Related papers: Beyond Phasors: Solving Non-Sinusoidal Electrical …
Using the ``composite harmonic mapping method," we construct exact solutions for cylindrically symmetric gravitational and electromagnetic waves within the Einstein-Maxwell system, focusing on the conversion dynamics between these types of…
In this paper we show how to extend the known algorithm of nodal analysis in such a way that, in the case of circuits without nullors and controlled sources (but allowing for both, independent current and voltage sources), the system of…
We describe a geometric method to quantify wave patterns observed in the nervous system, which are non-stationary and with a mixture of spiral, target, plane and irregular waves. The method analyzes fluctuations of the energy angular…
The dynamics of a pair of three-dimensional matter-wave harmonic oscillators (HOs) coupled by a repulsive cubic nonlinearity is investigated through direct simulations of the respective GrossPitaevskii equations (GPEs) and with the help of…
This contribution investigates the connection between isogeometric analysis and integral equation methods for full-wave electromagnetic problems up to the low-frequency limit. The proposed spline-based integral equation method allows for an…
The Phasor diagrams have long been used in Physics and Engineering. In telecommunications, this is particularly useful to clarify how the modulations work. This paper addresses rotating phasor pathways derived from different standard…
In this short survey article, we showcase a number of non-trivial geometric problems that have recently been resolved by marrying methods from functional calculus and real-variable harmonic analysis. We give a brief description of these…
We propose a method, based on a Generalized Heisenberg Algebra (GHA), to reproduce the anharmonic spectrum of diatomic molecules. The theoretical spectrum generated by GHA allows us to fit the experimental data and to obtain the…
We investigate nonlinear, higher-order dispersive equations with measure (or even less regular) potentials and initial data with low regularity. Our approach is of distributional nature and relies on the phase space analysis (via Gabor wave…
A new numerical scheme to solve the Einstein field equations based upon the generalized harmonic decomposition of the Ricci tensor is introduced. The source functions driving the wave equations that define generalized harmonic coordinates…
Motivated by the first detection of gravitational waves, this dissertation develops analytical, numerical, and data analysis techniques to address persistent blind spots in our understanding of gravity. Beginning with asymptotically flat…
We develop a geometric approach to Poisson electrodynamics, that is, the semi-classical limit of noncommutative $U(1)$ gauge theory. Our framework is based on an integrating symplectic groupoid for the underlying Poisson brackets, which we…
Non-Abelian geometric phases form the foundation of fault-tolerant holonomic quantum computation. An "all-geometric" approach leveraging these phases enables robust unitary operations in condensed matter systems. Photonics, with rich…
Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization…
Solving the holography equation has long been a numerical task. While effective, the numeric approach has its own set of limitations. Relying solely on numerical approaches often obscures the intricate interplay and influence of the…
Analog layout synthesis requires some elements in the circuit netlist to be matched and placed symmetrically. However, the set of symmetries is very circuit-specific and a versatile algorithm, applicable to a broad variety of circuits, has…
This article surveys the noncommutative-geometric (NCG) approach to fundamental physics, in which geometry is encoded spectrally by a generalized Dirac operator and where dynamics arise from the spectral action. I review historically how…
This research thesis presents a novel higher-order spectral element method (SEM) formulated in cylindrical coordinates for analyzing electromagnetic fields in waveguides filled with complex anisotropic media. In this study, we consider a…
Time-frequency analysis, such as the Gabor transform, plays an important role in many signal processing applications. The redundancy of such representations is often directly related to the computational load of any algorithm operating in…
Non-Euclidean geometry has recently emerged as a powerful tool, offering new insights and applications in optical microcavities supporting Whispering Gallery Modes (WGMs). In this study, we extend the concept of polygonal microcavities to…