Nonlinear saturation of electrostatic waves: mobile ions modify trapping scaling

The amplitude equation for an unstable electrostatic wave in a multi-species Vlasov plasma has been derived. The dynamics of the mode amplitude $\rho(t)$ is studied using an expansion in $\rho$; in particular, in the limit $\gamma\rightarrow0^+$, the singularities in the expansion coefficients are analyzed to predict the asymptotic dependence of the electric field on the linear growth rate $\gamma$. Generically $|E_k|\sim \gamma^{5/2}$, as $\gamma\rightarrow0^+$, but in the limit of infinite ion mass or for instabilities in reflection-symmetric systems due to real eigenvalues the more familiar trapping scaling $|E_k|\sim \gamma^{2}$ is predicted.Comment: 13 pages (Latex/RevTex), 4 postscript encapsulated figures which are included using the utility "uufiles". They should be automatically included with the text when it is downloaded. Figures also available in hard copy from the authors ([email protected]

Thrombolysis in Patients Aged over 80 Years Is Equally Effective and Safe

BACKGROUND: Despite stroke's high prevalence in the elderly, intravenous thrombolysis is licensed in Europe only for patients younger than 80 years old. We aimed to compare the functional outcomes and complication rates in patients older versus younger than 80 years old treated with intravenous thrombolysis. METHODS: A retrospective observational study of patients who received intravenous thrombolysis in a stroke unit between January 1, 2009, and June 30, 2012, was conducted. Variables were compared between 2 subgroups (≤80 and >80 years). RESULTS: Overall, 512 patients underwent intravenous thrombolysis, of which 13.1% were over 80 years. The mean age was 65.4 years in the younger subgroup and 82.9 years in the older subgroup. Prior independence rates did not differ between the subgroups. Prevalence of atrial fibrillation and cardioembolic stroke was higher in the older subgroup (P = .004 and .026). Only 3% of the elderly with atrial fibrillation were taking oral anticoagulants. Symptoms-to-needle time was lower in the older subgroup (P = .048). Stroke severity was higher in patients over 80 years (P = .026). There was significant improvement in the National Institutes of Health Stroke Scale score 7 days after intravenous thrombolysis (P < .001) in both subgroups. The proportion of patients with 3 months' favorable outcome and independence, hemorrhagic transformation, and mortality rates were similar in both subgroups. CONCLUSIONS: Elderly patients' benefits and outcomes from intravenous thrombolysis treatment were identical to the younger subgroup without excess hemorrhagic transformation or mortality. These results favor the use of intravenous thrombolysis in patients over 80 years.info:eu-repo/semantics/publishedVersio

Coercivity and stability results for an extended Navier-Stokes system

In this article we study a system of equations that is known to {\em extend} Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergence-free. Our aim is to contribute to an understanding of the role of divergence and pressure in developing energy estimates capable of controlling the nonlinear terms. We address questions of global existence and stability in bounded domains with no-slip boundary conditions. Even in two space dimensions, global existence is open in general, and remains so, primarily due to the lack of a self-contained $L^2$ energy estimate. However, through use of new $H^1$ coercivity estimates for the linear equations, we establish a number of global existence and stability results, including results for small divergence and a time-discrete scheme. We also prove global existence in 2D for any initial data, provided sufficient divergence damping is included.Comment: 29 pages, no figure

Stability of a Nonequilibrium Interface in a Driven Phase Segregating System

We investigate the dynamics of a nonequilibrium interface between coexisting phases in a system described by a Cahn-Hilliard equation with an additional driving term. By means of a matched asymptotic expansion we derive equations for the interface motion. A linear stability analysis of these equations results in a condition for the stability of a flat interface. We find that the stability properties of a flat interface depend on the structure of the driving term in the original equation.Comment: 14 pages Latex, 1 postscript-figur

On the Modulation Equations and Stability of Periodic GKdV Waves via Bloch Decompositions

In this paper, we complement recent results of Bronski and Johnson and of Johnson and Zumbrun concerning the modulational stability of spatially periodic traveling wave solutions of the generalized Korteweg-de Vries equation. In this previous work it was shown by rigorous Evans function calculations that the formal slow modulation approximation resulting in the Whitham system accurately describes the spectral stability to long wavelength perturbations. Here, we reproduce this result without reference to the Evans function by using direct Bloch-expansion methods and spectral perturbation analysis. This approach has the advantage of applying also in the more general multi-periodic setting where no conveniently computable Evans function is yet devised. In particular, we complement the picture of modulational stability described by Bronski and Johnson by analyzing the projectors onto the total eigenspace bifurcating from the origin in a neighborhood of the origin and zero Floquet parameter. We show the resulting linear system is equivalent, to leading order and up to conjugation, to the Whitham system and that, consequently, the characteristic polynomial of this system agrees (to leading order) with the linearized dispersion relation derived through Evans function calculation.Comment: 19 pages

Universal trapping scaling on the unstable manifold for a collisionless electrostatic mode

An amplitude equation for an unstable mode in a collisionless plasma is derived from the dynamics on the two-dimensional unstable manifold of the equilibrium. The mode amplitude $\rho(t)$ decouples from the phase due to the spatial homogeneity of the equilibrium, and the resulting one-dimensional dynamics is analyzed using an expansion in $\rho$. As the linear growth rate $\gamma$ vanishes, the expansion coefficients diverge; a rescaling $\rho(t)\equiv\gamma^2\,r(\gamma t)$ of the mode amplitude absorbs these singularities and reveals that the mode electric field exhibits trapping scaling $|E_1|\sim\gamma^2$ as $\gamma\rightarrow0$. The dynamics for $r(\tau)$ depends only on the phase $e^{i\xi}$ where $d\epsilon_{{k}} /dz=|{\epsilon_{{k}}}|e^{-i\xi/2}$ is the derivative of the dielectric as $\gamma\rightarrow0$.Comment: 11 pages (Latex/RevTex), 2 figures available in hard copy from the Author ([email protected]); paper accepted by Physical Review Letter

Blocking IL-17: A Promising Strategy in the Treatment of Systemic Rheumatic Diseases

Systemic rheumatic diseases are a heterogeneous group of autoimmune disorders that affect the connective tissue, characterized by the involvement of multiple organs, leading to disability, organ failure and premature mortality. Despite the advances in recent years, the therapeutic options for these diseases are still limited and some patients do not respond to the current treatments. Interleukin-17 (IL-17) is a cytokine essential in the defense against extracellular bacteria and fungi. Disruption of IL-17 homeostasis has been associated with the development and progression of rheumatic diseases, and the approval of different biological therapies targeting IL-17 for the treatment of psoriatic arthritis (PsA) and ankylosing spondylitis (AS) has highlighted the key role of this cytokine. IL-17 has been also implicated in the pathogenesis of systemic rheumatic diseases, including systemic lupus erythematosus (SLE), Sjogren's syndrome (SS) and systemic sclerosis (SSc). The aim of this review is to summarize and discuss the most recent findings about the pathogenic role of IL-17 in systemic rheumatic and its potential use as a therapeutic option

Scaling anomalies in the coarsening dynamics of fractal viscous fingering patterns

We analyze a recent experiment of Sharon \textit{et al.} (2003) on the coarsening, due to surface tension, of fractal viscous fingering patterns (FVFPs) grown in a radial Hele-Shaw cell. We argue that an unforced Hele-Shaw model, a natural model for that experiment, belongs to the same universality class as model B of phase ordering. Two series of numerical simulations with model B are performed, with the FVFPs grown in the experiment, and with Diffusion Limited Aggregates, as the initial conditions. We observed Lifshitz-Slyozov scaling $t^{1/3}$ at intermediate distances and very slow convergence to this scaling at small distances. Dynamic scale invariance breaks down at large distances.Comment: 4 pages, 4 eps figures; to appear in Phys. Rev.

Spectral stability of noncharacteristic isentropic Navier-Stokes boundary layers

Building on work of Barker, Humpherys, Lafitte, Rudd, and Zumbrun in the shock wave case, we study stability of compressive, or "shock-like", boundary layers of the isentropic compressible Navier-Stokes equations with gamma-law pressure by a combination of asymptotic ODE estimates and numerical Evans function computations. Our results indicate stability for gamma in the interval [1, 3] for all compressive boundary-layers, independent of amplitude, save for inflow layers in the characteristic limit (not treated). Expansive inflow boundary-layers have been shown to be stable for all amplitudes by Matsumura and Nishihara using energy estimates. Besides the parameter of amplitude appearing in the shock case, the boundary-layer case features an additional parameter measuring displacement of the background profile, which greatly complicates the resulting case structure. Moreover, inflow boundary layers turn out to have quite delicate stability in both large-displacement and large-amplitude limits, necessitating the additional use of a mod-two stability index studied earlier by Serre and Zumbrun in order to decide stability