12 papers
Extended Walk-on-Spheres Algorithm for Linear and Nonlinear Elliptic Problems of Divergence-type
Iulian Cîmpean, Andreea Grecu, Arghir Zarnescu
The Walk-on-Spheres algorithm, introduced by M. E. Muller in 1956, is a well known Monte Carlo method that leverages Brownian exit distributions from spheres to solve the Laplace e…
Variational principles for the interaction of liquid crystals and electric fields in the Oseen--Frank model
Giovanni Di Fratta, Valeriy Slastikov, Arghir Zarnescu
We develop a rigorous variational framework for uniaxial nematic liquid crystals interacting with an external electric field in the one-constant Oseen--Frank approximation. Equilib…
Effective Complexity Reduction of the Landau-de Gennes Elastic Energy: A Quantitative Framework and Numerical Validation
Razvan-Dumitru Ceuca, Simone Rusconi, Arghir-Dani Zarnescu
We revisit the elastic energy formulation of the Landau-de Gennes model for nematic liquid crystals, focusing on quantitative reductions of the multi-constant elastic energy. Build…
On the impact of clusters of rigid balls on the motion of a viscous fluid
Marco Bravin, Eduard Feireisl, Arnab Roy +1
We develop a new approach to the problem of the motion of a large number of rigid bodies immersed in a viscous fluid. The leading idea is the concept of cluster - a collection of i…
The Ginzburg-Landau system with general potential: maximum principle and gradient estimates
Radu Ignat, Luc Nguyen, Valeriy Slastikov +1
We study critical points of the Ginzburg-Landau energy functional $$\mathcal{F}_\varepsilon[u] = \int_Ω\Big[ \frac{1}{2}|\nabla u|^2 + \frac{1}{2\varepsilon^2} W(1 - |u|^2)\Big]\,…
On the long time behaviour of a system of several rigid bodies immersed in a viscous fluid
Marco Bravin, Eduard Feireisl, Arnab Roy +1
We consider several rigid bodies immersed in a viscous Newtonian fluid contained in a bounded domain in . We introduce a new concept of dissipative weak solution of the proble…