Edward L. Reiss's research while affiliated with Keele University and other places

... KRAKEN [40,41] is a normal mode model where range-dependent solutions are obtained using optionally adiabatic or coupled-mode theory [23]. The KRAKEN program takes an ENV file, computes the modes, and writes them to disk for use by other modules. ...

... Wrinkling of circular and annular plates and spherical shells appears in various engineering and biomechanical applications and has been studied by Adachi and Benicek (1964); Bushnell (1981); Panov and Feodosiev (1948). Under some loading types and boundary conditions a ring of large circumferential compressive stress develops near the edge of the plate (or shell) and may cause asymmetrical buckling (Cheo and Reiss, 1973;Voronkova, 2018, 2020)). Nonaxisymmetric buckling of circular plates subjected to surface load was first formulated and studied in Panov and Feodosiev (1948), and, later, existence and uniqueness of unsymmetric equilibrium states were proved by Morozov (1961); Piechocki (1969)). ...

... It is in fact very special and nongeneric for power series to directly solve a boundary value problem, even though the class of exceptions includes all Hough functions. (The range of applicability can be increased by domain decomposition, that is, by applying a swarm of power series, each evaluated only on its associated subdomain, and matching the piecewise approximations together as in Keller and Reiss [32] and Weinitschke [50].) The domain of convergence of power series approximations can be greatly extended by applying sum acceleration schemes such as the Euler sum acceleration [14,16,41] and Padé approximants [3,12]. ...

... The proof of convergence of the estimation procedure is given here (Theorem 2.1). It is expected to obtain good estimates only if the required matrix has a sparse structure (Beu 2015). In Sect. 3 the algorithm for estimating the unknown parameters of a matrix product is described which is based on solving a minimization problem by the SPSA (Simultaneous Perturbation Stochastic Approximation) (Spall 2003). ...

... In the context of elastic membranes, response curves exhibiting multiple solutions were studied by Callegari, Reiss 4nd Keller [8] and by Bauer, Callegari and Reiss [9]. ...

... We refer to the boundary-value problem (2.6) as Problem S. If X < 0 then Problem S has a unique solution [8], If X is positive and sufficiently large then Problem S may have non-unique solutions. We seek unsymmetric solutions of Problem B which branch from a solution of Problem S. For the pure buckling problem this corresponds to studying secondary buckling from a buckled axisymmetric state. ...

... But, it is a well known^fact that finite Taylor expansions usually furnish asymptotic approximations to exact solutions only on finite time interval though we need perturbation procedures which give asymptotic expansions approximating exact solutions uniformly on the whole time interval 0<ί<oo, which is quite difficult. To overcome this difficulty, one of the most powerful perturbation methods was first developed by Cole and Kevorkian [3] and was simplified by Reiss [38] later. The method is known under the various names, the method of multiple scales, or simply the two-timing method. ...

... Fourth-order boundary value problems which describe the deformations of an elastic beam in an equilibrium state whose both ends are simply supported have been extensively studied in the literature. For classical results obtained on elastic beam equations we refer to [6,12,14,15,38,44], in particular [44] is one of the pioneering works on extensible beams), while [12] settles the existence and multiplicity question for (P f ) in the physical situation p = 2, ρ = 0 and M of the form M (s) = as + b. Recently, the existence of solutions to fourth-order boundary value problems have been studied in many papers and we refer the reader to the papers [8,9,20,22,26,28,29,30,31,36] and the references therein. ...

... As e -0, the regular Hopfbifurcation becomes singular, and the mathematical problem is to investigate the perturbation of a double zero eigenvalue. It appears that this problem is quite different from other double zero eigenvalue bifurcation problems, which results from the coalescence of a Hopf bifurcation point and a steady bifurcation or limit point [12], [10], [8], [6]. In [1] we analyzed the bifurcation problem for (1.1) and discovered that it eventually reduces to the study of the following equations for x and y dx dy (1.2) y+ ef(x, y, L, e), ...

... The layer thickness is constrained to lie between 5 and 100 m, the compressional speed between 1540 and 1800 m/s, the gradient between 0 and 4 s À1 , and density between 1.2 and 2.0 g cm À3 . Wavenumbers for each candidate parameter vector x were computed using the Sturm sequence eigenvalue search 23 (the method used in KRAKEN 24 ) The objective function is minimized by performing a sequential 1D optimization over each parameter, holding the others fixed at their latest optimized value. Six iterations were seen to provide good convergence. ...