A simple analytical approach to estimate thermodynamic properties of model Yukawa systems is presented. The approach extends the traditional Debye-Hückel theory into the regime of moderate coupling and is able to qualitatively reproduce thermodynamics of Yukawa systems up to the fluid-solid phase transition. The simplistic equation of state (pressure equation) is derived and applied to the hydrodynamic description of the longitudinal waves in Yukawa fluids. The relevance of this study to the topic of complex (dusty) plasmas is discussed.

Extensive computer simulations have been carried out to study propagation of acoustic waves in a two-dimensional disordered fractured porous medium, as a prelude to studying elastic wave propagation in such media. The fracture network is represented by randomly distributed channels of finite width and length, the contrast in the properties of the porous matrix and the fractures is taken into account, and the propagation of the waves is studied over broad ranges of the fracture number density $\rho$ and width $b$. The most significant result of the study is that, at short distances from the wave source, the waves' amplitude, as well as their energy, decays exponentially with the distance from the source, which is similar to the classical problem of electron localization in disordered solids, whereas the amplitude decays as a stretched exponential function of the distance $x$ that corresponds to sublocalization, $exp(-x^{\alpha })$ with $\alpha <1$. Moreover, the exponent $\alpha$ depends on both $\rho$ and $b$. This is analogous to electron localization in percolation systems at the percolation threshold. Similar results are obtained for the decay of the waves' amplitude with the porosity of the fracture network. Moreover, the amplitude decays faster with distance from the source $x$ in a fractured porous medium than in one without fractures. The mean speed of wave propagation decreases linearly with the fractures' number density.

The dynamics of the Hamiltonian mean-field model is studied in the context of continuous-time random walks. We show that the sojourn times in cells in the momentum space are well described by a one-sided truncated Lévy distribution. Consequently, the system is nonergodic for long observation times that diverge with the number of particles. Ergodicity is attained only after very long times both at thermodynamic equilibrium and at quasistationary out-of-equilibrium states.

We report the results of experimental studies of the short-time–long-wavelength behavior of collective particle displacements in quasi-one-dimensional (q1D) and quasi-two-dimensional (q2D) colloid suspensions. Our results are reported via the $q\to 0$ behavior of the hydrodynamic function $H$($q$) that relates the effective collective diffusion coefficient $D_e$($q$), with the static structure factor $S$($q$) and the self-diffusion coefficient of isolated particles $D_0$: $H\left(q\right)\equiv D_e\left(q\right)S\left(q\right)/D_0$. We find an apparent divergence of $H$($q$) as $q\to 0$ with the form $H\left(q\right)\propto q^{-\gamma }$ (1.7 < $\gamma$ < 1.9) for both q1D and q2D colloid suspensions. Given that $S$($q$) does not diverge as $q\to 0$ we infer that $D_e$($q$) does. This behavior is qualitatively different from that of the three-dimensional $H$($q$) and $D_e$($q$) as $q\to 0$, and the divergence is of a different functional form from that predicted for the diffusion coefficient in one-component one-dimensional and two-dimensional fluids not subject to boundary conditions that define the dimensionality of the system. We provide support for the contention that the boundary conditions that define a confined system play a very important role in determining the long-wavelength behavior of the collective diffusion coefficient from two sources: (i) the results of simulations of $H$($q$) and $D_e$($q$) in quasi-1D and quasi-2D systems and (ii) verification, using data from the work of Lin, Rice and Weitz [Phys. Rev. E 51, 423 (1995)], of the prediction by Bleibel et al., arXiv:1305.3715, that $D_e$($q$) for a monolayer of colloid particles constrained to lie in the interface between two fluids diverges as $q^{-1}$ as $q\to 0$.

We present our conclusions of the investigation of the self-assembly and growth of an array of CdS nanotubes: a consequence of a fine balance of directed motion, diffusion, and aggregation of reacting ${\mathrm{Cd}}^{+2}$ and ${\mathrm{S}}^{-2}$ ions. In a previous communication [Kiruthiga and Chatterji, J. Chem. Phys. 138, 024905 (2013)], we identified the mechanism of an unexpected growth of a CdS nanocylinder of uniform radial cross section from the end of a nanochannel. Furthermore, the cylinder had a pore along the axis but was closed at one end. This unique phenomenon of self-assembly of very monodisperse CdS nanocylinders had been observed in a rather simple experiment where two chambers containing 0.1M $\mathrm{Cd}{\mathrm{Cl}}_2$ and 0.1M ${\mathrm{Na}}_2\mathrm{S}$ solutions were joined by an array of anodized aluminium oxide (AAO) nanochannels [ and , Phys. Rev. E 85, 056104 (2012)]. Interestingly, the growth of CdS nanotubes was observed only in the ${\mathrm{Na}}_2\mathrm{S}$ chamber. The primary focus of our previous study was on identifying the principles governing the growth of a single nanotube at the exit point of a single AAO nanochannel. In this communication, we identify factors affecting the self-assembly of a nanotube in the presence of other similar neighboring nanotubes growing out from an array of closely spaced AAO nanochannel exit points, a scenario closer to the experimental situation. Our model is not Cd${}^{+2}$ or ${\text{S}}^{-2}$ specific, thus our conclusions suggest that the experimental scheme can be extended to the self-assembly of a general class of reacting-diffusing A and B ions with A (in this case ${\mathrm{Cd}}^{+2}$ ions) selectively migrating out from a nanochannel. In particular, we note that after the initial growth of nanotubes for a period of time, there can arise a severe deficiency of B ions (${\text{S}}^{-2}$) near the AAO-nanochannel exits. The low concentration of B near the nanochannel exits impedes further growth of uniform CdS nanotubes. We further identify the parameters which can be tuned to obtain an improved crop of monodisperse nanotubes. Thereby we predict the necessary characteristics of reacting systems which can be self-assembled using suitable adaptations of experiments used to grow CdS cylinders.

Metallic alloys, such as Al and Cu or mild steel, display plastic instabilities in a well-defined range of temperatures and deformation rates, a phenomenon known as the Portevin–Le Chatelelier effect. The stick-slip behavior, or serration, typical of this effect is due to the discontinuous motion of dislocations as they interact with solute atoms. Here we study a simple model of interacting dislocations and show how the classical Einstein fluctuation-dissipation relation can be used to define the temperature over a range of model parameters and to construct a phase diagram of serration that can be compared to experimental results. Furthermore, by performing analytic calculations and numerically integrating the equations of motion, we clarify the crucial role played by dislocation mutual interactions in serration.

We study whether and how the energy scaling based on the single-ridge approximation is revised in an actual crumpled sheet, namely, in the presence of ridge-ridge interactions. Molecular dynamics simulation is employed for this purpose. In order to improve the data quality, modifications are introduced to the common protocol. As crumpling proceeds, we find that the average storing energy changes from being proportional to one-third of the ridge length to a linear relation, while the ratio of bending and stretching energies decreases from 5 to 2. The discrepancy between previous simulations and experiments on the material-dependence for the power-law exponent is resolved. We further determine the average ridge length to scale as $1/D^{1/3}$, the ridge number as $D^{2/3}$, and the average storing energy per unit ridge length as $D^{0.881}$ where $D$ denotes the volume density of the crumpled ball. These results are accompanied by experimental proofs and are consistent with mean-field predictions. Finally, we extend the existent simulations to the high-pressure region and verify the existence of a scaling relation that is more general than the familiar power law at covering the whole density range.

In vivo measurements of the passive movements of biomolecules or vesicles in cells consistently report “anomalous diffusion,” where mean-squared displacements scale as a power law of time with exponent $\alpha <1$ (subdiffusion). While the detailed mechanisms causing such behaviors are not always elucidated, movement hindrance by obstacles is often invoked. However, our understanding of how hindered diffusion leads to subdiffusion is based on diffusion amidst randomly located immobile obstacles. Here, we have used Monte Carlo simulations to investigate transient subdiffusion due to mobile obstacles with various modes of mobility. Our simulations confirm that the anomalous regimes rapidly disappear when the obstacles move by Brownian motion. By contrast, mobile obstacles with more confined displacements, e.g., Orstein-Ulhenbeck motion, are shown to preserve subdiffusive regimes. The mean-squared displacement of tracked protein displays convincing power laws with anomalous exponent $\alpha$ that varies with the density of Orstein-Ulhenbeck (OU) obstacles or the relaxation time scale of the OU process. In particular, some of the values we observed are significantly below the universal value predicted for immobile obstacles in two dimensions. Therefore, our results show that subdiffusion due to mobile obstacles with OU type of motion may account for the large variation range exhibited by experimental measurements in living cells and may explain that some experimental estimates are below the universal value predicted for immobile obstacles.

Evolution of cooperation is a widely studied problem in biology, social science, economics, and artificial intelligence. Most of the existing approaches that explain cooperation rely on some notion of direct or indirect reciprocity. These reciprocity based models assume agents recognize their partner and know their previous interactions, which requires advanced cognitive abilities. In this paper we are interested in developing a model that produces cooperation without requiring any explicit memory of previous game plays. Our model is based on the notion of inequity aversion, a concept introduced within behavioral economics, whereby individuals care about payoff equality in outcomes. Here we explore the effect of using income inequality to guide partner selection and interaction. We study our model by considering both the well-mixed and the spatially structured population and present the conditions under which cooperation becomes dominant. Our results support the hypothesis that inequity aversion promotes cooperative relationship among nonkin.

This paper tackles a destabilizing problem of a direct-current (dc) bus system with constant power loads, which can be considered a fundamental problem of dc power grid networks. The present paper clarifies scenarios of the destabilization and applies the well-known delayed-feedback control to the stabilization of the destabilized bus system on the basis of nonlinear science. Further, we propose a systematic procedure for designing the delayed feedback controller. This controller can converge the bus voltage exactly on an unstable operating point without accurate information and can track it using tiny control energy even when a system parameter, such as the power consumption of the load, is slowly varied. These features demonstrate that delayed feedback control can be considered a strong candidate for solving the destabilizing problem.

We study experimentally the influence of dissipation on stationary capillary wave turbulence on the surface of a liquid by changing its viscosity. We observe that the frequency power-law scaling of the capillary spectrum departs significantly from its theoretical value when the dissipation is increased. The energy dissipated by capillary waves is also measured and found to increase nonlinearly with the mean power injected within the liquid. Here we propose an experimental estimation of the energy flux at every scale of the capillary cascade. The latter is found to be nonconstant through the scales. For fluids of low enough viscosity, we found that both capillary spectrum scalings with the frequency and the newly defined mean energy flux are in good agreement with wave turbulence theory. The Kolmogorov-Zakharov constant is then experimentally estimated and compared to its theoretical value.

The Kolmogorov flow provides an ideal instance of a virtual channel flow: It has no boundaries, but it possesses well defined mean flow in each half wavelength. We exploit this remarkable feature for the purpose of investigating the interplay between the mean flow and the turbulent drag of the bulk flow. By means of a set of direct numerical simulations at increasing Reynolds number, we show the dependence of the bulk turbulent drag on the amplitude of the mean flow. Further, we present a detailed analysis of the scale-by-scale energy balance, which describes how kinetic energy is redistributed among different regions of the flow while being transported toward small dissipative scales. Our results allow us to obtain an accurate prediction for the spatial energy transport at large scales.

A general framework for analyzing the recently discovered phase transitions in the steady state of dissipation-driven open quantum systems is still lacking. To fill this gap, we extend the so-called fidelity approach to quantum phase transitions to open systems whose steady state is a Gaussian fermionic state. We endow the manifold of correlation matrices of steady states with a metric tensor $g$ measuring the distinguishability distance between solutions corresponding to a different set of control parameters. The phase diagram can then be mapped out in terms of the scaling behavior of $g$ and connections with the Liouvillean gap and the model correlation functions unveiled. We argue that the fidelity approach, thanks to its differential-geometric and information-theoretic nature, provides insights into dissipative quantum critical phenomena as well as a general and powerful strategy to explore them.

We provide an analytic solution to the first-passage time (FPT) problem of a piecewise-smooth stochastic model, namely Brownian motion with dry friction, using two different but closely related approaches which are based on eigenfunction decompositions on the one hand and on the backward Kolmogorov equation on the other. For the simple case containing only dry friction, a phase-transition phenomenon in the spectrum is found which relates to the position of the exit point, and which affects the tail of the FPT distribution. For the model containing as well a driving force and viscous friction the impact of the corresponding stick-slip transition and of the transition to ballistic exit is evaluated quantitatively. The proposed model is one of the very few cases where FPT properties are accessible by analytical means.

Motivated by recent findings, we discuss the existence of a direct and robust mechanism providing discontinuous absorbing transitions in short-range systems with single species, with no extra symmetries or conservation laws. We consider variants of the contact process, in which at least two adjacent particles (instead of one, as commonly assumed) are required to create a new species. Many interaction rules are analyzed, including distinct cluster annihilations and a modified version of the original pair contact process. Through detailed time-dependent numerical simulations, we find that for our modified models, the phase transitions are of first order, hence contrasting with their corresponding usual formulations in the literature, which are of second order. By calculating the order-parameter distributions, the obtained bimodal shapes as well as the finite-scale analysis reinforce coexisting phases and thus a discontinuous transition. These findings strongly suggest that the above particle creation requirements constitute a minimum and fundamental mechanism determining the phase coexistence in short-range contact processes.

We study the transport of heat along a chain of particles interacting through a harmonic potential and subject to heat reservoirs at its ends. Each particle has two degrees of freedom and is subject to a stochastic noise that produces infinitesimal changes in the velocity while keeping the kinetic energy unchanged. This is modeled by means of a Langevin equation with multiplicative noise. We show that the introduction of this energy-conserving stochastic noise leads to Fourier's law. By means of an approximate solution that becomes exact in the thermodynamic limit, we also show that the heat conductivity $\kappa$ behaves as $\kappa =aL/(b+\lambda L)$ for large values of the intensity $\lambda$ of the energy-conserving noise and large chain sizes $L$. Hence, we conclude that in the thermodynamic limit the heat conductivity is finite and given by $\kappa =a/\lambda$.