Related papers: Harmonic Balance for Differential Constitutive Mod…
The dynamics of a one-degree of freedom oscillator with arbitrary polynomial non-linearity subjected to an external periodic excitation is studied. The sequences (cascades) of harmonic and subharmonic stationary solutions to the equation of…
High harmonic generation (HHG) in solids has emerged as a powerful spectroscopic method for resolving ultrafast electron dynamics and band structure properties across a wide range of materials. However, quantitative HHG studies require…
Bayesian estimation is a vital tool in robotics as it allows systems to update the robot state belief using incomplete information from noisy sensors. To render the state estimation problem tractable, many systems assume that the motion and…
We investigate the perturbation dynamics in a supersonic shear layer using a combination of large-eddy simulations (LES) and linear-operator-based input-output analysis. The flow consists of two streams-a main stream (Mach 1.23) and a…
We report a hybrid numerical method for the solution of the model H fluctuating hydrodynamic equations for binary mixtures. The momentum conservation equations with Landau-Lifshitz stresses are solved using the fluctuating lattice Boltzmann…
The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…
We, herein, present a new model based on the framework of synchronization to describe a thermoacoustic system and capture the multiple bifurcations that such a system undergoes. Instead of applying flame describing function to depict the…
A nonlinear algebraic equation system of 5 variables is numerically solved, which is derived from the application of the Fourier transform to a differential equation system that allows modeling the behavior of the temperatures and the…
We propose a new spectral Lagrangian based deterministic solver for the non-linear Boltzmann Transport Equation for Variable Hard Potential (VHP) collision kernels with conservative or non-conservative binary interactions. The method is…
We rederive from first principles and generalize the theoretical framework of the nonlinear Gaussian noise model to the case of coherent optical systems with multiple fiber types per span and ideal Nyquist spectra. We focus on the accurate…
Here, we provide a unified framework for numerical analysis of stochastic nonlinear fractional diffusion equation driven by fractional Gaussian noise with Hurst index $H\in(0,1)$. A novel estimate of the second moment of the stochastic…
The flux reconstruction (FR) approach offers a flexible framework for describing a range of high-order numerical schemes; including nodal discontinuous Galerkin and spectral difference schemes. This is accomplished through the use of…
A global solution of the Schr\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is…
The rapid rise in inverter-based renewable resources has heightened concerns over subsynchronous resonance and oscillations, thereby challenging grid stability. This paper reviews approaches to identify and mitigate these issues, focusing…
This article investigates how a uniform high frequency (HF) drive applied to each site of a weakly-coupled discrete nonlinear resonator array can modulate the onsite natural stiffness and damping and thereby facilitate the active tunability…
The addition of suitable volume forces to the Navier-Stokes equation allows to simulate flows in the presence of a homogeneous shear. Because of the explicit form of the driving the flows are accessible to rigorous mathematical treatment…
The development of physical simulators, called Ising machines, that sample from low energy states of the Ising Hamiltonian has the potential to drastically transform our ability to understand and control complex systems. However, most of…
In this report, a novel methodology based on the static coherent states approach is introduced with the capability of calculating various strong-field laser-induced nonlinearities in full dimensional single-electron molecular systems; an…
Harmonic analysis has provided powerful tools to accurately determine the tune from turn-by-turn data originating from numerical simulations or beam measurements in circular accelerators and storage rings. Methods that have been developed…
The partitioned approach for the numerical integration of power system differential algebraic equations faces inherent numerical stability challenges due to delays between the computation of state and algebraic variables. Such delays can…