R^{3}$ phase space. We demonstrate that it accommodates the phase space dynamics of low dimensional dissipative systems such as the much studied Lorenz and…
We examine the deformation of homogeneous spherical fluid vesicles along their equator by a circular rigid ring. We consider deformations preserving the axial and equatorial mirror symmetries of the vesicles. The configurations of the…
Over the past few decades the experimental literature has consistently reported observations of attraction between like-charged colloidal particles and macromolecules in solution. Examples include nucleic acids and colloidal particles in…
Finite topology self translating surfaces to mean curvature flow of surfaces constitute a key element for the analysis of Type II singularities from a compact surface, since they arise in a limit after suitable blow-up scalings around the…
We study the combined effects of natural convection and rotation on the dissolution of a solute in a solvent-filled circular cylinder. The density of the fluid increases with the increasing concentration of the dissolved solute, and we…
Engineering synthetic materials that mimic the remarkable complexity of living organisms is a fundamental challenge in science and technology. We study the spatiotemporal patterns that emerge when an active nematicfilm of microtubules and…
Cosmological simulations of dark matter structures have identified a set of universal profiles, and similar characteristics have been seen in non-cosmological simulations. It has therefore been speculated whether these profiles of…
This work investigates experimentally and numerically the dynamics of rigid particles settling under gravity in a highly viscous fluid. We demonstrate that certain shapes: cones, crescent moons, arrowheads, and open flat rings reorient and…