The temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential (soft-KG) are investigated systematically. Similarly to the previously studied hard-KG lattices, the existence of renormalized phonons is also confirmed in soft-KG lattices. In particular, the temperature dependence of the renormalized phonon frequency predicted by a classical field theory is verified by detailed numerical simulations. However, the thermal conductivities of soft-KG lattices exhibit the opposite trend in temperature dependence in comparison with those of hard-KG lattices. The interesting thing is that the temperature-dependent thermal conductivities of both soft- and hard-KG lattices can be interpreted in the same framework of effective phonon theory. According to the effective phonon theory, the exponents of the power-law dependence of the thermal conductivities as a function of temperature are only determined by the exponents of the soft or hard on-site potentials. These theoretical predictions are consistently verified very well by extensive numerical simulations.

We compute the effective dispersion and vibrational density of states (DOS) of two-dimensional subregions of three-dimensional face-centered-cubic crystals using both a direct projection-inversion technique and a Monte Carlo simulation based on a common underlying Hamiltonian. We study both a (111) and (100) plane. We show that for any given direction of wave vector, both (111) and (100) show an anomalous ${\omega }^2\sim q$ regime at low $q$ where ${\omega }^2$ is the energy associated with the given mode and $q$ is its wave number. The ${\omega }^2\sim q$ scaling should be expected to give rise to an anomalous DOS, $D_{\omega }$, at low $\omega$: $D_{\omega }\sim {\omega }^3$ rather than the conventional Debye result: $D_{\omega }\sim {\omega }^2$. The DOS for (100) looks to be consistent with $D_{\omega }\sim {\omega }^3$, while (111) shows something closer to the conventional Debye result at the smallest frequencies. In addition to the direct projection-inversion calculation, we perform Monte Carlo simulations to study the effects of finite sampling statistics. We show that finite sampling artifacts act as an effective disorder and bias $D_{\omega }$, giving a behavior closer to $D_{\omega }\sim {\omega }^2$ than $D_{\omega }\sim {\omega }^3$. These results should have an important impact on the interpretation of recent studies of colloidal solids where the two-point displacement correlations can be obtained directly in real-space via microscopy.

We construct and analyze a rate-based neural network model in which self-interacting units represent clusters of neurons with strong local connectivity and random interunit connections reflect long-range interactions. When sufficiently strong, the self-interactions make the individual units bistable. Simulation results, mean-field calculations, and stability analysis reveal the different dynamic regimes of this network and identify the locations in parameter space of its phase transitions. We identify an interesting dynamical regime exhibiting transient but long-lived chaotic activity that combines features of chaotic and multiple fixed-point attractors.

We consider representative financial records (stocks and indices) on time scales between one minute and one day, as well as historical monthly data sets, and show that the distribution $P_Q\left(r\right)$ of the interoccurrence times $r$ between losses below a negative threshold $-Q$, for fixed mean interoccurrence times $R_Q$ in multiples of the corresponding time resolutions, can be described on all time scales by the same $q$ exponentials, $P_Q\left(r\right)\propto 1/\left\{{[1+(q-1)\beta r]}^{1/(q-1)}\right\}$. We propose that the asset- and time-scale-independent analytic form of $P_Q\left(r\right)$ can be regarded as an additional stylized fact of the financial markets and represents a nontrivial test for market models. We analyze the distribution $P_Q\left(r\right)$ as well as the autocorrelation $C_Q\left(s\right)$ of the interoccurrence times for three market models: (i) multiplicative random cascades, (ii) multifractal random walks, and (iii) the generalized autoregressive conditional heteroskedasticity [GARCH(1,1)] model. We find that only one of the considered models, the multifractal random walk model, approximately reproduces the $q$-exponential form of $P_Q\left(r\right)$ and the power-law decay of $C_Q\left(s\right)$.

Information processing machines at the nanoscales are unavoidably affected by thermal fluctuations. Efficient design requires understanding how nanomachines can operate at minimal energy dissipation. Here we focus on mechanical systems controlled by smoothly varying potential forces. We show that optimal control equations come about in a natural way if the energy cost to manipulate the potential is taken into account. When such a cost becomes negligible, an optimal control strategy can be constructed by transparent geometrical methods which recover the solution of optimal mass transport equations in the overdamped limit. Our equations are equivalent to hierarchies of kinetic equations of a form well known in the theory of dilute gases. From our results, optimal strategies for energy efficient nanosystems may be devised by established techniques from kinetic theory.

We describe direct measurements of the acceleration of an object impacting on a loosely packed granular bed under various pressures, using an instrumented sphere. The sphere acts as a noninvasive probe that measures and continuously transmits the acceleration as it penetrates into the sand, using a radio signal. The time-resolved acceleration of the sphere reveals the detailed dynamics during the impact that cannot be resolved from the position information alone. Because of the unobstructed penetration, we see a downward acceleration of the sphere at the moment the air cavity collapses. The compressibility of the sand bed is observed through the oscillatory behavior of the acceleration curve for various ambient pressures; it shows the influence of interstitial air on the compaction of the sand as a function of time.

Quantum-mechanical particles in a confining potential interfere with each other while undergoing thermodynamic processes far from thermal equilibrium. By evaluating the corresponding transition probabilities between many-particle eigenstates we obtain the quantum work distribution function for identical bosons and fermions, which we compare with the case of distinguishable particles. We find that the quantum work distributions for bosons and fermions significantly differ at low temperatures, while, as expected, at high temperatures the work distributions converge to the classical expression. These findings are illustrated with two analytically solvable examples, namely the time-dependent infinite square well and the parametric harmonic oscillator.

The plunging of a large intruder sphere into a prefluidized granular bed with various constant velocities and various sphere diameters is investigated using a state-of-the-art hybrid discrete particle and immersed boundary method, in which both the gas-induced drag force and the contact force exerted on the intruder can be investigated separately. We investigate low velocities, where velocity dependent effects first begin to appear. The results show a concave-to-convex dependence of the plunging force as a function of intruder depth. In the concave region the force fits to a power law with an exponent around 1.3, which is in good agreement with existing experimental observations. Our simulation results further show that the force exerted on the frontal hemisphere of the intruder is dominant. At larger intruder velocities, friction with the granular medium causes a velocity-dependent drag force. As long as the granular particles have not yet closed the gap behind the intruder, this drag force is independent of the actual intruder depth. In this regime, the drag force experienced by intruders of different diameter moving at different velocities all fall onto a single master curve if plotted against the Reynolds number, using a single value for the effective viscosity of the granular medium. This master curve corresponds well to the Schiller-Naumann correlation for the drag force between a sphere and a Newtonian fluid. After the gap behind the intruder has closed, the drag force increases not only with velocity but also with depth. We attribute this to the effect of increasing hydrostatic particle pressure in the granular medium, leading to an increase in effective viscosity.

Active turbulence in dense active systems is characterized by high vorticity on a length scale that is large compared to that of individual entities. We describe the properties of active turbulence as momentum propagation is screened by frictional damping. As friction is increased, the spacing between the walls in the nematic director field decreases as a consequence of the more rapid velocity decays. This leads to, first, a regime with more walls and an increased number of topological defects, and then to a jammed state in which the walls deliminate bands of opposing flow, analogous to the shear bands observed in passive complex fluids.

The phase behavior of Janus disks on a square lattice is studied using the Monte Carlo method. A particle is composed of two different parts, $A$ and $B$. The interactions between neighboring particles depend on their orientations. To control the strength of the interactions, we use energy parameters characterizing $AA,BB$, and $AB$ contacts. The phase diagrams are estimated. We found two phase transitions, namely first-order transitions between colloidal-rich and colloidal-poor phases, and continuous order-disorder transitions to different ordered phases. A variety of ordered structures occurs depending on the relation between the energy parameters and on the fluid density. The influence of energy parameters on the phase diagram topology and critical parameters is shown. The competition between phase transitions and self-organization is discussed.

We use homogenization theory to develop a multiscale model of colloidal dispersion of particles in nematic liquid crystals under weak-anchoring conditions. We validate the model by comparing it with simulations by using the Landau–de Gennes free energy and show that the agreement is excellent. We then use the multiscale model to study the effect that particle anisotropy has on the liquid crystal: spherically symmetric particles always reduce the effective elastic constant. Asymmetric particles introduce an effective alignment field that can increase the Fredericks threshold and decrease the switch-off time.

Parkinson's disease is marked by neurodegenerative processes that affect the pattern of discharge of basal ganglia neurons. The main features observed in the parkinsonian globus pallidus pars interna (GPi), a subdomain of the basal ganglia that is involved in the regulation of voluntary movement, are pathologically increased and synchronized neuronal activity. How these changes affect the implemented neuronal code is not well understood. Our experimental temporal structure-function analysis shows that in parkinsonian animals the rate-coding window of GPi neurons needed for the proper performance of voluntary actions is reduced. The model of the GPi network that we develop and discuss here reveals indeed that the size of the rate-coding window shrinks as the network activity increases and is expanded if the coupling strength among the neurons is increased. This leads to the novel interpretation that the pathological neuronal synchronization in Parkinson's disease in the GPi is the result of a collective attempt to counterbalance the shrinking of the rate-coding window due to increased activity in GPi neurons.

Two measurements are employed to quantitatively investigate the scaling properties of the spatial distribution of urban facilities: the $K$ function [whose derivative gives the radial distribution function $\rho \left(t\right)=K^{\prime }\left(t\right)/2\pi t$] by number counting and the variance-mean relationship by the method of expanding bins. The $K$ function and the variance-mean relationship are both power functions. This means that the spatial distributions of urban facilities are scaling invariant. Further analysis of more data (which includes eight types of facilities in 37 major Chinese cities) shows that the the power laws broadly hold for all combinations of facilities and cities. A double stochastic process (DSP) model is proposed as a mathematical mechanism by which spatial point patterns can be generated that resemble the actual distribution of urban facilities both qualitatively and quantitatively. Simulation of the DSP yields a better agreement with the urban data than the correlated percolation model.

This paper presents a smoothed particle hydrodynamics (SPH) and element bending group (EBG) coupling method for modeling the interaction of flexible fibers with moving viscous fluids. SPH is a well-developed mesh-free particle method for simulating viscous fluid flows. EBG is also a particle method for modeling flexible bodies. The interaction of flexible fibers with moving viscous fluids is rendered through the interaction of EBG particles for flexible fiber and SPH particles for fluid. In numerical simulation, flexible fibers of different lengths are immersed in a moving viscous fluid driven by a body force. The drag force on the fiber obtained from SPH-EBG simulation agrees well with experimental observations. It is shown that the flexible fiber demonstrates three typical bending modes, including the U-shaped mode, the flapping mode, and the closed mode, and that the flexible fiber experiences a drag reduction due to its reconfiguration by bending. It is also found that the $U$ drag scaling law for a flexible fiber is only valid for the U-shaped mode, but not valid for the flapping and closed modes. The results indicate that the reconfiguration of a flexible fiber is caused by the fluid force acting on it, while vortex shedding is of importance in the translations of bending modes.

We develop a method for multidimensional optimization using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimizing functional correspond to fixed points of the flow equation. While ideas based on Bayesian inference such as the maximum entropy method always depend on a prior probability, the additional step in our approach is to perform a continuous update of the prior during the homotopy flow. The prior probability thus enters the flow equation only as an initial condition. We demonstrate the applicability of this optimization method for two paradigmatic problems in theoretical condensed matter physics: numerical analytic continuation from imaginary to real frequencies and finding (variational) ground states of frustrated (quantum) Ising models with random or long-range antiferromagnetic interactions.

The $n$-index Rényi mutual information and transfer entropies for the two-dimensional kinetic Ising model with arbitrary single-spin dynamics in the thermodynamic limit are derived as functions of ensemble averages of observables and spin-flip probabilities. Cluster Monte Carlo algorithms with different dynamics from the single-spin dynamics are thus applicable to estimate the transfer entropies. By means of Monte Carlo simulations with the Wolff algorithm, we calculate the information flows in the Ising model with the Metropolis dynamics and the Glauber dynamics, respectively. We find that not only the global Rényi transfer entropy, but also the pairwise Rényi transfer entropy, peaks in the disorder phase.

Using a thermodynamic integration scheme, we compute the excess free energy, $\gamma$, of a glass-forming, binary Lennard-Jones liquid in contact with a frozen amorphous wall, formed by particles frozen into a similar structure as the liquid. We find that $\gamma$ is nonzero, becoming negative at low temperature. This indicates that the thermodynamics of the system is perturbed by the effect of the amorphous wall.

We suggest a generalization of the expression of the nonequilibrium (NE) density matrix obtained by Hershfield's method for the cases where both heat and charge steady-state currents are present in a quantum open system. The finite-size quantum system, connected to two temperature and particle reservoirs, is driven out of equilibrium by the presence of both a temperature gradient and a chemical potential gradient between the two reservoirs. We show that the NE density matrix is given by a generalized Gibbs-like ensemble and is in full agreement with the general results of the McLennan-Zubarev nonequilibrium ensembles. The extra nonequilibrium terms are related to the entropy production in the system and characterize the fluxes of heat and particle. An explicit example, for the lowest-order expansion, is provide for a model system of noninteracting fermions.

The states of an overdamped Brownian particle confined in a two-dimensional bilobal enclosure are considered to correspond to two binary values: 0 (left lobe) and 1 (right lobe). An ensemble of such particles represents bits of entropic information. An external bias is applied on the particles, equally distributed in two lobes, to drive them to a particular lobe erasing one kind of bit of information. It has been shown that the average work done for the entropic memory erasure process approaches the Landauer bound for a very slow erasure cycle. Furthermore, the detailed Jarzynski equality holds to a very good extent for the erasure protocol, so that the Landauer bound may be calculated irrespective of the time period of the erasure cycle in terms of the effective free-energy change for the process. The detailed Jarzynski equality applied to two subprocesses, namely the transition from entropic memory state 0 to state 1 and the transition from entropic memory state 1 to state 1, connects the work done on the system to the probability to occupy the two states under a time-reversed process. In the entire treatment, the work appears as a boundary effect of the physical confinement of the system not having a conventional potential energy barrier. Finally, an analytical derivation of the detailed and classical Jarzynski equality for Brownian movement in confined space with varying width has been proposed. Our analytical scheme supports the numerical simulations presented in this paper.

Directional switching in a self-propelled particle model with delayed interactions is investigated. It is shown that the average switching time is an increasing function of time delay. The presented results are applied to studying collective animal behavior. It is argued that self-propelled particle models with time delays can explain the state-dependent diffusion coefficient measured in experiments with locust groups. The theory is further generalized to heterogeneous groups where each individual can respond to its environment with a different time delay.