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A coupling approach is presented to combine a wave-based method to the standard finite element method. This coupling methodology is presented here for the Helmholtz equation but it can be applied to a wide range of wave propagation…
This chapter gives a self-contained review of the how standard open quantum system Hamiltonians can be mapped analytically onto representations in which the environments appear as one dimensional harmonic chains with nearest neighbour…
We have studied the emergence of bound states in weakly deformed and/or heterogeneous waveguides, comparing the analytical predictions obtained using a recently developed perturbative method, with precise numerical results, for different…
The aim of this lecture is to consider a concrete problem, namely the identification of situations of invisibility in waveguides, to present techniques and tools that may be useful in various fields of applied mathematics. To be more…
In this paper, we study numerical homogenization methods based on integral equations. Our work is motivated by materials such as concrete, modeled as composites structured as randomly distributed inclusions imbedded in a matrix. We…
It is shown that by means of the approach based on the Quantum Hamilton-Jacobi equation, it is possible to modify the WKB expressions for the energy levels of quantum systems, when incorrect, obtaining exact WKB-like formulae. This extends…
Coupled waveguides are convenient at implementing useful optical transformations. In this letter, we investigate the uncertainty of transformation by two coupled waveguides that stems from the perturbations of waveguide's mode indices~---…
We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do {\it not} request special choices of bases.…
A new variational method for studying the equilibrium states of an interacting particles system has been proposed. The statistical description of the system is realized by means of a density matrix. This method is used for description of…
Orthogonal frequency division multiplexing (OFDM) has been recently recognized as inadequate to meet the increased requirements of the next generation of communication systems. A number of alternative modulation solutions, based on the use…
The numerical complex coupled-mode method used in a metal thin-film optic element is applied to a planar multilayer optical waveguide. All modes are required to satisfy Helmholtz Vectorial equation in an optical waveguide including bound…
The generation of optical frequency combs via direct electrical pumping of semiconductor lasers is an attractive alternative to the well-established mode-locked laser sources in terms of compactness, robustness and integrability. However,…
This article discusses a useful tool in dimensionality reduction and low-rank matrix approximation called the CUR decomposition. Various viewpoints of this method in the literature are synergized and are compared and contrasted; included in…
Sequence classification has numerous applications in various fields. Despite extensive studies in the last decades, many challenges still exist, particularly in pattern-based methods. Existing pattern-based methods measure the…
In this thesis, we develop WKB techniques for the finite difference Schrodinger equation, following the construction of the WKB approach for the standard differential Schrodinger equation. In particular, we will develop an all-order WKB…
Coplanar waveguide resonators are central to the thriving field of circuit quantum electrodynamics. Recently, we have demonstrated the generation of a broadband microwave-frequency comb spectrum using a superconducting quantum interference…
The Wave Based Method (WBM) is a Trefftz method for the simulation of wave problems in vibroacoustics. Like other Trefftz methods, it employs a non-standard discretisation basis consisting of solutions of the partial differential equation…
A unified homogenization procedure for split ring metamaterials taking into account time and spatial dispersion is introduced. The procedure is based on two coupled systems of equations. The first one comes from an approximation of the…
The scope of this paper is to compare two different approaches for solving the Wheeler-DeWitt (WDW) equation in the presence of homogeneous matter (inflaton) and perturbations around it. The standard Born-Oppenheimer (BO) decomposition,…
We have designed and fabricated superconducting coplanar waveguide resonators with fundamental frequencies from 2 to $9 \rm{GHz}$ and loaded quality factors ranging from a few hundreds to a several hundred thousands reached at temperatures…