arXiv subjects

Oliver Tse

Publications and source records attributed to Oliver Tse.

41 records · Page 3Linked to original sources

arXiv2015

Mean field models for interacting ellipsoidal particles

We consider a mean field hierarchy of models for large systems of interacting ellipsoids suspended in an incompressible fluid. The models range from microscopic to macroscopic mean field models. The microscopic model is based on three ingredients. Starting from a Langevin type model for rigid body interactions, we use a Jefferys type term to model the influence of the fluid on the ellipsoids and a simplified interaction potential between the ellipsoids to model the interaction between the ellipsoids. A mean field equation and corresponding equations for the marginals of the distribution function are derived and a numerical comparison between the different levels of the model hierarchy is given. The results clearly justify the suitability of the proposed approximations for the example cases under consideration.

math.DS↗

arXiv2015

A Retarded Mean-Field Approach for Interacting Fiber Structures

We consider an interacting system of one-dimensional structures modelling fibers with fiber-fiber interaction in a fiber lay-down process. The resulting microscopic system is investigated by looking at different asymptotic limits of the corresponding stochastic model. Equations arising from mean-field and diffusion limits are considered. Furthermore, numerical methods for the stochastic system and its mean-field counterpart are discussed. A numerical comparison of solutions corresponding to the different scales (microscopic, mesoscopic and macroscopic) is included.

math.DS↗

arXiv2015

The Semi-Classical Limit of an Optimal Design Problem for the Stationary Quantum Drift-Diffusion Model

We consider an optimal semiconductor design problem for the quantum drift diffusion (QDD) model in the semiclassical limit. The design question is formulated as a PDE constrained optimal control problem, where the doping profile acts as control variable. The existence of minimizers for any scaled Planck constant allows for the investigation of the corresponding sequence. Using the concepts of Gamma-convergence and equi-coercivity we can show the convergence of minima and minimizers. Due to the lack of uniqueness for the state system and optimization problem, it was necessary to establish a new result for the QDD model ensuring the existence of a sequence of quantum solutions converging to an isolated classical solution. As a by-product, we obtain new insights into the regularizing property of the quantum Bohm potential. Finally, we present the numerical optimization of a MESFET device underlining our analytical results.

math.OC↗

arXiv2014

On the effects of Bohm's potential on a macroscopic system of self-interacting particles

We consider an instationary macroscopic system of self-interacting particles with an additional potential, the so called Bohm's potential. We study the existence of non-negative global solutions to the (4-th order) system of equations and allude the differences to results obtained for classical models. The problem is considered on a bounded domain up to three space dimension, subject to initial and Neumann boundary condition for the particle density, and Dirichlet boundary condition for the self-interacting potential. Moreover, the initial datum is only assumed to be non-negative and to satisfy a weak integrability condition.

math.AP↗

arXiv2014

On the Effects of Bohm's Potential on a Stationary Macroscopic System of Self-Interacting Particles

We consider a macroscopic model describing a system of self-gravitating particles. We study the existence and uniqueness of non-negative stationary solutions and allude the differences to results obtained from classical gravitational models. The problem is considered on a bounded domain up to three space dimension, subject to Neumann boundary condition for the particle density, and Dirichlet boundary condition for the self-interacting potential. Finally, we show numerical simulations that affirm our findings.

math.AP↗