Related papers: cPCWE -- Perturbed Convective Wave Equation based …
In this paper we present new results on the preservation of polynomial stability of damped wave equations under addition of perturbing terms. We in particular introduce sufficient conditions for the stability of perturbed two-dimensional…
We consider an undetermined coefficient inverse problem for a nonlinear partial differential equation describing high intensity ultrasound propagation as widely used in medical imaging and therapy. The usual nonlinear term in the standard…
The perturbation equation for aeroacoustics has been derived in a dissipative medium from the linearized compressible Navier-Stokes equation without any assumption, by expressing the same in spectral plane as in Continuum perturbation field…
The problem of recovering acoustic sources, more specifically monopoles, from point-wise measurements of the corresponding acoustic pressure at a limited number of frequencies is addressed. To this purpose, a family of sparse optimization…
Deterministic neural operators perform well on many PDEs but can struggle with the approximation of high-frequency wave phenomena, where strong input-to-output sensitivity makes operator learning challenging, and spectral bias blurs…
Fluid equations are nonlinear, dissipative, and non-Hamiltonian, which makes their relation to Schr\"odinger evolution and quantum algorithms nontrivial. We derive an exact Eulerian Cole-Hopf-type reformulation of isothermal compressible…
We consider an inverse problem for the compressible Euler's equations in polytropic fluid. We show that by taking active measurements near a particle trajectory one can determine the background flow in a set where pressure waves can…
Here, the acoustic equation for a lossy medium is derived from the first principle from the linearized compressible Navier-Stokes equation without Stokes' hypothesis. The dispersion relation of the governing equation is obtained, which…
Flow-based models are powerful tools for designing probabilistic models with tractable density. This paper introduces Convex Potential Flows (CP-Flow), a natural and efficient parameterization of invertible models inspired by the optimal…
In this paper we propose a {\it discontinuous} plane wave neural network (DPWNN) method with $hp-$refinement for approximately solving Helmholtz equation and time-harmonic Maxwell equations. In this method, we define a quadratic functional…
The scattering and transmission of harmonic acoustic waves at a penetrable material are commonly modelled by a set of Helmholtz equations. This system of partial differential equations can be rewritten into boundary integral equations…
Wave functions and energies are constructed in a short-range Poeschl-Teller well (= negative quadratic secans hyperbolicus) with a quartic perturbation. Within the framework of an innovated, Lanczos-inspired perturbation theory we show that…
We study acoustic wave propagation in a uniform stationary flow. We develop a method founded on the Lorentz transform and a hypothesis of irrotationality of the acoustic perturbation. After a transformation of the space-time and of the…
Particle methods play an important role in computational fluid dynamics, but they are among the most difficult to implement and solve. The most common method is smoothed particle hydrodynamics, which is suitable for problem settings that…
Here, the perturbation equation for a dissipative medium is derived from the first principle from the linearized compressible Navier-Stokes equation without Stokes's hypothesis. The dispersion relations of this generic governing equation…
We present Helmholtz or Helmholtz like equations for the approximation of the time-harmonic wave propagation in gases with small viscosity, which are completed with local boundary conditions on rigid walls. We derived approximative models…
Charge density wave (CDW) is a widely concerned emergent phenomenon in condensed matter physics. To establish a systematic understanding of CDW, we develop a diagrammatic self-consistent-field approach for cubic Holstein model employing…
We predict the development and propagation of the fluctuations in a perturbed ideally-expanded air jet. A non-propagating harmonic perturbation in the density, axial velocity, and pressure is introduced at the inflow with different…
Supersonic pre-transitional boundary layers flowing over porous flat and concave surfaces are studied using numerical and asymptotic methods. The porous wall is composed of thin equally-spaced cylindrical microcavities. The flow is…
We present a formal derivation of a simplified version of Compressible Primitive Equations (CPEs) for atmosphere modeling. They are obtained from $3$-D compressible Navier-Stokes equations with an \emph{anisotropic viscous stress tensor}…