A multiple replica approach to simulate reactive trajectories

A method to generate reactive trajectories, namely equilibrium trajectories leaving a metastable state and ending in another one is proposed. The algorithm is based on simulating in parallel many copies of the system, and selecting the replicas which have reached the highest values along a chosen one-dimensional reaction coordinate. This reaction coordinate does not need to precisely describe all the metastabilities of the system for the method to give reliable results. An extension of the algorithm to compute transition times from one metastable state to another one is also presented. We demonstrate the interest of the method on two simple cases: a one-dimensional two-well potential and a two-dimensional potential exhibiting two channels to pass from one metastable state to another one

Produit de solubilité de la calcite et constantes de dissociation de CaHCO3+ et CaCO30 entre 5 et 75 °C

Les valeurs du produit de solubilité de la calcite et des constantes de dissociation de CaHCO3+ et CaCO30, notées K3 et K4, ont été déterminées à différentes températures comprises entre 5 et 75 °C (la calcite est instable aux températures plus élevées) à partir des mesures [(Ca2+)T, pH] de solubilité de ce sel dans l'eau carboniquement pure. Les résultats obtenus ont permis d'établir les relations empiriques suivantes :pKs= 7,8156 + 0,03111 T + (1 502/T) - 5,518 log TpK3= 6,2447 + 0,00437 T + (864,479/T) - 0,363 log TpK4= 2,89636 + 0,00707 T + (102,87/T) - 0,44176 log Texpressions dans lesquelles T désigne la température absolue (K) et log le logarithme décimal.Des variations de pKS avec la température nous avons déduit, à 25 °C, les grandeurs thermodynamiques relatives à la dissolution de la calcite :∆H0 = -2510 cal. mol-1, ∆S0 = -47,2 cal. mol-1. K-1et ∆C∘p = -73,9 cal. mol-1. K-1The values of the solubility product of calcite and dissociation constants of CaHCO3+ and CaCO30, K3 and K4 respectively, were determined at several temperatures between 5 and 75 °C (calcite becomes unstable at higher temperatures) from measurements [(Ca2+)T, pH] of calcite solubility using carbonically pure water. The results obtained lead to the following empirical expressions for the dependence of equilibrium constants on the temperature :pKs= 7,8156 + 0,03111 T + (1 502/T) - 5,518 log TpK3= 6,2447 + 0,00437 T + (864,479/T) - 0,363 log TpK4= 2,89636 + 0,00707 T + (102,87/T) - 0,44176 log Twhere log T is the common logarithm of the absolute temperature T(K).Using this expression of pKS, the calculated thermodynamic properties of the calcite dissolution reaction at 25 °C are :∆H0 = -2510 cal. mol-1, ∆S0 = -47,2 cal. mol-1. K-1et ∆C∘p = -73,9 cal. mol-1. K-

Stacking order dynamic in the quasi-two-dimensional dichalcogenide 1T-TaS2_2 probed with MeV ultrafast electron diffraction

Transitions between different charge density wave (CDW) states in quasi-two-dimensional materials may be accompanied also by changes in the inter-layer stacking of the CDW. Using MeV ultrafast electron diffraction, the out-of-plane stacking order dynamics in the quasi-two-dimensional dichalcogenide 1T-TaS$_2$ is investigated for the first time. From the intensity of the CDW satellites aligned around the commensurate $l$ = 1/6 characteristic stacking order, it is found out that this phase disappears with a 0.5 ps time constant. Simultaneously, in the same experiment, the emergence of the incommensurate phase, with a slightly slower 2.0 ps time constant, is determined from the intensity of the CDW satellites aligned around the incommensurate $l$ = 1/3 characteristic stacking order. These results might be of relevance in understanding the metallic character of the laser-induced metastable "hidden" state recently discovered in this compound

Resonance modes in a 1D medium with two purely resistive boundaries: calculation methods, orthogonality and completeness

Studying the problem of wave propagation in media with resistive boundaries can be made by searching for "resonance modes" or free oscillations regimes. In the present article, a simple case is investigated, which allows one to enlighten the respective interest of different, classical methods, some of them being rather delicate. This case is the 1D propagation in a homogeneous medium having two purely resistive terminations, the calculation of the Green function being done without any approximation using three methods. The first one is the straightforward use of the closed-form solution in the frequency domain and the residue calculus. Then the method of separation of variables (space and time) leads to a solution depending on the initial conditions. The question of the orthogonality and completeness of the complex-valued resonance modes is investigated, leading to the expression of a particular scalar product. The last method is the expansion in biorthogonal modes in the frequency domain, the modes having eigenfrequencies depending on the frequency. Results of the three methods generalize or/and correct some results already existing in the literature, and exhibit the particular difficulty of the treatment of the constant mode

Central Limit Theorem for Adaptative Multilevel Splitting Estimators in an Idealized Setting

International audienceThe Adaptive Multilevel Splitting algorithm is a very powerful and versatile iterative method to estimate the probability of rare events, based on an interacting particle systems. In an other article, in a so-called idealized setting, the authors prove that some associated estimators are unbiased, for each value of the size n of the systems of replicas and of resampling number k. Here we go beyond and prove these estimator's asymptotic normality when h goes to infinity, for any fixed value of k. The main ingredient is the asymptotic analysis of a functional equation on an appropriate characteristic function. Some numerical simulations illustrate the convergence to rely on Gaussian confidence intervals

Production of η′\eta\prime Mesons in the pp→ppη′pp \to pp\eta\prime Reaction at 3.67 GeV/c

The ratio of the total exclusive production cross sections for $\eta\prime$ and $\eta$ mesons has been measured in the $pp$ reaction at $p_{beam}=3.67$ GeV/c. The observed $\eta\prime/\eta$ ratio is $(0.83\pm{0.11}^{+0.23}_{-0.18})\times 10^{-2}$ from which the exclusive $\eta\prime$ meson production cross section is determined to be $(1.12\pm{0.15}^{+0.42}_{-0.31})\mu b$. Differential cross section distributions have been measured. Their shape is consistent with isotropic $\eta\prime$ meson production.Comment: 14 pages, 5 figures, accepted by Phys.Lett.