Thermal collapse of a granular gas under gravity

Free cooling of a gas of inelastically colliding hard spheres represents a central paradigm of kinetic theory of granular gases. At zero gravity the temperature of a freely cooling homogeneous granular gas follows a power law in time. How does gravity, which brings inhomogeneity, affect the cooling? We combine molecular dynamics simulations, a numerical solution of hydrodynamic equations and an analytic theory to show that a granular gas cooling under gravity undergoes thermal collapse: it cools down to zero temperature and condenses on the bottom of the container in a finite time.Comment: 4 pages, 12 eps figures, to appear in PR

Velocity fluctuations of noisy reaction fronts propagating into a metastable state: testing theory in stochastic simulations

The position of a reaction front, propagating into a metastable state, fluctuates because of the shot noise of reactions and diffusion. A recent theory [B. Meerson, P.V. Sasorov, and Y. Kaplan, Phys. Rev. E 84, 011147 (2011)] gave a closed analytic expression for the front diffusion coefficient in the weak noise limit. Here we test this theory in stochastic simulations involving reacting and diffusing particles on a one-dimensional lattice. We also investigate a small noise-induced systematic shift of the front velocity compared to the prediction from the spatially continuous deterministic reaction-diffusion equation.Comment: 5 pages, 5 figure

Humanin G (HNG) protects age-related macular degeneration (AMD) transmitochondrial ARPE-19 cybrids from mitochondrial and cellular damage.

Age-related macular degeneration (AMD) ranks third among the leading causes of visual impairment with a blindness prevalence rate of 8.7%. Despite several treatment regimens, such as anti-angiogenic drugs, laser therapy, and vitamin supplementation, being available for wet AMD, to date there are no FDA-approved therapies for dry AMD. Substantial evidence implicates mitochondrial damage and retinal pigment epithelium (RPE) cell death in the pathogenesis of AMD. However, the effects of AMD mitochondria and Humanin G (HNG), a more potent variant of the mitochondrial-derived peptide (MDP) Humanin, on retinal cell survival have not been elucidated. In this study, we characterized mitochondrial and cellular damage in transmitochondrial cybrid cell lines that contain identical nuclei but possess mitochondria from either AMD or age-matched normal (Older-normal (NL)) subjects. AMD cybrids showed (1) reduced levels of cell viability, lower mtDNA copy numbers, and downregulation of mitochondrial replication/transcription genes and antioxidant enzyme genes; and (2) elevated levels of genes related to apoptosis, autophagy and ER-stress along with increased mtDNA fragmentation and higher susceptibility to amyloid-β-induced toxicity compared to NL cybrids. In AMD cybrids, HNG protected the AMD mitochondria, reduced pro-apoptosis gene and protein levels, upregulated gp130 (a component of the HN receptor complex), and increased the protection against amyloid-β-induced damage. In summary, in cybrids, damaged AMD mitochondria mediate cell death that can be reversed by HNG treatment. Our results also provide evidence of Humanin playing a pivotal role in protecting cells with AMD mitochondria. In the future, it may be possible that AMD patient's blood samples containing damaged mitochondria may be useful as biomarkers for this condition. In conclusion, HNG may be a potential therapeutic target for treatment of dry AMD, a debilitating eye disease that currently has no available treatment. Further studies are needed to establish HNG as a viable mitochondria-targeting therapy for dry AMD

Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas

We employ Navier-Stokes granular hydrodynamics to investigate the long-time behavior of clustering instability in a freely cooling dilute granular gas in two dimensions. We find that, in circular containers, the homogeneous cooling state (HCS) of the gas loses its stability via a sub-critical pitchfork bifurcation. There are no time-independent solutions for the gas density in the supercritical region, and we present analytical and numerical evidence that the gas develops thermal collapse unarrested by heat diffusion. To get more insight, we switch to a simpler geometry of a narrow-sector-shaped container. Here the HCS loses its stability via a transcritical bifurcation. For some initial conditions a time-independent inhomogeneous density profile sets in, qualitatively similar to that previously found in a narrow-channel geometry. For other initial conditions, however, the dilute gas develops thermal collapse unarrested by heat diffusion. We determine the dynamic scalings of the flow close to collapse analytically and verify them in hydrodynamic simulations. The results of this work imply that, in dimension higher than one, Navier-Stokes hydrodynamics of a dilute granular gas is prone to finite-time density blowups. This provides a natural explanation to the formation of densely packed clusters of particles in a variety of initially dilute granular flows.Comment: 18 pages, 19 figure

Switching between phenotypes and population extinction

Many types of bacteria can survive under stress by switching stochastically between two different phenotypes: the "normals" who multiply fast, but are vulnerable to stress, and the "persisters" who hardly multiply, but are resilient to stress. Previous theoretical studies of such bacterial populations have focused on the \emph{fitness}: the asymptotic rate of unbounded growth of the population. Yet for an isolated population of established (and not very large) size, a more relevant measure may be the population \emph{extinction risk} due to the interplay of adverse extrinsic variations and intrinsic noise of birth, death and switching processes. Applying a WKB approximation to the pertinent master equation of such a two-population system, we quantify the extinction risk, and find the most likely path to extinction under both favorable and adverse conditions. Analytical results are obtained both in the biologically relevant regime when the switching is rare compared with the birth and death processes, and in the opposite regime of frequent switching. We show that rare switches are most beneficial in reducing the extinction risk.Comment: 11 pages, 5 figures. Additional discussion paragraph, minor language improvements; content as published in Phys. Rev.

Oral History Transcript | Interview with Baruch Kirschenbaum, March 25, 2007

https://digitalcommons.risd.edu/archives_oralhistories_transcripts/1002/thumbnail.jp

Emergence of stability in a stochastically driven pendulum: beyond the Kapitsa effect

We consider a prototypical nonlinear system which can be stabilized by multiplicative noise: an underdamped non-linear pendulum with a stochastically vibrating pivot. A numerical solution of the pertinent Fokker-Planck equation shows that the upper equilibrium point of the pendulum can become stable even when the noise is white, and the "Kapitsa pendulum" effect is not at work. The stabilization occurs in a strong-noise regime where WKB approximation does not hold.Comment: 4 pages, 7 figure

Asymptotically false-positive-maximizing attack on non-binary Tardos codes

We use a method recently introduced by Simone and Skoric to study accusation probabilities for non-binary Tardos fingerprinting codes. We generalize the pre-computation steps in this approach to include a broad class of collusion attack strategies. We analytically derive properties of a special attack that asymptotically maximizes false accusation probabilities. We present numerical results on sufficient code lengths for this attack, and explain the abrupt transitions that occur in these results

Scaling and self-similarity in an unforced flow of inviscid fluid trapped inside a viscous fluid in a Hele-Shaw cell

We investigate quasi-two-dimensional relaxation, by surface tension, of a long straight stripe of inviscid fluid trapped inside a viscous fluid in a Hele-Shaw cell. Combining analytical and numerical solutions, we describe the emergence of a self-similar dumbbell shape and find non-trivial dynamic exponents that characterize scaling behavior of the dumbbell dimensions.Comment: 4 pages, 5 figures, to appear in PR