We study inference and reconstruction of couplings in a partially observed kinetic Ising model. With hidden spins, calculating the likelihood of a sequence of observed spin configurations requires performing a trace over the configurations of the hidden ones. This, as we show, can be represented as a path integral. Using this representation, we demonstrate that systematic approximate inference and learning rules can be derived using dynamical mean-field theory. Although naive mean-field theory leads to an unstable learning rule, taking into account Gaussian corrections allows learning the couplings involving hidden nodes. It also improves learning of the couplings between the observed nodes compared to when hidden nodes are ignored.

We present numerical results for various information theoretic properties of the square lattice Ising model. First, using a bond propagation algorithm, we find the difference $2H_L\left(w\right)-H_{2L}\left(w\right)$ between entropies on cylinders of finite lengths $L$ and $2L$ with open end cap boundaries, in the limit $L\to \infty$. This essentially quantifies how the finite length correction for the entropy scales with the cylinder circumference $w$. Secondly, using the transfer matrix, we obtain precise estimates for the information needed to specify the spin state on a ring encircling an infinitely long cylinder. Combining both results, we obtain the mutual information between the two halves of a cylinder (the “excess entropy” for the cylinder), where we confirm with higher precision but for smaller systems the results recently obtained by Wilms et al., and we show that the mutual information between the two halves of the ring diverges at the critical point logarithmically with $w$. Finally, we use the second result together with Monte Carlo simulations to show that also the excess entropy of a straight line of $n$ spins in an infinite lattice diverges at criticality logarithmically with $n$. We conjecture that such logarithmic divergence happens generically for any one-dimensional subset of sites at any two-dimensional second-order phase transition. Comparing straight lines on square and triangular lattices with square loops and with lines of thickness 2, we discuss questions of universality.

A heat engine undergoes a cyclic operation while in equilibrium with the net result of conversion of heat into work. Quantum effects such as superposition of states can improve an engine's efficiency by breaking detailed balance, but this improvement comes at a cost due to excess entropy generated from collapse of superpositions on measurement. We quantify these competing facets for a quantum ratchet composed of an ensemble of pairs of interacting two-level atoms. We suggest that the measurement postulate of quantum mechanics is intricately connected to the second law of thermodynamics. More precisely, if quantum collapse is not inherently random, then the second law of thermodynamics can be violated. Our results challenge the conventional approach of simply quantifying quantum correlations as a thermodynamic work deficit.

The constant surface tension assumption of the Classical Nucleation Theory (CNT) is known to be flawed. In order to probe beyond this limitation, we consider a microscopic, two-dimensional Lattice-Gas Automata (LGA) model of nucleation in a supersaturated system, with model input parameters $E_{ss}$ (solid particle-to-solid particle bonding energy), $E_{sw}$ (solid particle-to-water bonding energy), η (next-to-nearest-neighbor bonding coefficient in solid phase), and $C_{in}$ (initial solute concentration). The LGA method has the advantages of easy implementation, low memory requirements, and fast computation speed. Analytical results for the system's concentration and the crystal radius as functions of time are derived and the former is fit to the simulation data in order to determine the equilibrium concentration. The “Mean First-Passage Time” technique is used to obtain the nucleation rate and critical nucleus size from the simulation data. The nucleation rate and supersaturation data are evaluated using a modification to the CNT that incorporates a two-dimensional radius-dependent surface tension term. The Tolman parameter, δ, which controls the radius dependence of the surface tension, decreases (increases) as a function of the magnitude of $E_{ss}$ ($E_{sw}$), at fixed values of η and $E_{sw}$ ($E_{ss}$). On the other hand, δ increases as η increases while $E_{ss}$ and $E_{sw}$ are held constant. The constant surface tension term of the CNT, ${\Sigma }_0$, increases (decreases) with increasing magnitudes of $E_{ss}$ ($E_{sw}$) at fixed values of $E_{sw}$ ($E_{ss}$) and increases as η is increased. ${\Sigma }_0$ increases linearly as a function of the change in energy during an attachment or detachment reaction, $\left|\Delta E\right|$, however, with a slope less than that predicted for a crystal that is uniformly packed at maximum density. These results indicate an increase in the radius-dependent surface tension, Σ, with respect to increasing magnitude of the difference between $E_{ss}$ and $E_{sw}$.

In the eikonal approach, we describe sound propagation near topological defects of nematic liquid crystals as geodesics of a non-Euclidian manifold endowed with an effective metric tensor. The relation between the acoustics of the medium and this geometrical description is given by Fermat's principle. We calculate the ray trajectories and propose a diffraction experiment to retrieve information about the elastic constants.

We investigate light-induced patterning of a monodomain side-chain liquid crystal elastomer (SC-LCE) doped with light-sensitive azobenzene moiety in the temperature region close to the nematic-paranematic phase transition. We show that a strongly nonlinear relationship between the concentration of the cis isomers of the azomesogens and the refractive index modification of the material, which is characteristic for the phase transition region, results in nonmonotonous time dependence of the diffraction efficiency of a probe beam. From this effect we determine the sensitivity of the nematic transition temperature on the molar fraction of the cis isomers. The relation between the cis isomer molar fraction and nematic order also provides a possibility for recording hidden holograms, which can be made visible by cooling the sample from the paranematic to the nematic phase.

A critical step in the bacteriophage life cycle is genome ejection into host bacteria. The ejection process for double-stranded DNA phages has been studied thoroughly in vitro, where after triggering with the cellular receptor the genome ejects into a buffer. The experimental data have been interpreted in terms of the decrease in free energy of the densely packed DNA associated with genome ejection. Here we detail a simple model of genome ejection in terms of the hydrostatic and osmotic pressures inside the phage, a bacterium, and a buffer solution or culture medium. We argue that the hydrodynamic flow associated with the water movement from the buffer solution into the phage capsid and further drainage into the bacterial cytoplasm, driven by the osmotic gradient between the bacterial cytoplasm and culture medium, provides an alternative mechanism for phage genome ejection in vivo; the mechanism is perfectly consistent with phage genome ejection in vitro.

In this paper, we study dynamical traffic light strategies in the Biham-Middleton-Levine traffic flow model. The strategies use local vehicular information to control urban traffic, which take into account the interaction of vehicles traveling in different directions via considering their dynamical spatial configuration. Simulations find out two strategies, in which local information at nearby sites is used. The two strategies perform much better than the alternating strategy. Under these two strategies, vehicles can self-organize into a new intermediate state with band structure. The analytical solutions of velocity of this state have been presented, which are in good agreement with simulations.

Vaccination is an important measure available for preventing or reducing the spread of infectious diseases. In this paper, an epidemic model including susceptible, infected, and imperfectly vaccinated compartments is studied on Watts-Strogatz small-world, Barabási-Albert scale-free, and random scale-free networks. The epidemic threshold and prevalence are analyzed. For small-world networks, the effective vaccination intervention is suggested and its influence on the threshold and prevalence is analyzed. For scale-free networks, the threshold is found to be strongly dependent both on the effective vaccination rate and on the connectivity distribution. Moreover, so long as vaccination is effective, it can linearly decrease the epidemic prevalence in small-world networks, whereas for scale-free networks it acts exponentially. These results can help in adopting pragmatic treatment upon diseases in structured populations.

Permutation entropy (PE) has been recently suggested as a novel measure to characterize the complexity of nonlinear time series. In this paper, we propose a simple method to address some of PE's limitations, mainly its inability to differentiate between distinct patterns of a certain motif and the sensitivity of patterns close to the noise floor. The method relies on the fact that patterns may be too disparate in amplitudes and variances and proceeds by assigning weights for each extracted vector when computing the relative frequencies associated with every motif. Simulations were conducted over synthetic and real data for a weighting scheme inspired by the variance of each pattern. Results show better robustness and stability in the presence of higher levels of noise, in addition to a distinctive ability to extract complexity information from data with spiky features or having abrupt changes in magnitude.

Extensive Monte Carlo simulations are performed on a two-dimensional random field Ising model. The purpose of the present work is to study the disorder-induced changes in the properties of disordered spin systems. The time evolution of the domain growth, the order parameter, and the spin-spin correlation functions are studied in the nonequilibrium regime. The dynamical evolution of the order parameter and the domain growth shows a power law scaling with disorder-dependent exponents. It is observed that for weak random fields, the two-dimensional random field Ising model possesses long-range order. Except for weak disorder, exchange interaction never wins over pinning interaction to establish long-range order in the system.

We study full counting statistics for classical heat transport through anharmonic or nonlinear molecular junctions formed by interacting oscillators. An analytical result of the steady-state heat flux for an overdamped anharmonic junction with arbitrary temperature bias is obtained. It is found that the thermal conductance can be expressed in terms of a temperature-dependent effective force constant. The role of anharmonicity is identified. We also give the general formula for the second cumulant of heat in steady state, as well as the average geometric heat flux when two system parameters are modulated adiabatically. We present an anharmonic example for which all cumulants for heat can be obtained exactly. For a bounded single oscillator model with mass we found that the cumulants are independent of the nonlinear potential.

Using a bond-propagation algorithm, we study the finite-size behavior of the critical two-dimensional Ising model on a finite triangular lattice with free boundaries in five shapes: triangular, rhomboid, trapezoid, hexagonal, and rectangular. The critical free energy, internal energy, and specific heat are calculated. The accuracy of the free energy reaches ${10}^{-26}$. Based on accurate data on several finite systems with linear size up to $N=2000$, we extract the bulk, surface, and corner parts of the free energy, internal energy, and specific heat accurately. We confirm the conformal field theory prediction that the corner free energy is universal and find logarithmic corrections in higher-order terms in the critical free energy for the rhomboid, trapezoid, and hexagonal systems, which are absent for the triangular and rectangular systems. The logarithmic edge corrections due to edges parallel or perpendicular to the bond directions in the internal energy are found to be identical, while the logarithmic edge corrections due to corresponding edges in the specific heat are different. The corner internal energy and corner specific heat for angles $\pi /3$, $\pi /2$, and $2\pi /3$ are obtained, as well as higher-order corrections. Comparing with the corner internal energy and corner specific heat we previously found on a rectangle of the square lattice [Phys. Rev. E 86, 041149 (2012)], we conclude that the corner internal energy and corner specific heat for the rectangular shape are not universal.

Strong interaction with other particles or feedback from the medium on a Brownian particle entail memory effects in the effective dynamics. That motivates the extension of the fluctuation-dissipation theorem to nonequilibrium Langevin systems with memory. An important application is to the nonequilibrium modification of the Sutherland-Einstein relation between diffusion and mobility in the case of strong memory. Nonequilibrium corrections include the time correlation between the dynamical activity and the velocity of the particle, which in turn leads to information about the correlations between the driving force and the particle's displacement.

We derive exact predictions for universal scaling exponents and scaling functions associated with the statistics of maximum velocities $v_m$ during avalanches described by the mean-field theory of the interface depinning transition. In particular, we find a robust power-law regime in the statistics of maximum events that can explain the observed distribution of the peak amplitudes in acoustic emission experiments of crystal plasticity. Our results are expected to be broadly applicable to a broad range of systems in the mean-field interface depinning universality class, ranging from magnets to earthquakes.

The supersonic gas plume of a landing rocket entrains lunar regolith, which is the layer of loose solids covering the lunar surface. This ejection is problematic due to scouring and dust impregnation of surrounding hardware, reduction in visibility for the crew, and spoofing of the landing sensors. To date, model predictions of erosion and ejection dynamics have been based largely on single-trajectory models in which the role of interparticle collisions is ignored. In the present work, the parameters affecting the erosion rate of monodisperse solids are investigated using the discrete element method (DEM). The drag and lift forces exerted by the rocket exhaust are incorporated via one-way coupling. The results demonstrate that interparticle collisions are frequent in the region immediately above the regolith surface; as many as 20$\%$ of particles are engaged in a collision at a given time. These collisions play an important role both in the erosion dynamics and in the final trajectories of particles. In addition, a direct assessment of the influence of collisions on the erosion rate is accomplished via a comparison between a “collisionless” DEM model and the original DEM model. This comparison shows that the erosion dynamics change drastically when collisions are considered and that the erosion rate is dependent on the collision parameters (coefficient of restitution and coefficient of friction). Physical explanations for these trends are provided.

We investigate the static structure and diffusive dynamics of binary Lennard-Jones mixture upon supercooling in the presence of gold nanoparticle within the framework of the mode-coupling theory of the dynamic glass transition in the direct space by means of constant-NVT molecular dynamics simulations. It is found that the presence of gold nanoparticle causes the energy per particle and the pressure of this system to decrease with respect to the bulk binary Lennard-Jones mixture. Furthermore, the presence of nanoparticle has a direct effect on the liquid structure and causes the peaks of the radial distribution functions to become shorter with respect to the bulk binary Lennard-Jones liquid. The dynamics of the liquid at a given density is found to be consistent with the mode-coupling theory (MCT) predictions in a certain range at low temperatures. In accordance with the idealized MCT, the diffusion constants $D\left(T\right)$ show a power-law behavior at low temperatures for both types of binary Lennard-Jones (BLJ) particles as well as the gold atoms comprising the nanoparticle. The mode-coupling crossover temperature $T_c$ is the same for all particle types; however, $T_c=0.4$ is reduced with respect to that of the bulk BLJ liquid, and the $\gamma$ exponent is found to depend on the particle type. The existence of the nanoparticle causes the short-time $\beta$-relaxation regime to shorten and the range of validity of the MCT shrinks with respect to the bulk BLJ. It is also found that at intermediate and low temperatures the curves of the mean-squared displacements (MSDs) versus $tD\left(T\right)$ fall onto a master curve. The MSDs follow the master curve in an identical time range with the long-time $\alpha$-relaxation regime of the mode-coupling theory. By obtaining the viscosity, it is observed that the Stokes-Einstein relation remains valid at high and intermediate temperatures but breaks down as the temperatures approach $T_c$ as a result of the cooperative motion or activated processes.

Membrane flexoelectricity is an electromechanical coupling process that describes membrane electrical polarization due to bending and membrane bending under electric fields. In this paper we propose, formulate, and characterize a mechanical energy harvesting system consisting of a deformable soft flexoelectric thin membrane subjected to harmonic forcing from contacting bulk fluids. The key elements of the energy harvester are formulated and characterized, including (i) the mechanical-to-electrical energy conversion efficiency, (ii) the electromechanical shape equation connecting fluid forces with membrane curvature and electric displacement, and (iii) the electric power generation and efficiency. The energy conversion efficiency is cast as the ratio of flexoelectric coupling to the product of electric and bending elasticity. The device is described by a second-order curvature dynamics coupled to the electric displacement equation and as such results in mechanical power absorption with a resonant peak whose amplitude decreases with bending viscosity. The electric power generation is proportional to the conversion factor and the power efficiency decreases with frequency. Under high bending viscosity, the power efficiency increases with the conversion factor and under low viscosities it decreases with the conversion factor. The theoretical results presented contribute to the ongoing experimental efforts to develop mechanical energy harvesting from fluid flow energy through solid-fluid interactions and electromechanical transduction.

We study experimentally the fracture dynamics during the peeling at a constant velocity of a roller adhesive tape mounted on a freely rotating pulley. Thanks to a high speed camera, we measure, in an intermediate range of peeling velocities, high frequency oscillations between phases of slow and rapid propagation of the peeling fracture. This so-called stick-slip regime is well known as the consequence of a decreasing fracture energy of the adhesive in a certain range of peeling velocity coupled to the elasticity of the peeled tape. Simultaneously with stick slip, we observe low frequency oscillations of the adhesive roller angular velocity which are the consequence of a pendular instability of the roller submitted to the peeling force. The stick-slip dynamics is shown to become intermittent due to these slow pendular oscillations which produce a quasistatic oscillation of the peeling angle while keeping constant the peeling fracture velocity (averaged over each stick-slip cycle). The observed correlation between the mean peeling angle and the stick-slip amplitude questions the validity of the usually admitted independence with the peeling angle of the fracture energy of adhesives.

We report on an x-ray diffraction (XRD) study of helical poly[9,9-bis(2-ethylhexyl)fluorene] (PF2/6) under high quasihydrostatic pressure and show an effect of pressure on the torsion angle (dihedral angle) between adjunct repeat units and on the hexagonal unit cell. A model for helical backbone conformation is constructed. The theoretical position for the most prominent 00$l$ x-ray reflection is calculated as a function of torsion angle. The XRD of high molecular weight PF2/6 ($M_{\mathrm{n}}=30$ kg/mol) is measured through a diamond anvil cell upon pressure increase from 1 to 10 GPa. The theoretically considered $00l$ reflection is experimentally identified, and its shift with the increasing pressure is found to be consistent with the decreasing torsion angle between 2 and 6 GPa. This indicates partial backbone planarization towards a more open helical structure. The $h00$ peak is identified, and its shift together with the broadening of $00l$ implies impairment of the ambient hexagonal order, which begins at or below 2 GPa. Previously collected high-pressure photoluminescence data are reanalyzed and are found to be qualitatively consistent with the XRD data. This paper provides an example of how the helical π-conjugated backbone structure can be controlled by applying high quasihydrostatic pressure without modifications in its chemical structure. Moreover, it paves the way for wider use of high-pressure x-ray scattering in the research of π-conjugated polymers.