Related papers: Towards analytical solutions of the alloy solidifi…
Muon ionization cooling involves passing particles through solid or liquid absorbers. Careful simulations are required to design muon cooling channels. New features have been developed for inclusion in the transfer map code COSY Infinity to…
The explicit analytic solution of the Thomas Fermi equation thorough a new kind of analytic technique, namely the homotopy analysis method, was employed by Liao (Appl. Math. Comp. 144, (2003)). However, the base functions and the auxiliary…
A room temperature liquid metal features a melting point around room temperature. We use liquid metal gallium due to its non-toxicity. A physical maze is a connected set of Euclidean domains separated by impassable walls. We demonstrate…
This paper aims at obtaining, by means of integral transforms, analytical approximations in short times of solutions to boundary value problems for the one-dimensional reaction-diffusion equation with constant coefficients. The general form…
The present paper describes the development of a novel and comprehensive computational framework to simulate solidification problems in materials processing, specifically casting processes. Heat transfer, solidification and fluid flow due…
One of the main challenges in numerically solving partial differential equations is finding a discretisation for the computational domain that balances the accurate representation of the underlying field with computational efficiency.…
The one-dimensional (1D) Stefan problem is a prototypical heat and mass transfer problem that analyzes the temperature distribution in a material undergoing phase change. In addition, it describes the evolution of the phase change front…
We apply a proposal of Yuen and Tombesi, for treating stochastic problems with negative diffusion, to the analytically soluble problem of the single-mode anharmonic oscillator. We find that the associated stochastic realizations include…
The homotopy analysis method is studied in the present paper. The question of convergence of the homotopy analysis method is resolved. It is proven that under a special constraint the homotopy analysis method does converge to the exact…
Based on classical concept, solidification of alloys is a direct transition from liquid phase to solid phase, by which dendrites and dendritic segregation are produced. Through in-situ and real time morphology observation and XRD test…
This paper focuses on the regularization of backward time-fractional diffusion problem on unbounded domain. This problem is well-known to be ill-posed, whence the need of a regularization method in order to recover stable approximate…
In classical continuum theory, Volterra's principle [1, 2] is a long-known method to solve linear rheological (viscoelastic) problems derived from the corresponding elastic ones. Here, we introduce and present another approach that is…
We address the linear-mode analysis performed near an equilibrium configuration in the fluid rest frame with a dynamical magnetic field perturbed on a constant configuration. We develop a simple and general algorithm for an analytic…
The microsegregation and dendritic growth mode of Al-5wt%Cu alloy was investigated. In the early solidification stage, the crystal growth mode of interrupted growth and periodic boundary trapping will happen, which results in the…
The aim of this paper is to develop a stability theory and a numerical model for the three density-stratified electrically conductive liquid layers. Using regular perturbation methods to reduce the full 3d problem to the shallow layer…
With the previous results for the analytical blowup solutions of the N-dimensional Euler-Poisson equations, we extend the similar structure to construct an analytical family of solutions for the isothermal Navier-Stokes equations and…
Lubrication equations allow to describe many structurin processes of thin liquid films. We develop and apply numerical tools suitable for their analysis employing a dynamical systems approach. In particular, we present a time integration…
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…
In this article it is proved the existence of similarity solutions for a one-phase Stefan problem with temperature-dependent thermal conductivity and a Robin condition at the fixed face. The temperature distribution is obtained through a…
We study numerically stabilized solutions of the two-dimensional Schrodinger equation with a cubic nonlinearity. We discuss in detail the numerical scheme used and explain why choosing the right numerical strategy is very important to avoid…