Related papers: Semi-analytic techniques for calculating bubble wa…
We present a unified numerical method to determine the shapes of multiple Hele-Shaw bubbles in steady motion, and in the absence of surface tension, in three planar domains: free space, the upper half-plane, and an infinite channel. Our…
The performance of existing supervised layout estimation methods heavily relies on the quality of data annotations. However, obtaining large-scale and high-quality datasets remains a laborious and time-consuming challenge. To solve this…
Semi-Lagrangian methods are numerical methods designed to find approximate solutions to particular time-dependent partial differential equations (PDEs) that describe the advection process. We propose semi-Lagrangian one-step methods for…
In this article, a novel cluster analysis algorithm was employed in the study of polymer coil to globule transition via single chain Monte Carlo simulations. The algorithm, which has been recently applied in Molecular Dynamics simulations…
Bifurcation analysis collects techniques for characterizing the dependence of certain classes of solutions of a dynamical system on variations in problem parameters. Common solution classes of interest include equilibria and periodic…
In the following work we apply the boundary element method to two-phase flows in shallow microchannels, where one phase is dispersed and does not wet the channel walls. These kinds of flows are often encountered in microfluidic…
This paper addresses the modeling of fracture in quasi-brittle materials using a phase-field approach to the description of crack topology. Within the computational mechanics community, several studies have treated the issue of modeling…
This work is concerned with optimal control of partial differential equations where the control enters the state equation as a coefficient and should take on values only from a given discrete set of values corresponding to available…
In the present manuscript, we consider the practical problem of wave interaction with a vertical wall. However, the novelty here consists in the fact that the wall can move horizontally due to a system of springs. The water wave evolution…
We present a geometric algorithm for obtaining consistent solutions to systems of partial differential equations, mainly arising from singular covariant first-order classical field theories. This algorithm gives an intrinsic description of…
We present a new approach to studies of bubble dynamics in fluids. Relying on particle-based simulations, this method is general and suitable for cases where the commonly used perfect fluid description fails. We study expanding true vacuum…
In this paper, we propose a catalog of iterative methods for solving the Split Feasibility Problem in the non-convex setting. We study four different optimization formulations of the problem, where each model has advantageous in different…
In the context of bubble universes produced by a first-order phase transition with large nucleation rates compared to the inverse dynamical time scale of the parent bubble, we extend the usual analysis to non-vacuum backgrounds. In…
The double-well potential is a good example, where we can compute the splitting in the bound state energy of the system due to the tunneling effect with various methods, namely WKB or instanton calculations. All these methods are…
We investigate the hydrodynamic solutions for expanding bubbles in cosmological first-order phase transitions going beyond local thermal equilibrium approximation. Under the assumption of a tangenosidal field profile, we supplement the…
We study domain-walls and bubble nucleation in a non-relativistic vector field theory with different longitudinal and transverse speeds of sound. We describe analytical and numerical methods to calculate the orientation dependent…
The phase-field method is used as a basis to develop a strictly mass conserving, yet simple, model for simulation of two-phase flow. The model is aimed to be applied for the study of structure evolution in metallic foams. In this regard,…
Phase field equations describe the novel approach to the Stefan problems. We calculate these equations numerically performed in two-dimensions. We take full advantage of the phase field parameter $\varphi$ to track the interface on which…
We numerically examine the effect of thermal fluctuations on a first-order phase transition in 2+1 dimensions. By focusing on the expansion of a single bubble we are able to calculate changes in the bubble wall's velocity as well as changes…
Sandpiles have become paradigmatic systems for granular flow studies in statistical physics. New directions of investigations are discussed here. Rather than varying the nature of the pile (sand, salt, rice,..) we have investigated changes…