We discuss general multidimensional stochastic processes driven by a system of Langevin equations with multiplicative white noise. In particular, we address the problem of how time reversal diffusion processes are affected by the variety of conventions available to deal with stochastic integrals. We present a functional formalism to build up the generating functional of correlation functions without any type of discretization of the Langevin equations at any intermediate step. The generating functional is characterized by a functional integration over two sets of commuting variables, as well as Grassmann variables. In this representation, time reversal transformation became a linear transformation in the extended variables, simplifying in this way the complexity introduced by the mixture of prescriptions and the associated calculus rules. The stochastic calculus is codified in our formalism in the structure of the Grassmann algebra. We study some examples such as higher order derivative Langevin equations and the functional representation of the micromagnetic stochastic Landau-Lifshitz-Gilbert equation.

We consider the dependence of the electron transfer in photosynthetic complexes on correlation properties of random fluctuations of the protein environment. The electron subsystem is modeled by a finite network of connected electron (exciton) sites. The fluctuations of the protein environment are modeled by random telegraph processes, which act either collectively (correlated) or independently (uncorrelated) on the electron sites. We derived an exact closed system of first-order linear differential equations with constant coefficients, for the average density matrix elements and for their first moments. Under some conditions, we obtained analytic expressions for the electron transfer rates and found the range of parameters for their applicability by comparing with the exact numerical simulations. We also compared the correlated and uncorrelated regimes and demonstrated numerically that the uncorrelated fluctuations of the protein environment can, under some conditions, either increase or decrease the electron transfer rates.

In the present work, the two-equation $k\text{−}L$ model [G. Dimonte and R. Tipton, Phys. Fluids 18, 085101 (2006)] is extended by the addition of a third equation for the mass-flux velocity. A set of model constants is derived to satisfy an ansatz of self-similarity in the low Atwood number limit. The model is then applied to the simulation of canonical Rayleigh-Taylor and Richtmyer-Meshkov test problems in one dimension and is demonstrated to reproduce analytical self-similar growth and to recover growth rates used to constrain the model.

Prediction is a fundamental objective of science. It is more difficult for chaotic and complex systems like turbulence. Here we use information theory to quantify spatial prediction using experimental data from a turbulent soap film. At high Reynolds number, $\text{Re}$, where a cascade exists, turbulence becomes easier to predict as the inertial range broadens. The development of a cascade at low $\text{Re}$ is also detected.

The regimes and mechanisms of the Rayleigh-Taylor instability have been studied in the scope of the nonhydrostatic shallow water model with horizontally nonuniform density. As analysis shows, the nonhydrostaticity has a crucial influence on the instability. It is for this reason that at the final stage a collapse tendency predicted on the base of the hydrostatic scenario slows down and turns into the regime of algebraic instability. The numerical testing has shown that in spite of its simplicity, the model is quite able to describe realistically a number of effects. For example, the model captures the shallowing effect, which manifests itself as profile concavities on either side of the jet coming out of the boundary layer.

In a previous paper [M. Kundu, Phys. Plasmas 21, 013302 (2014)], fractional collisional absorption $\left(\alpha \right)$ of laser light in underdense plasma was studied by using a classical scattering model of electron-ion collision frequency ${\nu }_{\mathrm{ei}}$, where total velocity $v=\sqrt{v_{\mathrm{th}}^2+v_0^2}$ (with $v_{\mathrm{th}}$ and $v_0$ as the thermal and the ponderomotive velocity of an electron) dependent Coulomb logarithm $ln\Lambda \left(v\right)$ was shown to be responsible for the anomalous (unconventional) increase of ${\nu }_{\mathrm{ei}}$ and $\alpha \left(\propto {\nu }_{\mathrm{ei}}\right)$ with the laser intensity $I_0$ up to a maximum value about an intensity $I_{\mathrm{c}}$ in the low temperature $(T_{\mathrm{e}}<15\mathrm{eV})$ regime and a conventional $\approx I_0^{-3/2}$ decrease when $I_0\gg I_{\mathrm{c}}$. One may object that the anomalous increase in ${\nu }_{\mathrm{ei}}$ and $\alpha$ were partly due to the artifact introduced in $ln\Lambda$ through the maximum cutoff distance $b_{\max }\propto v$. In this work, we show similar anomalous increase in ${\nu }_{\mathrm{ei}}$ and $\alpha$ versus $I_0$ (in the low temperature and underdense density regime) with more accurate quantum and classical kinetic models of ${\nu }_{\mathrm{ei}}$ without using $ln\Lambda$, but with a proper choice of the total velocity dependent inverse cutoff length $k_{\max }\propto v^2$ (classical) or $k_{\max }\propto v$ (quantum). For a given $I_0<5\times {10}^{14}{\mathrm{W}\mathrm{cm}}^{-2}$, ${\nu }_{\mathrm{ei}}$ versus $T_{\mathrm{e}}$ also exhibits so far unnoticed identical anomalous increase as ${\nu }_{\mathrm{ei}}$ versus $I_0$, even if the conventional $k_{\max }\propto v_{\mathrm{th}}^2$ or $k_{\max }\propto v_{\mathrm{th}}$ (without $v_0$) is chosen. The total velocity dependent $k_{\max }$ in the kinetic models, as proposed here, is found to explain the anomalous increase of $\alpha$ with $I_0$ measured in some earlier laser-plasma experiments.

The understanding of the transport of suprathermal ions in the presence of turbulence is important for fusion plasmas in the burning regime that will characterize reactors, and for space plasmas to understand the physics of particle acceleration. Here, three-dimensional measurements of a suprathermal ion beam in the toroidal plasma device TORPEX are presented. These measurements demonstrate, in a turbulent plasma, the existence of subdiffusive and superdiffusive transport of suprathermal ions, depending on their energy. This result stems from the unprecedented combination of uniquely resolved measurements and first-principles numerical simulations that reveal the mechanisms responsible for the nondiffusive transport. The transport regime is determined by the interaction of the suprathermal ion orbits with the turbulent plasma dynamics, and is strongly affected by the ratio of the suprathermal ion energy to the background plasma temperature.

In common descriptions of phase transitions, first-order transitions are characterized by discontinuous jumps in the order parameter and normal fluctuations, while second-order transitions are associated with no jumps and anomalous fluctuations. Outside this paradigm are systems exhibiting “mixed-order” transitions displaying a mixture of these characteristics. When the jump is maximal and the fluctuations range over the entire range of allowed values, the behavior has been coined an “extreme Thouless effect.” Here we report findings of such a phenomenon in the context of dynamic, social networks. Defined by minimal rules of evolution, it describes a population of extreme introverts and extroverts, who prefer to have contacts with, respectively, no one or everyone. From the dynamics, we derive an exact distribution of microstates in the stationary state. With only two control parameters, $N_{I,E}$ (the number of each subgroup), we study collective variables of interest, e.g., $X$, the total number of $I\text{−}E$ links, and the degree distributions. Using simulations and mean-field theory, we provide evidence that this system displays an extreme Thouless effect. Specifically, the fraction $X/\left(N_I{N}_E\right)$ jumps from 0 to 1 (in the thermodynamic limit) when $N_I$ crosses $N_E$, while all values appear with equal probability at $N_I=N_E$.

We have studied the three-dimensional lattice glass of Pica Ciamarra et al. [Phys. Rev. E 67, 057105 (2003)], which has been shown to reproduce several features of the structural glass phenomenology, such as the cage effect, exponential increase of relaxation times, and aging. We show, using short-time dynamics, that the metastability limit is above the estimated Kauzmann temperature. We also find that in the region where the metastable liquid exists the aging exponent is lower than 0.5, indicating that equilibrium is reached relatively quickly. We conclude that the usefulness of this model to study the deeply supercooled regime is rather limited.

Inspired by the experimental observation that the maximum peeling force of elastic films on rigid substrates does not always emerge at the steady-state peeling stage, but sometimes at the initial one, a theoretical model is established in this paper, in which not only the effect of the film's bending stiffness on the peeling force is considered, but also the whole peeling process, from the initiation of debonding to the steady-state stage, is characterized. Typical peeling force-displacement curves and deformed profiles of the film reappear for the whole peeling process. For the case of a film with relatively large bending stiffness, the maximum peeling force is found arising at the initial peeling stage and the larger the stiffness of the film, the larger the maximum peeling force is. With the peeling distance increasing, the peeling force is reduced from the maximum to a constant at the steady-state stage. For the case of a film with relatively small stiffness, the peeling force increases monotonically at the initial stage and then achieves a constant as the maximum at the steady-state stage. Furthermore, the peeling forces in the steady-state stage are compared with those of the classical Kendall model. All the theoretical predictions agree well with the existing experimental and numerical observations, from which the maximum peeling force can be predicted precisely no matter what the stiffness of the film is. The results in this paper should be very helpful in the design and assessment of the film-substrate interface.

We consider the motion of a diffusive population on a growing domain, $0<x<L\left(t\right)$, which is motivated by various applications in developmental biology. Individuals in the diffusing population, which could represent molecules or cells in a developmental scenario, undergo two different kinds of motion: (i) undirected movement, characterized by a diffusion coefficient, $D$, and (ii) directed movement, associated with the underlying domain growth. For a general class of problems with a reflecting boundary at $x=0$, and an absorbing boundary at $x=L\left(t\right)$, we provide an exact solution to the partial differential equation describing the evolution of the population density function, $C(x,t)$. Using this solution, we derive an exact expression for the survival probability, $S\left(t\right)$, and an accurate approximation for the long-time limit, $\mathcal{S}={lim}_{t\to \infty }S\left(t\right)$. Unlike traditional analyses on a nongrowing domain, where $\mathcal{S}\equiv 0$, we show that domain growth leads to a very different situation where $\mathcal{S}$ can be positive. The theoretical tools developed and validated in this study allow us to distinguish between situations where the diffusive population reaches the moving boundary at $x=L\left(t\right)$ from other situations where the diffusive population never reaches the moving boundary at $x=L\left(t\right)$. Making this distinction is relevant to certain applications in developmental biology, such as the development of the enteric nervous system (ENS). All theoretical predictions are verified by implementing a discrete stochastic model.

Classical chaos is known to affect wave propagation because it signifies the presence of broken symmetries. The effect of chaos has been observed experimentally for matter waves, electromagnetic waves, and acoustic waves. When these three types of waves propagate through a spatially periodic medium, the allowed propagation energies form bands. For energies in the band gaps, no wave propagation is possible. We show that optical lattices provide a well-defined system that allows a study of the effect of chaos on band structure. We have determined the band structure of a body-centered-cubic optical lattice for all theoretically possible couplings, and we find that the band structure for those lattices realizable in the laboratory differs significantly from that expected for the bands in an “empty” body-centered-cubic crystal. However, as coupling is increased, the lattice becomes increasingly chaotic and it becomes possible to produce band structure that has behavior qualitatively similar to the “empty” body-centered-cubic band structure, although with fewer degeneracies.

A linear stability analysis is carried out for the flow through a tube with a soft wall in order to resolve the discrepancy of a factor of 10 for the transition Reynolds number between theoretical predictions in a cylindrical tube and the experiments of Verma and Kumaran [J. Fluid Mech. 705, 322 (2012)]. Here the effect of tube deformation (due to the applied pressure difference) on the mean velocity profile and pressure gradient is incorporated in the stability analysis. The tube geometry and dimensions are reconstructed from experimental images, where it is found that there is an expansion and then a contraction of the tube in the streamwise direction. The mean velocity profiles at different downstream locations and the pressure gradient, determined using computational fluid dynamics, are found to be substantially modified by the tube deformation. The velocity profiles are then used in a linear stability analysis, where the growth rates of perturbations are calculated for the flow through a tube with the wall modeled as a neo-Hookean elastic solid. The linear stability analysis is carried out for the mean velocity profiles at different downstream locations using the parallel flow approximation. The analysis indicates that the flow first becomes unstable in the downstream converging section of the tube where the flow profile is more pluglike when compared to the parabolic flow in a cylindrical tube. The flow is stable in the upstream diverging section where the deformation is maximum. The prediction for the transition Reynolds number is in good agreement with experiments, indicating that the downstream tube convergence and the consequent modification in the mean velocity profile and pressure gradient could reduce the transition Reynolds number by an order of magnitude.

Network models are useful tools for studying the dynamics of social interactions in a structured population. After a round of interactions with the players in their local neighborhood, players update their strategy based on the comparison of their own payoff with the payoff of one of their neighbors. Here we show that the assumptions made on strategy updating are of crucial importance for the strategy dynamics. In the first step, we demonstrate that seemingly small deviations from the standard assumptions on updating have major implications for the evolutionary outcome of two cooperation games: cooperation can more easily persist in a Prisoner's Dilemma game, while it can go more easily extinct in a Snowdrift game. To explain these outcomes, we develop a general model for the updating of states in a network that allows us to derive conditions for the steady-state coexistence of states (or strategies). The analysis reveals that coexistence crucially depends on the number of agents consulted for updating. We conclude that updating rules are as important for evolution on a network as network structure and the nature of the interaction.

Quasi-two-dimensional (quasi-2D) foams consist of monolayers of bubbles squeezed between two narrowly spaced plates. These simplified foams have served successfully in the past to shed light on numerous issues in foam physics. Here we consider the electrical conductivity of such model foams. We compare experiments to a model which we propose, and which successfully relates the structural and the conductive properties of the foam over the full range of the investigated liquid content. We show in particular that in the case of quasi-2D foams the liquid in the nodes needs to be taken into account even at low liquid content. We think that these results may provide different approaches for the characterization of foam properties and for the in situ characterization of the liquid content of foams in confining geometries, such as microfluidics.

Electric-field-induced patterns of diverse morphology have been observed over a wide frequency range in a recently synthesized bent-core nematic (BCN) liquid crystal. At low frequencies (up to ∼25 Hz), the BCN exhibited unusual polarity-dependent patterns. When the amplitude of the ac field was enhanced, these two time-asymmetrical patterns turned into time-symmetrical prewavylike stripes. At ac frequencies in the middle-frequency range (∼50–3000 Hz), zigzag patterns were detected whose obliqueness varied with the frequency. Finally, if the frequency was increased above 3 kHz, the zigzag pattern was replaced by another, prewavylike pattern, whose threshold voltage depended on the frequency; however, the wave vector did not. For a more complete characterization, material parameters such as elastic constants, dielectric permittivities, and the anisotropy of the diamagnetic susceptibility were also determined.

Recent studies of athermal systems such as dry grains and dense, non-Brownian suspensions have shown that shear can lead to solidification through the process of shear jamming in grains and discontinuous shear thickening in suspensions. The similarities observed between these two distinct phenomena suggest that the physical processes leading to shear-induced rigidity in athermal materials are universal. We present a nonequilibrium statistical mechanics model, which exhibits the phenomenology of these shear-driven transitions, shear jamming and discontinuous shear thickening, in different regions of the predicted phase diagram. Our analysis identifies the crucial physical processes underlying shear-driven rigidity transitions, and clarifies the distinct roles played by shearing forces and the packing fraction of grains.

We present molecular dynamics simulations for active one-particle microrheology of an unentangled polymer melt. The tracer particle is forced to oscillate by an oscillating harmonic potential, which models an experiment using optical tweezers. The amplitude and phase shift of this oscillation are related to the complex shear modulus of the polymer melt. In the linear response regime at low frequencies, the active microrheology gives the same result as the passive microrheology, where the thermal motion of a tracer particle is related to the complex modulus. We expand the analysis to include full hydrodynamic effects instead of stationary Stokes friction only, and show that different approaches suggested in the literature lead to completely different results, and that none of them improves on the description using the stationary Stokes friction.

The temporal evolutions of electromagnetic fields generated by the interaction between ultraintense lasers ($1.3\times {10}^{18}$ and $8.2\times {10}^{18}\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$) and solid targets at a distance of several millimeters from the laser-irradiated region have been investigated by electron deflectometry. For three types of foil targets (insulating foil, conductive foil, and insulating foil onto which a metal disk was deposited), transient changes in the fields were observed. We found that the direction, strength, and temporal evolution of the generated fields differ markedly for these three types of targets. The results provide an insight for studying the emission dynamics of laser-accelerated fast electrons.