Asymptotic Properties of Solutions to the Cauchy Problem for Degenerate Parabolic Equations with Inhomogeneous Density on Manifolds

We consider the Cauchy problem for doubly nonlinear degenerate parabolic equations with inhomogeneous density on noncompact Riemannian manifolds. We give a qualitative classification of the behavior of the solutions of the problem depending on the behavior of the density function at infinity and the geometry of the manifold, which is described in terms of its isoperimetric function. We establish for the solutions properties as: stabilization of the solution to zero for large times, finite speed of propagation, universal bounds of the solution, blow up of the interface. Each one of these behaviors of course takes place in a suitable range of parameters, whose definition involves a universal geometrical characteristic function, depending both on the geometry of the manifold and on the asymptotics of the density at infinity.

Fatal outcome of SARS-CoV-2 infection (B1.1.7) in a 4-year-old child

This case report highlights details of a case of critical acute respiratory syndrome coronavirus type 2 (SARS-CoV-2) with B1.1.7 variant in a 4-year-old girl who died due to pneumonia and pulmonary hemorrhage. The girl was referred to our University ECMO Center from another University hospital for veno-arterial extracorporeal membrane oxygenation (VA-ECMO). In the clinical course, superinfection with Pseudomonas aeruginosa was detected. Virological evidence of herpes simplex sepsis was also obtained in blood samples on her day of death. Transcription polymerase chain reaction (PCR) confirmed SARS-CoV-2 infection in lung tissue. Postmortem computed tomography showed pulmonary hemorrhage with inhomogeneous density values in both lungs. Lung tissue showed no ventilated areas. Autopsy revealed a massively congested lung with evidence of acute respiratory distress syndrome (ARDS) and pneumonia with multiple abscesses. Histopathology showed a mixture of diffuse alveolar injury with hyaline membranes, massive hemorrhage, and bronchopneumonia with multiple granulocytic abscesses. Cardiac examination revealed pericarditis. Suspicion of myocarditis or myocardial infarction could not be confirmed microscopically. To our knowledge, this is the first autopsy-based case report of the death of a previously healthy child due to the new variant B 1.1.7 in Germany.

Granulomatous Mucormycosis of the Temporal Bone extending Into Temporomandibular Joint and Infratemporal Fossa: A Case Report

Mucormycosis of temporal bone is extremely rare. They are usually associated with host immunodeficiency, are difficult to diagnose, and many cases are fatal. We performed a literature review and found only 10 reported cases of temporal bone mucormycosis. We present a case of temporal bone mucormycosis involving the temporomandibular joint and infratemporal fossa in a 53-year-old woman with diabetes mellitus who presented with unbearable otalgia. Computed tomography and magnetic resonance imaging demonstrate inhomogeneous density mass in the parapharyngeal and retropharyngeal space accompanied with lytic bone destruction on the temporomandibular joint. After undergoing a biopsy of the left infratemporal fossa, the patient’s pathology exhibited fungal hyphae consistent with mucormycosis. To our knowledge, this is the first report of temporal bone mucormycosis with extensive involvement of temporomandibular joint and its adjacent structures, which exhibited no otologic or rhinologic signs. A definitive diagnosis is made by biopsy.

A numerical study of gravity-driven instability in strongly coupled dusty plasma. Part 1. Rayleigh–Taylor instability and buoyancy-driven instability

Rayleigh–Taylor (RT) and buoyancy-driven (BD) instabilities are driven by gravity in a fluid system with inhomogeneous density. The paper investigates these instabilities for a strongly coupled dusty plasma medium. This medium has been represented here in the framework of the generalized hydrodynamics (GHD) fluid model which treats it as a viscoelastic medium. The incompressible limit of the GHD model is considered here. The RT instability is explored both for gradual and sharp density gradients stratified against gravity. The BD instability is discussed by studying the evolution of a rising bubble (a localized low-density region) and a falling droplet (a localized high-density region) in the presence of gravity. Since both the rising bubble and falling droplet have symmetry in spatial distribution, we observe that a falling droplet process is equivalent to a rising bubble. We also find that both the gravity-driven instabilities get suppressed with increasing coupling strength of the medium. These observations have been illustrated analytically as well as by carrying out two-dimensional nonlinear simulations. Part 2 of this paper is planned to extend the present study of the individual evolution of a bubble and a droplet to their combined evolution in order to understand the interaction between them.

Electromagnetic electron hole generation: theory and PIC simulations

<div> <div> <div> <p>Recent MMS observations (<em>e.g.</em> [Holmes et al, 2018, Steinvall et al., 2019]) exploring various regions of the magnetosphere have found solitary potential structures call Electron phase-space Hole (EH). These structures have kinetic scale (dozens of Debye lengths) and persist during long time (dozens of plasma frequency periods). EH are characterized by a bipolar electric field parallel to ambient magnetic field and fastly propagate along this latter (a few tenths of speed light). We have created a 3D Bernstein-Greene-Kruskal (BGK) model (as [Chen et al, 2004]) adapted to various magnetospheric ambient magnetic fields. BGK model results depend on choice of potential shape and passing distribution function at infinity (before EH potential interaction).</p> <p>2D-3V Particle-In-Cell simulations have been developed with the fully kinetic code Smilei [Derouillat et al, 2017], using real magnetosphere plasma parameters. Solitary waves in the magnetotail are three-dimensional potentials which can be generated through nonlinear evolution of an electron beam instability (or bump on tail). The simulated EH are comparable to the EH observed in the magnetosphere with the same parameters.</p> <p>We have also investigated the EH formation with density inhomogeneities using a BGK stability model we have developed. Indeed, density inhomogeneities exist notably in interplanetary plasmas. As a result taking into account the background density inhomogeneities, significantly alters the stability criteria. We have performed 2D-3V PIC simulations with realistic inhomogeneous density background (smaller than 10% of mean density) to understand such a type of EH formation.</p> <p><strong>References:</strong></p> <ul><li>Holmes et al., J. Geophys. Res. Space Phys. 123, 9963, 2018</li> <li>Steinvall et al., Phys. Rev. Lett. 123, 255101, 2019</li> <li>Chen et al., Phys. Rev. E 69, 055401, 2004</li> <li>Derouillat et al., Comput. Phys. Commun. 222, 351, 2017</li> </ul><div> <div> <div> <div> <div> <div> <div> <div> <div> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div> </div>

Oscillating collective motion of active rotors in confinement

Due to its inherent out-of-equilibrium nature, active matter in confinement may exhibit collective behavior absent in unconfined systems. Extensive studies have indicated that hydrodynamic or steric interactions between active particles and boundary play an important role in the emergence of collective behavior. However, besides introducing external couplings at the single-particle level, the confinement also induces an inhomogeneous density distribution due to particle-position correlations, whose effect on collective behavior remains unclear. Here, we investigate this effect in a minimal chiral active matter composed of self-spinning rotors through simulation, experiment, and theory. We find that the density inhomogeneity leads to a position-dependent frictional stress that results from interrotor friction and couples the spin to the translation of the particles, which can then drive a striking spatially oscillating collective motion of the chiral active matter along the confinement boundary. Moreover, depending on the oscillation properties, the collective behavior has three different modes as the packing fraction varies. The structural origins of the transitions between the different modes are well identified by the percolation of solid-like regions or the occurrence of defect-induced particle rearrangement. Our results thus show that the confinement-induced inhomogeneity, dynamic structure, and compressibility have significant influences on collective behavior of active matter and should be properly taken into account.

Resonant absorption of kink oscillations in coronal flux tubes with continuous magnetic twist

ABSTRACT There are observational evidences for the existence of twisted magnetic field in the solar corona. Here, we have investigated resonant damping of the magnetohydrodynamic (MHD) kink waves in magnetic flux tubes. A realistic model of the tube with continuous magnetic twist and radially inhomogeneous density profile has been considered. We have obtained the dispersion relation of the kink wave using the solution to the linear MHD equations outside the density inhomogeneity and the appropriate connection formula to the solutions across the thin transitional boundary layer. The dependence of the oscillation frequency and damping rate of the waves on the twist parameter and longitudinal wavenumber has been investigated. For the flux tube parameters considered in this paper, we obtain rapid damping of the kink waves comparable to the observations. In order to justify this rapid damping, depending on the sign of the azimuthal kink mode number, $m=+1$ or $-1$, the background magnetic field must have left- or right-handed twisted profile, respectively. For the model considered here, the resonant absorption occurs only when the twist parameter is in a range specified by the density contrast.

Five Years of Phase Space Dynamics of the Standard & Poor’s 500

Inhomogeneous density of states in a discrete model of Standard & Poor’s 500 phase space leads to inequitable predictability of market events. Most frequent events might be efficiently predicted in the long run as expected from Mean reversion theory. Stocks have different mobility in phase space. Highly mobile stocks are associated with less unsystematic risk. Less mobile stocks might be cast into disfavor almost indefinitely. Relations between information components in Standard & Poor’s 500 phase space resemble of those in unfair coin tossing.