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We consider an Ising model with quenched surface disorder, the disorder average of the free energy is the main object of interest. Explicit expressions for the free energy distribution are difficult to obtain if the quenched surface spins…
We study the energy balance for weak solutions of the three-dimensional compressible Navier--Stokes equations in a bounded domain. We establish an $L^p$-$L^q$ regularity conditions on the velocity field for the energy equality to hold,…
Starting from an energy comprised of both a bulk term and a surface term, set in the space of special functions of bounded hessian, $SBH$, a relaxation problem in the context of second-order structured deformations was studied in…
This paper investigates an initial boundary value problem for the relaxed one-dimensional compressible Navier-Stokes-Fourier equations. By transforming the system into Lagrangian coordinates, the resulting formulation exhibits a uniform…
In this paper, we investigate the effect of boundary surface roughness on numerical simulations of incompressible fluid flow past a cylinder in two and three spatial dimensions furnished with slip boundary conditions. The governing…
Membranes are an important subject of study in physical chemistry and biology. They can be considered as material surfaces with a surface energy depending on the curvature tensor. Usually, mathematical models developed in the literature…
In many fields of application, dynamic processes that evolve through time are well described by systems of ordinary differential equations (ODEs). The analytical solution of the ODEs is often not available and different methods have been…
The smoothing spline is one of the most popular curve-fitting methods, partly because of empirical evidence supporting its effectiveness and partly because of its elegant mathematical formulation. However, there are two obstacles that…
We investigate equilibrium configurations for surface energies which contain the squared $L^2$ norm of the difference of the mean curvature H and the spontaneous curvature $c_o$ coupled with the elastic energy of the boundary curve, which…
We present a novel framework based on semi-bounded spatial operators for analyzing and discretizing initial boundary value problems on moving and deforming domains. This development extends an existing framework for well-posed problems and…
We reexamine cosmological applications of the holographic energy density in the framework of sourced Friedmann equations. This framework is suitable because it can accommodate a macroscopic interaction between holographic and ordinary…
We consider the optimal arrangement of two diffusion materials in a bounded open set $\Omega\subset \mathbb{R}^N$ in order to maximize the energy. The diffusion problem is modeled by the $p$-Laplacian operator. It is well known that this…
Cohesive laws are stress-strain curves used in finite element calculations to describe the debonding of interfaces such as grain boundaries. It would be convenient to describe grain boundary cohesive laws as a function of the parameters…
Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies…
Snow density estimates as a function of depth are used for understanding climate processes, evaluating water accumulation trends in polar regions, and estimating glacier mass balances. The common and interpretable physically-derived…
We describe an energy-enstrophy conserving discretisation for the rotating shallow water equations with slip boundary conditions. This relaxes the assumption of boundary-free domains (periodic solutions or the surface of a sphere, for…
This paper presents a Bayesian framework for manipulating mesh surfaces with the aim of improving the positional integrity of the geological boundaries that they seek to represent. The assumption is that these surfaces, created initially…
In this survey article, we present two applications of surface curvatures in theoretical physics. The first application arises from biophysics in the study of the shape of cell vesicles involving the minimization of a mean curvature type…
The differential-geometric structure of the manifold of smooth shapes is applied to the theory of shape optimization problems. In particular, a Riemannian shape gradient with respect to the first Sobolev metric and the Steklov-Poincar\'{e}…
We study critical surfaces for a surface energy which contains the squared $L^2$ norm of the difference of the mean curvature $H$ and the spontaneous curvature $c_o$, coupled to the elastic energy of the boundary curve. We investigate the…