Inviscid Large deviation principle and the 2D Navier Stokes equations with a free boundary condition

Using a weak convergence approach, we prove a LPD for the solution of 2D stochastic Navier Stokes equations when the viscosity converges to 0 and the noise intensity is multiplied by the square root of the viscosity. Unlike previous results on LDP for hydrodynamical models, the weak convergence is proven by tightness properties of the distribution of the solution in appropriate functional spaces

Loop algorithm for Heisenberg models with biquadratic interaction and phase transitions in two dimensions

We present a new algorithm for quantum Monte Carlo simulation based on global updating with loops. While various theoretical predictions are confirmed in one dimension, we find, for S=1 systems on a square lattice with an antiferromagnetic biquadratic interaction, that the intermediate phase between the antiferromagnetic and the ferromagnetic phases is disordered and that the two phase transitions are both of the first order in contrast to the one-dimensional case. It is strongly suggested that the transition points coincide those at which the algorithm changes qualitatively.Comment: 4 pages including 4 figures, to appear in JPS

Ground state of the Kagome-like S=1/2 antiferromagnet, Volborthite Cu3V2O7(OH)2.2H2O

Volborthite compound is one of the very few realizations of S=1/2 quantum spins on a highly frustrated kagome-like lattice. Low-T SQUID measurements reveal a broad magnetic transition below 2K which is further confirmed by a peak in the 51V nuclear spin relaxation rate (1/T1) at 1.4K$\pm$0.2K. Through 51V NMR, the ground state (GS) appears to be a mixture of different spin configurations, among which 20% correspond to a well defined short range order, possibly of the $\sqrt{3} \times \sqrt{3}$ type. While the freezing involve all the Cu$^{2+}$ spins, only 40% of the copper moment is actually frozen which suggests that quantum fluctuations strongly renormalize the GS.Comment: 4 pages, 4 figures, to appear in PR

Jointly Optimal Channel Pairing and Power Allocation for Multichannel Multihop Relaying

We study the problem of channel pairing and power allocation in a multichannel multihop relay network to enhance the end-to-end data rate. Both amplify-and-forward (AF) and decode-and-forward (DF) relaying strategies are considered. Given fixed power allocation to the channels, we show that channel pairing over multiple hops can be decomposed into independent pairing problems at each relay, and a sorted-SNR channel pairing strategy is sum-rate optimal, where each relay pairs its incoming and outgoing channels by their SNR order. For the joint optimization of channel pairing and power allocation under both total and individual power constraints, we show that the problem can be decoupled into two subproblems solved separately. This separation principle is established by observing the equivalence between sorting SNRs and sorting channel gains in the jointly optimal solution. It significantly reduces the computational complexity in finding the jointly optimal solution. It follows that the channel pairing problem in joint optimization can be again decomposed into independent pairing problems at each relay based on sorted channel gains. The solution for optimizing power allocation for DF relaying is also provided, as well as an asymptotically optimal solution for AF relaying. Numerical results are provided to demonstrate substantial performance gain of the jointly optimal solution over some suboptimal alternatives. It is also observed that more gain is obtained from optimal channel pairing than optimal power allocation through judiciously exploiting the variation among multiple channels. Impact of the variation of channel gain, the number of channels, and the number of hops on the performance gain is also studied through numerical examples.Comment: 15 pages. IEEE Transactions on Signal Processin

Logarithmic asymptotics of the densities of SPDEs driven by spatially correlated noise

We consider the family of stochastic partial differential equations indexed by a parameter \eps\in(0,1], \begin{equation*} Lu^{\eps}(t,x) = \eps\sigma(u^\eps(t,x))\dot{F}(t,x)+b(u^\eps(t,x)), \end{equation*} (t,x)\in(0,T]\times\Rd with suitable initial conditions. In this equation, $L$ is a second-order partial differential operator with constant coefficients, $\sigma$ and $b$ are smooth functions and $\dot{F}$ is a Gaussian noise, white in time and with a stationary correlation in space. Let p^\eps_{t,x} denote the density of the law of u^\eps(t,x) at a fixed point (t,x)\in(0,T]\times\Rd. We study the existence of \lim_{\eps\downarrow 0} \eps^2\log p^\eps_{t,x}(y) for a fixed $y\in\R$. The results apply to a class of stochastic wave equations with $d\in\{1,2,3\}$ and to a class of stochastic heat equations with $d\ge1$.Comment: 39 pages. Will be published in the book " Stochastic Analysis and Applications 2014. A volume in honour of Terry Lyons". Springer Verla

Membrane binding proteins of coronaviruses

Coronaviruses (CoVs) infect many species causing a variety of diseases with a range of severities. Their members include zoonotic viruses with pandemic potential where therapeutic options are currently limited. Despite this diversity CoVs share some common features including the production, in infected cells, of elaborate membrane structures. Membranes represent both an obstacle and aid to CoV replication – and in consequence – virus-encoded structural and nonstructural proteins have membrane-binding properties. The structural proteins encounter cellular membranes at both entry and exit of the virus while the nonstructural proteins reorganize cellular membranes to benefit virus replication. Here, the role of each protein in membrane binding is described to provide a comprehensive picture of their role in the CoV replication cycle

The Determinants of the Preferred Walking Speed in Individuals with Obesity.

The preferred walking speed (PWS), also known as the "spontaneous" or "self-selected" walking speed, is the speed normally used during daily living activities and may represent an appropriate exercise intensity for weight reduction programs aiming to enhance a more negative energy balance. The aim of this study was to examine, simultaneously, the energetics, mechanics, and perceived exertion determinants of PWS in individuals with obesity. Twenty-three adults with obesity (age 32.7 ± 6.8 years, body mass index 33.6 ± 2.6 kg/m2) were recruited. The participants performed 10 min of treadmill familiarization, and PWS was determined. Each subject performed six 5-min walking trials (PWS 0.56, 0.83, 1.11, 1.39, and 1.67 m/s). Gas exchanges were collected and analyzed to obtain the gross energy cost of walking (GCw), rated perceived exertion (RPE) was measured using a 6-20 Borg scale, and the external mechanical work (Wext) and the fraction of mechanical energy recovered by the pendular mechanism (Recovery) were computed using an instrumented treadmill. Second-order least-squares regression was used to calculate the optimal walking speed (OWS) of each variable. No significant difference was found between PWS (1.28 ± 0.13 m/s) and OWS for GCw (1.28 ± 0.10 m/s), RPE cost of walking (1.38 ± 0.14 m/s), and Recovery (1.48 ± 0.27 m/s; p > 0.06 for all), but the PWS was significantly faster than the OWS for Wext (0.98 ± 0.56 m/s; p < 0.02). Multiple regression (r = 0.72; p = 0.003) showed that ∼52% of the variance in PWS was explained by Recovery, Wext, and height. The main finding of this study was that obese adults may select their PWS in function of several competing demands, since this speed simultaneously minimizes pendular energy transduction, energy cost, and perceived exertion during walking. Moreover, recovery of mechanical work, external work, and height seem to be the major determinants of PWS in these individuals

Magnetic properties of NaV2O5, a one-dimensional spin 1/2 antiferromagnet with finite chains

We have performed measurements of the magnetic susceptibility of NaV$_2$O$_5$ between 2 and 400 K. The high temperature part is typical of spin 1/2 chains with a nearest--neighbour antiferromagnetic exchange integral $J$ of 529 K. We develop a model for the susceptibility of a system with finite chains to account for the low temperature part of the data, which cannot be fitted by a standard Curie-Weiss term. These results suggest that the next nearest--neighbour exchange integral $J_2$ in CaV$_4$O$_9$ should be of the order of 500 K because, like $J$ in NaV$_2$O$_5$, it corresponds to corner sharing VO$_5$ square pyramids.Comment: An early version of the manuscript was mistakenly submitted. Although relatively minor, the changes concern the list of authors, the main text, the references and the figure captions. 10 pages of latex, 2 figure