10 research outputs found
Antenna Q and stored energy expressed in the fields, currents, and input impedance
Although the stored energy of an antenna is instrumental in the evaluation of antenna Q and the associated physical bounds, it is difficult to strictly define stored energy. Classically, the stored energy is either determined from the input impedance of the antenna or the electromagnetic fields around the antenna. The new energy expressions proposed by Vandenbosch express the stored energy in the current densities in the antenna structure. These expressions are equal to the stored energy defined from the difference between the energy density and the far field energy for many but not all cases. Here, the different approaches to determine the stored energy are compared for dipole, loop, inverted L-antennas, and bow-tie antennas. We use Brune synthesized circuit models to determine the stored energy from the input impedance. We also compare the results with differentiation of the input impedance and the obtained bandwidth. The results indicate that the stored energy in the fields, currents, and circuit models agree well for small antennas. For higher frequencies, the stored energy expressed in the currents agrees with the stored energy determined from Brune synthesized circuit models whereas the stored energy approximated by differentiation of input impedance gives a lower value for some cases. The corresponding results for the bandwidth suggest that the inverse proportionality between the fractional bandwidth and Q-factor depends on the threshold level of the reflection coefficient
Asymptotic wave-splitting in anisotropic linear acoustics
Linear acoustic wave-splitting is an often used tool in describing sound-wave
propagation through earth's subsurface. Earth's subsurface is in general
anisotropic due to the presence of water-filled porous rocks. Due to the
complexity and the implicitness of the wave-splitting solutions in anisotropic
media, wave-splitting in seismic experiments is often modeled as isotropic.
With the present paper, we have derived a simple wave-splitting procedure for
an instantaneously reacting anisotropic media that includes spatial variation
in depth, yielding both a traditional (approximate) and a `true amplitude'
wave-field decomposition. One of the main advantages of the method presented
here is that it gives an explicit asymptotic representation of the linear
acoustic-admittance operator to all orders of smoothness for the smooth,
positive definite anisotropic material parameters considered here. Once the
admittance operator is known we obtain an explicit asymptotic wave-splitting
solution.Comment: 20 page
Solitary Wave Dynamics in an External Potential
We study the behavior of solitary-wave solutions of some generalized
nonlinear Schr\"odinger equations with an external potential. The equations
have the feature that in the absence of the external potential, they have
solutions describing inertial motions of stable solitary waves.
We construct solutions of the equations with a non-vanishing external
potential corresponding to initial conditions close to one of these solitary
wave solutions and show that, over a large interval of time, they describe a
solitary wave whose center of mass motion is a solution of Newton's equations
of motion for a point particle in the given external potential, up to small
corrections corresponding to radiation damping.Comment: latex2e, 41 pages, 1 figur
Nonlinear coherent states and Ehrenfest time for Schrodinger equation
We consider the propagation of wave packets for the nonlinear Schrodinger
equation, in the semi-classical limit. We establish the existence of a critical
size for the initial data, in terms of the Planck constant: if the initial data
are too small, the nonlinearity is negligible up to the Ehrenfest time. If the
initial data have the critical size, then at leading order the wave function
propagates like a coherent state whose envelope is given by a nonlinear
equation, up to a time of the same order as the Ehrenfest time. We also prove a
nonlinear superposition principle for these nonlinear wave packets.Comment: 27 page
Limitations on the effective area and bandwidth product for Array Antennas
An upper bound on the effective area and bandwidth product for linearly polarized array antennas is derived. The bound is based on the forward scattering sum rule that relates the antenna properties with the polarizability of the antenna structure. The results are illustrated for a dipole array and a capacitively loaded dipole array with numerical simulations
Physical bounds on the partial realized gain
An antenna identity, derived from the forward scattering sum rule, shows that the partial realized gain of an antenna is related to the polarizability of the antenna structure. The partial realized gain contains the mismatch, directivity, efficiency, and polarization properties of the antenna. The antenna identity expresses how the performance depends on the electrical size and shape of the antenna structure. It is also the starting point for several antenna bounds. In this paper, the identity, its associated physical bounds, and computational aspects of the polarizability dyadics are discussed
Freezing of Energy of a Soliton in an External Potential
In this paper we study the dynamics of a soliton in the generalized NLS with a small external potential \u3f5V of Schwartz class. We prove that there exists an effective mechanical system describing the dynamics of the soliton and that, for any positive integer r, the energy of such a mechanical system is almost conserved up to times of order \u3f5 12r. In the rotational invariant case we deduce that the true orbit of the soliton remains close to the mechanical one up to times of order \u3f5 12r