Numerical investigation of trapped modes in an irregular waveguide

It is shown by means of a numerical experiment that an arbitrary asymmetric perturbation of the function describing a dielectric insert in a waveguide, in the general case, results in vanishing of the trapped mode; i.e., it ceases to exist.     

Numerical solution of the Goursat problem by a nonlinear trapezoidal formula

In this paper the solution of the Goursat problem is obtained by the use of a nonlinear Trapezoidal formula based on geometric means. The numerical results indicate the new strategy to be superior.     

The resolvent of a periodic optical waveguide the continuous spectrum

We consider a two-dimensional optical waveguide with periodic media interface. We study the resolvent of the waveguide in a neighborhood of a purely imaginary point of the spectral parameter. We prove that the resolvent exists on the subspace of functions orthogonal ina certain sense to the singular functions of the continuous spectrum. Bibliography: 7 titles. Translated fromProblemy Matematicheskogo Analiza, No. 13, 1992, pp. 79–89.     

Eigenfunctions of the continuous spectrum of a two-dimensional periodic optical waveguide

One proves the existence of the eigenfunctions of the continuous spectrum of a two-dimensional periodic optical waveguide. One gives a normalization of the eigenfunctions of the continuous spectrum relative to an indefinite inner product. One defines the concept of the genus of the multipliers of a Hamiltonian equation, corresponding to the continuous spectrum of the optical waveguide.Translated from Problemy Matematicheskogo Analiza, No. 9, pp. 18–34, 1984.     

Numerical calculation of incomplete gamma functions by the trapezoidal rule

Summary The trapezoidal rule is applied to the numerical calculation of a known integral representation of the complementary incomplete gamma function (a,x) in the regiona<–1 andx>0. Since this application of the rule is not standard, a careful investigation of the remainder terms using the Euler-Maclaurin formula is carried out. The outcome is a simple numerical procedure for obtaining values of incomplete gamma functions with surprising accuracy in the stated region.This work has been supported by the Ministero della Pubblica Istruzione and the Consiglio Nazionale delle Ricerche     

Numerical investigation of a multiserver retrial model

We consider a queueing model in which customers arrive in a Poisson stream to be served by one ofc servers. Each arriving customer enters a pool of active customers and starts generating requests for service at exponentially distributed time intervals at rate until he finds a free server and begins service. An analytical solution of this model is difficult and does not lend itself to numerical implementation. In this paper, we make a simplifying approximation, based on understanding of the physical behavior of the system, which yields an infinitesimal generator with a modified matrix-geometric equilibrium probability vector. That vector can be very efficiently computed even for high congestion levels. Illustrative numerical examples demonstrate the effectiveness of the approximation as well as the effect of the retrial rate on the system behavior for various levels of congestion. This study shows how numerical results for analytically intractable systems can be obtained by combining intuition with efficient algorithmic methods.This author's research was supported in part by Grants Nos. ECS-88-03061 from the National Science Foundation and AFOSR-88-0076 from the Air Force Office of Scientific Research.     

Numerical analysis of dissipative instabilities in toroidal plasma configurations with a noncircular cross-section

Translated from Pryamye i Obratnye Zadachi Matematicheskoi Fiziki, pp. 198–203, 1991.     

Nested 2D finite-element function-spaces formulation for the mode-matching problem of arbitrary cross-section waveguide devices

A large class of microwave, millimeter-wave and terahertz waveguide devices for high-frequency electronic systems are made up of waveguide steps cascaded along the propagation direction, giving rise to diverse modal and numerical analysis techniques to solve Maxwell equations for this problem. In this paper, a novel formulation is proposed to compute the numerical modes in all arbitrary cross-sections and characterize all waveguide steps involved in this kind of structures with a modular and straightforward approach through block-matrix operations. The key idea is expressing the modal fields in terms of 2D nested function spaces (each one for a different cross-section) made up of finite-element basis functions. This leads to finite-element matrices used to compute the modes in all different arbitrary waveguides of the structure from a single inter-cross-section conforming 2D mesh. Moreover, these finite-element matrices and results are used to build directly the mode-matching solution of all steps in the structure. After comparison with analytical results for canonical steps, this flexible and efficient approach is validated with various examples of waveguide devices (two filters, a polarizer, a transformer and a polarization rotator), showing excellent agreement with other numerical methods and measurements.     

Numerical investigation of a developmental pneumatically fed impact pulveriser

The current work has been carried out on a pneumatically fed impact pulveriser. A recent build of the proposed device, and early experiments have shown promising size reduction ratios and energy savings in comparison with conventional milling techniques.     

On a conjecture of ridge

The conjecture of Ridge on the numerical range of a shift of periodic weights is resolved in the affirmative, i.e., if the weights are nonzero, the numerical range of the corresponding shift is an open disc centered at the origin. The radius of the disc can be expressed as the Perron root of a nonnegative irreducible symmetric matrix. Some related results are obtained.

     

Numerical investigation of a liquid displacing a gas in thin porous layers

This article deals with a liquid displacing a gas in a thin heterogeneous porous material, which occurs e.g. during the filling process of a lithium-ion battery with an electrolyte. The investigation is based upon the local volume-averaged Navier-Stokes equations, using a Volume-of-Fluid method to treat the interface. For the flow the wall effect and capillary forces have to be considered. Capillary rise experiments are used to determine the permeability. Since the layers are thin and the characteristic size of the particles is comparatively large, friction with the electrode is taken into account with respect to the mobility of the contact line. The implemented models are validated against analytical results, showing a good agreement. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the multistability of spatial solitons in waveguide and optical lattice

Properties of spatial solitons in channel waveguide and optical lattice are studied with the help of projection operator approach. The nonlinearity is assumed to be of cubic-quintic type. The stability consideration of the fixed point solutions of the ODE’s governing the evolution of soliton parameters indicates to the existence of more than one branch of soliton, giving rise to multistability. Explicit numerical analysis gives more information than the standard Vakhitov–Kolokov criterion. A systematic numerical simulation of the soliton profile gives detailed information about the nature of trapping and structure of the different branches of the pulse. It is observed that even under different launching conditions the solitons do not radiate but get trapped.     

Numerical investigation of the Liebau phenomenon

The Liebau phenomenon is the occurrence of valveless pumping through the application of a periodic force at a place which lies asymmetric with respect to system configuration. This paper is concerned with two different physical configurations and respective models. Comparison and derivation among the models is discussed. Accurate numerical schemes which solve these models are presented. By means of numerical simulations it is investigated under which conditions valveless pumping takes place.     

The critical cross-section of a vortex

Summary This paper discusses the problem of critical-flow cross-sections in vortex flows. It is shown that there are two different types of vortex flows, A-type and B-type vortices (say). An A-type vortex approaches its critical flow state as its cross-sectional area increases and departs from the critical state as the cross-sectional area is decreased. This property is associated with the particular dependence of total pressure and circulation on the stream function, and it holds for both subcritical and supercritical A-type vortices. On the other hand, both subcritical and supercritical B-type vortices approach their critical flow states as their cross-sectional areas are decreased and depart from their critical states for increasing cross-sectional area. As was shown by Benjamin, setting the first variation of the flow force with respect to the stream function equal to zero leads to Euler's equation of motion. The second variation also vanishes if the corresponding flow state is critical. In this case the sign of the third variation decides whether the flow is an A-type or a B-type vortex. Within the framework of inviscid-fluid flow theory the type of a vortex is preserved unless vortex breakdown occurs. Making use of the knowledge that vortex flows are controlled by two different types of critical-flow cross-sections a variety of vortex flow phenomena are investigated, including the two types of inlet vortices that are observed upstream of jet engines, the behavior of vortex valves, the flow characteristics of liquid-fuel atomizers and the bath tub vortex.     

Numerical investigation of the Liebau phenomenon

The Liebau phenomenon is the occurrence of valveless pumping through the application of a periodic force at a place which lies asymmetric with respect to system configuration. This paper is concerned with two different physical configurations and respective models. Comparison and derivation among the models is discussed. Accurate numerical schemes which solve these models are presented. By means of numerical simulations it is investigated under which conditions valveless pumping takes place.     

Numerical investigation of pressure loss reduction in a power plant stack

The strengthened environmental laws require the power plants to reduce the emissions. Flue gas desulphurization and deNO_x involve adding chemicals to the flow stream, thereby resulting in increased mass flow. This problem could be overcome by reducing the pressure drop in the duct work and stack combination, so that a higher flow at reduced pressure drop can be handled by the existing fans. In this study, a power plant stack model of 1:40 was investigated numerically. The pressure reduction was achieved by introduction of baffles with various orientations and turning vanes at the inlet of the stack. The flows were modeled and analyzed using commercial computational fluid dynamics (CFD) software Fluent 6.2. The numerical results were validated with the experimental data. The 30° baffle without turning vanes was found to be the optimum baffle angle in terms of the pressure loss reduction. Variation of axial velocity, swirling component and turbulence kinetic energy along the axis of the stack was analyzed to understand the mechanism of the pressure loss reduction in a power plant stack. Guidelines for further pressure loss reduction were provided based on the insight gained from the simulation results.