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The aim of this paper is to highlight recent progress in using conic optimization methods to study geometric packing problems. We will look at four geometric packing problems of different kinds: two on the unit sphere -- the kissing number…
We propose a direct numerical method for the solution of an optimal control problem governed by a two-side space-fractional diffusion equation. The presented method contains two main steps. In the first step, the space variable is…
We investigate a one-dimensional model describing the motion of liquid drops sliding down an inclined plane (the so-called quasi-static approximation model). We prove existence and uniqueness of a solution and investigate its long time…
We present results on a series of 2D atomistic computer simulations of amorphous systems subjected to simple shear in the athermal, quasistatic limit. The athermal quasistatic trajectories are shown to separate into smooth, reversible…
Continuum models of plasticity fail to capture the richness of microstructural evolution because the continuum is a homogeneous construction. The present study shows that an alternative way is available at the mesoscale in the form of truly…
We introduce a convergent finite difference method for solving the optimal transportation problem on the sphere. The method applies to both the traditional squared geodesic cost (arising in mesh generation) and a logarithmic cost (arising…
Generating time-optimal, collision-free trajectories for autonomous mobile robots involves a fundamental trade-off between guaranteeing safety and managing computational complexity. State-of-the-art approaches formulate spline-based motion…
We design the conforming virtual element method for the numerical approximation of the two dimensional elastodynamics problem. We prove stability and convergence of the semi-discrete approximation and derive optimal error estimates under…
A fast, parallel algorithm for distant-dependent calculation and simulation of crystal properties is presented along with speedup results and methods of application. An illustrative example is used to compute the Lennard-Jones lattice…
An explicitly solvable quasi 1D model of oil displacement is studied. The problem of recovering of the reservoir geometry is solved by means of a fixed point algorithm. The stability of solution is studied in various functional classes.
We analyze the convergence rates to a planar interface in the Mullins-Sekerka model by applying a relaxation method based on relationships among distance, energy, and dissipation. The relaxation method was developed by two of the authors in…
Accurate photometric and kinematic modelling of disc galaxies requires the inclusion of radiative transfer models. Due to the complexity of the radiative transfer equation (RTE), sophisticated techniques are required. Various techniques…
We propose a novel iterative process to establish the minimum separation between two ellipsoids. The method maintains one point on each surface and updates their locations in the theta-phi parametric space. The tension along the connecting…
We consider a class of relaxation problems mixing slow and fast variations which can describe population dynamics models or hyperbolic systems, with varying stiffness (from non-stiff to strongly dissipative), and develop a multi-scale…
This paper is an extension of the result by Christowiak and Kreisbeck (2017), which addresses the Gamma-convergence approach to a homogenization problem for composite materials consisting of two distinct types of parallel layers. In…
We consider enstrophy dissipation in two-dimensional (2D) Navier-Stokes flows and focus on how this quantity behaves in thelimit of vanishing viscosity. After recalling a number of a priori estimates providing lower and upper bounds on this…
Plasticity in hexagonal close-packed zirconium is controlled by screw dislocations which easily glide in the prismatic planes where they are dissociated. At high enough temperatures, these dislocations can deviate out of the prism planes to…
This paper presents an analysis of optimal impact strategies to deflect potentially dangerous asteroids. To compute the increase in the minimum orbit intersection distance of the asteroid due to an impact with a spacecraft, simple…
In this paper, we deal with the convergence of an iterative scheme for the 2-D stochastic Navier-Stokes Equations on the torus suggested by the Lie-Trotter product formulas for stochastic differential equations of parabolic type. The…
In this article we approach a class of stochastic reachability problems with state constraints from an optimal control perspective. Preceding approaches to solving these reachability problems are either confined to the deterministic setting…