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

Noise Prevents Singularities in Linear Transport Equations

A stochastic linear transport equation with multiplicative noise is considered and the question of no-blow-up is investigated. The drift is assumed only integrable to a certain power. Opposite to the deterministic case where smooth initial conditions may develop discontinuities, we prove that a certain Sobolev degree of regularity is maintained, which implies H\"older continuity of solutions. The proof is based on a careful analysis of the associated stochastic flow of characteristics

The Bismut-Elworthy-Li type formulae for stochastic differential equations with jumps

Consider jump-type stochastic differential equations with the drift, diffusion and jump terms. Logarithmic derivatives of densities for the solution process are studied, and the Bismut-Elworthy-Li type formulae can be obtained under the uniformly elliptic condition on the coefficients of the diffusion and jump terms. Our approach is based upon the Kolmogorov backward equation by making full use of the Markovian property of the process.Comment: 29 pages, to appear in Journal of Theoretical Probabilit

Statistical Analysis of a Semilinear Hyperbolic System Advected by a White in Time Random Velocity Field

We study a system of semilinear hyperbolic equations passively advected by smooth white noise in time random velocity fields. Such a system arises in modeling non-premixed isothermal turbulent flames under single-step kinetics of fuel and oxidizer. We derive closed equations for one-point and multi-point probability distribution functions (PDFs) and closed form analytical formulas for the one point PDF function, as well as the two-point PDF function under homogeneity and isotropy. Exact solution formulas allows us to analyze the ensemble averaged fuel/oxidizer concentrations and the motion of their level curves. We recover the empirical formulas of combustion in the thin reaction zone limit and show that these approximate formulas can either underestimate or overestimate average concentrations when reaction zone is not tending to zero. We show that the averaged reaction rate slows down locally in space due to random advection induced diffusion; and that the level curves of ensemble averaged concentration undergo diffusion about mean locations.Comment: 18 page

Improved linear response for stochastically driven systems

The recently developed short-time linear response algorithm, which predicts the average response of a nonlinear chaotic system with forcing and dissipation to small external perturbation, generally yields high precision of the response prediction, although suffers from numerical instability for long response times due to positive Lyapunov exponents. However, in the case of stochastically driven dynamics, one typically resorts to the classical fluctuation-dissipation formula, which has the drawback of explicitly requiring the probability density of the statistical state together with its derivative for computation, which might not be available with sufficient precision in the case of complex dynamics (usually a Gaussian approximation is used). Here we adapt the short-time linear response formula for stochastically driven dynamics, and observe that, for short and moderate response times before numerical instability develops, it is generally superior to the classical formula with Gaussian approximation for both the additive and multiplicative stochastic forcing. Additionally, a suitable blending with classical formula for longer response times eliminates numerical instability and provides an improved response prediction even for long response times

Associação entre características de desempenho de tilápia-do-nilo ao longo do período de cultivo.

O objetivo deste trabalho foi estimar as herdabilidades e a estrutura de correlações genéticas entre as características de desempenho de tilápia-do-nilo (Oreochromis niloticus) da linhagem GIFT, em diferentes estágios do ciclo de produção. As tilápias foram cultivadas em tanques - rede. Mediu-se ganho em peso diário total, peso vivo e ganho em peso diário, em quatro períodos, com intervalos de aproximadamente 30 dias. Foram realizadas análises unicaracter para as medidas, em todas as biometrias e, nas análises bicaracter, as medidas de mesma característica foram combinadas duas a duas e com o ganho em peso diário total. As estimações de herdabilidade variaram de 0,15 a 0,11 para peso vivo, 0,16 a 0,09 para ganho em peso diário e 0,17 a 0,12 para ganho em peso diário total, nas análises unicaracter. Os valores estimados de correlação genética para peso vivo e ganho em peso diário, associados ao ganho em peso diário total, variaram entre 0,37 a 0,98 e 0,74 a 0,8 respectivamente. A forte associação genética estimada entre peso vivo em biometrias intermediárias e ganho em peso diário total sugere que a seleção para velocidade de crescimento pode ser realizada de forma precoce

Loss of ALS2/Alsin Exacerbates Motor Dysfunction in a SOD1H46R-Expressing Mouse ALS Model by Disturbing Endolysosomal Trafficking

BACKGROUND: ALS2/alsin is a guanine nucleotide exchange factor for the small GTPase Rab5 and involved in macropinocytosis-associated endosome fusion and trafficking, and neurite outgrowth. ALS2 deficiency accounts for a number of juvenile recessive motor neuron diseases (MNDs). Recently, it has been shown that ALS2 plays a role in neuroprotection against MND-associated pathological insults, such as toxicity induced by mutant Cu/Zn superoxide dismutase (SOD1). However, molecular mechanisms underlying the relationship between ALS2-associated cellular function and its neuroprotective role remain unclear. METHODOLOGY/PRINCIPAL FINDINGS: To address this issue, we investigated the molecular and pathological basis for the phenotypic modification of mutant SOD1-expressing mice by ALS2 loss. Genetic ablation of Als2 in SOD1(H46R), but not SOD1(G93A), transgenic mice aggravated the mutant SOD1-associated disease symptoms such as body weight loss and motor dysfunction, leading to the earlier death. Light and electron microscopic examinations revealed the presence of degenerating and/or swollen spinal axons accumulating granular aggregates and autophagosome-like vesicles in early- and even pre-symptomatic SOD1(H46R) mice. Further, enhanced accumulation of insoluble high molecular weight SOD1, poly-ubiquitinated proteins, and macroautophagy-associated proteins such as polyubiquitin-binding protein p62/SQSTM1 and a lipidated form of light chain 3 (LC3-II), emerged in ALS2-deficient SOD1(H46R) mice. Intriguingly, ALS2 was colocalized with LC3 and p62, and partly with SOD1 on autophagosome/endosome hybrid compartments, and loss of ALS2 significantly lowered the lysosome-dependent clearance of LC3 and p62 in cultured cells. CONCLUSIONS/SIGNIFICANCE: Based on these observations, although molecular basis for the distinctive susceptibilities to ALS2 loss in different mutant SOD1-expressing ALS models is still elusive, disturbance of the endolysosomal system by ALS2 loss may exacerbate the SOD1(H46R)-mediated neurotoxicity by accelerating the accumulation of immature vesicles and misfolded proteins in the spinal cord. We propose that ALS2 is implicated in endolysosomal trafficking through the fusion between endosomes and autophagosomes, thereby regulating endolysosomal protein degradation in vivo

Well-posedness of the transport equation by stochastic perturbation

We consider the linear transport equation with a globally Holder continuous and bounded vector field. While this deterministic PDE may not be well-posed, we prove that a multiplicative stochastic perturbation of Brownian type is enough to render the equation well-posed. This seems to be the first explicit example of partial differential equation that become well-posed under the influece of noise. The key tool is a differentiable stochastic flow constructed and analysed by means of a special transformation of the drift of Ito-Tanaka type.Comment: Addition of new part

Path Integrals on a Compact Manifold with Non-negative Curvature

A typical path integral on a manifold, $M$ is an informal expression of the form \frac{1}{Z}\int_{\sigma \in H(M)} f(\sigma) e^{-E(\sigma)}\mathcal{D}\sigma, \nonumber where $H(M)$ is a Hilbert manifold of paths with energy $E(\sigma) < \infty$, $f$ is a real valued function on $H(M)$, $\mathcal{D}\sigma$ is a \textquotedblleft Lebesgue measure \textquotedblright and $Z$ is a normalization constant. For a compact Riemannian manifold $M$, we wish to interpret $\mathcal{D}\sigma$ as a Riemannian \textquotedblleft volume form \textquotedblright over $H(M)$, equipped with its natural $G^{1}$ metric. Given an equally spaced partition, ${\mathcal{P}}$ of $[0,1],$ let H_{{\mathcal{P}}%}(M) be the finite dimensional Riemannian submanifold of $H(M)$ consisting of piecewise geodesic paths adapted to $\mathcal{P.}$ Under certain curvature restrictions on $M,$ it is shown that $$\frac{1}{Z_{{\mathcal{P}}}}e^{-{1/2}E(\sigma)}dVol_{H_{{\mathcal{P}}}}(\sigma)\to\rho(\sigma)d\nu(\sigma)\text{as}\mathrm{mesh}({\mathcal{P}})\to0,$$ where $Z_{{\mathcal{P}}}$ is a \textquotedblleft normalization\textquotedblright constant, $E:H(M) \to\lbrack0,\infty)$ is the energy functional, Vol_{H_{{\mathcal{P}}%}} is the Riemannian volume measure on $H_{\mathcal{P}}(M) ,$ $\nu$ is Wiener measure on continuous paths in $M,$ and $\rho$ is a certain density determined by the curvature tensor of $M.

Elliptic flow in Pb+Pb collisions at sqrt{s_{NN}} = 2.76 TeV: hybrid model assessment of the first data

We analyze the elliptic flow parameter v_2 in Pb+Pb collisions at sqrt{s_{NN}} = 2.76 TeV and in Au+Au collisions at sqrt{s_{NN}} =200 GeV using a hybrid model in which the evolution of the quark gluon plasma is described by ideal hydrodynamics with a state-of-the-art lattice QCD equation of state, and the subsequent hadronic stage by a hadron cascade model. For initial conditions, we employ Monte-Carlo versions of the Glauber and the Kharzeev-Levin-Nardi models and compare results with each other. We demonstrate that the differential elliptic flow v_2(p_T) hardly changes when the collision energy increases, whereas the integrated v_2 increases due to the enhancement of mean transverse momentum. The amount of increase of both v_2 and mean p_T depends significantly on the model of initialization.Comment: 5 pages, 5 figure