Resolvent estimates for 2 dimensional perturbations of plane Couette Flow

We present results concerning resolvent estimates for the linear operator associated with the system of differential equations governing perturbations of the Couette flow. We prove estimates on the L_2 norm of the resolvent of this operator showing this norm to be proportional to the Reynolds number R for a region of the unstable half plane. For the remaining region, we show that the problem can be reduced to estimating the solution of a homogeneous ordinary differential equation with non-homogeneous boundary conditions. Numerical approximations indicate that the norm of the resolvent is proportional to R in the whole region of interest.Comment: 16 pages, 4 figures. A mistake in the proof of Theorem 1 was corrected. The presentation was changed a little, and typos were correcte

Computational modeling of acute myocardial infarction

This is an Accepted Manuscript of an article published by Taylor & Francis Group in Computer Methods in Biomechanics and Biomedical Engineering on October, 2016, available online at: http://www.tandfonline.com/10.1080/10255842.2015.1105965Myocardial infarction, commonly known as heart attack, is caused by reduced blood supply and damages the heart muscle because of a lack of oxygen. Myocardial infarction initiates a cascade of biochemical and mechanical events. In the early stages, cardiomyocytes death, wall thinning, collagen degradation, and ventricular dilation are the immediate consequences of myocardial infarction. In the later stages, collagenous scar formation in the infarcted zone and hypertrophy of the non-infarcted zone are auto-regulatory mechanisms to partly correct for these events. Here we propose a computational model for the short-term adaptation after myocardial infarction using the continuum theory of multiplicative growth. Our model captures the effects of cell death initiating wall thinning, and collagen degradation initiating ventricular dilation. Our simulations agree well with clinical observations in early myocardial infarction. They represent a first step toward simulating the progression of myocardial infarction with the ultimate goal to predict the propensity toward heart failure as a function of infarct intensity, location, and size.Peer ReviewedPostprint (author's final draft

SNAKE ASSEMBLAGE STRUCTURES AND SEASONAL ACTIVITY PATTERNS ON A MILITARY BASE IN SOUTH-CENTRAL PENNSYLVANIA:: LAND MANAGEMENT IMPLICATIONS FOR SNAKE CONSERVATION

We ascertained the assemblage structures of snakes occurring in a mixed habitat matrix of natural and disturbed habitats during 2008–2011 at Letterkenny Army Depot (LEAD), a 7200 ha U.S. Army base in south-central Pennsylvania, to understand the patterns of species abundance as they related to habitat type of managed lands. We detected eight species in 12 sites comprising natural and disturbed habitats of wetlands, forest, and thicket and open fields. The Common Gartersnake (Thamnophis sirtalis) occurred in the most sites, the Red-bellied Snake (Storeria occipitomaculata) was the rarest species in the study. Two to six species occupied each site and were distributed unevenly. Dynamics of assemblages could be explained in part by habitat and also by the presence of the North American Racer (Coluber constrictor). All species for which data were available exhibited a unimodal pattern to their seasonal activity (mostly May and June); however, seasonal activity peaks differed between sexes. Sex ratios varied among species but were consistently female–biased in the Common Gartersnake and Ring-necked Snake (Diadophis punctatus) in Pennsylvania and surrounding areas. As elsewhere in Pennsylvania and the Northeast, body sizes of adults were larger for species syntopic with the North American Racer than for species not syntopic with this potential predator. We found a degree of predictability with respect to snake assemblage dynamics among habitats at LEAD, which in turn can prove useful in resource management of this large and protected human-impacted system

Velocity and Distribution of Primordial Neutrinos

The Cosmic Neutrinos Background (\textbf{CNB}) are Primordial Neutrinos decoupled when the Universe was very young. Its detection is complicated, especially if we take into account neutrino mass and a possible breaking of Lorentz Invariance at high energy, but has a fundamental relevance to study the Big-Bang. In this paper, we will see that a Lorentz Violation does not produce important modification, but the mass does. We will show how the neutrinos current velocity, with respect to comobile system to Universe expansion, is of the order of 1065 $[\frac{km}{s}]$, much less than light velocity. Besides, we will see that the neutrinos distribution is complex due to Planetary motion. This prediction differs totally from the usual massless case, where we would get a correction similar to the Dipolar Moment of the \textbf{CMB}.Comment: 16 pages, latex, 7 figure

Bounding the size of a vertex-stabiliser in a finite vertex-transitive graph

In this paper we discuss a method for bounding the size of the stabiliser of a vertex in a $G$-vertex-transitive graph $\Gamma$. In the main result the group $G$ is quasiprimitive or biquasiprimitive on the vertices of $\Gamma$, and we obtain a genuine reduction to the case where $G$ is a nonabelian simple group. Using normal quotient techniques developed by the first author, the main theorem applies to general $G$-vertex-transitive graphs which are $G$-locally primitive (respectively, $G$-locally quasiprimitive), that is, the stabiliser $G_\alpha$ of a vertex $\alpha$ acts primitively (respectively quasiprimitively) on the set of vertices adjacent to $\alpha$. We discuss how our results may be used to investigate conjectures by Richard Weiss (in 1978) and the first author (in 1998) that the order of $G_\alpha$ is bounded above by some function depending only on the valency of $\Gamma$, when $\Gamma$ is $G$-locally primitive or $G$-locally quasiprimitive, respectively

Fourier methods for smooth distribution function estimation

In this paper we show how to use Fourier transform methods to analyze the asymptotic behavior of kernel distribution function estimators. Exact expressions for the mean integrated squared error in terms of the characteristic function of the distribution and the Fourier transform of the kernel are employed to obtain the limit value of the optimal bandwidth sequence in its greatest generality. The assumptions in our results are mild enough so that they are applicable when the kernel used in the estimator is a superkernel, or even the sinc kernel, and this allows to extract some interesting consequences, as the existence of a class of distributions for which the kernel estimator achieves a first-order improvement in efficiency over the empirical distribution function.Comment: 12 pages, 2 figure