Dynamical Monte Carlo Study of Equilibrium Polymers : Static Properties

We report results of extensive Dynamical Monte Carlo investigations on self-assembled Equilibrium Polymers (EP) without loops in good solvent. (This is thought to provide a good model of giant surfactant micelles.) Using a novel algorithm we are able to describe efficiently both static and dynamic properties of systems in which the mean chain length \Lav is effectively comparable to that of laboratory experiments (up to 5000 monomers, even at high polymer densities). We sample up to scission energies of $E/k_BT=15$ over nearly three orders of magnitude in monomer density $\phi$, and present a detailed crossover study ranging from swollen EP chains in the dilute regime up to dense molten systems. Confirming recent theoretical predictions, the mean-chain length is found to scale as \Lav \propto \phi^\alpha \exp(\delta E) where the exponents approach $\alpha_d=\delta_d=1/(1+\gamma) \approx 0.46$ and $\alpha_s = 1/2 [1+(\gamma-1)/(\nu d -1)] \approx 0.6, \delta_s=1/2$ in the dilute and semidilute limits respectively. The chain length distribution is qualitatively well described in the dilute limit by the Schulz-Zimm distribution \cN(s)\approx s^{\gamma-1} \exp(-s) where the scaling variable is s=\gamma L/\Lav. The very large size of these simulations allows also an accurate determination of the self-avoiding walk susceptibility exponent $\gamma \approx 1.165 \pm 0.01$. ....... Finite-size effects are discussed in detail.Comment: 15 pages, 14 figures, LATE

Circular Jacobi ensembles and deformed Verblunsky coefficients

Using the spectral theory of unitary operators and the theory of orthogonal polynomials on the unit circle, we propose a simple matrix model for the following circular analogue of the Jacobi ensemble: $$c_{\delta,\beta}^{(n)} \prod_{1\leq k -1/2$. If$e$is a cyclic vector for a unitary$n\times n$matrix$U$, the spectral measure of the pair$(U,e)$is well parameterized by its Verblunsky coefficients$(\alpha_0, ..., \alpha_{n-1})$. We introduce here a deformation$(\gamma_0, >..., \gamma_{n-1})$of these coefficients so that the associated Hessenberg matrix (called GGT) can be decomposed into a product$r(\gamma_0)... r(\gamma_{n-1})$of elementary reflections parameterized by these coefficients. If$\gamma_0, ..., \gamma_{n-1}$are independent random variables with some remarkable distributions, then the eigenvalues of the GGT matrix follow the circular Jacobi distribution above. These deformed Verblunsky coefficients also allow to prove that, in the regime$\delta = \delta(n)$with$\delta(n)/n \to \dd$, the spectral measure and the empirical spectral distribution weakly converge to an explicit nontrivial probability measure supported by an arc of the unit circle. We also prove the large deviations for the empirical spectral distribution. Formula with Formula . If e is a cyclic vector for a unitary n x n matrix U, the spectral measure of the pair (U, e) is well parameterized by its Verblunsky coefficients ({alpha}0, ..., {alpha}n-1). We introduce here a deformation ({gamma}0, ..., {gamma}n-1) of these coefficients so that the associated Hessenberg matrix (called GGT) can be decomposed into a product r({gamma}0)··· r({gamma}n-1) of elementary reflections parameterized by these coefficients. If {gamma}0, ..., {gamma}n-1 are independent random variables with some remarkable distributions, then the eigenvalues of the GGT matrix follow the circular Jacobi distribution above. These deformed Verblunsky coefficients also allow us to prove that, in the regime {delta} = {delta} (n) with {delta} (n)/ n -> β d/2, the spectral measure and the empirical spectral distribution weakly converge to an explicit nontrivial probability measure supported by an arc of the unit circle. We also prove the large deviations for the empirical spectral distributio

Wind changes above warm Agulhas Current eddies

Sea surface temperature (SST) estimated from the Advanced Microwave Scanning Radiometer E onboard the Aqua satellite and altimetry-derived sea level anomalies are used south of the Agulhas Current to identify warm-core mesoscale eddies presenting a distinct SST perturbation greater than to 1 °C to the surrounding ocean. The analysis of twice daily instantaneous charts of equivalent stability-neutral wind speed estimates from the SeaWinds scatterometer onboard the QuikScat satellite collocated with SST for six identified eddies shows stronger wind speed above the warm eddies than the surrounding water in all wind directions, if averaged over the lifespan of the eddies, as was found in previous studies. However, only half of the cases showed higher wind speeds above the eddies at the instantaneous scale; 20 % of cases had incomplete data due to partial global coverage by the scatterometer for one path. For cases where the wind is stronger above warm eddies, there is no relationship between the increase in surface wind speed and the SST perturbation, but we do find a linear relationship between the decrease in wind speed from the centre to the border of the eddy downstream and the SST perturbation. SST perturbations range from 1 to 6 °C for a mean eddy SST of 15.9 °C and mean SST perturbation of 2.65 °C. The diameter of the eddies range from 100 to 250 km. Mean background wind speed is about 12 m s−1 (mostly southwesterly to northwesterly) and ranging mainly from 4 to 16 m s−1. The mean wind increase is about 15 %, which corresponds to 1.8 m s−1. A wind speed increase of 4 to 7 m s−1 above warm eddies is not uncommon. Cases where the wind did not increase above the eddies or did not decrease downstream had higher wind speeds and occurred during a cold front associated with intense cyclonic low-pressure systems, suggesting certain synoptic conditions need to be met to allow for the development of wind speed anomalies over warm-core ocean eddies. In many cases, change in wind speed above eddies was masked by a large-scale synoptic wind speed deceleration/acceleration affecting parts of the eddies

Genetic properties of North African Drosophila melanogaster and comparison with European and Afrotropical populations

International audienc

Reactions at polymer interfaces: A Monte Carlo Simulation

Reactions at a strongly segregated interface of a symmetric binary polymer blend are investigated via Monte Carlo simulations. End functionalized homopolymers of different species interact at the interface instantaneously and irreversibly to form diblock copolymers. The simulations, in the framework of the bond fluctuation model, determine the time dependence of the copolymer production in the initial and intermediate time regime for small reactant concentration $\rho_0 R_g^3=0.163 ... 0.0406$. The results are compared to recent theories and simulation data of a simple reaction diffusion model. For the reactant concentration accessible in the simulation, no linear growth of the copolymer density is found in the initial regime, and a $\sqrt{t}$-law is observed in the intermediate stage.Comment: to appear in Macromolecule

The reversible polydisperse Parking Lot Model

We use a new version of the reversible Parking Lot Model to study the compaction of vibrated polydisperse media. The particle sizes are distributed according to a truncated power law. We introduce a self-consistent desorption mechanism with a hierarchical initialization of the system. In this way, we approach densities close to unity. The final density depends on the polydispersity of the system as well as on the initialization and will reach a maximum value for a certain exponent in the power law.Comment: 7 pages, Latex, 12 figure

On Sharp Large Deviations for the bridge of a general Diffusion

We provide sharp Large Deviation estimates for the probability of exit from a domain for the bridge of a $d$-dimensional general diffusion process $X$, as the conditioning time tends to $0$. This kind of results is motivated by applications to numerical simulation. In particular we investigate the influence of the drift $b$ of $X$. It turns out that the sharp asymptotics for the exit time probability are independent of the drift, provided $b$ enjoyes a simple condition that is always satisfied in dimension $1$. On the other hand, we show that the drift can be influential if this assumption is not satisfied.