Parametric Analysis of Linear Periodic Arrays Generating Flat-Top Beams

Several synthesis techniques are available to optimize amplitude and phase excitations of periodic linear arrays to generate flat-top beams. Clearly, the optimal tapering depends on design parameters such as the array length, the number of array elements, the beam flatness, the beam width, the side lobe levels, and others. In this paper, in order to derive useful guidelines and rule of thumb for the synthesis of periodic array antennas, relations between these parameters are derived employing linear programming techniques, which guarantee optimality of the solutions. Such relations are then plotted and used in some design examples.

Linear optical properties of a linear chain of interacting gold nanoparticles

In a Drude-like model for the conduction electrons of Metal Nanoparticles (MNPs) in a periodic linear chain, considering dipole-dipole interactions of adjacent particles, an analytical expression is derived for each particle permittivity for two different polarizations of incident light: parallel with and perpendicular to the chain line. A numerical analysis is carried out for a chain including 10 identical gold Nanoparticles (NPs) for two different sizes of NPs and two different host media of air and glass. It is shown that in the parallel case of polarization, interaction of NPs leads to a substantial increase in the extinction cross section and the red-shift of the Surface Plasmon Resonance (SPR) wavelength. In comparison with the linear properties of a single NP, the second and penultimate particles have the most increase in the extinction cross section and SPR wavelength displacement while the first and last particles experience the least variations due to the mutual interactions. For the perpendicular polarization, inversely, the dipolar coupling causes the decrease in extinction cross section of all particles and the blue-shift of SPR wavelength. For the parallel polarization, the absolute values of the real and imaginary parts of complex permittivity of each MNP decrease in comparison with the single particle case while they increase for the perpendicular state of polarization.

Dispersive fractalisation in linear and nonlinear Fermi–Pasta–Ulam–Tsingou lattices

We investigate, both analytically and numerically, dispersive fractalisation and quantisation of solutions to periodic linear and nonlinear Fermi–Pasta–Ulam–Tsingou systems. When subject to periodic boundary conditions and discontinuous initial conditions, e.g., a step function, both the linearised and nonlinear continuum models for FPUT exhibit fractal solution profiles at irrational times (as determined by the coefficients and the length of the interval) and quantised profiles (piecewise constant or perturbations thereof) at rational times. We observe a similar effect in the linearised FPUT chain at times t where these models have validity, namely t = O(h−2), where h is proportional to the intermass spacing or, equivalently, the reciprocal of the number of masses. For nonlinear periodic FPUT systems, our numerical results suggest a somewhat similar behaviour in the presence of small nonlinearities, which disappears as the nonlinear force increases in magnitude. However, these phenomena are manifested on very long time intervals, posing a severe challenge for numerical integration as the number of masses increases. Even with the high-order splitting methods used here, our numerical investigations are limited to nonlinear FPUT chains with a smaller number of masses than would be needed to resolve this question unambiguously.

Computational insights into the calcium ions role in protein-glycosaminoglycan systems

Glycosaminoglycans (GAGs) are anionic periodic, linear polysaccharides which are composed of periodic disaccharide units. They play a vital role in many biological processes ongoing in the extracellular matrix. In terms...