Large-deviation properties of the extended Moran model

The distributions of the times to the first common ancestor t_mrca is numerically studied for an ecological population model, the extended Moran model. This model has a fixed population size N. The number of descendants is drawn from a beta distribution Beta(alpha, 2-alpha) for various choices of alpha. This includes also the classical Moran model (alpha->0) as well as the uniform distribution (alpha=1). Using a statistical mechanics-based large-deviation approach, the distributions can be studied over an extended range of the support, down to probabilities like 10^{-70}, which allowed us to study the change of the tails of the distribution when varying the value of alpha in [0,2]. We find exponential distributions p(t_mrca)~ delta^{t_mrca} in all cases, with systematically varying values for the base delta. Only for the cases alpha=0 and alpha=1, analytical results are known, i.e., delta=\exp(-2/N^2) and delta=2/3, respectively. We recover these values, confirming the validity of our approach. Finally, we also study the correlations between t_mrca and the number of descendants.Comment: 8 pages, 8 figure

Non-linear fate of internal wave attractors

We present a laboratory study on the instability of internal wave attractors in a trapezoidal fluid domain filled with uniformly stratified fluid. Energy is injected into the system via standing-wave-type motion of a vertical wall. Attractors are found to be destroyed by parametric subharmonic instability (PSI) via a triadic resonance which is shown to provide a very efficient energy pathway from long to short length scales. This study provides an explanation why attractors may be difficult or impossible to observe in natural systems subject to large amplitude forcing

Regulation by small RNAs via coupled degradation: mean-field and variational approaches

Regulatory genes called small RNAs (sRNAs) are known to play critical roles in cellular responses to changing environments. For several sRNAs, regulation is effected by coupled stoichiometric degradation with messenger RNAs (mRNAs). The nonlinearity inherent in this regulatory scheme indicates that exact analytical solutions for the corresponding stochastic models are intractable. Here, we present a variational approach to analyze a well-studied stochastic model for regulation by sRNAs via coupled degradation. The proposed approach is efficient and provides accurate estimates of mean mRNA levels as well as higher order terms. Results from the variational ansatz are in excellent agreement with data from stochastic simulations for a wide range of parameters, including regions of parameter space where mean-field approaches break down. The proposed approach can be applied to quantitatively model stochastic gene expression in complex regulatory networks.Comment: 4 pages, 3 figure

A New Pseudopolymorph of Hexakis-(4-cynaophenyl)benzene

The title compound (systematic name: benzene-4,4′,4′′,4′′′,-4′′′′,4′′′′′-hexaylhexabenzonitrile dichloromethane disolvate), C48H24N6•2CH2Cl2, crystallizes as an inclusion compound during the slow diffusion of methanol into a solution of hexakis(4-cyanophenyl)benzene in CH2Cl2. The hexakis(4- cyanophenyl)benzene molecule lies on an axis of twofold rotation in the space group Pbcn. Weak C—H•••N interactions between hexakis(4-cyanophenyl)benzene molecules define an open network with space for including guests. The resulting structure is a new pseudopolymorph of hexakis-(4-cyanophenyl)benzene. The eight known pseudopolymorphs have few shared architectural features, in part because none of the intermolecular interactions that are present plays a dominant role or forces neighboring molecules to assume particular relative orientations

Depinning of domain walls with an internal degree of freedom

Taking into account the coupling between the position of the wall and an internal degree of freedom, namely its phase $\phi$, we examine, in the rigid wall approximation, the dynamics of a magnetic domain wall subject to a weak pinning potential. We determine the corresponding force-velocity characteristics, which display several unusual features when compared to standard depinning laws. At zero temperature, there exists a bistable regime for low forces, with a logarithmic behavior close to the transition. For weak pinning, there occurs a succession of bistable transitions corresponding to different topological modes of the phase evolution. At finite temperature, the force-velocity characteristics become non-monotonous. We compare our results to recent experiments on permalloy nanowires