Related papers: Numerical Approach to Multi Dimensional Phase Tran…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…
Using a recently proposed classification scheme for phase transitions in finite systems [Phys.Rev.Lett.{\bf 84},3511 (2000)] we show that within the statistical standard model of nuclear multifragmentation the predicted phase transition is…
We develop a method for multidimensional optimisation using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimising functional correspond to fixed points of the…
We introduce a modified molecular dynamics algorithm that allows one to freeze the dynamics of parts of a physical system, and thus concentrate the simulation effort on selected, central degrees of freedom. This freezing, in contrast to…
We study the numerical algorithm and error analysis for the Cahn-Hilliard equation with dynamic boundary conditions. A second-order in time, linear and energy stable scheme is proposed, which is an extension of the first-order stabilized…
We discuss an algorithm for the numerical evaluation of NLO multiparton processes. We focus hereby on the virtual part of the NLO calculation, i.e. on evaluating the one-loop integration numerically. We employ and extend the ideas of the…
We construct the thermal bounce solution in holographic models that describes first-order phase transitions between the deconfined and confined phases in strongly-coupled gauge theories. This new, periodic Euclidean solution represents…
Fractional order models have proven to be a very useful tool for the modeling of the mechanical behaviour of viscoelastic materials. Traditional numerical solution methods exhibit various undesired properties due to the non-locality of the…
One-dimensional model of a system where first-order phase transition occurs is examined in the present paper. It is shown that basic properties of the phenomenon, such as a well defined temperature of transition, are caused both by…
In this article, firstly we develop a method for a type of difference equations, applicable to solve approximately a class of first order ordinary differential equation systems. In a second step, we apply the results obtained to solve a…
We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested…
Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
We develop an efficient numerical method to study the quantum critical behavior of disordered systems with $\mathcal{O}(N)$ order-parameter symmetry in the large$-N$ limit. It is based on the iterative solution of the large$-N$ saddle-point…
The Hubbard model has occupied the minds of condensed matter physicists for most part of the last century. This model provides insight into a range of phenomena in correlated electron systems. We wish to examine the paradigm of quantum…
We introduce a new Forward-Flux Sampling in Time (FFST) algorithm to efficiently measure transition times in rare-event processes in non-equilibrium systems, and apply it to study the first-order (discontinuous) kinetic transition in the…
We present a hierarchical approach for enhancing the robustness of numerical solvers for modelling radiative MHD flows in multi-dimensions. This approach is based on clustering the entries of the global Jacobian in a hierarchical manner…
To address the magnetization dynamics in ferromagnetic materials described by the Landau-Lifshitz-Gilbert equation under large damping parameters, a third-order accurate numerical scheme is developed by building upon a second-order method…
The replica exchange method is a powerful tool for overcoming slow relaxation in molecular simulations, but its efficiency depends strongly on the choice of the number and interval of replicas and their exchange probabilities. Here, we…