It is proven that the ”horizon condition”, which was found to characterize the fundamental modular region in continuum theory and the thermodynamic limit of gauge theory on a periodic lattice, holds for every (transverse) configuration on a finite lattice with free boundary conditions.

The classical integrability the O(N) nonlinear sigma model on a half-line is examined, and the existence of an infinity of conserved charges in involution is established for the free boundary condition. For the case N = 3 other possible boundary conditions are considered briefly.

This paper presents a new and efficient method to calculate point mobilities from subcomponents of a full structure. When performing dynamic analyses of subcomponents the result normally tends to strongly depend on the boundary condition selected for the component. The goal is to simulate the results one would have received if the full model would be analysed. Normally free or clamped boundary ...

The higher rank analogue of the XXZ model with a boundary is considered on the basis of the vertex operator approach. We derive difference equations of the quantum Knizhnik-Zamolodchikov type for 2N-point correlations of the model. We present infinite product formulae of two point functions with free boundary condition by solving those difference equations with N = 1.

In this article, element free Galerkin method is used for static analysis of thin micro/nanoscale plates based on the nonlocal plate theory. The problem is solved for the plates with arbitrary boundary conditions. Since shape functions of the element free Galerkin method do not satisfy the Kronecker’s delta property, the penalty method is used to impose the essential boundary conditions. Discre...

We establish the saddle point property of the focusing selfsimilar solution of a free boundary problem for the heat equation with free boundary conditions given by u = 0 and ∂u ∂ν = 1.

In this paper, free vibration analysis of orthotropic functionally graded material (FGM) cylinders was carried out by a Mesh-Free method. In this analysis, moving least squares shape functions are used for approximation of displacement field in the weak form of equilibrium equation. Essential boundary conditions are imposed by transformation method. In this simulation, an axisymmetric model is ...

boundary layer growth and hence displacement thickness are the key factors in shock position over aerodynamical surfaces at transonic regimes. since boundary layer growth is a function of free stream reynolds number and also of the transition location, the free stream reynolds number and also the other parameters involved in the boundary layer growth and its transition location are determinant ...

In this paper, free longitudinal vibration of nanorods is investigated from the wave viewpoint. The Eringen’s nonlocal elasticity theory is used for nanorods modelling. Wave propagation in a medium has a similar formulation as vibrations and thus,  it can be used to describe the vibration behavior. Boundaries reflect the propagating waves after incident. Firstly, the governing quation of nanoro...