Related papers: Constrained maximization of conformal capacity
This papers shows the convergence of optimal control problems where the constraint function is discretised by a particle method. In particular, we investigate the viscous Burgers equation in the whole space $\mathbb R$ by using…
We study the $k$-center problem in a kinetic setting: given a set of continuously moving points $P$ in the plane, determine a set of $k$ (moving) disks that cover $P$ at every time step, such that the disks are as small as possible at any…
A finite element analysis of a Dirichlet boundary control problem governed by the linear parabolic equation is presented in this article. The Dirichlet control is considered in a closed and convex subset of the energy space $H^1(\Omega…
This paper is concerned with the distributed control and stabilization problems for linear discrete-time large scale systems with imposed constraints. The main contributions of this paper are: Firstly, by using the maximum principle…
In this paper we prove a theorem that provides an upper bound for the density of packings of congruent copies of a given convex body in $\mathbb{R}^n$; this theorem is a generalization of the linear programming bound for sphere packings. We…
This paper investigates the bounds on channel capacity and constellation shaping under memoryless mixed noise, which is composed of impulsive noise (IN) and white Gaussian noise (WGN). The capacity bounds are derived using the entropy power…
In this paper we consider the problem of locating $k$ obnoxious facilities (congruent disks of maximum radius) amidst $n$ demand points (existing repulsive facility sites) ordered from left to right in the plane so that none of the existing…
We study the sphere packing problem in Euclidean space where we impose additional constraints on the separations of the center points. We prove that any sphere packing in dimension $48$, with spheres of radii $r$, such that no two centers…
This paper is devoted to confront two different approaches to the problem of dynam-ical perfect plasticity. Interpreting this model as a constrained boundary value Friedrichs' system enables one to derive admissible hyperbolic boundary…
We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…
An investigation is made of disk accretion of matter onto a rotating star with an aligned dipole magnetic field. A new aspect of this work is that when the angular velocity of the star and disk differ substantially we argue that the $\bf B$…
We study the numerical approximation by space-time finite element methods of a multi-physics system coupling hyperbolic elastodynamics with parabolic transport and modeling poro- and thermoelasticity. The equations are rewritten as a…
In many cosmological models, including the $\Lambda$CDM concordance model, there exist a theoretical upper bounds on the size of collapsing structures. The most common formulations in the literature refer to a turnaround radius in spherical…
Stars form in dense cores of molecular clouds that are observed to be significantly magnetized. In the simplest case of a laminar (non-turbulent) core with the magnetic field aligned with the rotation axis, both analytic considerations and…
We study rapidly accreting, gravitationally unstable disks with a series of global, three dimensional, numerical experiments using the code ORION. In this paper we conduct a numerical parameter study focused on protostellar disks, and show…
Studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the distribution of particles at `microscales' to predict physical properties at `macroscales', whether for a liquid, composite material, or…
The thermodynamic properties of disks moving in a channel sufficiently narrow that they can collide only with their nearest neighbors can be solved exactly by determining the eigenvalues and eigenfunctions of an integral equation. Using it…
The existence of hyperbolic orbits is proved for a class of restricted three-body problems with a fixed energy by taking limit for a sequence of periodic solutions which are obtained by variational methods.
In this paper, we study the problem of hyperball (hypersphere) packings in $n$-dimensional hyperbolic space ($n \ge 4$). We prove that to each $n$-dimensional congruent saturated hyperball packing, there is an algorithm to obtain a…
The hard disk model is a 2D Gibbsian process of particles interacting via pure hard core repulsion. At high particle density the model is believed to show orientational order, however, it is known not to exhibit positional order. Here we…