In 1, 2 , we have considered a lossless transmission line terminated by a nonlinear resistive load and parallel connected capacitance cf. Figure 1 . The nonlinear boundary condition is caused by the polynomial type V-I characteristics of the nonlinear load at the second end of the transmission line cf. Figure 1 . The voltage and current u x, t , i x, t of the lossless transmission line can be f...

We study the O(n) loop model on a dynamically triangulated disk, with a new type of boundary conditions, discovered recently by Jacobsen and Saleur. The partition function of the model is that of a gas of self and mutually avoiding loops covering the disk. The Jacobsen-Saleur (JS) boundary condition prescribes that the loops that do not touch the boundary have fugacity n ∈ [−2, 2], while the lo...

We show that a minimal disk satisfying the free boundary condition in a constant curvature ball of any dimension is totally geodesic. We weaken the condition to parallel mean curvature vector in which case we show that the disk lies in a three dimensional constant curvature submanifold and is totally umbilic. These results extend to higher dimensions earlier three dimensional work of J. C. C. N...

The BEM is applied to the solution of the torsion problem of non-homogeneous anisotropic non-circular prismatic bars. The problem is formulated in terms of the warping function. This formulation leads to a second order partial differential equation with variable coefficients, subjected to a generalized Neumann type boundary condition. The problem is solved using the Analog Equation Method (AEM)...

Boltzmann’s one-dimensional non-linear non-stationary moment system of equations in the third approximation is presented, which first, and fourth corresponds to laws conservation mass, momentum energy, respectively. This contains six represents a nonlinear hyperbolic type equations. For six- an initial boundary value problem formulated. The macroscopic condition moments incident particles distr...

We consider an initial boundary value problem for a symmetrizable mixed hyperbolic-parabolic system of conservation laws with a small viscosity ε, ut +F (u )x = ε(B(u)ux)x. When the boundary is noncharacteristic for both the viscous and the inviscid system, and the boundary condition dissipative, we show that uε converges to a solution of the inviscid system before the formation of shocks if th...

We study the condition number of the system matrices that appear in the Boundary Element Method when solving the Stokes equations at a two-dimensional domain. At the boundary of the domain we impose Dirichlet conditions or mixed conditions. We show that for certain critical boundary contours the underlying boundary integral equation is not solvable. As a consequence, the condition number of the...