Related papers: Minimal surfaces in random environment
In this paper, we investigate the ruled surfaces generated by a straight line according to rotation minimizing frame (RMF). Using this frame of a straight line, we obtained the necessary and sufficient conditions when the ruled surface is…
When calculating the index of a minimal surface, the set of smooth functions on a domain with compact support is the standard setting to describe admissible variations. We show that the set of admissible variations can be widened in a…
We study the minimal error of the Empirical Risk Minimization (ERM) procedure in the task of regression, both in the random and the fixed design settings. Our sharp lower bounds shed light on the possibility (or impossibility) of adapting…
Most known examples of doubly periodic minimal surfaces in $\mathbb{R}^3$ with parallel ends limit as a foliation of $\mathbb{R}^3$ by horizontal noded planes, with the location of the nodes satisfying a set of balance equations.…
The proliferation of 3D representations, from explicit meshes to implicit neural fields and more, motivates the need for simulators agnostic to representation. We present a data-, mesh-, and grid-free solution for elastic simulation for any…
We present a connection between minimal surfaces of index one and General Relativity. First, we show that for a certain class of (electro)static systems, each of its unstable horizons is the solution of a one-parameter min-max problem for…
Molecular Dynamics (MD) simulations of standard systems of interacting particles ("atoms") give excellent agreement with the equipartition theorem for the average energy, but we find that these simulations exhibit finite-size effects in the…
Locating the global minimum of a complex potential energy surface is facilitated by considering a homotopy, namely a family of surfaces that interpolate continuously from an arbitrary initial potential to the system under consideration.…
For each integer m>1 and l>0 we construct a pair of compact embedded minimal surfaces of genus 1+4m(m-1)l. These surfaces desingularize the m Clifford tori meeting each other along a great circle at the angle of \pi/m. They are invariant…
We study the propagation and scattering of electromagnetic waves by random arrays of dipolar cylinders in a uniform medium. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is…
We simulate a growth model with restricted surface relaxation process in d=1 and d=2, where d is the dimensionality of a flat substrate. In this model, each particle can relax on the surface to a local minimum, as the Edwards-Wilkinson…
For a class of functions (called minimal Rad\'o functions) that arise naturally in minimal surface theory, we bound the number of interior critical points (counting multiplicity) in terms of the boundary data and the Euler characteristic of…
Since the seminal work of Schoen-Uhlenbeck, many authors have studied properties of harmonic maps satisfying Dirichlet boundary conditions. In this article, we instead investigate regularity and symmetry of $\mathbb{S}^2-$valued minimizing…
Theoretical background is provided towards the mathematical foundation of the minimum enclosing ball problem. This problem concerns the determination of the unique spherical surface of smallest radius enclosing a given bounded set in the…
In recent work we have shown how an accurate reduced model can be utilized to perform mesh refinement in random space. That work relied on the explicit knowledge of an accurate reduced model which is used to monitor the transfer of activity…
The origin of rigidity in disordered materials is an outstanding open problem in statistical physics. Previously, a class of 2D cellular models has been shown to undergo a rigidity transition controlled by a mechanical parameter that…
The problem of binary minimization of a quadratic functional in the configuration space is discussed. In order to increase the efficiency of the random-search algorithm it is proposed to change the energy functional by raising to a power…
We consider the "thin one-phase" free boundary problem, associated to minimizing a weighted Dirichlet energy of the function in $\mathbb R^{n+1}_+$ plus the area of the positivity set of that function in $\mathbb R^n$. We establish full…
Dielectric relaxation in disordered dielectric mixtures are presented by emphasizing the interfacial polarization. The obtained results coincide with and cause confusion with those of the low frequency dispersion behavior. The considered…
The recently established threshold theorem for energy critical wave maps states that wave maps with energy less than that of the ground state (i.e., a minimal energy nontrivial harmonic map) are globally regular and scatter on…