Existence Of Complex Modes Research Articles

Analysis of the acoustical behavior of cavities using impedance functions

The acoustic design of cavities is an important task in a variety of engineering applications, from automotive or aerospace industries to equipment coating designs. In this work, the acoustic impedance functions (a frequency domain model) were calculated using analytical, numerical, and experimental methods. Those different approaches were presented in a unified manner in order to allow comparisons among them. The relationship of the impedance function and a classical frequency response function (FRF) was also established. A circular duct of rigid walls was assumed with different boundary conditions as closed end, as well as opened and absorbed extremities. Three duct configurations were implemented in order to compare analytical, numerical, and experimental results. Finally, it could be possible to evaluate some aspects that are characteristic of a large range of acoustic systems applications as the existence of complex modes and frequency-dependent behavior of absorption material. This study aims the usage of the impedance functions to analyze the acoustic behavior of cavities, as well as to compose the background in order to develop, in the future, an acoustic modeling process using impedance functions.

Condition for the existence of complex modes in a trapped Bose-Einstein condensate with a highly quantized vortex

We consider a trapped Bose-Einstein condensate (BEC) with a highly quantized vortex. For the BEC with a doubly, triply, or quadruply quantized vortex, the numerical calculations have shown that the Bogoliubov-de Gennes equations, which describe the fluctuation of the condensate, have complex eigenvalues. In this paper, we obtain the analytic expression of the condition for the existence of complex modes, using the method developed by Rossignoli and Kowalski [R. Rossignoli and A. M. Kowalski, Phys. Rev. A 72, 032101 (2005)] for the small coupling constant. To derive it, we make the two-mode approximation. With the derived analytic formula, we can identify the quantum numbers of the complex modes for each winding number of the vortex. Our result is consistent with those obtained by the numerical calculation in the case that the winding number is two, three, or four. We prove that the complex modes always exist when the condensate has a highly quantized vortex.

On the mechanism of occurrence of chaotic dynamics in a vacuum microwave generator with a virtual cathode

The nonlinear dynamics of an electron beam with a virtual cathode in a transit-current vircator system is numerically studied. The existence of complex modes, including chaotic ones, is shown. The physical processes in the electron beam are examined. It is found that the chaotic dynamics in an electron beam with a virtual cathode is due to the nonlinear interaction between the structures organized in it.

Planar bianisotropic waveguides

This paper presents an analysis of several planar bianisotropic waveguides including grounded slabs and strip lines. The bianisotropic properties of the materials are prescribed in a special but practical form so that the propagating waves are either transverse electric or transverse magnetic modes. Certain unique characteristics of the waves are discussed including mode elimination, unidirectional propagation, and the existence of complex modes. Both analytical and numerical results of guided wave properties are discussed.

Role of complex modes in coplanar‐waveguide‐to‐coplanar‐waveguide discontinuity calculations

AbstractThe existence of complex modes in the lossless symmetrical shielded coplanar waveguide is demonstrated. Complex modes are found to occur only within a range of frequency and structural parameters. It is shown that exclusion of these modes in the analysis of coplanar waveguide discontinuities can cause the imput reflection and transmission coefficients to converge to incorrect values, thus highlighting their importance in such problems.

Complex modes in shielded suspended coupled microstrip lines

The existence of complex modes in electrically shielded suspended coupled microstrip lines has been studied extensively, and the results are presented. A rigorous full-wave spectral-domain approach (SDA) with a newly proposed and tested set of basis functions can efficiently and accurately determine the propagation characteristics of the dominant, higher-order, and complex modes for planar or quasi-planar transmission lines. These basis functions are validated by comparing the convergence study of field solutions with those obtained by various sets of preconditioned bases and by the unconditioned subdomain ones. Excellent agreement is obtained for the propagation constants and the normalized complex longitudinal and transverse current distributions on conducting strips for the strongly coupled microstrip lines. For all the particular case studies discussed, it is shown that the complex modes may exist in all the shielded suspended coupled microstrip lines, even when the substrate dielectric constant is low. Theoretical results for the fundamental, higher-order, evanescent, and complex modes are presented for suspended coupled microstrip lines.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nature of complex time eigenvalues of the one speed transport equation in a homogeneous sphere

The complex time eigenvalues of the transport equation have been studied for one speed neutrons, scattered isotropically in a homogeneous sphere with vacuum boundary conditions. It is shown that the complex decay constants vary continuously with the radius of the sphere. Our earlier conjecture (Dahl and Sahni (1983–1984)) regarding disjoint arcs is thus shown to be true. We also indicate that complex decay constants exist even for large assemblies, though with rapid oscillations in the corresponding eigenvectors. These modes can not be predicted by the diffusion equation as this nature of eigenvectors contradicts the assumption of ‘slowly varying flux’ needed to derive the diffusion approximation from the transport equation. For an infinite system, the existence of complex modes is related to the solution of a homogeneous equation.

Modeling discontinuities in dielectric-loaded waveguides

The mode-matching technique is applied to model step discontinuities in dielectric-loaded cylindrical waveguides excited by hybrid modes. It is shown that the field solution obtained by mode matching does not converge unless complex modes are included in the field expansion. If the structure parameters and operating frequency allow for the existence of complex modes, then the purely propagating and evanescent mode fields do not form a complete set unless complemented by the complex mode field. Numerical results that clearly illustrate the role of the complex mode fields in the modeling of step discontinuities are presented. Examples illustrating the representation of the step discontinuities by a multiport scattering matrix are included. >

Complex modes in lossless shielded microstrip lines

The possible existence of complex modes in lossless shielded microstrip lines was investigated using the singular integral equation method. The method is used for the analysis of three lossless shielded microstrip line structures with different substrate permittivities. To confirm the validity of the method, results are compared with existing data for propagating modes. Complex modes were found in the moderate and high permittivity structures.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>