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The concept of nonradiative dielectric resonator is generalized in order to include axially open configurations having rotational invariance. The resulting additional nonradiative conditions are established for the different resonance modes…
Time-domain wave scattering in an unbounded two-dimensional acoustic medium by sound-hard scatterers is considered. Two canonical geometries, namely a split-ring resonator (SRR) and an array of cylinders, are used to highlight the theory,…
Incomplete multi-view clustering presents significant challenges due to missing views. Although many existing graph-based methods aim to recover missing instances or complete similarity matrices with promising results, they still face…
The stochastic series expansion (SSE) algorithm is one of the most powerful quantum Monte Carlo methods and has been extensively applied to the study of quantum many body systems. Its efficiency is particularly enhanced with a deterministic…
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…
The asymptotic completeness of a set of the eigenmodes of an open system with increasing number of modes enables an accurate calculation of the system response in terms of these modes. Using the exact eigenmodes, such completeness is…
Deregulation of energy markets, penetration of renewables, advanced metering capabilities, and the urge for situational awareness, all call for system-wide power system state estimation (PSSE). Implementing a centralized estimator though is…
We study truncations of hierarchical equations of motion (HEOM) for finite-dimensional open quantum systems. We prove that for finite-dimensional approximations constructed with a Schur-complement type of terminator, the spectrum converges…
3D fragment reassembly aims to recover the rigid poses of unordered fragment point clouds or meshes in a common object coordinate system to reconstruct the complete shape. The problem becomes particularly challenging as the number of…
We investigate the effectiveness of the stabilizer R\'enyi entropy (SRE), a quantifier associated with non-stabilizer resources (quantum magic), as an indicator of quantum phase transitions. Specifically, we analyze the behavior of the…
The idea of the modal expansion in electromagnetics is derived from the research on electromagnetic resonators, which play an essential role in developments in nanophotonics. All of the electromagnetic resonators share a common property:…
Recent advances in nanophotonics have demonstrated that various optical resonances in nanostructures can achieve strong field confinement with substantially suppressed scattering. This study investigates the optical Kerr effect (OKE)…
Spectral element methods (SEM), which are extensions of finite element methods (FEM), are important emerging techniques for solving partial differential equations in physics and engineering. SEM can potentially deliver better accuracy due…
Sextic oscillator in D dimensions is considered as a typical quasi-exactly solvable (QES) model. Usually, its QES N-plets of bound states have to be computed using the coupled Magyari's nonlinear algebraic equations. We propose and describe…
With the discovery of gravitational waves and fast radio bursts, wave optics has become increasingly relevant in astrophysics. This paper studies the behaviour of random gravitational and plasma lenses, presenting the refractive and…
This paper introduces an accurate edge-based smoothed finite element method (ES-FEM) for electromagnetic analysis for both two dimensional cylindrical and three dimensional cartesian systems, which shows much better performance in terms of…
The Stochastic Series Expansion method (SSE) is a Quantum Monte Carlo (QMC) technique working directly in the imaginary time continuum and thus avoiding "Trotter discretization" errors. Using a non-local "operator-loop update" it allows…
Partial Differential Equations (PDEs) describe phenomena ranging from turbulence and epidemics to quantum mechanics and financial markets. Despite recent advances in computational science, solving such PDEs for real-world applications…
Frequency domain Mie solutions to scattering from spheres have been used for a long time. However, deriving their transient analogue is a challenge as it involves an inverse Fourier transform of the spherical Hankel functions (and their…
Reconfigurable intelligent surface (RIS) devices have emerged as an effective way to control the propagation channels for enhancing the end-users' performance. However, RIS optimization involves configuring the radio frequency response of a…