We investigate the one-dimensional pair contact process with diffusion (PCPD) by extensive Monte Carlo simulations, mainly focusing on the critical density decay exponent $\delta$. To obtain an accurate estimate of $\delta$, we first find the strength of corrections to scaling using the recently introduced method [S.-C. Park. J. Korean Phys. Soc. 62, 469 (2013)]. For small diffusion rate ($d\le 0.5$), the leading corrections-to-scaling term is found to be $\sim t^{-0.15}$, whereas for large diffusion rate ($d=0.95$) it is found to be $\sim t^{-0.5}$. After finding the strength of corrections to scaling, effective exponents are systematically analyzed to conclude that the value of critical decay exponent $\delta$ is $0.173\left(3\right)$ irrespective of $d$. This value should be compared with the critical decay exponent of the directed percolation, 0.1595. In addition, we study two types of crossover. At $d=0$, the phase boundary is discontinuous and the crossover from the pair contact process to the PCPD is found to be described by the crossover exponent $\varphi =2.6\left(1\right)$. We claim that the discontinuity of the phase boundary cannot be consistent with the theoretical argument supporting the hypothesis that the PCPD should belong to the DP. At $d=1$, the crossover from the mean field PCPD to the PCPD is described by $\varphi =2$ which is argued to be exact.

We have considered the underdamped motion of a Brownian particle in the presence of a correlated external random force. The force is modeled by an Ornstein-Uhlenbeck process. We investigate the fluctuations of the work done by the external force on the Brownian particle in a given time interval in the steady state. We calculate the large deviation functions as well as the complete asymptotic form of the probability density function of the performed work. We also discuss the symmetry properties of the large deviation functions for this system. Finally we perform numerical simulations and they are in a very good agreement with the analytic results.

The mechanical properties of molecules are today captured by single molecule manipulation experiments, so that polymer features are tested at a nanometric scale. Yet devising mathematical models to get further insight beyond the commonly studied force-elongation relation is typically hard. Here we draw from techniques developed in the context of disordered systems to solve models for single and double-stranded DNA stretching in the limit of a long polymeric chain. Since we directly derive the marginals for the molecule local orientation, our approach allows us to readily calculate the experimental elongation as well as other observables at wish. As an example, we evaluate the correlation length as a function of the stretching force. Furthermore, we are able to fit successfully our solution to real experimental data. Although the model is admittedly phenomenological, our findings are very sound. For single-stranded DNA our solution yields the correct (monomer) scale and yet, more importantly, the right persistence length of the molecule. In the double-stranded case, our model reproduces the well-known overstretching transition and correctly captures the ratio between native DNA and overstretched DNA. Also in this case the model yields a persistence length in good agreement with consensus, and it gives interesting insights into the bending stiffness of the native and overstretched molecule, respectively.

In this paper, we study an adaptive spatial network. We consider a susceptible-infected-susceptible (SIS) epidemic on the network, with a link or contact rewiring process constrained by spatial proximity. In particular, we assume that susceptible nodes break links with infected nodes independently of distance and reconnect at random to susceptible nodes available within a given radius. By systematically manipulating this radius we investigate the impact of rewiring on the structure of the network and characteristics of the epidemic. We adopt a step-by-step approach whereby we first study the impact of rewiring on the network structure in the absence of an epidemic, then with nodes assigned a disease status but without disease dynamics, and finally running network and epidemic dynamics simultaneously. In the case of no labeling and no epidemic dynamics, we provide both analytic and semianalytic formulas for the value of clustering achieved in the network. Our results also show that the rewiring radius and the network's initial structure have a pronounced effect on the endemic equilibrium, with increasingly large rewiring radiuses yielding smaller disease prevalence.

We present a detailed experimental study of the symmetry properties and the momentum space representation of the field distributions of a dielectric square resonator as well as the comparison with a semiclassical model. The experiments have been performed with a flat ceramic microwave resonator. Both the resonance spectra and the field distributions were measured. The momentum space representations of the latter evidenced that the resonant states are each related to a specific classical torus, leading to the regular structure of the spectrum. Furthermore, they allow for a precise determination of the refractive index. Measurements with different arrangements of the emitting and the receiving antennas were performed and their influence on the symmetry properties of the field distributions was investigated in detail, showing that resonances with specific symmetries can be selected purposefully. In addition, the length spectrum deduced from the measured resonance spectra and the trace formula for the dielectric square resonator are discussed in the framework of the semiclassical model.

We design and simulate the motion of a swimmer, the Quadroar, with three-dimensional translation and reorientation capabilities in low-Reynolds-number conditions. The Quadroar is composed of an $\mathtt{I}$-shaped frame whose body link is a simple linear actuator and four disks that can rotate about the axes of flange links. The time symmetry is broken by a combination of disk rotations and the one-dimensional expansion or contraction of the body link. The Quadroar propels on forward and transverse straight lines and performs full three-dimensional reorientation maneuvers, which enable it to swim along arbitrary trajectories. We find continuous operation modes that propel the swimmer on planar and three-dimensional periodic and quasiperiodic orbits. Precessing quasiperiodic orbits consist of slow lingering phases with cardioid or multiloop turns followed by directional propulsive phases. Quasiperiodic orbits allow the swimmer to access large parts of its neighboring space without using complex control strategies. We also discuss the feasibility of fabricating a nanoscale Quadroar by photoactive molecular rotors.

We develop a thorough analytical study of the $O(1/N)$ correction to the spectrum of regular random graphs with $N\to \infty$ nodes. The finite-size fluctuations of the resolvent are given in terms of a weighted series over the contributions coming from loops of all possible lengths, from which we obtain the isolated eigenvalue as well as an analytical expression for the $O(1/N)$ correction to the continuous part of the spectrum. The comparison between this analytical formula and direct diagonalization results exhibits an excellent agreement, confirming the correctness of our expression.

We show how to obtain all the models of the continuous description of membranes by constructing the appropriate nonlinear realizations of the Euclidean symmetries of the embedding. The procedure has the advantage of giving a unified formalism with which the models are generated and highlights the relevant order parameters in each phase. We use our findings to investigate a fluid description of both tethered and hexatic membranes, showing that both the melting and the loss of local order induce long-range interactions in the high-temperature fluid phase. The results can be used to understand the appearance of intrinsic ripples in crystalline membranes in a thermal bath.

We consider an array of units each of which can be in one of three states. Unidirectional transitions between these states are governed by Markovian rate processes. The interactions between units occur through a dependence of the transition rates of a unit on the states of the units with which it interacts. This coupling is nonlocal, that is, it is neither an all-to-all interaction (referred to as global coupling), nor is it a nearest neighbor interaction (referred to as local coupling). The coupling is chosen so as to disfavor the crowding of interacting units in the same state. As a result, there is no global synchronization. Instead, the resultant spatiotemporal configuration is one of clusters that move at a constant speed and that can be interpreted as traveling waves. We develop a mean field theory to describe the cluster formation and analyze this model analytically. The predictions of the model are compared favorably with the results obtained by direct numerical simulations.

We discuss sets of measures with the goal of describing dynamical properties of force networks in dense particulate systems. The presented approach is based on persistent homology and allows for extracting precise, quantitative measures that describe the evolution of geometric features of the interparticle forces, without necessarily considering the details related to individual contacts between particles. The networks considered emerge from discrete element simulations of two-dimensional particulate systems consisting of compressible frictional circular disks. We quantify the evolution of the networks for slowly compressed systems undergoing jamming transition. The main findings include uncovering significant but localized changes of force networks for unjammed systems, global (systemwide) changes as the systems evolve through jamming, to be followed by significantly less dramatic evolution for the jammed states. We consider both connected components, related in a loose sense to force chains, and loops and find that both measures provide a significant insight into the evolution of force networks. In addition to normal, we consider also tangential forces between the particles and find that they evolve in the consistent manner. Consideration of both frictional and frictionless systems leads us to the conclusion that friction plays a significant role in determining the dynamical properties of the considered networks. We find that the proposed approach describes the considered networks in a precise yet tractable manner, making it possible to identify features which could be difficult or impossible to describe using other approaches.

The actin cytoskeleton in living cells exhibits a high degree of capacity for dynamic self-organization. Recent experiments have observed propagating actin waves in Dictyostelium cells recovering from complete depolymerization of their actin cytoskeleton. The propagation of these waves appear to be dependent on a programmed recruitment of a few proteins that control actin assembly and disassembly. Such waves also arise spontaneously along the plasma membrane of the cell, and it has been suggested that actin waves enable the cell to scan a surface for particles to engulf. Based on known molecular components involved in wave propagation, we present and study a minimal reaction-diffusion model for actin wave production observed in recovering cells.

Topological cycles in excitable networks can play an important role in maintaining the network activity. When properly activated, cycles act as dynamic pacemakers, sustaining the activity of the whole network. Most previous research has focused on the contributions of short cycles to network dynamics. Here, we identify the specific cycles that are used during different runs of activation in sparse random graphs, as a basis of characterizing the contribution of cycles of any length. Both simulation and a refined mean-field approach evidence a decrease in the cycle usage when the cycle length increases, reflecting a trade-off between long time for recovery after excitation and low vulnerability to out-of-phase external excitations. In spite of this statistical observation, we find that the successful usage of long cycles, though rare, has important functional consequences for sustaining network activity: The average cycle length is the main feature of the cycle length distribution that affects the average lifetime of activity in the network. Particularly, use of long, rather than short, cycles correlates with higher lifetime, and cutting shortcuts in long cycles tends to increase the average lifetime of the activity. Our findings, thus, emphasize the essential, previously underrated role of long cycles in sustaining network activity. On a more general level, the findings underline the importance of network topology, particularly cycle structure, for self-sustained network dynamics.

Time delays have been commonly used in modeling biological systems and can significantly change the dynamics of these systems. Quite a few works have been focused on analyzing the effect of small delays on the pattern formation of biological systems. In this paper, we investigate the effect of any delay on the formation of Turing patterns of reaction-diffusion equations. First, for a delay system in a general form, we propose a technique calculating the critical value of the time delay, above which a Turing instability occurs. Then we apply the technique to a predator-prey model and study the pattern formation of the model due to the delay. For the model in question, we find that when the time delay is small it has a uniform steady state or irregular patterns, which are not of Turing type; however, in the presence of a large delay we find spiral patterns of Turing type. For such a model, we also find that the critical delay is a decreasing function of the ratio of carrying capacity to half saturation of the prey density.

The effective surface dilatational viscosity is calculated of a flat interface separating two immiscible fluids laden with half-immersed monodisperse rigid spherical non-Brownian particles in the limit of high particle concentration. The derivation is based upon the facts that (i) highly concentrated particle arrays in a plane form a hexagonal structure and (ii) the dominant contribution to the viscous dissipation rate arises in the thin gaps between neighboring particles.

A ballistic atom pump is a system containing two reservoirs of neutral atoms or molecules and a junction connecting them containing a localized time-varying potential. Atoms move through the pump as independent particles. Under certain conditions, these pumps can create net transport of atoms from one reservoir to the other. While such systems are sometimes called “quantum pumps,” they are also models of classical chaotic transport, and their quantum behavior cannot be understood without study of the corresponding classical behavior. Here we examine classically such a pump's effect on energy and temperature in the reservoirs, in addition to net particle transport. We show that the changes in particle number, of energy in each reservoir, and of temperature in each reservoir vary in unexpected ways as the incident particle energy is varied.

A class of generalized exclusion processes with symmetric nearest-neighbor hopping which are parametrized by the maximal occupancy, $k\ge 1$, is investigated. For these processes on hypercubic lattices we compute the diffusion coefficient in all spatial dimensions. In the extreme cases of $k=1$ (symmetric simple exclusion process) and $k=\infty$ (noninteracting symmetric random walks) the diffusion coefficient is constant, while for $2\le k<\infty$ it depends on the density and $k$. We also study the evolution of the tagged particle, show that it exhibits a normal diffusive behavior in all dimensions, and probe numerically the coefficient of self-diffusion.

We present a study on the effects of particle shape (disks, hexagons, and pentagons) on the macroscopic coefficient of friction of a two-dimensional, monodisperse, single-shaped, granular system, subjected to shear. We found that the mechanism of stress relaxation in disks is based on the sliding of adjacent planes parallel to the applied deformation direction. In hexagons, stress is relaxed through the creation of rigid pivots, which require hexagonal domains to nucleate and are responsible for the large fluctuations in the dilatancy and shear force. In pentagons the stress relaxation mechanism is through the rotation of individual pentagons, which is a consequence of their permanent misalignment, and are responsible for the small but relatively rapid fluctuations in the shear force. We observed that the friction coefficient is larger for polygonal particles than for the rounded ones. A maximum in the friction coefficient is observed in hexagon granulates with an initial width around $6.5$ grains caused by the increased frequency in nucleation of rigid pivots. In mixtures of disks and hexagons we observed three different friction coefficient behaviors, which depended on the relative concentration of hexagons; in low concentrations of hexagons, $<20\%$, the friction coefficient corresponds to that obtained in solely disks, at intermediate concentrations, $<80\%$, the coefficient varies linearly with concentration, and at larger concentrations the friction coefficient corresponds to the values obtained for solely hexagons. On the contrary, mixtures of pentagons and hexagons showed two regimes; a low constant friction regime at concentrations lower than $60\%$, and an increased in friction observed with higher concentrations of hexagons.

A self-consistent generalized Langevin-equation theory is proposed to describe the self- and collective dynamics of a liquid of linear Brownian particles. The equations of motion for the spherical harmonics projections of the collective and self-intermediate-scattering functions, $F_{lm,lm}(\mathbf{k},t)$ and $F_{lm,lm}^S(\mathbf{k},t)$, are derived as a contraction of the description involving the stochastic equations of the corresponding tensorial one-particle density $n_{lm}(\mathbf{k},t)$ and the translational $(\alpha =T)$ and rotational $(\alpha =R)$ current densities ${\mathbf{j}}_{lm}^{\alpha }(\mathbf{k},t)$. Similar to the spherical case, these dynamic equations require as an external input the equilibrium structural properties of the system contained in the projections of the static structure factor, denoted by $S_{lm,lm}\left(\mathbf{k}\right)$. Complementing these exact equations with simple (Vineyard-like) approximate relations for the collective and the self-memory functions we propose a closed self-consistent set of equations for the dynamic properties involved. In the long-time asymptotic limit, these equations become the so-called bifurcation equations, whose solutions (the nonergodicity parameters) can be written, extending the spherical case, in terms of one translational and one orientational scalar dynamic order parameter, ${\gamma }_T$ and ${\gamma }_R$, which characterize the possible dynamical arrest transitions of the system. As a concrete illustrative application of this theory we determine the dynamic arrest diagram of the dipolar hard-sphere fluid. In qualitative agreement with mode coupling theory, the present self-consistent equations also predict three different regions in the state space spanned by the macroscopic control parameters $\eta$ (volume fraction) and T* (scaled temperature): a region of fully ergodic states, a region of mixed states, in which the translational degrees of freedom become arrested while the orientational degrees of freedom remain ergodic, and a region of fully nonergodic states.

Lipid monolayers and bilayers have been used as experimental models for the investigation of membrane thermal transitions. The main transition takes place near ambient temperatures for several lipids and reflects the order-disorder transition of lipid hydrocarbonic chains, which is accompanied by a surface density gap. Equivalence between the transitions in the two systems has been argued by several authors. The two-state statistical model adopted by numerous authors for different properties of the membrane, such as permeability, diffusion, and mixture or insertion of cholesterol or protein, is inadequate for the description of charged membranes, since it lacks a proper description of surface density. We propose a lattice solution model which adds interactions with water molecules to lipid-lipid interactions and obtain its thermal properties under a mean-field approach. Density variations, although concomitant with chain order variations, are independent of the latter. The model presents both chain order and gas-liquid transitions, and extends the range of applicability of previous models, yielding Langmuir isotherms in the full range of pressures and areas.