相关论文: Spectral Analysis and Hydrodynamic Manifolds for t…
We perform a complete spectral analysis of the linear three-dimensional Boltzmann BGK operator resulting in an explicit transcendental equation for the eigenvalues. Using the theory of finite-rank perturbations, we confirm the existence of…
We present the optimal hydrodynamic model for rarefied gas flows relative to a given kinetic model by combining the recent theory of slow spectral closure with machine learning techniques. We learn generalized transport coefficients from…
The accurate modeling of mode hybridization and calculation of radiative relaxation rates have been crucial to the design and optimization of superconducting quantum devices. In this work, we introduce a spectral theory for the…
We study the spectrum of the linearization around standing wave profiles for two quantum hydrodynamics systems with linear and nonlinear viscosity. The essential spectrum for such profiles is stable; we investigate the point spectrum using…
Within the relaxation time approximation under a constant mass profile, we investigate the collective dynamics of a system of massive relativistic particles described by the Maxwell-Boltzmann equilibrium distribution. We analytically derive…
We review the spectral analysis and the time-dependent approach of scattering theory for manifolds with asymptotically cylindrical ends. For the spectral analysis, higher order resolvent estimates are obtained via Mourre theory for both…
One manifestation of quantum chaos is a random-matrix-like fine-grained energy spectrum. Prior to the inverse level spacing time, random matrix theory predicts a `ramp' of increasing variance in the connected part of the spectral form…
We use the recent theory of Spectral Submanifolds (SSM) for model reduction of nonlinear mechanical systems subject to parametric excitations. Specifically, we develop expressions for higher-order nonautonomous terms in the parameterization…
We prove an explicit, non-local hydrodynamic closure for the linear one-dimensional kinetic equation independent on the size of the relaxation time. We compare this dynamical equation to the local approximations obtained from the…
Shakhov model is a relaxation approximation of the Boltzmann equation proposed to overcome the deficiency of the original BGK model, namely, the incorrect production of the Prandtl number. In this paper, we address the existence and the…
In this paper, we present a detailed analysis of normal modes based on the Boltzmann equation within the mutilated relaxation time approximation (RTA). Using this linearized effective kinetic description, our analysis encompasses a complete…
We present a linear analysis of inviscid, incompressible, magnetohydrodynamic (MHD) shallow water systems. In spherical geometry, a generic property of such systems is the existence of five wave modes. Three of them (two magneto-Poincare…
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…
We argue that the gravitational shock wave computation used to extract the scrambling rate in strongly coupled quantum theories with a holographic dual is directly related to probing the system's hydrodynamic sound modes. The information…
Linear stability of stratified two-phase flows in horizontal channels to arbitrary wavenumber disturbances is studied. The problem is reduced to Orr-Sommerfeld equations for the stream function disturbances, defined in each sublayer and…
We consider the linear water-wave problem in a periodic channel $\Pi^h \subset \mathbb{R}^3$, which is shallow except for a periodic array of deep potholes in it. Motivated by applications to surface wave propagation phenomena, we study the…
For many applications, critical information about system dynamics is encoded in associated eigenvalue problems that can be posed as linear Hamiltonian systems with suitable boundary conditions. Motivated by examples from hydrodynamics,…
This work investigates a three-dimensional slow-fast stochastic system with quadratic nonlinearity and additive noise, inspired by fluid dynamics. The deterministic counterpart exhibits a periodic orbit and a slow manifold. We demonstrate…
The normal mode model is one of the most popular approaches for solving underwater sound propagation problems. Among other methods, the finite difference method is widely used in classic normal mode programs. In many recent studies, the…
This paper focuses on the analysis of stratified steady periodic water waves that contain stagnation points. The initial step involves transforming the free-boundary problem into a quasilinear pseudodifferential equation through a conformal…