Viscous evolution of point vortex equilibria: The collinear state

When point vortex equilibria of the 2D Euler equations are used as initial conditions for the corre- sponding Navier-Stokes equations (viscous), typically an interesting dynamical process unfolds at short and intermediate time scales, before the long time single peaked, self-similar Oseen vortex state dom- inates. In this paper, we describe the viscous evolution of a collinear three vortex structure that cor- responds to an inviscid point vortex fixed equilibrium. Using a multi-Gaussian 'core-growth' type of model, we show that the system immediately begins to rotate unsteadily, a mechanism we attribute to a 'viscously induced' instability. We then examine in detail the qualitative and quantitative evolution of the system as it evolves toward the long-time asymptotic Lamb-Oseen state, showing the sequence of topological bifurcations that occur both in a fixed reference frame, and in an appropriately chosen rotating reference frame. The evolution of passive particles in this viscously evolving flow is shown and interpreted in relation to these evolving streamline patterns.Comment: 17 pages, 15 figure

A Variational Principle Based Study of KPP Minimal Front Speeds in Random Shears

Variational principle for Kolmogorov-Petrovsky-Piskunov (KPP) minimal front speeds provides an efficient tool for statistical speed analysis, as well as a fast and accurate method for speed computation. A variational principle based analysis is carried out on the ensemble of KPP speeds through spatially stationary random shear flows inside infinite channel domains. In the regime of small root mean square (rms) shear amplitude, the enhancement of the ensemble averaged KPP front speeds is proved to obey the quadratic law under certain shear moment conditions. Similarly, in the large rms amplitude regime, the enhancement follows the linear law. In particular, both laws hold for the Ornstein-Uhlenbeck process in case of two dimensional channels. An asymptotic ensemble averaged speed formula is derived in the small rms regime and is explicit in case of the Ornstein-Uhlenbeck process of the shear. Variational principle based computation agrees with these analytical findings, and allows further study on the speed enhancement distributions as well as the dependence of enhancement on the shear covariance. Direct simulations in the small rms regime suggest quadratic speed enhancement law for non-KPP nonlinearities.Comment: 28 pages, 14 figures update: fixed typos, refined estimates in section

A stochastic perturbation of inviscid flows

We prove existence and regularity of the stochastic flows used in the stochastic Lagrangian formulation of the incompressible Navier-Stokes equations (with periodic boundary conditions), and consequently obtain a \holderspace{k}{\alpha} local existence result for the Navier-Stokes equations. Our estimates are independent of viscosity, allowing us to consider the inviscid limit. We show that as $\nu \to 0$, solutions of the stochastic Lagrangian formulation (with periodic boundary conditions) converge to solutions of the Euler equations at the rate of $O(\sqrt{\nu t})$.Comment: 13 pages, no figures

Apoptotic changes in the myocardium in the course of experimentally-induced pleurisy

The secreted proinflammatory interleukins IL-1, IL-6 and TNF in the course of experimentally-induced pleurisy can be the cause of pathological changes in the ultrastructure of cardiac muscle and of apoptosis. The pleurisy was induced in rats by means of carrageenin. The scraps of cardiac muscle obtained during the inflammatory reaction in the pleura were analysed by means of an electron microscope. The scraps were also stained with the TUNEL method in order to find the apoptotic foci. It was proved by the experiment that the inflammatory process affected mitochondria in the cardiomyocytes, enhanced collagen fibre synthesis and contributed to the formation of apoptotic foci in the cardiac muscle

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

Vanishing viscosity limit for an expanding domain in space

We study the limiting behavior of viscous incompressible flows when the fluid domain is allowed to expand as the viscosity vanishes. We describe precise conditions under which the limiting flow satisfies the full space Euler equations. The argument is based on truncation and on energy estimates, following the structure of the proof of Kato's criterion for the vanishing viscosity limit. This work complements previous work by the authors, see [Kelliher, Comm. Math. Phys. 278 (2008), 753-773] and [arXiv:0801.4935v1].Comment: 23 pages, submitted for publicatio

On the dynamics of a self-gravitating medium with random and non-random initial conditions

The dynamics of a one-dimensional self-gravitating medium, with initial density almost uniform is studied. Numerical experiments are performed with ordered and with Gaussian random initial conditions. The phase space portraits are shown to be qualitatively similar to shock waves, in particular with initial conditions of Brownian type. The PDF of the mass distribution is investigated.Comment: Latex, figures in eps, 23 pages, 11 figures. Revised versio

Right to Access Information in Decentralized Indonesia: a Socio-legal Inquiry

Indonesia is no longer an authoritarian country, and no longer centralized government. Decentralization processes since 1999 has changed local democratization in a wider participation. Nevertheless, the culture of openness and incorrupt have been far from the more ideal situation. Bribery, corruption and unresponsive public services have been continuously and more systematic taking place. In that context, the Government of Indonesia enacted Law No. 14 of 2008 concerning Public Information Openness (Keterbukaan Informasi Publik or called PIO Law), which is implemented since 30 April 2010. The PIO law is believed to contribute to the better decentralization processes and economic-political democratization at local level. Nevertheless, although right to access information was guaranteed by law, but it has been applied in limited process. Such situation actually gives clear evidence that decentralized Indonesia should be questioned, especially in terms of how the right to access information has been applied in a meaningful way after the enactment PIO Law in 2008 and, what the dominant problems in implementing right to access information are. This article will elaborate the norms and practices of PIO Law by using the rule of law point of view

Chemotactic Collapse and Mesenchymal Morphogenesis

We study the effect of chemotactic signaling among mesenchymal cells. We show that the particular physiology of the mesenchymal cells allows one-dimensional collapse in contrast to the case of bacteria, and that the mesenchymal morphogenesis represents thus a more complex type of pattern formation than those found in bacterial colonies. We finally compare our theoretical predictions with recent in vitro experiments