A mushy zone model with an exact solution

An exact Solution for a Finite Solution Server Model

An Exact Solution to a Three Dimensional Ising Model

A high temperature expansion is employed to map some complex anisotropic nonhermitian three dimensional Ising models with algebraic long range interactions into a solvable two dimensional variant. Some solutions are presented. This framework further allows for some very simple general observations. It will be seen that the absence of a “phase interference” effect plays an important role in high...

The rapid advance and slow retreat of a mushy zone

We discuss a model for the evolution of a mushy zone which forms during the solidification of a binary alloy cooled from below in a tank with finite height. Our focus is on behaviours of the system that do not appear when either a semi-infinite domain or negligible solute diffusion is assumed. The problem is simplified through an assumption of negligible latent heat, and we develop a numerical ...

An Exact Solution for Kelvin-Voigt Model Classic Coupled Thermo Viscoelasticity in Spherical Coordinates

In this paper, the classic Kelvin-Voigt model coupled thermo-viscoelasticity model of hollow and solid spheres under radial symmetric loading condition is considered. A full analytical method is used and an exact unique solution of the classic coupled equations is presented. The thermal and mechanical boundary conditions, the body force, and the heat source are considered in the most general fo...

An Exact Isotropic Solution

The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients of order three. We prove that this difference equation can be solved in general. Consequently we can find an exact solution to the field equations corresponding to a static spherically symmetric gravitational potential in terms of elementary functions. The metric functions, the energy de...