Averaged Boundary Conditions Research Articles

Complicated dynamics of scalar reaction diffusion equations with a nonlocal term

SynopsisWe consider the dynamics of scalar equations ut, = uxx + f(x, u) + c(x)α(u), 0 < x < l, where α denotes some weighted spatial average and Dinchlet boundary conditions are assumed. Prescribing f, c, α appropriately, it is shown that complicated dynamics can occur. Specifically, linearisations at equilibria can have any number of purely imaginary eigenvalues. Moreover, the higher order terms of the reduced vector field in an associated centre manifold can be prescribed arbitrarily, up to any finite order. These results are in marked contrast with the case α = 0, where bounded solutions are known to converge to equilibrium.

A resistive sheet approximation for mesh reflector antennas

A simplified method of estimating the equivalent surface resistance of a reflecting mesh is presented. The equivalent resistance is obtained from the approximate mesh reflection coefficients, which are based on averaged boundary conditions. This resistance approximation allows an integral equation solution for the mesh reflector that is a simple extension of that for the perfectly conducting reflector. Paraboloid radiation patterns using physical optics in conjunction with the reflection coefficients are compared to an E-field integral equation solution for a resistive surface. The agreement is excellent for low to moderate resistance values, even in the sidelobe regions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Plenum chamber effect on wind-tunnel resonance by the finite-elementmethod

A finite-element approach is developed for predicting the so-called frequencies of subsonic wind tunnels with plenum chambers. The resulting computer code has been applied to various wind tunnels. For example, the resonant frequencies for both the rectangular wind tunnel (rectangular cross section) and the NASA Langley Research Center 16 x 16 ft Transonic Dynamics Tunnel (octagonal cross section) have been calculated. Plenum chamber effects on wind-tunnel resonance is significant in a Mach number range of 0-0.5. The results are more accurate than theoretical values obtained by using an averaged homogeneous boundary condition on the slot. [B] b F {/) H i [K] [k] M [ m ] [M] |_7VJ p

On the electromagnetic scattering from infinite rectangular grids with finite conductivity

-The development of a new numerical technique for the analysis of electromagnetic scattering from a rectangular wire (or strip) mesh. According to this technique the conjugate gradient method (CGM) and the fast Fourier transform (FFT) are used to solved for the aperture fields and the induced current densities. The method is efficient because 1) it makes use of the fast Fourier transform, 2) it converts a set of integrodifferential equations into a set of algebraic equations, and 3) it does not require inversion of any matrices. Unlike the moment method, the spectral iteration approach (SIT), and the averaged boundary conditions method, this technique can be used for arbitrary size and spacing between adjacent strips. The equivalent radius principle is used to determine the reflection coefficient from a wire mesh. Results, examples, and comparisons of this method with other methods support the validity of the algorithm.

Image Theory for Dipole Excitation of Fields above and below a Wire Grid with Square Cells

The exact imnage theory, recently introduced by two of the present authors for the Sommerfeld problem, is applied to the problem of a vertical electric dipole above a plane metallic grid with rectangular cells. The mesh size is assumed small compared to the wavelength and the wire diameter small compared to the mesh size, whence the Kontorovich averaged boundary condition concept is applicable. The image current consists of two exponential-line-current waves located in complex space. The theory is seen to produce simple asymptotic expressions for the field close to the grid surface. Also, an integral expression for the calculation of the change in the vertical-electric-dipole impedance due to the grid is constructed.

Nucleons in nuclei in the selfconsistent soliton model to QCD

In the scalar Soliton model of QCD the gluon field operators are replaced by a classical selfcoupling scalar field with solitontype interaction. The quark wave-functions and the soliton field are calculated for the free nucleon as compared to a nucleon inside nuclear matter approximated by averaged boundary conditions to simulate the surrounding nucleons. The mass of the nucleon as well as its mean effective radius are given in terms of the nuclear-matter density and the model parameters. For large quark-soliton coupling the EMC-effect is seen, and then at high densities a plasma of free quarks and free localized solitons is the lowest energy solution.

Electromagnetic Wave Propagation along a Pair of Rectangular Bonded Wire Meshes

A mode equation is derived for propagation between a pair of rectangular wire meshes, and numerical results for the propagation constant of the quasi-TEM mode are presented. An approximate method based on averaged boundary conditions is found to agree, if the mesh dimensions are small and the mesh separation is large. The field distribution of the quasi-TEM mode is also examined.

Electromagnetic Surface-Wave Propagation over a Rectangular-Bonded Wire Mesh

The electromagnetic surface wave which can propagate over a rectangular wire mesh of infinite extent is considered. The propagaton constant is determined both from a rigorous Floquet formulation and an approximate method using averaged boundary conditions. The agreement is fairly good for sufflciently small mesh dimensions. The rectangular mesh is found to be highly anisotropic, and the possibility of an effective anisotropic transfer inductance representation for the mesh is discussed briefly.

Electromagnetic Surface Wave Propagation over a Bonded Wire Mesh

The electromagnetic surface wave that can propagate over a square mesh of intersecting parallel wires is considered. A combined analytical and numerical method developed earlier is employed to deal with the interacting wire currents. For small mesh spacings, the propagation constant is found to be almost independent of the azimuthal direction of propagation. This is in agreement with previous results obtained by Soviet investigators who utilize averaged boundary conditions for analyzing such bonded wire meshes. However, for larger wire spacings, greater than about one tenth of a wavelength, there is a significant dependence on the direction of propagation over the mesh. The validity of describing the wire mesh in terms of an effective transfer inductance and related questions are discussed briefly in the Appendix.

Average boundary conditions in Cauchy problems

We consider the general Cauchy problem with initial data in a Hilbert space and with a formal dissipative linear generator. A complete parametrization is known of the (abstract) boundary conditions which make this problem well set. We exhibit a distinguished subset B E of the set B of boundary conditions and demonstrate explicitly that the evolution associated with each B in B can be represented as a (time independent) average over the evolutions associated with B′ in B E . Applications are discussed to Schrödinger equations in bounded regions or with singular potentials.

On the reflection properties of periodically supported metallic wire gratings with rectangular mesh showing small sag

Ideal reflector simulation of wire gratings is considered. Results for infinite plane gratings under linearly polarized plane waves, based on Astrakhan's averaged boundary conditions, yield conclusions on influence of wire orientation, mesh size, and wire connection. The grating sag is considered. Its influence on strength and phase shift of the reflection is estimated from a simple scatter problem, using Kirchhoff's approximation. A smoothness criterion is given. The results of the work are related to an unstationary method to measure radiation patterns of aircraft antennas in flight.

On the theory of ventilated wind tunnels

This paper gives a new and more accurate treatment of the theory of rectangular wind tunnels that are ventilated by means of longitudinal slots on one pair of opposite walls. An aerofoil is placed at zero incidence midway between the slotted walls. The cross-flow, which is induced by the slots on the basic two-dimensional flow, is calculated accurately. This permits an averaged boundary condition to be obtained which is more accurate than those previously published. In the final section of the paper the wake and solid blockage caused by the slotted walls is calculated. Let the slots have a width 2σa and be spaced 2a apart and let the tunnel height be H. Then the theory yields the σ, 2a H relation for zero blockage without any limit on the ratio 2a H , which in earlier treatments is required to be small.