B. L. G. Jonsson

Solitary Wave Dynamics in an External Potential

We study the behavior of solitary-wave solutions of some generalized nonlinear Schrödinger 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 consider 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.

Physical Bounds and Optimal Currents on Antennas

Physical bounds on the directivity Q-factor quotient and optimal current distributions are determined for antennas of arbitrary shape and size using an optimization formulation. A variational approach offers closed form solutions for small antennas expressed in the polarizability of the antenna structure. Finite sized antennas are solved using Lagrangian parameters in a method of moments formulation. It is also shown that the optimal charge density for a small antenna can be generated by several current densities. Numerical examples for small and large antennas are used to illustrate the results.

Stored Electromagnetic Energy and Antenna Q

Decomposition of the electromagnetic energy into its stored and radiated parts is instrumental in the evaluation of antenna Q and the corresponding fundamental limitations on antennas. This decomposition is not unique and there are several proposals in the literature. Here, it is shown that stored energy defined from the difference between the energy density and the far field energy equals the energy expressions proposed by Vandenbosch for many but not all cases. This also explains the observed cases with negative stored energy and suggests a possible remedy to them. The results are compared with the classical explicit expressions for spherical regions where the results only differ by the electrical size ka that is interpreted as the far-field energy in the interior of the sphere.

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.

A Circularly Polarized Cylindrical Dielectric Resonator Antenna Using a Helical Exciter

A novel circularly polarized cylindrical dielectric resonator antenna excited by an external tape helix is presented. The helix is fed by a coaxial line through a small hole on a finite size ground plane. The configuration offers a compact and easy to fabricate feeding network providing a 3 dB axial-ratio bandwidth of 6.4%. A prototype of the proposed configuration is fabricated and measured. Measured and simulated return loss, axial-ratio, radiation pattern, and realized gain are presented and discussed together with design guidelines.

Effective dynamics for boson stars

We study solutions close to solitary waves of the pseudo-relativistic Hartree equation describing boson stars under the influence of an external gravitational field. In particular, we analyse the long-time effective dynamics of such solutions. In essence, we establish a (long-time) stability result for solutions describing boson stars that move under the influence of an external gravitational field. The proof of our main result tackles difficulties that are absent when deriving similar results on effective solitary wave motions for nonlinear Schrodinger equations or nonlinear wave equations. This is due to the fact that the pseudo-relativisitic Hartree equation does not exhibit Galilean or Lorentz covariance.

Array Antenna Limitations

This letter defines a physical-bound-based array figure of merit for both single and multiband array antennas. It provides a measure to compare their performance with respect to return loss, bandwidth(s), thickness of the array over the ground plane, and scan range. The result is based on a sum-rule result of Rozanov-type for linear polarization. For single-band antennas, it extends an existing limit for a given fixed scan-angle to include the whole scan range of the array, as well as the unit-cell structure in the bound. The letter ends with an investigation of the array figure of merit for some wideband and/or wide-scan antennas with linear polarization. We find arrays with a figure of merit >0.6 that empirically defines high-performance antennas with respect to this measure.

A Helix Excited Circularly Polarized Hollow Cylindrical Dielectric Resonator Antenna

In this letter, we use a helix to excite two orthogonal HE11δ modes in phase quadrature in a hollow cylindrical dielectric resonator antenna to generate circular polarization. As compared to our previous work, it is shown that replacing the cylindrical dielectric resonator antenna with a hollow cylindrical-shaped one leads to a significant enhancement in the 3-dB axial-ratio bandwidth. A design guideline is provided, and three design cases are presented. A prototype for one of the designs is fabricated and measured. Measured and simulated data are presented and discussed. It is shown that the 3-dB axial-ratio bandwidth increases as the wall thickness of the hollow cylindrical dielectric resonator decreases. Furthermore, a reduction in the wall thickness requires a longer helix exciter for similar performance .

Communication: Band bending at the interface in polyethylene-MgO nanocomposite dielectric

Polymer nanocomposite dielectrics are promising materials for electrical insulation in high voltage applications. However, the physics behind their performance is not yet fully understood. We use density functional theory to investigate the electronic properties of the interfacial area in magnesium oxide-polyethylene nanocomposite. Our results demonstrate polyethylene conduction band matching with conduction bands of different surfaces of magnesium oxide. Such band bending results in long range potential wells of up to 2.6 eV deep. Furthermore, the fundamental influence of silicon treatment on magnesium oxide surface properties is assessed. We report a reduction of the surface-induced states at the silicon-treated interface. The simulations provide information used to propose a new model for charge trapping in nanocomposite dielectrics.

Long-time dynamics of variable coefficient modified Korteweg-de Vries solitary waves

We study the long-time behavior of solutions to the Korteweg-de Vries-type equation partial derivative(t)u=-partial derivative(x)(partial derivative(2)(x)u+f(u)-b(t,x)u), with initial conditions cl ...