In this paper, the exact analytical and numerical solutions for rotating variable-thickness annular disk are presented. The inner and outer edges of the rotating variable-thickness annular disk are considered to have free boundary conditions. Two different annular disks for the radially varying thickness are given. The numerical Runge-Kutta solution as well as the exact analytical solution is a...

We consider Monte-Carlo discretizations of partial differential equations based on a combination of semi-lagrangian schemes and probabilistic representations of the solutions. We study the Monte-Carlo error in a simple case, and show that under an anti-CFL condition on the time-step δt and on the mesh size δx and for N the number of realizations reasonably large, we control this error by a term...

We consider nonlinear diffusion problems of the form ut = ∆u + f(u) with Stefan type free boundary conditions, where the nonlinear term f(u) is of monostable, bistable or combustion type. Such problems arise as an alternative model (to the corresponding Cauchy problem) to describe the spreading of a biological or chemical species, where the free boundary represents the expanding front. We are i...

Every solution of a linear elliptic equation on a bounded domain may be considered as an equilibrium of a free boundary problem. The free boundary problem consists of the corresponding parabolic equation on a variable unknown domain with free boundary conditions prescribing both Dirichlet and Neumann data. We establish a rigorous stability analysis of such equilibria, including the construction...

We extend the well-known method of calculating bulk correlation functions of the conformal Ising model via bosonisation to situations with boundaries. Oshikawa and Affleck have found the boundary states of two decoupled Ising models in terms of the orbifold of a single free boson compactified on a circle of radius r=1; we adapt their results to include disorder operators. Using these boundary s...

We present a procedure in which known solutions to reflection equations for interactionround-a-face lattice models are used to construct new solutions. The procedure is particularly well-suited to models which have a known fusion hierarchy and which are based on graphs containing a node of valency 1. Among such models are the AndrewsBaxter-Forrester models, for which we construct reflection equ...

This paper describes modal testing of a wooden baseball bat with the purpose of finding the peak frequencies and vibration modes and their relation to the so-called “sweet spot”. Initial vibration testing was done by performing a tap test along a Louisville Slugger wooden baseball bat. The bat was suspended by elastic rubber bands to approximate free-free boundary conditions. The peak frequenci...

In quantum theory Hamilton operators with spininteractions have a long history [1 – 5]. Triple spin interaction have been studied by several authors [6 – 19]. Iglói [6] investigated an Ising model with three-spin interaction by finite-size scaling and applying free boundary conditions. Vanderzande and Iglói [7] studied the critical behaviour and logarithmic corrections of a quantum model with t...

We consider a linear elastic plate with stress-free boundary conditions in the limit of vanishing Poisson coefficient. We prove that under a local change of Young’s modulus infinitely many eigenvalues arise in the essential spectrum which accumulate at a positive threshold. We give estimates on the accumulation rate and on the asymptotical behaviour of the eigenvalues.

The shape of two-dimensional invasion percolation clusters are studied numerically for both nontrapping (NTIP) and trapping (TIP) invasion percolation processes. Two different anisotropy quantifiers, the anisotropy parameter and the asphericity are used for probing the degree of anisotropy of clusters. We observe that in spite of the difference in scaling properties of NTIP and TIP, there is no...