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We introduce and study a class of models of free fermions hopping between neighbouring sites with random Brownian amplitudes. These simple models describe stochastic, diffusive, quantum, unitary dynamics. We focus on periodic boundary…
A coupled hybridizable discontinuous Galerkin (HDG) and boundary integral (BI) method is proposed to efficiently analyze electromagnetic scattering from inhomogeneous/composite objects. The coupling between the HDG and the BI equations is…
A non-${\cal{PT}}$-symmetric Hamiltonian system of a Duffing oscillator coupled to an anti-damped oscillator with a variable angular frequency is shown to admit periodic solutions. The result implies that ${\cal{PT}}$-symmetry of a…
In this paper we develop a class of efficient Galerkin boundary element methods for the solution of two-dimensional exterior single-scattering problems. Our approach is based upon construction of Galerkin approximation spaces confined to…
The aim of this paper is to substantiate the importance of non-normality of shear flow linear operators and its consequence -- the non-modal dynamics of the perturbations -- in the formation of acoustic wave output of time-developing free…
Assessment of voice signals has long been performed with the assumption of periodicity as this facilitates analysis. Near periodicity of normal voice signals makes short-time harmonic modeling an appealing choice to extract vocal feature…
A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…
We propose homotopy analysis method in combination with Galerkin projections to approximate the natural response of non-smooth oscillators with discontinuities of type Heaviside, signum, modulus etc. While constructing the homotopy, we…
Utilizing spherical harmonic (SH) domain has been established as the default method of obtaining continuity over space in head-related transfer functions (HRTFs). This paper concerns different variants of extending this solution by…
Manipulating the dispersive characteristics of vibrational waves is beneficial for many applications, e.g., high-precision instruments. architected hierarchical phononic materials have sparked promise tunability of elastodynamic waves and…
Solving real-world nonlinear semiconductor device problems modeled by the drift-diffusion equations coupled with the Poisson equation (also known as the Poisson-Nernst-Planck equations) necessitates an accurate and efficient numerical…
We propose a novel method for the efficient and accurate iterative solution of frequency domain integral equations (IEs) that are used for large/multi-scale electromagnetic scattering problems. The proposed method uses a novel…
In this paper, we present the Stroboscopic Averaging Method (SAM), recently introduced in [7,8,10,12], which aims at numerically solving highly-oscillatory differential equations. More specifically, we first apply SAM to the Schr\"odinger…
Chaotic oscillators have gained significant attention in the research community because of their ability to reproduce and investigate the complex dynamics of real-world phenomena. Recent advances in the design of chaotic oscillator…
If the duration of the input pulse resonantly interacting with a system is comparable or smaller than the time required for the system to achieve the steady state, transient effects become important. For complex systems, a quantitative…
Many processes of scientific and technological interest are characterized by time scales that render their simulation impossible if one uses present day simulation capabilities. To overcome this challenge a variety of enhanced simulation…
We investigate the feasibility of modelling turbulence via numeric functional integration. By transforming the Burgers' equation into a functional integral we are able to calculate equal-time spatial correlation of system variables using…
The self-consistent procedure in electronic structure calculations is revisited using a highly efficient and robust algorithm for solving the non-linear eigenvector problem i.e. H({{\psi}}){\psi} = E{\psi}. This new scheme is derived from a…
For autoregressive modeling of chaotic dynamical systems over long time horizons, the stability of both training and inference is a major challenge in building scientific foundation models. We present a hybrid technique in which an…
This paper presents a robust fixed lag smoother for a class of nonlinear uncertain systems. A unified scheme, which combines a nonlinear robust estimator with a stable fixed lag smoother, is presented to improve the error covariance of the…