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Spherically symmetric solutions to a model for interface motion by interface diffusion

Zhu, Peicheng (2013)

Applications of Mathematics 2013

The existence of spherically symmetric solutions is proved for a new phase-field model that describes the motion of an interface in an elastically deformable solid, here the motion is driven by configurational forces. The model is an elliptic-parabolic coupled system which consists of a linear elasticity system and a non-linear evolution equation of the order parameter. The non-linear equation is non-uniformly parabolic and is of fourth order. One typical application is sintering.

Steady and unsteady 2D numerical solution of generalized Newtonian fluids flow

Keslerová, Radka, Kozel, Karel (2012)

Applications of Mathematics 2012

This article presents the numerical solution of laminar incompressible viscous flow in a branching channel for generalized Newtonian fluids. The governing system of equations is based on the system of balance laws for mass and momentum. The generalized Newtonian fluids differ through choice of a viscosity function. A power-law model with different values of power-law index is used. Numerical solution of the described models is based on cell-centered finite volume method using explicit Runge–Kutta...

The convergence of explicit Runge-Kutta methods combined with Richardson extrapolation

Faragó, István, Havasi, Ágnes, Zlatev, Zahari (2012)

Applications of Mathematics 2012

Runge-Kutta methods are widely used in the solution of systems of ordinary differential equations. Richardson extrapolation is an efficient tool to enhance the accuracy of time integration schemes. In this paper we investigate the convergence of the combination of any explicit Runge-Kutta method with active Richardson extrapolation and show that the obtained numerical solution converges under rather natural conditions.

Uniform L 1 error bounds for semi-discrete finite element solutions of evolutionary integral equations

Lin, Qun, Xu, Da, Zhang, Shuhua (2012)

Applications of Mathematics 2012

In this paper, we consider the second-order continuous time Galerkin approximation of the solution to the initial problem u t + 0 t β ( t - s ) A u ( s ) d s = 0 , u ( 0 ) = v , t > 0 , where A is an elliptic partial-differential operator and β ( t ) is positive, nonincreasing and log-convex on ( 0 , ) with 0 β ( ) < β ( 0 + ) . Error estimates are derived in the norm of L t 1 ( 0 , ; L x 2 ) , and some estimates for the first order time derivatives of the errors are also given.

Use of a differential evolution algorithm for the optimization of the heat radiation intensity

Mlýnek, Jaroslav, Knobloch, Roman, Srb, Radek (2015)

Application of Mathematics 2015

This article focuses on the heat radiation intensity optimization on the surface of an aluminium shell mould. The outer mould surface is heated by infrared heaters located above the mould and the inner mould surface is sprinkled with a special PVC powder. This is an economic way of producing artificial leathers in the automotive industry (e.g. the artificial leather on car dashboards). The article includes a description of a mathematical model that allows us to calculate the heat radiation intensity...

Viscosity solutions to a new phase-field model for martensitic phase transformations

Zhu, Peicheng (2015)

Application of Mathematics 2015

We investigate a new phase-field model which describes martensitic phase transitions, driven by material forces, in solid materials, e.g., shape memory alloys. This model is a nonlinear degenerate parabolic equation of second order, its principal part is not in divergence form in multi-dimensional case. We prove the existence of viscosity solutions to an initial-boundary value problem for this model.

Why quintic polynomial equations are not solvable in radicals

Křížek, Michal, Somer, Lawrence (2015)

Application of Mathematics 2015

We illustrate the main idea of Galois theory, by which roots of a polynomial equation of at least fifth degree with rational coefficients cannot general be expressed by radicals, i.e., by the operations + , - , · , : , and · n . Therefore, higher order polynomial equations are usually solved by approximate methods. They can also be solved algebraically by means of ultraradicals.

Wildland fire propagation modelling: A novel approach reconciling models based on moving interface methods and on reaction-diffusion equations

Kaur, Inderpreet, Mentrelli, Andrea, Bosseur, Frederic, Filippi, Jean Baptiste, Pagnini, Gianni (2015)

Application of Mathematics 2015

A novel approach to study the propagation of fronts with random motion is presented. This approach is based on the idea to consider the motion of the front, split into a drifting part and a fluctuating part; the front position is also split correspondingly. In particular, the drifting part can be related to existing methods for moving interfaces, for example, the Eulerian level set method and the Lagrangian discrete event system specification. The fluctuating part is the result of a comprehensive...

Zero points of quadratic matrix polynomials

Opfer, Gerhard, Janovská, Drahoslava (2013)

Applications of Mathematics 2013

Our aim is to classify and compute zeros of the quadratic two sided matrix polynomials, i.e. quadratic polynomials whose matrix coefficients are located at both sides of the powers of the matrix variable. We suppose that there are no multiple terms of the same degree in the polynomial 𝐩 , i.e., the terms have the form 𝐀 j 𝐗 j 𝐁 j , where all quantities 𝐗 , 𝐀 j , 𝐁 j , j = 0 , 1 , ... , N , are square matrices of the same size. Both for classification and computation, the essential tool is the description of the polynomial 𝐩 by a matrix equation...

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