A stochastic-Lagrangian particle system for the Navier-Stokes equations

This paper is based on a formulation of the Navier-Stokes equations developed by P. Constantin and the first author (\texttt{arxiv:math.PR/0511067}, to appear), where the velocity field of a viscous incompressible fluid is written as the expected value of a stochastic process. In this paper, we take $N$ copies of the above process (each based on independent Wiener processes), and replace the expected value with $\frac{1}{N}$ times the sum over these $N$ copies. (We remark that our formulation requires one to keep track of $N$ stochastic flows of diffeomorphisms, and not just the motion of $N$ particles.) We prove that in two dimensions, this system of interacting diffeomorphisms has (time) global solutions with initial data in the space \holderspace{1}{\alpha} which consists of differentiable functions whose first derivative is $\alpha$ H\"older continuous (see Section \ref{sGexist} for the precise definition). Further, we show that as $N \to \infty$ the system converges to the solution of Navier-Stokes equations on any finite interval $[0,T]$. However for fixed $N$, we prove that this system retains roughly $O(\frac{1}{N})$ times its original energy as $t \to \infty$. Hence the limit $N \to \infty$ and $T\to \infty$ do not commute. For general flows, we only provide a lower bound to this effect. In the special case of shear flows, we compute the behaviour as $t \to \infty$ explicitly.Comment: v3: Typo fixes, and a few stylistic changes. 17 pages, 2 figure

Zero-Reachability in Probabilistic Multi-Counter Automata

We study the qualitative and quantitative zero-reachability problem in probabilistic multi-counter systems. We identify the undecidable variants of the problems, and then we concentrate on the remaining two cases. In the first case, when we are interested in the probability of all runs that visit zero in some counter, we show that the qualitative zero-reachability is decidable in time which is polynomial in the size of a given pMC and doubly exponential in the number of counters. Further, we show that the probability of all zero-reaching runs can be effectively approximated up to an arbitrarily small given error epsilon > 0 in time which is polynomial in log(epsilon), exponential in the size of a given pMC, and doubly exponential in the number of counters. In the second case, we are interested in the probability of all runs that visit zero in some counter different from the last counter. Here we show that the qualitative zero-reachability is decidable and SquareRootSum-hard, and the probability of all zero-reaching runs can be effectively approximated up to an arbitrarily small given error epsilon > 0 (these result applies to pMC satisfying a suitable technical condition that can be verified in polynomial time). The proof techniques invented in the second case allow to construct counterexamples for some classical results about ergodicity in stochastic Petri nets.Comment: 20 page

Tracing very high energy neutrinos from cosmological distances in ice

Astrophysical sources of ultrahigh energy neutrinos yield tau neutrino fluxes due to neutrino oscillations. We study in detail the contribution of tau neutrinos with energies above PeV relative to the contribution of the other flavors. We consider several different initial neutrino fluxes and include tau neutrino regeneration in transit through the Earth and energy loss of charged leptons. We discuss signals of tau neutrinos in detectors such as IceCube, RICE and ANITA.Comment: 27 pages, 19 figure

Meigs syndrome presenting with axillary vein thrombosis and lymphadenopathy: a case report.

INTRODUCTION: Meigs syndrome is a rare condition, occurring in less than 1% of ovarian tumors and has the characteristic features of a benign ovarian tumor, ascites and a pleural effusion. We present a case of Meigs syndrome in a young patient presenting initially with an axillary vein thrombosis and local lymphadenopathy. CASE PRESENTATION: A 28-year-old Caucasian woman presented with a short history of right arm swelling and shortness of breath as a result of an axillary vein thrombosis and pulmonary embolus.The initial assessment also demonstrated right axillary and subclavian lymphadenopathy, a pleural effusion, ascites and a large ovarian mass. Serum levels of the tumor markers human chorionic gonadotropin and alpha-fetoprotein were normal and the CA-125 level was only moderately elevated.The combination of thrombosis, lymphadenopathy and an ovarian mass raised the possibility of a disseminated malignancy potentially an epithelial ovarian cancer, a germ cell tumor or an ovarian sex cord-stromal tumor.Surgery, performed after a short period of anticoagulation, demonstrated a 13.5cm ovarian cellular fibroma of low malignant potential. Postoperatively the patient made an excellent recovery and the ascites, pleural effusion and lymphadenopathy all resolved promptly. CONCLUSIONS: In Meigs syndrome the classical findings of ascites, pleural effusion in combination with an ovarian mass can mimic disseminated malignancy but resolve spontaneously after surgery. In this current case, the patient also had lymphadenopathy and venous thrombosis, two other findings that are frequently associated with malignancy and was acutely unwell at presentation.It is unclear if the thrombosis and lymphadenopathy were simply coincidental or shared the same etiology as the ascites and pleural effusion. This case indicates that Meigs syndrome may on occasion present with additional findings that can further mimic disseminated malignancy and may lead to diagnostic uncertainty

Stochastic Lagrangian Particle Approach to Fractal Navier-Stokes Equations

In this article we study the fractal Navier-Stokes equations by using stochastic Lagrangian particle path approach in Constantin and Iyer \cite{Co-Iy}. More precisely, a stochastic representation for the fractal Navier-Stokes equations is given in terms of stochastic differential equations driven by L\'evy processes. Basing on this representation, a self-contained proof for the existence of local unique solution for the fractal Navier-Stokes equation with initial data in \mW^{1,p} is provided, and in the case of two dimensions or large viscosity, the existence of global solution is also obtained. In order to obtain the global existence in any dimensions for large viscosity, the gradient estimates for L\'evy processes with time dependent and discontinuous drifts is proved.Comment: 19 page

DNMTs are required for delayed genome instability caused by radiation

This is an open-access article licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License. The article may be redistributed, reproduced, and reused for non-commercial purposes, provided the original source is properly cited - Copyright @ 2012 Landes Bioscience.The ability of ionizing radiation to initiate genomic instability has been harnessed in the clinic where the localized delivery of controlled doses of radiation is used to induce cell death in tumor cells. Though very effective as a therapy, tumor relapse can occur in vivo and its appearance has been attributed to the radio-resistance of cells with stem cell-like features. The molecular mechanisms underlying these phenomena are unclear but there is evidence suggesting an inverse correlation between radiation-induced genomic instability and global hypomethylation. To further investigate the relationship between DNA hypomethylation, radiosensitivity and genomic stability in stem-like cells we have studied mouse embryonic stem cells containing differing levels of DNA methylation due to the presence or absence of DNA methyltransferases. Unexpectedly, we found that global levels of methylation do not determine radiosensitivity. In particular, radiation-induced delayed genomic instability was observed at the Hprt gene locus only in wild-type cells. Furthermore, absence of Dnmt1 resulted in a 10-fold increase in de novo Hprt mutation rate, which was unaltered by radiation. Our data indicate that functional DNMTs are required for radiation-induced genomic instability, and that individual DNMTs play distinct roles in genome stability. We propose that DNMTS may contribute to the acquirement of radio-resistance in stem-like cells.This study is funded by NOTE, BBSRC and the Royal Society Dorothy Hodgkin Research Fellowship

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

On naked singularities in higher dimensional Vaidya space-times

We investigate the end state of gravitational collapse of null fluid in higher dimensional space-times. Both naked singularities and black holes are shown to be developing as final outcome of the collapse. The naked singularity spectrum in collapsing Vaidya region (4D) gets covered with increase in dimensions and hence higher dimensions favor black hole in comparison to naked singularity. The Cosmic Censorship Conjecture will be fully respected for a space of infinite dimension.Comment: 9 pages, LateX, Minor changes. Accepted in Phys. Rev.

Quantum Entanglement and Teleportation in Higher Dimensional Black Hole Spacetimes

We study the properties of quantum entanglement and teleportation in the background of stationary and rotating curved space-times with extra dimensions. We show that a maximally entangled Bell state in an inertial frame becomes less entangled in curved space due to the well-known Hawking-Unruh effect. The degree of entanglement is found to be degraded with increasing the extra dimensions. For a finite black hole surface gravity, the observer may choose higher frequency mode to keep high level entanglement. The fidelity of quantum teleporation is also reduced because of the Hawking-Unruh effect. We discuss the fidelity as a function of extra dimensions, mode frequency, black hole mass and black hole angular momentum parameter for both bosonic and fermionic resources.Comment: 15 pages, 10 figures,contents expande