相关论文: Pattern Formation in Landau-de Gennes Theory

We study droplet-impact problems in a three-dimensional cylindrical or equivalent two-dimensional Cartesian geometry. Such structures do have an approximate experimental realization, and they are often simulated a test-bed for computational…

We consider a typical hard scattering process in a heat bath of photons and electrons at temperature, $T$, in finite temperature QED. We show that, when the hard scattering scale is much larger than the temperature, the infrared pieces of…

Light-scattering in the terahertz region is demonstrated for granular matter. A quantum-cascade laser is used in a benchtop setup to determine the angle-dependent scattering of spherical grains as well as coffee powder and sugar grains. For…

We calculate using perturbative calculations and Ward identities the basic parameters of the Fermi Liquid: the scattering vertex, the Landau interaction function, the effective mass, specific heat, and physical susceptibilities for a model…

In this study, we investigate the clustering of 5000 droplets, each originating from one of five distinct droplet classes, each representing a unique geometry. The shape coordinates of the droplets are mapped to a 2D latent space through a…

We theoretically investigate droplet quasi-Bessel beams for different shapes of the round-tip axicon. Exact solutions for the Fresnel diffraction integrals describing the axial distribution of the electric field amplitude behind the axicon…

A framework is developed for a robust and highly accurate numerical solution of the coupled Stokes-Darcy system in three dimensions. The domain decomposition method is based on a Dirichlet-Neumann type splitting of the interface conditions…

Understanding the continuum limit of a theory of discrete random geometries is a beautiful but difficult challenge. In this optic, we review here the insights that can be obtained for Causal Dynamical Triangulations (CDT) by employing the…

We use Ginzburg-Landau theory to study the $H_{c2}$ transition in layered superconductors with field parallel to the layers, finding a continuous 3d freezing transition to a triangular vortex super-solid in the three-dimensional XY…

The spherically symmetric layer of matter is considered within the frameworks of general relativity. We perform generalization of the already known theory for the case of nonconstant surface entropy and finite temperature. We also propose…

Framing the glass formation within standard statistical mechanics is an outstanding problem of condensed matter theory. To provide new insight, we investigate the structural properties of the Lennard-Jones fluid in the very-low temperature…

We use the method of $\Gamma$-convergence to study the behavior of the Landau-de Gennes model for a nematic liquid crystalline film in the limit of vanishing thickness. In this asymptotic regime, surface energy plays a greater role and we…

We study the general properties of fluid spheres satisfying the heuristic assumption that their areas and proper radius are equal (the Euclidean condition). Dissipative and non-dissipative models are considered. In the latter case, all…

We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…

Static and dynamic phenomena in overheated free-standing smectic-A films are studied using a generalization of de Gennes' theory for a confined presmectic liquid. A static application is to determine the profile of the film meniscus and the…

In this paper, we shall study the Dirichlet problem for the minimal surfaces equation. We prove some results about the boundary behaviour of a solution of this problem. We describe the behaviour of a non-converging sequence of solutions in…

We describe experimental investigations of the structure of two-dimensional spherical crystals. The crystals, formed by beads self-assembled on water droplets in oil, serve as model systems for exploring very general theories about the…

A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. For this, a mathematical model is developed to incorporate homogeneous Dirichlet and Neumann type boundary conditions. The…

We prove that the 3-D free-surface incompressible Euler equations with regular initial geometries and velocity fields have solutions which can form a finite-time "splash" (or "splat") singularity first introduced in [9], wherein the…

We analyze isothermal aging of a four dimensional Edwards-Anderson model in detail by Monte Carlo simulations. We analyze the data in the view of an extended version of the droplet theory proposed recently (cond-mat/0202110) which is based…