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The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
Employing the phase-space representation of second order ordinary differential equations we developed a method to find the eigenvalues and eigenfunctions of the 1-dimensional time independent Schr\"odinger equation for quantum model…
Key properties of physical systems can be described by the eigenvalues of matrices that represent the system. Computational algorithms that determine the eigenvalues of these matrices exist, but they generally suffer from a loss of…
We investigate the quasinormal modes of a massless scalar field on an effective rotating loop quantum black hole background, constructed from a covariant spherical model via an improved Newman-Janis algorithm. Using the continued fraction…
We report on recent extensions and improvements to the Legolas code, which is an open-source, finite element-based numerical framework to solve the linearised (magneto)hydrodynamic equations for a three-dimensional force- and thermally…
We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…
In this work we investigate a binned version of Quantum Phase Estimation (QPE) set out by [Somma 2019] and known as the Quantum Eigenvalue Estimation Problem (QEEP). Specifically, we determine whether the circuit decomposition techniques we…
The perturbations of the Kerr metric and the miracle of their exact solutions play a critical role in the comparison of predictions of general relativity with astrophysical observations of compact massive objects. The differential equations…
This paper presents a novel approach for computing substructure characteristic modes. This method leverages electromagnetic scattering matrices and spherical wave expansion to directly decompose electromagnetic fields. Unlike conventional…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
In this paper, a new rigorous numerical method to compute fundamental matrix solutions of non-autonomous linear differential equations with periodic coefficients is introduced. Decomposing the fundamental matrix solutions $\Phi(t)$ by their…
Quantum subspace methods (QSMs) are a class of quantum computing algorithms where the time-independent Schrodinger equation for a quantum system is projected onto a subspace of the underlying Hilbert space. This projection transforms the…
Over short time intervals planetary ephemerides have been traditionally represented in analytical form as finite sums of periodic terms or sums of Poisson terms that are periodic terms with polynomial amplitudes. Nevertheless, this…
Reliable and efficient computation of the pseudospectral abscissa in the large-scale setting is still not settled. Unlike the small-scale setting where there are globally convergent criss-cross algorithms, all algorithms in the large-scale…
The Physalis method is suitable for the simulation of flows with suspended spherical particles. It differs from standard immersed boundary methods due to the use of a local spectral representation of the solution in the neighborhood of each…
We investigate quasinormal modes (QNMs) of scalar, electromagnetic, and axial gravitational perturbations in slowly rotating Kalb-Ramond (KR) black holes, where an antisymmetric tensor field induces spontaneous Lorentz symmetry breaking.…
We provide an analytical approximation to the dynamics in each of the three most important low order secondary resonances (1:1, 2:1, and 3:1) bifurcating from the synchronous primary resonance in the gravitational spin-orbit problem. To…
Quantum phase estimation is the workhorse behind any quantum algorithm and a promising method for determining ground state energies of strongly correlated quantum systems. Low-cost quantum phase estimation techniques make use of circuits…
A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…
We report a self-consistent quasinormal mode theory for nanometer scale electromagnetism where the possible nonlocal and quantum effects are treated through quantum surface responses. With Feibelman's frequency-dependent \textit{d}…