Much of the progress achieved in understanding plasticity and failure in amorphous solids had been achieved using experiments and simulations in which the materials were loaded using strain control. There is paucity of results under stress control. Here we present a method that was carefully geared to allow loading under stress control either at $T=0$ or at any other temperature, using Monte Carlo techniques. The method is applied to a model-perfect crystalline solid, to a crystalline solid contaminated with topological defects, and to a generic glass. The highest yield stress belongs to the crystal, the lowest to the crystal with a few defects, with the glass in between. Although the glass is more disordered than the crystal with a few defects, it yields stress much higher than that of the latter. We explain this fact by considering the actual microscopic interactions that are typical of glass-forming materials, pointing out the reasons for the higher cohesive nature of the glass. The main conclusion of this paper is that the instabilities encountered in stress-control condition are the identical saddle-node bifurcation seen in strain control. Accordingly one can use the latter condition to infer the former. Finally we discuss temperature effects and comment on the time needed to see a stress-controlled material failure.

In order to describe two-dimensionally packed cells in epithelial tissues both mathematically and physically, there have been developed several sorts of geometrical models, such as the vertex model, the finite element model, the cell-centered model, and the cellular Potts model. So far, in any case, pressures have not neatly been dealt with and the curvatures of the cell boundaries have been even omitted through their approximations. We focus on these quantities and formulate them in the vertex model. Thus, a model with the curvatures is constructed, and its algorithm for simulation is provided. The possible extensions and applications of this model are also discussed.

In this paper we study the interplay between stochastic gene expression and system design using simple stochastic models of autoactivation and autoinhibition. Using the Poisson representation, a technique whose particular usefulness in the context of nonlinear gene regulation models we elucidate, we find exact results for these feedback models in the steady state. Further, we exploit this representation to analyze the parameter spaces of each model, determine which dimensionless combinations of rates are the shape determinants for each distribution, and thus demarcate where in the parameter space qualitatively different behaviors arise. These behaviors include power-law-tailed distributions, bimodal distributions, and sub-Poisson distributions. We also show how these distribution shapes change when the strength of the feedback is tuned. Using our results, we reexamine how well the autoinhibition and autoactivation models serve their conventionally assumed roles as paradigms for noise suppression and noise exploitation, respectively.

A procedure for solving Poisson's equation using plane waves in adaptive coordinates $\left(\mathbf{u}\right)$ is described. The method, based on Gygi's work, writes a trial potential $\xi$ as the product of a preselected Coulomb weight $\mu$ times a plane-wave expansion depending on $\mathbf{u}$. Then, the Coulomb potential generated by a given density $\rho$ is obtained by variationally optimizing $\xi$, so that the error in the Coulomb energy is second-order with respect to the error in $\xi$. The Coulomb weight $\mu$ is chosen to provide to each $\xi$ the typical long-range tail of a Coulomb potential, so that calculations on atoms and molecules are made possible without having to resort to the supercell approximation. As a proof of concept, the method is tested on the helium atom and the ${\mathrm{H}}_2$ and ${\mathrm{H}}_3^{+}$ molecules, where Hartree-Fock energies with better than milli-Hartree accuracy require only a moderate number of plane waves.

Understanding the dynamics of human movements is key to issues of significant current interest such as behavioral prediction, recommendation, and control of epidemic spreading. We collect and analyze big data sets of human movements in both cyberspace (through browsing of websites) and physical space (through mobile towers) and find a superlinear scaling relation between the mean frequency of visit $\langle f\rangle$ and its fluctuation $\sigma :\sigma \sim \langle f{\rangle }^{\beta }$ with $\beta \approx 1.2$. The probability distribution of the visiting frequency is found to be a stretched exponential function. We develop a model incorporating two essential ingredients, preferential return and exploration, and show that these are necessary for generating the scaling relation extracted from real data. A striking finding is that human movements in cyberspace and physical space are strongly correlated, indicating a distinctive behavioral identifying characteristic and implying that the behaviors in one space can be used to predict those in the other.

The quantum Szilard engine (QSZE) is a conceptual quantum engine for understanding the fundamental physics of quantum thermodynamics and information physics. We generalize the QSZE to an arbitrary spin case, i.e., a spin QSZE (SQSZE), and we systematically study the basic physical properties of both fermion and boson SQSZEs in a low-temperature approximation. We give the analytic formulation of the total work. For the fermion SQSZE, the work might be absorbed from the environment, and the change rate of the work with temperature exhibits periodicity and even-odd oscillation, which is a generalization of a spinless QSZE. It is interesting that the average absorbed work oscillates regularly and periodically in a large-number limit, which implies that the average absorbed work in a fermion SQSZE is neither an intensive quantity nor an extensive quantity. The phase diagrams of both fermion and boson SQSZEs give the SQSZE doing positive or negative work in the parameter space of the temperature and the particle number of the system, but they have different behaviors because the spin degrees of the fermion and the boson play different roles in their configuration states and corresponding statistical properties. The critical temperature of phase transition depends sensitively on the particle number. By using Landauer's erasure principle, we give the erasure work in a thermodynamic cycle, and we define an efficiency (we refer to it as information-work efficiency) to measure the engine's ability of utilizing information to extract work. We also give the conditions under which the maximum extracted work and highest information-work efficiencies for fermion and boson SQSZEs can be achieved.

We investigate, using exact diagonalization techniques, the distribution of conductance peak heights in Coulomb blockade regime of a quantum dot connected to two leads under generic dot conditions. The study reveals a three-parametric dependence of the distribution: (i) two dot-lead contact characteristics and (ii) the complexity parameter, mimicking the combined effect of all dot conditions. This also indicates the presence of an infinite range of universality classes of conductance statistics, dominantly characterized just by the complexity parameter and global symmetry constraints.

Catastrophic failure of natural and engineered materials is often preceded by an acceleration and localization of damage that can be observed indirectly from acoustic emissions (AE) generated by the nucleation and growth of microcracks. In this paper we present a detailed investigation of the statistical properties and spatiotemporal characteristics of AE signals generated during triaxial compression of a sandstone sample. We demonstrate that the AE event amplitudes and interevent times are characterized by scaling distributions with shapes that remain invariant during most of the loading sequence. Localization of the AE activity on an incipient fault plane is associated with growth in AE rate in the form of a time-reversed Omori law with an exponent near 1. The experimental findings are interpreted using a model that assumes scale-invariant growth of the dominating crack or fault zone, consistent with the Dugdale-Barenblatt “process zone” model. We determine formal relationships between fault size, fault growth rate, and AE event rate, which are found to be consistent with the experimental observations. From these relations, we conclude that relatively slow growth of a subcritical fault may be associated with a significantly more rapid increase of the AE rate and that monitoring AE rate may therefore provide more reliable predictors of incipient failure than direct monitoring of the growing fault.

We consider the dynamics and the cyclization kinetics of Gaussian semiflexible chains, in which the interaction potential tends to align successive bonds. We provide asymptotic expressions for the cyclization time, for the eigenvalues and eigenfunctions, and for the mean square displacement at all time and length scales, with explicit dependence on the capture radius, on the positions of the reactive monomers in the chain, and on the finite number of beads. For the cyclization kinetics, we take into account non-Markovian effects by calculating the distribution of reactive conformations of the polymer, which are not taken into account in the classical Wilemski-Fixman theory. Comparison with numerical simulations confirms the accuracy of this non-Markovian theory.

We show that sensory noise can enhance the nonlinear response of neuronal networks, and when delivered together with a weak signal, it improves the signal detection by the network. We reveal this phenomenon in neuronal networks that are in a dynamical state preceding a saddle-node bifurcation corresponding to the appearance of sustained network oscillations. In this state, even a weak subthreshold pulse can evoke a large-amplitude oscillation of neuronal activity. The signal-to-noise ratio reaches a maximum at an optimum level of sensory noise, manifesting stochastic resonance (SR) at the population level. We demonstrate SR by use of simulations and numerical integration of rate equations in a cortical model. Using this model, we mimic the experiments of Gluckman et al. [Phys. Rev. Lett. 77, 4098 (1996)] that have given evidence of SR in mammalian brain. We also study neuronal networks in which neurons are grouped in modules and every module works in the regime of SR. We find that even a few modules can strongly enhance the reliability of signal detection in comparison with the case when a modular organization is absent.

The behavior of lipid vesicles near solid surfaces, despite its scientific and technological significance, is poorly understood. By simultaneously taking into account (i) the dynamics of spontaneous pore opening and closing in surface bound vesicles; (ii) their volume loss via leakage through the pores; (iii) and the propagation of their contact line, we have developed a simple model that can fully describe the detailed mechanism of and provide the necessary conditions for the rupture of vesicles and the subsequent formation of supported lipid bilayers. The predictions of the model are in qualitative agreement with many of the experimental observations.

Mixing two nonconducting hydrogen-bonded liquids, each exhibiting a low dielectric relaxation strength, can result in a highly electrically absorbing fluid. This susceptibility amplification effect is demonstrated for mixtures of monohydroxy alcohols. Whereas in the pure liquids a tendency to form ringlike low-dipole moment clusters prevails, in the mixtures such supramolecular structures are disfavored leading to an up to tenfold enhancement of the dielectric loss. The compositional evolution of density and mean cluster-cluster separation is traced using x-ray scattering and indicates deviations from ideal mixing with decreased C-C but simultaneously increased O-O correlation lengths. Thus, the variation in the supramolecular absorption strength could be tracked using a static scattering technique. These observations are in harmony with volume exclusion and ring open effects that predict an optimized susceptibility amplification for mixtures in which the two components occupy equal volume fractions as experimentally observed.

Eigenvector centrality is a common measure of the importance of nodes in a network. Here we show that under common conditions the eigenvector centrality displays a localization transition that causes most of the weight of the centrality to concentrate on a small number of nodes in the network. In this regime the measure is no longer useful for distinguishing among the remaining nodes and its efficacy as a network metric is impaired. As a remedy, we propose an alternative centrality measure based on the nonbacktracking matrix, which gives results closely similar to the standard eigenvector centrality in dense networks where the latter is well behaved but avoids localization and gives useful results in regimes where the standard centrality fails.

This paper provides insight into when, why, and how forecast strategies fail when they are applied to complicated time series. We conjecture that the inherent complexity of real-world time-series data, which results from the dimension, nonlinearity, and nonstationarity of the generating process, as well as from measurement issues such as noise, aggregation, and finite data length, is both empirically quantifiable and directly correlated with predictability. In particular, we argue that redundancy is an effective way to measure complexity and predictive structure in an experimental time series and that weighted permutation entropy is an effective way to estimate that redundancy. To validate these conjectures, we study 120 different time-series data sets. For each time series, we construct predictions using a wide variety of forecast models, then compare the accuracy of the predictions with the permutation entropy of that time series. We use the results to develop a model-free heuristic that can help practitioners recognize when a particular prediction method is not well matched to the task at hand: that is, when the time series has more predictive structure than that method can capture and exploit.

We present a detailed experimental characterization of the autocorrelation properties of a delayed feedback semiconductor laser for different dynamical regimes. We show that in many cases the autocorrelation function of laser intensity dynamics can be approximated by the analytically derived autocorrelation function obtained from a linear stochastic model with delay. We extract a set of dynamic parameters from the fit with the analytic solutions and discuss the limits of validity of our approximation. The linear model captures multiple fundamental properties of delay systems, such as the shift and asymmetric broadening of the different delay echoes. Thus, our analysis provides significant additional insight into the relevant physical and dynamical properties of delayed feedback lasers.

The $\mathrm{C}{\mathrm{O}}_2$ behavior within the reservoirs of carbon capture and storage projects is usually predicted from large-scale simulations of the reservoir. A key parameter in reservoir simulation is relative permeability. However, mineral precipitation alters the pore structure over time, and leads correspondingly to permeability changing with time. In this study, we numerically investigate the influence of carbonate precipitation on relative permeability during $\mathrm{C}{\mathrm{O}}_2$ storage. The pore spaces in rock samples were extracted by high-resolution microcomputed tomography (CT) scanned images. The fluid velocity field within the three-dimensional pore spaces was calculated by the lattice Boltzmann method, while reactive transport with calcite deposition was modeled by an advection-reaction formulation solved by the finite volume method. To increase the computational efficiency and reduce the processing time, we adopted a graphics processing unit parallel computing technique. The relative permeability of the sample rock was then calculated by a highly optimized two-phase lattice Boltzmann model. We also proposed two pore clogging models. In the first model, the clogging processes are modeled by transforming fluid nodes to solid nodes based on their precipitated mass level. In the second model, the porosity is artificially reduced by adjusting the gray scale threshold of the CT images. The developed method accurately simulates the mineralization process observed in laboratory experiment. Precipitation-induced evolution of pore structure significantly influenced the absolute permeability. The relative permeability, however, was much more influenced by pore reduction in the nonwetting phase than in the wetting phase. The output of the structural changes in pore geometry by this model could be input to $\mathrm{C}{\mathrm{O}}_2$ reservoir simulators to investigate the outcome of sequestered $\mathrm{C}{\mathrm{O}}_2$.

Fundamental biological processes such as transcription and translation, where a genetic sequence is sequentially read by a macromolecule, have been well described by a classical model of nonequilibrium statistical physics, the totally asymmetric exclusion principle (TASEP). This model describes particles hopping between sites of a one-dimensional lattice, with the particle current determining the transcription or translation rate. An open problem is how to analyze a TASEP where particles can pause randomly, as has been observed during transcription. In this work, we report that surprisingly, a simple mean-field model predicts well the particle current for all values of the average pause duration, using a simple description of blocking behind paused particles.

We consider an Ising model on the triangular Apollonian network (AN), with a thermalized distribution of vacant sites. The statistical problem is formulated in a grand canonical ensemble, in terms of the temperature $T$ and a chemical potential $\mu$ associated with the concentration of active magnetic sites. We use a well-known transfer-matrix method, with a number of adaptations, to write recursion relations between successive generations of this hierarchical structure. We also investigate the analogous model on the diamond hierarchical lattice (DHL). From the numerical analysis of the recursion relations, we obtain various thermodynamic quantities. In the $\mu \to \infty$ limit, we reproduce the results for the uniform models: in the AN, the system is magnetically ordered at all temperatures, while in the DHL there is a ferromagnetic-paramagnetic transition at a finite value of $T$. Magnetic ordering, however, is shown to disappear for sufficiently large negative values of the chemical potential.

Physical parameters characterizing electrokinetic transport in a confined electrolyte solution are reconstructed from the generic transport coefficients obtained within the classical nonequilibrium statistical thermodynamic framework. The electro-osmotic flow, the diffusio-osmotic flow, the osmotic current, as well as the pressure-driven Poiseuille-type flow, the electric conduction, and the ion diffusion are described by this set of transport coefficients. The reconstruction is demonstrated for an aqueous NaCl solution between two parallel charged surfaces with a nanoscale gap, by using the molecular dynamic (MD) simulations. A Green-Kubo approach is employed to evaluate the transport coefficients in the linear-response regime, and the fluxes induced by the pressure, electric, and chemical potential fields are compared with the results of nonequilibrium MD simulations. Using this numerical scheme, the influence of the salt concentration on the transport coefficients is investigated. Anomalous reversal of diffusio-osmotic current, as well as that of electro-osmotic flow, is observed at high surface charge densities and high added-salt concentrations.

We present theoretical and experimental results of Lévy flights of light originating from a random walk of photons in a hot atomic vapor. In contrast to systems with quenched disorder, this system does not present any correlations between the position and the step length of the random walk. In an analytical model based on microscopic first principles including Doppler broadening we find anomalous Lévy-type superdiffusion corresponding to a single-step size distribution $P\left(x\right)\propto x^{-(1+\alpha )}$, with $\alpha \approx 1$. We show that this step size distribution leads to a violation of Ohm's law [$T_{\mathrm{diff}}\propto L^{-\alpha /2}\ne L^{-1}$], as expected for a Lévy walk of independent steps. Furthermore, the spatial profile of the transmitted light develops power-law tails [$T_{\mathrm{diff}}\left(r\right)\propto r^{-3-\alpha }$]. In an experiment using a slab geometry with hot Rb vapor, we measured the total diffuse transmission $T_{\mathrm{diff}}$ and the spatial profile of the transmitted light $T_{\mathrm{diff}}\left(r\right)$. We obtained the microscopic Lévy parameter $\alpha$ under macroscopic multiple scattering conditions paving the way to investigation of Lévy flights in different atomic physics and astrophysics systems.