Related papers: On attractors for a sharp interface model of exoth…
We consider a semi-scale invariant version of the Poisson cylinder model which in a natural way induces a random fractal set. We show that this random fractal exhibits an existence phase transition for any dimension $d\geq 2,$ and a…
Epitaxially grown heterogeneous nanowires present dislocations at the interface between the phases if their radius is big. We consider a corresponding variational discrete model with quadratic pairwise atomic interaction energy. By…
Particles bound to an interface interact because they deform its shape. The stresses that result are fully encoded in the geometry and described by a divergence-free surface stress tensor. This stress tensor can be used to express the force…
In this paper, we consider a damped Navier-Stokes-Bardina model posed on the whole three-dimensional. These equations have an important physical motivation and they arise from some oceanic model. From the mathematical point of view, they…
We study Lorentz-violating models of massive gravity which preserve rotations and are invariant under time-dependent shifts of the spatial coordinates. In the linear approximation the Newtonian potential in these models has an extra…
The aim of this paper is to find an upper bound for the box-counting dimension of uniform attractors for non-autonomous dynamical systems. Contrary to the results in literature, we do not ask the symbol space to have finite box-counting…
Slightly compressible Brinkman-Forchheimer equations in a bounded 3D domain with Dirichlet boundary conditions are considered. These equations model fluids motion in porous media. The dissipativity of these equations in higher order energy…
This paper reviews (and expands) some recent results on the modeling of aggregation-diffusion phenomena at various scales, focusing on the emergence of collective dynamics as a result of the competition between attractive and repulsive…
We study the near-the-interface behavior of a compact convex scalar curvature flow with a flat side. Under suitable initial conditions on the flat side, we show that the interface propagates with a finite and non-degenerate speed until the…
The effect of thermal fluctuations near a contact line of a liquid interface partially wetting an impenetrable substrate is studied analytically and numerically. Promoting both the interface profile and the contact line position to random…
We discuss the solution of the Mott transition problem in a fully frustrated lattice with a semicircular density of states in the limit of infinite dimensions from the point of view of a Landau free energy functional. This approach provides…
The dynamical behaviors of two interacting dark energy models are considered. In addition to the scaling attractors found in the non-interacting quintessence model with exponential potential, new accelerated scaling attractors are also…
An important component in studying mathematical models in many biochemical systems, such as those found in developmental biology, is phase transition. The purpose of this work is to analyze the phase transition property of a…
The fundamental problem of friction in the presence of macroscopic adhesion, as in soft bodies, is receiving interest from many experimentalists. Since the first fracture mechanics `purely brittle' model of Savkoor and Briggs, models have…
We consider fluids where the attractive interaction at distances slightly larger than the particle size is dominated at larger distances by a repulsive contribution. A previous investigation of the effects of the competition between…
We study flat FLRW $\alpha$-attractor $\mathrm{E}$- and $\mathrm{T}$-models by introducing a dynamical systems framework that yields regularized unconstrained field equations on two-dimensional compact state spaces. This results in both…
We investigate the attractor solution in the coupled Yang-Mills field dark energy models with the general interaction term, and obtain the constraint equations for the interaction if the attractor solution exists. The research also shows…
We consider the intersections of fractal k-cubes of order n and intersections of their respective opposite l-faces. The main result of the paper is the theorem on representation of such intersection as the attractor of a graph-directed…
A model describing the three-dimensional folding of the triangular lattice on the face-centered cubic lattice is generalized allowing the presence of defects corresponding to cuts in the two-dimensional network. The model can be expressed…
We study the long time behavior of solutions to a nonlinear partial differential equation arising in the description of trapped rotating Bose-Einstein condensates. The equation can be seen as a hybrid between the well-known nonlinear…