Related papers: Numerical Approach to Multi Dimensional Phase Tran…
In the present article an endeavor is made to solve the variable order fractional diffusion equations using a powerful method viz., Homotopy Analysis method. It is demonstrated how the method can be used while solving approximately two…
Characterizing thermally activated transitions in high-dimensional rugged energy surfaces is a very challenging task for classical computers. Here, we develop a quantum annealing scheme to solve this problem. First, the task of finding the…
In a trapped Bose-Einstein condensate, subject to the action of an alternating external field, coherent topological modes can be resonantly excited. Depending on the amplitude of the external field and detuning parameter, there are two…
Quantum process tomography is a critical task for characterizing the dynamics of quantum systems and achieving precise quantum control. In this paper, we propose a two-stage solution for both trace-preserving and non-trace-preserving…
In this paper, we derive two bound-preserving and mass-conserving schemes based on the fractional-step method and high-order compact (HOC) finite difference method for nonlinear convection-dominated diffusion equations. We split the…
In this paper we present a numerical solution of a two-phase fractional Stefan problem with time derivative described in the Caputo sense. In the proposed algorithm, we use a special case of front-fixing method supplemented by the iterative…
This paper deals with the problem of simulating dense dispersed systems composed by large numbers of particles undergoing ballistic aggregation. The most classical approaches for dealing with such problems are represented by the so-called…
We calculate two-body scattering phase shifts on a quantum computer using a leading order short-range effective field theory Hamiltonian. The algorithm combines the variational quantum eigensolver and the quantum subspace expansion. As an…
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 study various dynamical aspects of systems possessing a first order phase transition in their phase diagram. We isolate three qualitatively distinct types of theories depending on the structure of instabilities and the nature of the low…
The dynamics of phase transitions plays a crucial r\^ole in the so-called interface between high energy particle physics and cosmology. Many of the interesting results generated during the last fifteen years or so rely on simplified…
This work aims at the goal whether the artificial intelligence can recognize phase transition without the prior human knowledge. If this becomes successful, it can be applied to, for instance, analyze data from quantum simulation of…
In this paper, we design, analyze, and numerically validate positive and energy-dissipating schemes for solving the time-dependent multi-dimensional system of Poisson-Nernst-Planck (PNP) equations, which has found much use in the modeling…
A one-dimensional reaction-diffusion model consisting of two species of particles and vacancies on a ring is introduced. The number of particles in one species is conserved while in the other species it can fluctuate because of creation and…
Quantum computers, with parallel computing and entanglement effects, excel in cryptography analysis and big data processing. However, they are not fully developed yet, and their performance needs further evaluation. Traditional computer…
This paper is devoted to the derivation of a digital quantum algorithm for the Cauchy problem for symmetric first order linear hyperbolic systems, thanks to the reservoir technique. The reservoir technique is a method designed to avoid…
In this Letter, three physical predictions on the phase separation of binary systems are derived based on a dynamic transition theory developed recently by the authors. First, the order of phase transitions is precisely determined by the…
Relying on the recently proposed multicanonical algorithm, we present a numerical simulation of the first order phase transition in the 2d 10-state Potts model on lattices up to sizes $100\times100$. It is demonstrated that the new…
This paper is concerned with moving mesh finite difference solution of partial differential equations. It is known that mesh movement introduces an extra convection term and its numerical treatment has a significant impact on the stability…
This paper applies Benders decomposition to two-stage stochastic problems for energy planning under climate uncertainty, a key problem for the design of renewable energy systems. To improve performance, we adapt various refinements for…