We have studied the dependence of the thermal conductivity $\kappa$ on the strength of the interparticle potential $\lambda$ and the strength of the external potential $\beta$ in the Frenkel-Kontorova model. We found that the functional relation can be expressed in a scaling form, $\kappa \propto \frac{{\lambda }^{3∕2}}{{\beta }^2}$. This result is first obtained by nonequilibrium molecular dynamics. It is then confirmed by two analytical methods, the self-consistent phonon theory and the self-consistent stochastic reservoirs method. The thermal conductivity $\kappa$ is therefore a decreasing functon of $\beta$ and an increasing function of $\lambda$.

The transport of interacting Brownian particles in a periodic asymmetric (ratchet) substrate is studied numerically. In a zero-temperature regime, the system behaves as a reversible step motor, undergoing multiple sign reversals of the particle current as any of the following parameters are varied: the pinning potential parameters, the particle occupation number, and the excitation amplitude. The reversals are induced by successive changes in the symmetry of the effective ratchet potential produced by the substrate and the fraction of particles which are effectively pinned. At high temperatures and low frequencies, thermal noise assists delocalization of the pinned particles, rendering the system to recover net motion along the gentler direction of the substrate potential. The joint effect of high temperature and high frequency, on the other hand, induces an additional current inversion, this time favoring motion along the direction where the ratchet potential is steeper. The dependence of these properties on the ratchet parameters and particle density is analyzed in detail.

The susceptible-infectious-recovered (SIR) model describes the evolution of three species of individuals which are subject to an infection and recovery mechanism. A susceptible $S$ can become infectious with an infection rate $\beta$ by an infectious $I$ type provided that both are in contact. The $I$ type may recover with a rate $\gamma$ and from then on stay immune. Due to the coupling between the different individuals, the model is nonlinear and out of equilibrium. We adopt a stochastic individual-based description where individuals are represented by nodes of a graph and contact is defined by the links of the graph. Mapping the underlying master equation onto a quantum formulation in terms of spin operators, the hierarchy of evolution equations can be solved exactly for arbitrary initial conditions on a linear chain. In the case of uncorrelated random initial conditions, the exact time evolution for all three individuals of the SIR model is given analytically. Depending on the initial conditions and reaction rates $\beta$ and $\gamma$, the $I$ population may increase initially before decaying to zero. Due to fluctuations, isolated regions of susceptible individuals evolve, and unlike in the standard mean-field SIR model, one observes a finite stationary distribution of the $S$ type even for large population size. The exact results for the ensemble-averaged population size are compared with simulations for single realizations of the process and also with standard mean-field theory, which is expected to be valid on large fully connected graphs.

Using both numerical simulations and exact expressions for the free energy and microcanonical entropy for a modified Hamiltonian mean-field (HMF) model, we show that when two similar systems with the same intensive parameters but with negative specific heat are weakly coupled, they undergo a process in which the total entropy increases irreversibly. We find that the final equilibrium is such that two phases appear at a temperature (equal in both systems) that is generally different from the initial temperature. We corroborate our results using two different kinds of couplings between the HMF systems. We confirm that our results hold also for the Ising model with long- and short-range interactions, which also has a parameter region with negative specific heat in the microcanonical ensemble. Further, we show that we can couple each system having negative specific heat to a third system that can be used as a thermometer, as long as this thermometer is small enough not to drive the system out of the microcanonical ensemble. Therefore, we show an instance of violation of the zeroth law of thermodynamics.

The flow properties of powders are mainly due to the interplay of cohesive forces and intergrain frictional forces. We have experimentally investigated a “smart granular system” for which the interparticle cohesion can be tuned by a magnetic field $\vec{B}$. We show that the rheological features of such a system can be controlled. Indeed, the granular flow can be controlled or even stopped by the magnetic field. Depending on the orientation of $\vec{B}$, different dynamical regimes can be obtained like a “dry liquid state” forming conical droplets as well as a “layered soft state.” Scaling laws are given for the flow rate outside a funnel as a function of $B$ and for the stopping threshold of the flow as a function of the funnel output diameter $D$. From this analysis, it appears that the flowing properties are related to the dimensionality of the magnetic aggregates.

Monte Carlo simulations are presented for the observation of the dynamics of a self-avoiding polymer in three types of confinement: slit, tube, and cube. We pay special attention to the parameter regime where the characteristic confinement dimension is smaller than the radius of gyration of the unconfined polymer. On the basis of the bond-fluctuation model, we measured the rotation time of the end-to-end vector of the polymer, the diffusion time for the center of the polymer to move a distance comparable to the root mean square end-to-end distance, and the looping time for the ends of the polymer to approach each other from an open position. As functions of the confinement width and polymer length, these three time scales are discussed in light of scaling theories.

In forced polymer translocation, the average translocation time $\tau$ scales with respect to pore force $f$ and polymer length $N$ as $\tau \sim f^{-1}{N}^{\beta }$. We demonstrate that an artifact in the Metropolis Monte Carlo method resulting in breakage of the force scaling with large $f$ may be responsible for some of the controversies between different computationally obtained results and also between computational and experimental results. Using Langevin dynamics simulations we show that the scaling exponent $\beta ⩽1+\nu$ is not universal, but depends on $f$. Moreover, we show that forced translocation can be described by a relatively simple force balance argument and $\beta$ to arise solely from the initial polymer configuration.

We report a theoretical study highlighting the fundamental effects of backbone disorder which simulates the environmental complications on charge transport properties of biological and synthetic DNA molecules. Based on effective tight-binding models of duplex DNA, the Lyapunov coefficient and current-voltage characteristics are numerically calculated by varying the backbone disorder degree. In contrast to the localization picture that the conduction of duplex DNA becomes poorer when the backbone disorder degree is increased, we find that the backbone disorder can enhance the charge transport ability of the DNA molecules when the environment-induced disorder surpasses a critical value, giving rise to a semiconducting-metallic transition. The physical origin for this is traced back to the antiresonant effects. These results provide a scenario to interpret a variety of transport behaviors observed in DNA molecules and suggest perspectives for future experiments intending to control the charge transport through DNA-based nanodevices.

Recent high resolution x-ray diffraction experiments have determined the structure of nucleosomes. In it 147 base pair long DNA B superhelix is wrapped around the eight nucleohistone proteins. They have found that there are many hydrogen-bonds (H-bonds) between the negative sites phosphate ($\mathrm{P}{\mathrm{O}}_4^{-}$) groups DNA, and first of all there is the positively charged lysine and arginine side chains of the histones. This means that there is a non-negligible charge transfer from DNA to the proteins causing a hole current in DNA and an electronic one in the proteins. If the relative positions of the two macromolecules change due to some external disturbances, the DNA moves away from the protein and can be read. If this happens simultaneously at several nucleosomes and at many places in chromatin (built up from the nucleosomes), undesired genetic information becomes readable. This final end can cause the occurrence of oncoproteins at an undesired time point which most probably disturbs the self-regulation of a differentiated cell. The connection of these chain of events with the initiation of cancer is obvious. To look into the details of these events we have used the detailed band structures of the four homopolynucleotides in the presence of water and natrium (${\mathrm{Na}}^{+}$) ions calculated previously with the help of the ab initio Hartree-Fock crystal orbital method. We have found that in the case of three homopolynucleotides the width of their valence band is broad enough ($\sim 10$ times broader than the thermal energy at $300\mathrm{K}$) for the application of the simple deformation potential approximation for transport calculations. With the help of this we have determined the hole mobilities at $300\mathrm{K}$ and $180\mathrm{K}$ of poly(guanilic acid), poly(adenilic acid), and polythimidine (polycytidine has a too narrow valence band for the application of the deformation potential method). The obtained mobilities are large enough to allow Bloch-type conduction in these systems. At the end of the paper we discuss briefly the possible mechanism of charge transport in aperiodic DNA as a combination of Bloch-type conduction, hopping, and tunneling.

We derive expressions for shock formation based on the local curvature of the flow characteristics during dynamic compression. Given a specific ramp adiabat, calculated for instance from the equation of state for a substance, the ideal nonlinear shape for an applied ramp loading history can be determined. We discuss the region affected by lateral release, which can be presented in compact form for the ideal loading history. Example calculations are given for representative metals and plastic ablators. Continuum dynamics (hydrocode) simulations were in good agreement with the algebraic forms. Example applications are presented for several classes of laser-loading experiment, identifying conditions where shocks are desired but not formed, and where long-duration ramps are desired.

We propose and analyze a stochastic model which explains, analytically, the cutoff behavior of real scale-free networks previously modeled computationally by Amaral et al. [Proc. Natl. Acad. Sci. U.S.A. 97, 11149 (2000)] and others. We present a mathematical model that can explain several existing computational scale-free network generation models. This yields a theoretical basis to understand cutoff behavior in complex networks, previously treated only with simulations using distinct models. Therefore, ours is an integrative approach that unifies the existing literature on cutoff behavior in scale-free networks. Furthermore, our mathematical model allows us to reach conclusions not hitherto possible with computational models: the ability to predict the equilibrium point of active vertices and to relate the growth of networks with the probability of aging. We also discuss how our model introduces a useful way to classify scale free behavior of complex networks.

The modeling of human behavior is an important approach to reproduce realistic phenomena for pedestrian flow. In this paper, an extended lattice gas model is proposed to simulate pedestrian counter flow under the open boundary conditions by considering the human subconscious behavior and different maximum velocities. The simulation results show that the presented model can capture some essential features of pedestrian counter flows, such as lane formation, segregation effect, and phase separation at higher densities. In particular, an interesting feature that the faster walkers overtake the slower ones and then form a narrow-sparse walkway near the central partition line is discovered. The phase diagram comparison and analysis show that the subconscious behavior plays a key role in reducing the occurrence of jam cluster. The effects of the symmetrical and asymmetrical injection rate, different partition lines, and different combinations of maximum velocities on pedestrian flow are investigated. An important conclusion is that it is needless to separate faster and slower pedestrians in the same direction by a partition line. Furthermore, the increase of the number of faster walkers does not always benefit the counter flow in all situations. It depends on the magnitude and asymmetry of injection rate. And at larger maximum velocity, the obtained critical transition point corresponding to the maximum flow rate of the fundamental diagram is in good agreement with the empirical results.

We propose a Wigner-function-based parameter that can be used as an indicator of quantum chaos. This parameter is defined as “entropy” from the time dependence of “nonclassicality” proposed by A. Kenfack and K. Życzkowski [J. Opt. B 6, 394 (2004)]. We perform our considerations for the system of damped nonlinear (Kerr-like) oscillator excited by a series of ultrashort external pulses.

Populations of uncoupled limit-cycle oscillators receiving common random impulses show various types of phase-coherent states, which are characterized by the distribution of phase differences between pairs of oscillators. We develop a theory to predict the stationary distribution of pairwise phase differences from the phase response curve, which quantitatively encapsulates the oscillator dynamics, via averaging of the Frobenius-Perron equation describing the impulse-driven oscillators. The validity of our theory is confirmed by direct numerical simulations using the FitzHugh-Nagumo neural oscillator receiving common Poisson impulses as an example.

We study reconnection phenomena in magnetohydrodynamics on the basis of a magnetohydrodynamic version of the Eulerian-Lagrangian analysis. We find that the methods are useful in capturing time scales associated with magnetic reconnection both in two and three dimensions. Visualizations show that the determinants of the Jacobian determinants of the diffusive labels are small where active reconnection takes place. The resetting of the diffusive labels extracts a short time scale during reconnection.

We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schrödinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and three-lattice-site contours in the form of both discrete multipole solitons and discrete vortices. Additionally to identifying the possible states, we analytically track their linear stability both qualitatively and quantitatively. We find that among the six-site configurations, the “hexapole” of alternating phases $\left(0\text{−}\pi \right)$, as well as the vortex of topological charge $S=2$ have intervals of stability; among three-site states, only the vortex of topological charge $S=1$ may be stable in the case of focusing nonlinearity. These conclusions are confirmed both for hexagonal and for honeycomb lattices by means of detailed numerical bifurcation analysis of the stationary states from the anticontinuum limit, and by direct simulations to monitor the dynamical instabilities, when the latter arise. The dynamics reveal a wealth of nonlinear behavior resulting not only in single-site solitary wave forms, but also in robust multisite breathing structures.

We study the quantum version of the random $K$-satisfiability problem in the presence of an external magnetic field $\Gamma$ applied in the transverse direction. We derive the replica-symmetric free-energy functional within the static approximation and the saddle-point equation for the order parameter: the distribution $P\left[h\left(m\right)\right]$ of functions of magnetizations. The order parameter is interpreted as the histogram of probability distributions of individual magnetizations. In the limit of zero temperature and small transverse fields, to leading order in $\Gamma$ magnetizations $m\approx 0$ become relevant in addition to purely classical values of $m\approx \pm 1$. Self-consistency equations for the order parameter are solved numerically using a quasi–Monte Carlo method for $K=3$. It is shown that for an arbitrarily small $\Gamma$ quantum fluctuations destroy the phase transition present in the classical limit $\Gamma =0$, replacing it with a smooth crossover transition. The implications of this result with respect to the expected performance of quantum optimization algorithms via adiabatic evolution are discussed. The replica-symmetric solution of the classical random $K$-satisfiability problem is briefly reexamined. It is shown that the phase transition at $T=0$ predicted by the replica-symmetric theory is of continuous type with atypical critical exponents.

We present the full thermodynamics of an interacting fluid confined by an arbitrary external potential. We show that for each confining potential, there emerge “generalized” volume and pressure variables $\mathcal{V}$ and $\mathcal{P}$, that replace the usual volume and hydrostatic pressure of a uniform system. This scheme is validated with the derivation of the virial expansion of the grand potential. We discuss how this approach yields experimentally amenable procedures to find the equation of state of the fluid, $\mathcal{P}=\mathcal{P}(\mathcal{V}∕N,T)$ with $N$ the number of atoms, as well as its heat capacity at constant generalized volume $C_{\mathcal{V}}=C_{\mathcal{V}}(\mathcal{V},N,T)$. With these two functions, all the thermodynamics properties of the system may be found. As specific examples we study weakly interacting Bose gases trapped by harmonic and by linear quadrupolar potentials within the Hartree-Fock approximation. We claim that this route provides an additional and useful tool to analyze both the thermodynamic variables of an ultracold trapped gas as well as its elementary excitations.

We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces. We use the well-known family of $NK$ landscapes as an example. In our case the inherent network is the graph whose vertices represent the local maxima in the landscape, and the edges account for the transition probabilities between their corresponding basins of attraction. We exhaustively extracted such networks on representative $NK$ landscape instances, and performed a statistical characterization of their properties. We found that most of these network properties are related to the search difficulty on the underlying $NK$ landscapes with varying values of $K$.

The unpinning of spiral waves by the application of high-frequency wave trains was studied in cultured cardiac myocytes. Successful unpinning was observed when the frequency of the paced waves exceeded a critical level. The unpinning process was analyzed by a numerical simulation with a model of cardiac tissue. The mechanism of unpinning by high-frequency stimuli is discussed in terms of local entrainment failure, through a reduction of the two-dimensional spatial characteristics into one dimension.