We study the maximum temperature rise induced by a rotating or dithering Gaussian laser beam on a two-layer body. First, we derive semi-analytical solutions by solving the transient threedimensional heat equation in a semi-infinite domain with insulating surface. Second, we provide numerical solutions for a two-layer structure in a finite domain. Our results show that the maximum temperature ri...

We study optical bistability of stationary light transmission in nonlinear periodic structures of finite and semi-infinite length. For finite-length structures, the system exhibits instability mechanisms typical for dissipative dynamical systems. We construct a LeraySchauder stability index and show that it equals the sign of the Evans function in λ = 0. As a consequence, stationary solutions w...

In this paper, we will study optimality conditions of semi-infinite programs and generalized semi-infinite programs, for which the gradient objective function when evaluated at any feasible direction for the linearized constraint set is non-negative. We consider three types of penalty functions for semi-infinite program and investigate the relationship among the exactness of these penalty funct...

In this paper, the boundary layer flow of an Eyring-Powell non-Newtonian fluid over a linearly stretching sheet is solved using the combination of the quasilinearization method and the Fractional order of Rational Chebyshev function (FRC) collocation method on a semi-infinite domain. The quasilinearization method converts the equation into a sequence of linear equations then, using the FRC coll...

In this work, we develop a numerical fitting routine to extract multiple thermal parameters using frequency-domain thermoreflectance (FDTR) for materials having non-standard, non-semi-infinite geometries. The is predicated on either 2D or 3D finite element analysis that permits the inclusion of boundary conditions, which cannot be considered in analytical solution heat diffusion equation freque...

A special class of differentiable functions on an infinite integral domain which is not a field is introduced. Some facts about these functions are established and the special case of z is studied in more detail

We present an approach for the solution of a class of generalized semi-infinite optimization problems. Our approach uses augmented Lagrangians to transform generalized semi-infinite min-max problems into ordinary semi-infinite min-max problems, with the same set of local and global solutions as well as the same stationary points. Once the transformation is effected, the generalized semi-infinit...