Related papers: Phase field models for two-dimensional branched tr…
The paper considers a class of linear Boltzmann transport equations which models a charged particle transport. The equation is an approximation of the original exact transport equation which involves hyper-singular integrals in their…
This work reports an extensive study of three-dimensional topological ordered phases that, in one of the directions behave like usual topological order concerning mobility of excitations, but in the perpendicular plane manifest type-II…
We construct a driven sandpile slope model and study it by numerical simulations in one dimension. The model is specified by a threshold slope $\sigma_c\/$, a parameter $\alpha\/$, governing the local current-slope relation (beyond…
We consider the following geometric optics problem: Construct a system of two reflectors which transforms a spherical wavefront generated by a point source into a beam of parallel rays. This beam has a prescribed intensity distribution. We…
Phase field models for two-phase flow with a surfactant soluble in possibly both fluids are derived from balance equations and an energy inequality so that thermodynamic consistency is guaranteed. Via a formal asymptotic analysis, they are…
The formalism based on the equal-time Wigner function of the two-point correlation function for a quantized Klein--Gordon field is presented. The notion of the gauge-invariant Wigner transform is introduced and equations for the…
In this paper we propose a quaternion formulation for the orientation variable in the three dimensional Kobayashi--Warren model for the dynamics of polycrystals. We obtain existence of solutions to the $L^2$-gradient descent flow of the…
One of the simplest models used in studying the dynamics of large-scale structure in cosmology, known as the Zeldovich approximation, is equivalent to the three-dimensional inviscid Burgers equation for potential flow. For smooth initial…
We propose numerical schemes for the approximate solution of problems defined on the edges of a one-dimensional graph. In particular, we consider linear transport and a drift-diffusion equations, and discretize them by extending Finite…
An imitation of 2d field theory is formulated by means of a model on the hierarchic tree (with branching number close to one) with the same potential and the free correlators identical to those of 2d ones. Such a model possesses some…
The concept of dispatchable region plays a pivotal role in quantifying the capacity of power systems to accommodate renewable generation. In this paper, we extend the previous approximations of the dispatchable regions on direct current…
We prove the well-posedness of entropy solutions for a wide class of nonlocal transport equations with nonlinear mobility in one spatial dimension. The solution is obtained as the limit of approximations constructed via a deterministic…
The optimal power flow (OPF) problem seeks to control power generation/demand to optimize certain objectives such as minimizing the generation cost or power loss in the network. It is becoming increasingly important for distribution…
In this Doctoral Dissertation we propose new variational principles for traffic assignment problems. So to find equillibrium we have to solve large-scale convex optimization problem of special (multilevel) type. We propose different…
The Optimal Power Flow (OPF) problem can be reformulated as a nonconvex Quadratically Constrained Quadratic Program (QCQP). There is a growing body of work on the use of semidefinite programming relaxations to solve OPF. The relaxation is…
In order to analyze numerically inverse problems several techniques based on linear and nonlinear stability analysis are presented. These techniques are illustrated on the problem of estimating mobilities and capillary pressure in…
We describe the implementation of a topological constraint in finite element simulations of phase field models which ensures path-connectedness of preimages of intervals in the phase field variable. Two main applications of our method are…
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…
We develop a phase-field approximation of the relaxation of the perimeter functional in the plane under a connectedness constraint based on the classical Modica-Mortola functional and the connectedness constraint of (Dondl, Lemenant,…
We study different forms of linear and non-linear field equations, so-called `phase-field' equations, in relation to the de~Broglie-Bohm double solution program. This defines a framework in which elementary particles are described by…