The typical behavior of the relay-without-delay channel under low-density parity-check coding and its multiple-unit generalization, termed the relay array, is studied using methods of statistical mechanics. A demodulate-and-forward strategy is analytically solved using the replica symmetric ansatz which is exact in the system studied at Nishimori’s temperature. In particular, the typical level of improvement in communication performance by relaying messages is shown in the case of a small and a large number of relay units.

The dynamic behavior of a social group influenced by both a strong leader and the mass media, which is modeled according to the social impact theory, is studied under two situations: (i) The strong leader changes his/her state of opinion periodically while the mass media are not considered. In this case, the leader is capable of driving the group between a dynamically ordered state with a weak leader-group coupling (high-frequency regime) and a dynamically disordered state where the group follows the opinion of the leader (low-frequency regime). (ii) The mass-media change periodically their message and have to compete with a strong leader that keeps his/her state of opinion unchanged. In this case, the mass media require an amplitude threshold in order to overcome the influence of the leader and drive the system into a dynamically disordered state. The dynamic behavior characteristic of the studied social opinion model shares many features of physical systems that are relevant in the fields of statistical mechanics and condensed matter.

The dynamical properties of semidilute solutions of supramolecular polymers formed from molecular recognition directed association between monomers bearing complementary hydrogen bonding groups were investigated by rheological and dynamic light scattering experiments. The steady-state flow curves showed a shear banding type instability, namely the occurrence of a stress plateau ${\sigma }_p$ above a critical shear rate ${\dot{\gamma }}_c$. The values of ${\sigma }_p$ and ${\dot{\gamma }}_c$ were found to be of the same order of magnitude as those of the elastic plateau modulus and the inverse stress relaxation time, respectively. The above features are in agreement with the theoretical predictions based on the reptation model. Dynamic light scattering experiments showed the presence in the autocorrelation function of the concentration fluctuations of a slow viscoelastic relaxation process that is likely to be of Rouse type.

We study the buckling instability of filaments or elastic rods in two spatial dimensions in the presence of thermal fluctuations. We present an analytical solution based on a renormalizationlike procedure where we integrate out short wavelength fluctuations in order to obtain an effective theory governing the buckling instability. We calculate the resulting shift of the critical force by fluctuation effects and the average projected filament length parallel to the force direction as a function of the applied force and of the contour length of the filament. We find that, in the buckled state, thermal fluctuations lead to an increase in the mean projected length of the filament in the force direction. As a function of the contour length, the mean projected length exhibits a cusp at the buckling instability, which becomes rounded by thermal fluctuations. Our analytic results are confirmed by Monte Carlo simulations.

We study the dynamics of denaturation bubbles in double-stranded DNA on the basis of the Poland-Scheraga model. We show that long time distributions for the survival of DNA bubbles and the size autocorrelation function can be derived from an asymptotic weak noise approach. In particular, below the melting temperature the bubble closure corresponds to a noisy finite time singularity. We demonstrate that the associated Fokker-Planck equation is equivalent to a quantum Coulomb problem. Below the melting temperature, the bubble lifetime is associated with the continuum of scattering states of the repulsive Coulomb potential; at the melting temperature, the Coulomb potential vanishes and the underlying first exit dynamics exhibits a long time power law tail; above the melting temperature, corresponding to an attractive Coulomb potential, the long time dynamics is controlled by the lowest bound state. Correlations and finite size effects are discussed.

Details of condensed matter structure can alter microscopic-scale response to electric fields by orders of magnitude. It is shown that dipolar liquids near boundaries is an exception where the response can be virtually insensitive to such details and can sense mainly the macroscopic dielectric permittivity. This insensitivity is due to fluidity, symmetry properties, and location of the fields’ charges outside the liquid or inside impermeable solute cavities, which is the ubiquitous location in molecular scale phenomena.

It is now an accepted fact that the size at which dunes form from a flat sand bed as well as their “minimal size” scales on the flux saturation length. This length is by definition the relaxation length of the slowest mode toward equilibrium transport. The model presented by Parteli, Durán, and Herrmann [Phys. Rev. E 75, 011301 (2007)] predicts that the saturation length decreases to zero as the inverse of the wind shear stress far from the threshold. We first show that their model is not self-consistent: even under large wind, the relaxation rate is limited by grain inertia and thus cannot decrease to zero. A key argument presented by these authors comes from the discussion of the typical dune wavelength on Mars (650 m) on the basis of which they refute the scaling of the dune size with the drag length evidenced by Claudin and Andreotti [Earth Planet. Sci. Lett. 252, 30 (2006)]. They instead propose that Martian dunes, composed of large grains $\left(500\mu \text{m}\right)$, were formed in the past under very strong winds. We emphasize that this saltating grain size, estimated from thermal diffusion measurements, is far from straightforward. Moreover, the microscopic photographs taken by the rovers on Martian Aeolian bedforms show a grain size of $87\pm 25\mu \text{m}$ together with hematite spherules at millimeter scale. As those so-called “blueberries” cannot be entrained more frequently than a few hours per century, we conclude that the saltating grains on Mars are the small ones, which gives a second strong argument against the model of Parteli et al.

We reply to the preceding comment by Andreotti and Claudin [Phys. Rev. E 76, 063301 (2007)] on our paper [Phys. Rev. E 75, 011301 (2007)]. We show that the equations of the dune model used in our calculations are self-consistent and effectively lead to a dependence of the minimal dune size on the wind speed through the saturation length. Furthermore, we show that Meridiani Planum ripples are probably not a good reference to estimate the grain size of Martian dune sands: the soil in the ripple troughs at the landing site is covered with nonerodible elements (“blueberries”), which increase the minimal threshold for saltation by a factor of 2.0. We conclude that, in the absence of large fragments as the ones found at the landing site, basaltic grains of diameter $d=500\pm 100\mu \text{m}$ that compose the large, typical dark Martian dunes [K. S. Edgett and P. R. Christensen, J. Geophys. Res. 96, 22765 (1991)] probably saltate during the strongest storms on Mars. We also show that the wind friction speed $u_{\ast }\approx 3.0\text{m}/\text{s}$ that we found from the calculations of Martian dunes is within the values of maximum wind speeds that occur during Martian storms a few times a decade [R. E. Arvidson et al., Science 222, 463 (1983); H. J. Moore, J. Geophys. Res. 90, 163 (1985); R. Sullivan et al., Nature (London) 436, 58 (2005); D. J. Jerolmack et al., J. Geophys. Res. 111, E12S02 (2006)]. In this manner, the dune model predicts that Martian dunes can be formed under present Martian conditions, with no need to assume other conditions of wind and atmosphere that could have prevailed in the past.

Most real-world networks are weighted graphs with the weight of the edges reflecting the relative importance of the connections. In this work, we study nondegree dependent correlations between edge weights, generalizing thus the correlations beyond the degree dependent case. We propose a simple method to introduce weight-weight correlations in topologically uncorrelated graphs. This allows us to test different measures to discriminate between the different correlation types and to quantify their intensity. We also discuss here the effect of weight correlations on the transport properties of the networks, showing that positive correlations dramatically improve transport. Finally, we give two examples of real-world networks (social and transport graphs) in which weight-weight correlations are present.

Chaotic Hamiltonian systems with time scale separation display features known from nonequilibrium statistical physics even when no thermodynamic limit is involved. In particular, fast chaotic degrees of freedom can be modeled by suitable stochastic forces and a Fokker-Planck equation governing the slow parts of the motion can be derived. It turns out that the underlying Hamiltonian structure results in fluctuation-dissipation relations which link the parameters of the effective stochastic model. Such properties are crucial to ensure the correct stationary state of the stochastic description. Our results demonstrate that concepts from thermodynamics can be transferred to dynamical systems with few degrees of freedom.

An extensive nonequilibrium steady-state kinetics model incorporating collisional and radiative processes is developed to study the electrical breakdown and discharge maintenance of laser-induced atmospheric plasma channels formed in externally applied electric fields. The model is based upon a self-consistent numerical solution of the Boltzmann equation for the electron energy distribution function coupled with the electron energy balance equation and the population balance equations for electrons and air species. Using the electron energy distribution function, the ionization and electron attachment rates as a function of the reduced applied electric field at different degrees of ionization are calculated. We find that the ionization rate as a function of applied electric field in a laser-induced plasma channel is orders of magnitude larger than that obtained for a natural atmospheric air discharge. Therefore, the electrical breakdown of these plasma channels may occur at significantly lower applied electric fields. The present model predicts a breakdown electric field of $10\mathrm{kV}∕\mathrm{cm}$, while the experimentally determined breakdown field strength is $\sim 5.7\mathrm{kV}∕\mathrm{cm}$ [A. P. Baronavski et al., NRL Memorandum Report No. NRL/MR/6110–02-8642, 2002 (unpublished)], a reduction of about a factor of 5 from the natural Paschen electrical breakdown field of $\sim 30\mathrm{kV}∕\mathrm{cm}$.

In this paper, a lattice Boltzmann method (LBM) for weakly ionized isothermal plasmas is presented by introducing a rescaling scheme for the Boltzmann transport equation. Without using this rescaling, we found that the nondimensional relaxation time used in the LBM is too large and the LBM does not produce physically realistic results. The developed model was applied to the electrostatic wave problem and the diffusion process of singly ionized helium plasmas with a 1–3% degree of ionization under an electric field. The obtained results agree well with theoretical values.

Anomalous transport of a particle subjected to non-Ohmic damping of the power $\delta$ in a tilted periodic potential is investigated via Monte Carlo simulation of the generalized Langevin equation. It is found that the system exhibits two relative motion modes: the locked state and the running state. In an environment of sub-Ohmic damping $(0<\delta <1)$, the particle should transfer into a running state from a locked state only when local minima of the potential vanish; hence a synchronization oscillation occurs in the particle’s mean displacement and mean square displacement (MSD). In particular, the two motion modes are allowed to coexist in the case of super-Ohmic damping $(1<\delta <2)$ for moderate driving forces, namely, where double centers exist in the velocity distribution. This causes the particle to have faster diffusion, i.e., its MSD reads $⟨\mathrm{\Delta }{x}^2\left(t\right)⟩=2D_{\mathrm{eff}}^{\left(\delta \right)}{t}^{{\delta }_{\mathrm{eff}}}$. Our result shows that the effective power index ${\delta }_{\mathrm{eff}}$ can be enhanced and is a nonmonotonic function of the temperature and the driving force. The mixture of the two motion modes also leads to a breakdown of the hysteresis loop of the mobility.

In this paper, we study the application of the concept of finite-time thermodynamics to first-order phase transitions. As an example, we investigate the transition from the gaseous to the liquid state by modeling the liquification of the gas in a finite time. In particular, we introduce, state, and solve an optimal control problem in which we aim at achieving the gas-liquid first-order phase transition through supersaturation within a fixed time in an optimal fashion, in the sense that the work required to supersaturate the gas, called excess work, is minimized by controlling the appropriate thermodynamic parameters. The resulting set of coupled nonlinear differential equations is then solved for three systems, nitrogen ${\text{N}}_2$, oxygen ${\text{O}}_2$, and water vapor ${\text{H}}_2\text{O}$.

In a very long Gaussian polymer on time scales shorter than the maximal relaxation time, the mean squared distance traveled by a tagged monomer grows as $\sim t^{1∕2}$. We analyze such subdiffusive behavior in the presence of one or two absorbing boundaries and demonstrate the differences between this process and the subdiffusion described by the fractional Fokker-Planck equation. In particular, we show that the mean absorption time of diffuser between two absorbing boundaries is finite. Our results restrict the form of the effective dispersion equation that may describe such subdiffusive processes.

A probabilistic framework is developed that gives a unifying perspective on both the classical and quantum versions of two-player games. We suggest exploiting peculiar joint probabilities involved in Einstein-Podolsky-Rosen (EPR) experiments to construct a quantum game when the corresponding classical game is obtained from factorizable joint probabilities. We analyze how nonfactorizability changes Nash equilibria in three well-known games of prisoner’s dilemma, stag hunt, and chicken. In this framework we find that for the game of prisoner’s dilemma even nonfactorizable EPR joint probabilities cannot be helpful to escape from the classical outcome of the game. For a particular version of the chicken game, however, we find that the two nonfactorizable sets of joint probabilities, which maximally violate the Clauser-Holt-Shimony-Horne sum of correlations, indeed result in new Nash equilibria.

After a brief discussion of the concepts of fractional exchange and fractional exclusion statistics, we report partly analytical and partly numerical results on thermodynamic properties of assemblies of particles obeying fractional exclusion statistics. The effect of dimensionality is one focal point, the ratio $\mu ∕k_{B}T$ of chemical potential to thermal energy being obtained numerically as a function of a scaled particle density. Pair correlation functions are also presented as a function of the statistical parameter, with Friedel oscillations developing close to the fermion limit, for sufficiently large density.

We analyze the crystallization and collapse transition of a simple model for flexible polymer chains on simple-cubic and face-centered-cubic lattices by means of sophisticated chain-growth methods. In contrast to the bond-fluctuation polymer model in certain parameter ranges, where these two conformational transitions were found to merge in the thermodynamic limit, we conclude from our results that the two transitions remain well separated in the limit of infinite chain lengths. The reason for this qualitatively distinct behavior is presumably due to the ultrashort attractive interaction range in the lattice models considered here.

We study the mechanical property of a two-dimensional filament with constant spontaneous curvature and under uniaxial applied force. We derive the equation that governs the stable shape of the filament and obtain analytical solutions for the equation. We find that for a long filament with positive initial azimuth angle (the azimuth angle is the angle between $x$ axis and the tangent of the filament) and under large stretching force, the azimuth angle is a two-valued function of the arclength, decreases first, and then increases with increasing arclength. Otherwise, the azimuth angle is a monotonic function of arclength. At finite temperature, we derive the differential equation that governs the partition function and find exact solution of the partition function for a filament free of force. We obtain closed-form expressions on the force-extension relation for a filament under low force and for a long filament under strong stretching force. Our results show that for a biopolymer with moderate length and not too small spontaneous curvature, the effect of the spontaneous curvature cannot be replaced by a simple renormalization of the persistence length in the wormlike chain model.

We present an analytical study describing a method for the control of spatiotemporal patterns of synchrony in networks of coupled oscillators. Delayed feedback applied through a small number of electrodes effectively induces spatiotemporal dynamics at minimal stimulation intensities. Different arrangements of the delays cause different spatial patterns of synchrony, comparable to central pattern generators (CPGs), i.e., interacting clusters of oscillatory neurons producing patterned output, e.g., for motor control. Multisite delayed feedback stimulation might be used to restore CPG activity in patients with incomplete spinal cord injury or gait ignition disorders.