We consider the large deviations of the smallest eigenvalue of the Wishart-Laguerre Ensemble. Using the Coulomb gas picture we obtain rate functions for the large fluctuations to the left and the right of the hard edge. Our results are compared with known exact results for $\beta =1$ finding good agreement. We also consider the case of almost square matrices finding new universal rate functions describing large fluctuations.

Bidirectional variants of stochastic many particle models for transport by molecular motors show a strong tendency to form macroscopic clusters on static lattices. Inspired by the fact that the microscopic tracks for molecular motors are dynamical, we study the influence of different types of lattice dynamics on stochastic bidirectional transport. We observe a transition toward efficient transport (corresponding to the dissolution of large clusters) controlled by the lattice dynamics.

Properties of computing Boolean circuits composed of noisy logical gates are studied using the statistical physics methodology. A formula-growth model that gives rise to random Boolean functions is mapped onto a spin system, which facilitates the study of their typical behavior in the presence of noise. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding macroscopic phase transitions. The framework is employed for deriving results on error-rates at various function-depths and function sensitivity, and their dependence on the gate-type and noise model used. These are difficult to obtain via the traditional methods used in this field.

We address the issue of a system that has been tacitly made thermodynamically open by externally driving the associated heat bath in an attempt to gain better insight regarding many physical situations that are akin to this problem. This work embodies the study of the quantum effects in the rate of decay from a metastable state of a Brownian particle which is in contact with a correlated noise-driven bath. We do this by initiating from a suitable system-reservoir model to derive the operator-valued Langevin equation. This further leads us to the corresponding $c$-number analog that includes quantum effects in leading order. Suitable mathematical treatment culminates in the quantum Fokker-Planck equation, the solution to which yields the rate expression. Finally, we put this to thorough numerical analysis.

Predicting the statistics of realistic wave-chaotic scattering systems requires, in addition to random matrix theory, introduction of system-specific information. This paper investigates experimentally one aspect of system-specific behavior, namely, the effects of short ray trajectories in wave-chaotic systems open to outside scattering channels. In particular, we consider ray trajectories of limited length that enter a scattering region through a channel (port) and subsequently exit through a channel (port). We show that a suitably averaged value of the impedance can be computed from these trajectories and that this can improve the ability to describe the statistical properties of the scattering systems. We illustrate and test these points through experiments on a realistic two-port microwave scattering billiard.

Weak bonds are ubiquitous in biological structures. They often act as adhesive contacts within an extended structure, for example, the internal bonds in a folded protein or a DNA/RNA loop. They also act as linkers between two structures, for example, a protein grafted in a cell membrane or a protein linking the cell membranes of two neighboring cells. Typically, the breakage of a bond depends on the strength of the binding potential and viscosity of the medium. But when extended structures couple to the bond, as in the above examples, the dynamics of the structure also has to be considered in order to understand the bond breakage phenomenon. Here we consider a generic model, a stretched polymer (an extended structure) tethered to a soft bond and study how the dynamics of the polymer, in addition to thermal noise, influences bond breakage. We also explore how the hydrodynamic interaction due to the fluid medium, which couples the distant parts of the polymer, change the bond breakage rate. We find that hydrodynamic interaction enhances the breakage rate and also makes the motion of the unstable collective mode of the polymer more coherent.

The bioengineering design principles evolved in silkworm cocoons make them ideal natural prototypes and models for structural composites. Cocoons depend for their stiffness and strength on the connectivity of bonding between their constituent materials of silk fibers and sericin binder. Strain-activated mechanisms for loss of bonding connectivity in cocoons can be translated directly into a surprisingly simple yet universal set of physically realistic as well as predictive quantitative structure-property relations for a wide range of technologically important fiber and particulate composite materials.

We investigate the displacement of one fluid by another in a deformable medium with pore-scale disorder. We develop a model that captures the dynamic pressure redistribution at the invasion front and the feedback between fluid invasion and microstructure rearrangement. Our results suggest how to collapse the transition between invasion percolation and viscous fingering in the presence of quenched disorder. We predict the emergence of a fracturing pattern for sufficiently deformable media, in agreement with observations of drainage in granular material. We identify a dimensionless number that appears to govern the crossover from fingering to fracturing.

We discuss methods that allow us to increase the step size in a parallel tempering simulation of statistical models and test them at the example of the three-dimensional Heisenberg spin glass. We find an overall speedup of about 2 for contemporary lattices.

Using Monte Carlo simulations, we determine the phase diagram of a diffusive two-temperature conserved order parameter $XY$ model. When the two temperatures are equal the system becomes the equilibrium $XY$ model with the continuous Kosterlitz-Thouless (KT) vortex-antivortex unbinding phase transition. When the two temperatures are unequal the system is driven by an energy flow from the higher temperature heat-bath to the lower temperature one and reaches a far-from-equilibrium steady state. We show that the nonequilibrium phase diagram contains three phases: A homogenous disordered phase and two phases with long range, spin texture order. Two critical lines, representing continuous phase transitions from a homogenous disordered phase to two phases of long range order, meet at the equilibrium KT point. The shape of the nonequilibrium critical lines as they approach the KT point is described by a crossover exponent $\phi =2.52\pm 0.05$. Finally, we suggest that the transition between the two phases with long-range order is first-order, making the KT-point where all three phases meet a bicritical point.

Nonextensive statistics, characterized by a nonextensive parameter $q$, is a promising and practically useful generalization of the Boltzmann statistics to describe power-law behaviors from physical and social observations. We here explore the unevenness of the first-digit distribution of nonextensive statistics analytically and numerically. We find that the first-digit distribution follows Benford’s law and fluctuates slightly in a periodical manner with respect to the logarithm of the temperature. The fluctuation decreases when $q$ increases, and the result converges to Benford’s law exactly as $q$ approaches 2. The relevant regularities between nonextensive statistics and Benford’s law are also presented and discussed.

A gradient of director through the thickness of a nematic glass cantilever gives a gradient in the large distortions such materials suffer in response to temperature or illumination changes. We first sketch, within isotropic elasticity, how such gradients cause these cantilevers to respond by bending. We then derive the response within the anisotropic elasticity expected for uniaxial solids. Because, in general, spontaneously bending cantilevers have regions of elongation and contraction (with respect to their neutral state), internal stresses are generated, the magnitude of which depends on the anisotropic, fourth rank modulus tensor and in particular on its local alignment arising from the director’s spatial distribution. We show that despite elastic complexity, bend is simply linear in the anisotropy of thermo-optical response, with a slope depending on the structure of the modulus tensor, justifying the previous literature on spontaneously bending cantilevers. We also explicitly consider two important director distributions—splay-bend and twist. Splay-bend cantilevers have no anticlastic (double-bend, saddle) response in the isotropic case or for some values of the anisotropic modulus tensor. Twist cantilevers have maximal anticlasticity in the isotropic case which we show to be weakly modified by anisotropy of elastic moduli.

We studied avalanches of cohesionless granular materials down a rough inclined plane and overflowing a wall normal to the incoming flow and to the bottom. This paper focuses on the transient time-varying mean force exerted by the granular stream on the obstacle at various slope inclinations. A nearly triangular dead zone is formed upstream of the obstacle. It largely contributes to the overall force signal at low slope inclinations. It also drives the residual force corresponding to the avalanche tail until its standstill whatever the slope inclination. An analytical hydrodynamic model based on depth-averaged momentum conservation was successfully developed for steady-flow conditions to predict the steady-state force computed from discrete numerical simulations [T. Faug, R. Beguin, and B. Chanut, Phys. Rev. E 80, 021305 (2009)]. The basic equations of the model are briefly reviewed and adapted to transient time-varying flows. The modified hydrodynamic model quite accurately represents the force peak produced by the granular avalanche flows computed from discrete numerical simulations reported in previous studies. A fitting procedure is needed to represent the decrease of the force after the force peak, thus quantifying the different contributions to the mean force on the wall. We show that the weight of each contribution is largely dependent on the slope inclination.

We have carried out a numerical study of both the structural and thermodynamic properties of free-standing smectic films (FSSFs) for two cases of enhanced pair interactions in the bounding layers. Calculations, based upon the extended McMillan’s approach with anisotropic forces, shows a stepwise reduction of the value of the heat capacity as the temperature is raised above the bulk smectic A-isotropic transition. The effects of surface “enhanced” pair interactions in the bounding layers and of film thickness on the orientational and translational order parameters, the Helmholtz free energy, and entropy of FSSFs have also been investigated. Reasonable agreement between the theoretically predicted and the experimentally obtained—by means of calorimetric techniques—data on the heat capacity of the partially fluorinated$5-n-\text{alkyl}-2-(4-n-(\text{perfluoroalkyl}-\text{metheleneoxy}\left)\text{phenyl}\right)$ (H10F5MOPP) films has been obtained.

A simple theory for glassy-polymeric mechanical response that accounts for large-scale chain relaxation is presented. It captures the crossover from perfect-plastic response to Gaussian strain hardening as the degree of polymerization $N$ increases, without invoking entanglements. By relating hardening to interactions on the scale of monomers and chain segments, we correctly predict its magnitude. Strain-activated relaxation arising from the need to maintain constant chain contour length reduces the characteristic relaxation time by a factor $\sim \dot{ϵ}N$ during active deformation at strain rate $\dot{ϵ}$. This prediction is consistent with results from recent experiments and simulations, and we suggest how it may be further tested experimentally.

The experimental data of Takahashi et al. [Physica D 43, 318 (1990)], on the response of squid giant axons stimulated by periodic sequence of short current pulses is interpreted within the Hodgkin-Huxley model. The minimum of the firing rate as a function of the stimulus amplitude $I_0$ in the high-frequency regime is due to the multimodal transition. Below this singular point only odd multiples of the driving period remain and the system is sensitive to noise. The coefficient of variation has a maximum and the firing rate has a minimum as a function of the noise intensity, which is an indication of the stochastic coherence antiresonance. The model calculations reproduce the frequency of occurrence of the most common modes in the vicinity of the transition. A linear relation of output frequency vs $I_0$ above the transition is also confirmed.

Wave pattern formation and transition in chemical and biochemical reaction systems can reveal the system properties. We investigate the pattern transition from target waves to spiral waves upon the increment of inactive beads in a discrete system model, where ion-exchange resin loaded with Belousov-Zhabotinsky catalyst corresponds to the active beads. The results show that inactive beads slow the propagation speed of target waves and increase the wave frequency. As the population of inactive beads increases, clusters are formed, which then break waves into segments where bounded spiral pairs are generated and separated into individual spirals. From this observation, we conclude that the population of inactive resin beads acts as the bifurcation parameter controlling the wave pattern transition from targets to spirals.

Weak selection, which means a phenotype is slightly advantageous over another, is an important limiting case in evolutionary biology. Recently, it has been introduced into evolutionary game theory. In evolutionary game dynamics, the probability to be imitated or to reproduce depends on the performance in a game. The influence of the game on the stochastic dynamics in finite populations is governed by the intensity of selection. In many models of both unstructured and structured populations, a key assumption allowing analytical calculations is weak selection, which means that all individuals perform approximately equally well. In the weak selection limit many different microscopic evolutionary models have the same or similar properties. How universal is weak selection for those microscopic evolutionary processes? We answer this question by investigating the fixation probability and the average fixation time not only up to linear but also up to higher orders in selection intensity. We find universal higher order expansions, which allow a rescaling of the selection intensity. With this, we can identify specific models which violate (linear) weak selection results, such as the one-third rule of coordination games in finite but large populations.

A vibrating plate is set into a chaotic state of wave turbulence by a forcing having periodic and random components. Both components are weighted in order to explore continuously intermediate forcing from the periodic to the random one, but keeping constant its rms value. The transverse velocity of the plate is measured at the application point of the force. It is found that whatever the detail of the forcing is, the velocity spectra exhibit a universal cascade for frequencies larger than the forcing frequency range. In contrast, the velocity spectra strongly depend on the nature of the forcing within the range of forcing frequencies. The coherence function is used to extract the contribution of the velocity fluctuations that display a linear relationship with the forcing. The nonlinear contribution to the velocity fluctuations is found to be almost constant, about 55% of the total velocity fluctuations whatever the nature of the forcing from random to periodic. On the other hand, the nonlinear contribution to the fluctuations of the injected power depends on the nature of the forcing; it is significantly larger for the periodic forcing (60%) and decreases continuously as the randomness is increased, reaching a value of 40% for the pure random forcing. For all the cases of intermediate forcing from random to periodic, a simple model of the velocity response recovers in a fairly good agreement the probability density function of the injected power. The consequence of the existence of a linear-response component is discussed in the context of the fluctuation-dissipation theorem validation in experiments of out-of-equilibrium systems.

The assembly of molecular networks into structures such as random tilings and glasses has recently been demonstrated for a number of two-dimensional systems. These structures are dynamically arrested on experimental time scales, so the critical regime in their formation is that of initial growth. Here, we identify a transition from energetic to entropic stabilization in the nucleation and growth of a molecular rhombus tiling. Calculations based on a lattice-gas model show that clustering of topological defects and the formation of faceted boundaries followed by a slow relaxation to equilibrium occur under conditions of energetic stabilization. We also identify an entropically stabilized regime in which the system grows directly into an equilibrium configuration without the need for further relaxation. Our results provide a methodology for identifying equilibrium and nonequilibrium randomness in the growth of molecular tilings, and we demonstrate that equilibrium spatial statistics are compatible with exponentially slow dynamical behavior.