We consider the six-vertex model with anti-periodic boundary conditions across a finite strip. The row-to-row transfer matrix is diagonalised by the ‘commuting transfer matrices’ method. From the exact solution we obtain an independent derivation of the interfacial tension of the six-vertex model in the anti-ferroelectric phase. The nature of the corresponding integrable boundary condition on t...

Transfer-matrix methods on finite-width strips with free boundary conditions are applied to lattice site animals, which provide a model for randomly branched polymers in a good solvent. By assigning a distinct fugacity to sites along the strip edges, critical properties at the special (adsorption) and ordinary transitions are assessed. The crossover exponent at the adsorption point is estimated...

Using a transfer matrix method, we present some results for directed lattice walkers in a horizontal strip of finite width. Some cases with two walkers in a small width are solved exactly, as are a couple of cases with vicious walkers in a small width; a conjecture is made for a case with three walkers. We also derive the general transfer matrix for two walkers. Lastly, we examine the dependenc...

(an Abel equation in canonical form, see [1, p. 24]) is a useful instrument to display rich qualitative properties such as extendability and finite escape time, stability and instability, boundedness, and periodicity. We show the following: (a) The equation has a unique solution that is defined on (−∞,∞). This solution is periodic. (b) As t increases, each solution is attracted into the strip |...

Goulden, I.P., A linear operator for symmetric functions and tableaux in a strip with given trace, Discrete Mathematics 99 (1992) 69-77. The sum of Schur symmetric functions in a countable set of variables, over partitions with given trace and upper bound on the number of parts, is evaluated. This generalizes results of Gordon (1971). The method is to extend an analogous sum in a finite set of ...

In this paper, wide-angle infrared perfect absorption has been demonstrated by using a double-layer graphene strip grating coupled with silicon dioxide grating. Numerical simulation of the finite-difference time-domain method indicates that can be achieved due to effective impedance matching, and all incident electromagnetic energy is confined in Al 2 O 3 layer between silver substrate Dual-ban...

In this study, dynamic bearing capacity of adjacent shallow strip foundations located on sandy soil was examined using a numerical finite difference modeling, FLAC. The behavioral interference of shallow strip foundations under different conditions was investigated. The effect of soil strength parameters, geometric characteristics of shallow foundations and cyclic loads at different distance ra...

There can be many reasons for engineers to place the footings near a slope such as leakage of suitable sites or architectural considerations. One of the approaches to increase the amount of bearing capacity, especially in soft soils, is adding stone columns to the soil. In this research, the behavior of a strip footing placed near a stone column reinforced clayey slope was investigated. For thi...

Temper rolling or skin pass rolling is one of cold rolling processes composed of a horizontal pass cold rolling mill stand. In this process, the thick strip is subjected to very light reduction (0.5–4%) in thickness in the presence of high friction amplitudes. One of the basic parameters of strip rolling processes is temper rolling force. A new rolling force model has been proposed for temper r...