Our aim in this paper is to study a generalization of the Caginalp phasefield system based on the theory of type III thermomechanics with two temperatures for the heat conduction. In particular, we obtain well-posedness results and study the dissipativity of the associated solution operators. We consider here both regular and singular nonlinear terms. Furthermore, we endow the equations with tw...

Analytical solutions of the diffusion equation for a radially N-layered cylinder were derived in the steady-state, frequency, and time domains. Solutions for axially infinite and finite cylinders are presented. The derived formulas were compared to a known solution of the diffusion equation for a layered semi-infinite geometry and to Monte Carlo simulations, showing excellent and good agreement...

A semi-Lagrangian code for the solution of the electrostatic drift-kinetic equations in straight cylinder configuration is presented. The code, CYGNE, is part of a project with the long term aim of studying microturbulence in fusion devices. The code has been constructed in such a way as to preserve a good control of the constants of motion, possessed by the drift-kinetic equations, until the n...

Loading conditions and complex geometry have led the cylinder heads to become the most challenging parts of diesel engines. The aim of this study is to compare the distribution of temperature and stress in the aluminum and magnesium cylinder heads under thermo-mechanical loads. The three-dimensional model of the cylinder heads was simulated in abaqus software and a two-layer viscoplasticity mod...

We study solution techniques for parabolic equations with fractional diffusion and Caputo fractional time derivative, the latter being discretized and analyzed in a general Hilbert space setting. The spatial fractional diffusion is realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic problem posed on a semi-infinite cylinder in one more spatial dimension. We write our evolution ...

The Razumov-Stroganov correspondence, an important link between statistical physics and combinatorics proved in 2011 by L. Cantini and A. Sportiello, relates the ground state eigenvector of the O(1) dense loop model on a semi-infinite cylinder to a refined enumeration of fully-packed loops, which are in bijection with alternating sign matrices. This paper reformulates a key component of this pr...

The polarizability of a nanostructure is an important parameter that determines the optical properties. An exact semi-analytical solution of the electrostatic polarizability of a general geometry consisting of two segments forming a cylinder that can be arbitrarily buried in a substrate is derived using bipolar coordinates, cosine-, and sine-transformations. Based on the presented expressions, ...

Suppressing mode instabilities (MI) by optimizing the fiber coiling methods has been studied numerically. By employing our semi-analytical model, the MI threshold of two typical high power fibers in various coiling methods has been calculated. It reveals that fiber laser systems with gain fibers being coiled in cylinder shape has higher MI threshold than those with gain fibers being coiled in s...

We present a numerical method to study convective heat transfer in a high Reynolds number incompressible flow around a cylinder subject to uncertain boundary conditions. We exploit the one-way coupling of the energy and momentum transport to derive a semi-intrusive uncertainty propagation scheme, which combines Galerkin and collocation approaches for computing approximate statistics of the stoc...

We study a discretization technique for the parabolic fractional obstacle problem in bounded domains. The fractional Laplacian is realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic equation posed on a semi-infinite cylinder, which recasts our problem as a quasi-stationary elliptic variational inequality with a dynamic boundary condition. The rapid decay of the solution suggest...