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We present an analytic theory unraveling the microscopic mechanism of instabilities within interacting $D$-dimensional Fermi liquid. Our model consists of a $D$-dimensional electron gas subject to an instantaneous electron-electron…
Physics Informed Neural Networks (PINNs) often exhibit failure modes in which the PDE residual loss converges while the solution error stays large, a phenomenon traditionally blamed on local optima separated from the true solution by steep…
Functionally graded materials (FGMs) are two-phase composites with continuously changing microstructure adapted to performance requirements. Traditionally, the overall behavior of FGMs has been determined using local averaging techniques or…
In this paper, we show that the quasi-one-dimensional flow of an ideal inviscid fluid in a corrugated pipe is parametrically unstable in certain frequency bands. First-order perturbation theory is used to analyze the stability of the flow,…
Instabilities are common phenomena frequently observed in nature, sometimes leading to unexpected catastrophes and disasters in seemingly normal conditions. The simplest form of instability in a distributed system is its response to a…
We investigate the nontrivial characteristics of modulational instability (MI) in a system of Bragg gratings with saturable nonlinearity. We also introduce an equal amount of gain and loss into the existing system which gives rise to an…
The proportional-integral-derivative (PID) controller and its variants are widely used in control engineering, but they often rely on linearization around equilibrium points and empirical parameter tuning, making them ineffective for…
In order to perform physically faithful particle-in-cell (PIC) simulations, the Gauss's law stands as a critical requirement, since its violation often leads to catastrophic errors in long-term plasma simulations. This work proposes a novel…
The pseudo-spectral analytical time-domain (PSATD) particle-in-cell (PIC) algorithm solves the vacuum Maxwell's equations exactly, has no Courant time-step limit (as conventionally defined), and offers substantial flexibility in plasma and…
The effects of noise in particle-in-cell (PIC) and Vlasov simulations of the Buneman instability in unmagnetized plasmas are studied. It is found that, in the regime of low drift velocity, the linear stage of the instability in PIC…
We explore the possibilities of applying structure-preserving numerical methods to a plasma hybrid model with kinetic ions and mass-less fluid electrons satisfying the quasi-neutrality relation. The numerical schemes are derived by finite…
Particle-in-cell (PIC) simulations are essential for studying kinetic plasma processes, but they often suffer from statistical noise, especially in plasmas with fast flows. We have also found that the typical central difference scheme used…
We study the spatio-temporal instability generated by a universal unstable attractor in normal dispersion graded-index multimode fiber (GRIN MMF) for femtosecond pulses. Our results present the generation of geometric parametric instability…
Across many plasma applications, the underlying phenomena and interactions among the involved processes are known to exhibit three-dimensional characteristics. Furthermore, the global properties and evolution of plasma systems are often…
This study investigates the streaming instability triggered by ion motion in a plasma system that is finite in length, collisionless, and inhomogeneous. Employing numerical simulations using Particle-In-Cell (PIC) techniques and kinetic…
Explicit structure-preserving geometric Particle-in-Cell (PIC) algorithm in curvilinear orthogonal coordinate systems is developed. The work reported represents a further development of the structure-preserving geometric PIC algorithm…
The rapid development of AI highlights the pressing need for sustainable energy, a critical global challenge for decades. Nuclear fusion, generally seen as an ultimate solution, has been the focus of intensive research for nearly a century,…
The problem of existence and stability of equilibria of DC microgirds with constant power loads methods is addressed in this paper. Constant power loads (CPLs) often cause instability due to its negative impedance characteristics. What is…
Since the classical proportional-integral-derivative (PID) controller has continued to be the most widely used feedback methods in engineering systems by far, it is crucial to investigate the working mechanism of PID in dealing with…
In the presence of strong electronic interactions, a partially filled Chern band may stabilize a fractional Chern insulator (FCI) state, the zero-field analog of the fractional quantum Hall phase. While FCIs have long been hypothesized,…