Related papers: Counterexamples to the sonic criterion
We establish the existence and stability of cylindrical transonic shock solutions under three dimensional perturbations of the incoming flows and the exit pressure without any further restrictions on the background transonic shock…
The existence and stability of a spherical transonic shock in a hemispherical shell under the three dimensional perturbations of the incoming flows and the exit pressure is established without any further restrictions on the background…
A method is described for the determination of the effective electromagnetic parameters of a metamaterial based only on external measurements or simulations, taking boundary effects at the interfaces between a conventional material and…
In this paper, we first investigate the mathematical aspects of supersonic flow of a Chaplygin gas past a conical wing with diamond-shaped cross sections in the case of a shock wave detached from the leading edges. The flow under…
We discuss the reflection of light by a rheoscopic fluid (a suspension of microscopic rod-like crystals) in a steady two-dimensional flow. This is determined by an order parameter which is a non-oriented vector, obtained by averaging…
The phenomena of self-sustained shock wave oscillations over conical bodies with a blunt axisymmetric base subject to uniform high-speed flow are investigated in a hypersonic wind tunnel at Mach number $M = 6$. The flow and shock wave…
We consider the long-time behavior of irrotational solutions of the three-dimensional compressible Euler equations with shocks, hypersurfaces of discontinuity across which the Rankine-Hugoniot conditions for irrotational flow hold. Our…
We develop a general framework for the identification of counterfactual parameters in a class of nonlinear semiparametric panel models with fixed effects and time effects. Our method applies to models for discrete outcomes (e.g., two-way…
We establish the existence and stability of the transonic shock solution to three-dimensional axisymmetric Euler system with an external force in a cylinder under perturbations of the incoming supersonic flow, the exit pressure, the…
We consider reflection of the first and the second sound waves by a rigid flat wall in superfluid. Nontrivial dependence of the reflection coefficients on the angle of incidence is obtained. Sound conversion is predicted at slanted…
We consider reflection of electromagnetic waves from layered structures with various dielectric and magnetic properties, including metamaterials. Assuming periodic variations in the permittivity, we find that the reflection is in general…
We study a 2D scalar harmonic wave transmission problem between a classical dielectric and a medium with a real-valued negative permittivity/permeability which models a metal at optical frequency or an ideal negative metamaterial. We…
We establish existence, uniqueness and stability of transonic shocks for steady compressible non-isentropic potential flow system in a multidimensional divergent nozzle with an arbitrary smooth cross-section, for a prescribed exit pressure.…
We consider linear and nonlinear waves in a stratified hydrostatic fluid within a channel of variable area, under the restriction of one-dimensional flow. We derive a modified version of Riemann's invariant that is related to the wave…
In a prior paper, the author described an instability in a nonlinear wavefunction model. Proposed in connection with the Measurement Problem, the model contained an external potential creating a ``classical'' instability. However, it is…
We develop a new approach and employ it to establish the global existence and nonlinear structural stability of attached weak transonic shocks in steady potential flow past three-dimensional wedges; in particular, the restriction that the…
We prove the existence of ``pure tone'' nonlinear sound waves of all frequencies. These are smooth, space and time periodic, oscillatory solutions of the $3\times3$ compressible Euler equations in one space dimension. Being perturbations of…
In this paper, we consider inverse time-harmonic acoustic and electromagnetic scattering from locally perturbed rough surfaces in three dimensions. The scattering interface is supposed to be the graph of a Lipschitz continuous function with…
It has recently been shown that periodic layered media can reflect strongly for all incident angles and polarizations in a given frequency range. The standard treatment gets these band gaps from an eigenvalue equation for the Bloch factor…
In this paper, we rigorously prove the existence of self-similar converging shock wave solutions for the non-isentropic Euler equations for $\gamma\in (1,3]$. These solutions are analytic away from the shock interface before collapse, and…