A one-dimensional stochastic exclusion process with two species of particles, $+$ and $-$, is studied where density of each species can fluctuate but the total particle density is conserved. From the exact stationary state weights we show that, in the limiting case where density of negative particles vanishes, the system undergoes a phase separation transition where a macroscopic domain of vacancies form in front of a single surviving negative particle. We also show that the phase-separated state is associated with a diverging correlation length for any density and that the critical exponents characterizing the behavior in this region are different from those at the transition line. The static and the dynamical critical exponents are obtained from the exact solution and numerical simulations, respectively.

A dissipative stochastic sandpile model is constructed and studied on small-world networks in one and two dimensions with different shortcut densities $\varphi$, where $\varphi =0$ represents regular lattice and $\varphi =1$ represents random network. The effect of dimension, network topology, and specific dissipation mode (bulk or boundary) on the the steady-state critical properties of nondissipative and dissipative avalanches along with all avalanches are analyzed. Though the distributions of all avalanches and nondissipative avalanches display stochastic scaling at $\varphi =0$ and mean-field scaling at $\varphi =1$, the dissipative avalanches display nontrivial critical properties at $\varphi =0$ and 1 in both one and two dimensions. In the small-world regime $(2^{-12}\le \varphi \le 0.1)$, the size distributions of different types of avalanches are found to exhibit more than one power-law scaling with different scaling exponents around a crossover toppling size $s_c$. Stochastic scaling is found to occur for $s<s_c$ and the mean-field scaling is found to occur for $s>s_c$. As different scaling forms are found to coexist in a single probability distribution, a coexistence scaling theory on small world network is developed and numerically verified.

We study the dynamics of nonlinear oscillators coupled through environmental diffusive coupling. The interaction between the dynamical systems is maintained through its agents which, in turn, interact globally with each other in the common dynamical environment. We show that this form of coupling scheme can induce an important transition like phase-flip transition as well transitions among oscillation quenching states in identical limit-cycle oscillators. This behavior is analyzed in the parameter plane by analytical and numerical studies of specific cases of the Stuart-Landau oscillator and van der Pol oscillator. Experimental evidences of the phase-flip transition and quenching states are shown using an electronic version of the van der Pol oscillators.

A general framework combining perturbation theory and coupled-mode theory is developed for analyzing nonlinear resonant structures comprising dispersive bulk and sheet materials. To allow for conductive sheet materials, a nonlinear current term is introduced in the formulation in addition to the more common nonlinear polarization. The framework is applied to model bistability in a graphene-based traveling-wave resonator system exhibiting third-order nonlinearity. We show that the complex conductivity of graphene disturbs the equality of electric and magnetic energies on resonance (a condition typically taken for granted), due to the reactive power associated with the imaginary part of graphene's surface conductivity. Furthermore, we demonstrate that the dispersive nature of conductive materials must always be taken into account, since it significantly impacts the nonlinear response. This is explained in terms of the energy stored in the surface current, which is zeroed-out when linear dispersion is neglected. The results obtained with the proposed framework are compared with full-wave nonlinear finite-element simulations with excellent agreement. Very low characteristic power for bistability is obtained, indicating the potential of graphene for nonlinear applications.

In this paper we investigate the in vitro dynamics of a single rabbit red blood cell (RBC) in a planar linear flow as a function of a shear stress $\sigma$ and the dynamic viscosity of outer fluid ${\eta }_o$. A linear flow is a generalization of previous studies dynamics of soft objects including RBC in shear flow and is realized in the experiment in a microfluidic four-roll mill device. We verify that the RBC stable orientation dynamics is found in the experiment being the in-shear-plane orientation and the RBC dynamics is characterized by observed three RBC dynamical states, namely tumbling (TU), intermediate (INT), and swinging (SW) [or tank-treading (TT)] on a single RBC. The main results of these studies are the following. (i) We completely characterize the RBC dynamical states and reconstruct their phase diagram in the case of the RBC in-shear-plane orientation in a planar linear flow and find it in a good agreement with that obtained in early experiments in a shear flow for human RBCs. (ii) The value of the critical shear stress ${\sigma }_c$ of the TU-TT(SW) transition surprisingly coincides with that found in early experiments in spite of a significant difference in the degree of RBC shape deformations in both the SW and INT states. (iii) We describe the INT regime, which is stationary, characterized by strong RBC shape deformations and observed in a wide range of the shear stresses. We argue that our observations cast doubts on the main claim of the recent numerical simulations that the only RBC spheroidal stress-free shape is capable to explain the early experimental data. Finally, we suggest that the amplitude dependence of both $\theta$ and the shape deformation parameter $D$ on $\sigma$ can be used as the quantitative criterion to determine the RBC stress-free shape.

We analyze the dynamics of comb-of-comb-network polymers in the presence of external random flows. The dynamics of such structures is evaluated through relevant physical quantities, viz., average square displacement (ASD) and the velocity autocorrelation function (VACF). We focus on comparing the dynamics of the comb-of-comb network with the linear polymer. The present work displays an anomalous diffusive behavior of this flexible network in the random layered flows. The effect of the polymer topology on the dynamics is analyzed by varying the number of generations and branch lengths in these networks. In addition, we investigate the influence of external flow on the dynamics by varying flow parameters, like the flow exponent $\alpha$ and flow strength $W_{\alpha }$. Our analysis highlights two anomalous power-law regimes, viz., subdiffusive (intermediate-time polymer stretching and flow-induced diffusion) and superdiffusive (long-time flow-induced diffusion). The anomalous long-time dynamics is governed by the temporal exponent $\nu$ of ASD, viz., $\nu =2-\alpha /2$. Compared to a linear polymer, the comb-of-comb network shows a shorter crossover time (from the subdiffusive to superdiffusive regime) but a reduced magnitude of ASD. Our theory displays an anomalous VACF in the random layered flows that scales as $t^{-\alpha /2}$. We show that the network with greater total mass moves faster.

Employing theory and numerical simulations, we demonstrate discontinuous force thinning due to the driven motion of an external probe in a host medium. We consider two cases: an ideal structureless medium (modeling ultrasoft materials such as polymer melts) and a dilute bath of interacting repulsive particles. When the driving of the probe exceeds a critical force, the microviscosity of the medium drops abruptly by about an order of magnitude. This phenomenon occurs for strong attractive interactions between a large probe and a sufficiently dense host medium.

Nematic liquid crystals exhibit both crystallike and fluidlike features. In particular, the propagation of an acoustic wave shows an interesting occurrence of some of the solidlike features at the hydrodynamic level, namely, the frequency-dependent anisotropy of sound velocity and acoustic attenuation. The non-Newtonian behavior of nematics also emerges from the frequency-dependent viscosity coefficients. To account for these phenomena, we put forward a viscoelastic model of nematic liquid crystals, and we extend our previous theory to fully include the combined effects of compressibility, anisotropic elasticity, and dynamic relaxation, at any shear rate. The low-frequency limit agrees with the compressible Ericksen-Leslie theory, while at intermediate frequencies the model correctly captures the relaxation mechanisms underlying finite shear and bulk elastic moduli. We show that there are only four relaxation times allowed by the uniaxial symmetry.

Wertheim predicted strong density-density correlations at free liquid surfaces, produced by capillary wave fluctuations of the interface [M. S. Wertheim, J. Chem. Phys. 65, 2377 (1976)]. That prediction has been used to search for a link between capillary wave (CW) theory and density functional (DF) formalism for classical fluids. In particular, Parry et al. have recently analyzed the decaying tails of these CW effects moving away from the interface as a clue for the extended CW theory [A. O. Parry et al., J. Phys.: Condens. Matter 28, 244013 (2016)], beyond the strict long-wavelength limit studied by Wertheim. Some apparently fundamental inconsistencies between the CW and the DF theoretical views of the fluid interfaces arose from the asymptotic analysis of the CW signal. In this paper we revisit the problem of the CW asymptotic decay with a separation of local non-CW surface correlation effects from those that are a truly nonlocal propagation of the CW fluctuations from the surface towards the liquid bulk.

A challenge in soft robotics and soft actuation is the determination of an elastic system that spontaneously recovers its trivial path during postcritical deformation after a bifurcation. The interest in this behavior is that a displacement component spontaneously cycles around a null value, thus producing a cyclic soft mechanism. An example of such a system is theoretically proven through the solution of the elastica and a stability analysis based on dynamic perturbations. It is shown that the asymptotic self-restabilization is driven by the development of a configurational force, of similar nature to the Peach-Koehler interaction between dislocations in crystals, which is derived from the principle of least action. A proof-of-concept prototype of the discovered elastic system is designed, realized, and tested, showing that this innovative behavior can be obtained in a real mechanical apparatus.

We investigate the application of the dissipative particle dynamics method to the instability problem of a long liquid thread surrounded by another fluid. The dispersion curves obtained from simulations are compared with classic theoretical predictions. The results from standard dissipative particle dynamics (DPD) simulations at first have a tendency of gradually approaching to Tomotika's Stokes flow prediction when the Reynolds number is decreased. But they then abnormally deviate again when the viscosity is very large. The same phenomenon is also confirmed in droplet retraction simulations when also compared with theoretical Stokes flow results. On the other hand, when a hard-core DPD model is used, with the decrease of the Reynolds number the simulation results did finally approach Tomotika's predictions when $\mathrm{Re}\approx 0.1$. A combined presentation of the hard-core DPD results and the standard DPD results, excluding the abnormal ones, demonstrates that they are approximately on a continuum when labeled with Reynolds number. These results suggest that the standard DPD method is a suitable method for investigation of the instability problem of immersed liquid thread in the inertioviscous regime ($0.1<\mathrm{Re}<10$), which is relevant for microfluidics applications but there is currently no theory. It cannot reach the $\mathrm{Re}\approx 0.1$ regime because of some irregular properties of highly viscous DPD fluid, while the hard-core DPD is suitable to overcome this inferiority with standard DPD.

The swimming of a two-sphere system and of a three-sphere chain in an incompressible viscous fluid is studied on the basis of simplified equations of motion which take account of both Stokes friction and added mass effects. The analysis is based on an explicit expression for the asymptotic periodic swimming velocity and a corresponding evaluation of the mean rate of dissipation. The mean swimming velocity of the two-sphere system is found to be nonvanishing provided that the two spheres are not identical. The swimming of a comparable chain of three identical spheres is much more efficient.

We present a comparative study of gaseous microflow systems using the recently introduced Fokker-Planck approach and other methods such as: direct simulation Monte Carlo, lattice Boltzmann, and variational solution of Boltzmann-BGK. We show that this Fokker-Plank approach performs efficiently at intermediate values of Knudsen number, a region where direct simulation Monte Carlo becomes expensive and lattice Boltzmann becomes inaccurate. We also investigate the effectiveness of a recently proposed Fokker-Planck model in simulations of heat transfer, as a function of relevant parameters such as the Prandtl, Knudsen numbers. Furthermore, we present simulation of shock wave as a function of Mach number in transonic regime. Our results suggest that the performance of the Fokker-Planck approach is superior to that of the other methods in transition regime for rarefied gas flow and transonic regime for shock wave.

A method for analytic continuation of imaginary-time correlation functions (here obtained in quantum Monte Carlo simulations) to real-frequency spectral functions is proposed. Stochastically sampling a spectrum parametrized by a large number of $\delta$ functions, treated as a statistical-mechanics problem, it avoids distortions caused by (as demonstrated here) configurational entropy in previous sampling methods. The key development is the suppression of entropy by constraining the spectral weight to within identifiable optimal bounds and imposing a set number of peaks. As a test case, the dynamic structure factor of the $S=1/2$ Heisenberg chain is computed. Very good agreement is found with Bethe ansatz results in the ground state (including a sharp edge) and with exact diagonalization of small systems at elevated temperatures.

We characterize the properties of the asymptotic stage of modulational instability arising from localized perturbations of a constant background, including the number and location of the individual peaks in the oscillation region. We show that, for long times, the solution tends to an ensemble of classical (i.e., sech-shaped) solitons of the focusing nonlinear Schrödinger equation (as opposed to the various breatherlike solutions of the same equation with a nonzero background). We also confirm the robustness of the theoretical results by comparing the analytical predictions with careful numerical simulations with a variety of initial conditions, which confirm that the evolution of modulationally unstable media in the presence of localized initial perturbations is indeed described by the same asymptotic state.

An infinite array of globally coupled overdamped constituents moving in a double-well potential with $n\mathrm{th}$ order saturation term under the influence of additive Gaussian white noise is investigated. The system exhibits a continuous phase transition from a symmetric phase to a symmetry-broken phase. The qualitative behavior is independent on $n$. The critical point is calculated for strong and for weak noise; these limits are also bounds for the critical point. Introducing an additional nonlinearity, such that the potential can have up to three minima, leads to richer behavior. There the parameter space divides into three regions: a region with a symmetric phase, a region with a phase of broken symmetry and a region where both phases coexist. The region of coexistence collapses into one of the others via a discontinuous phase transition, whereas the transition between the symmetric phase and the phase of broken symmetry is continuous. The tricritical point where the three regions intersect can be calculated for strong and for weak noise. These limiting values form tight bounds on the tricritical point. In the region of coexistence simulations of finite systems are performed. One finds that the stationary distribution of finite but large systems differs qualitatively from the one of the infinite system. Hence the limits of stationarity and large system size do not commute.

We consider a generic reaction-diffusion-advection system where the flow velocity of the advection term is subjected to dichotomous noise with zero mean and Ornstein-Zernike correlation. A general condition for noisy-flow-induced instability is derived in the flow velocity-correlation rate parameter plane. Full numerical simulations on Gierer-Meinhardt model with activator-inhibitor kinetics have been performed to show how noisy differential flow can lead to symmetry breaking of a homogeneous stable state in the presence of noise resulting in traveling waves.

Epidemic control is of great importance for human society. Adjusting interacting partners is an effective individualized control strategy. Intuitively, it is done either by shortening the interaction time between susceptible and infected individuals or by increasing the opportunities for contact between susceptible individuals. Here, we provide a comparative study on these two control strategies by establishing an epidemic model with nonuniform stochastic interactions. It seems that the two strategies should be similar, since shortening the interaction time between susceptible and infected individuals somehow increases the chances for contact between susceptible individuals. However, analytical results indicate that the effectiveness of the former strategy sensitively depends on the infectious intensity and the combinations of different interaction rates, whereas the latter one is quite robust and efficient. Simulations are shown to verify our analytical predictions. Our work may shed light on the strategic choice of disease control.

An active participation of players in evolutionary games depends on several factors, ranging from personal stakes to the properties of the interaction network. Diverse activity patterns thus have to be taken into account when studying the evolution of cooperation in social dilemmas. Here we study the weak prisoner's dilemma game, where the activity of each player is determined in a probabilistic manner either by its degree or by its payoff. While degree-correlated activity introduces cascading failures of cooperation that are particularly severe on scale-free networks with frequently inactive hubs, payoff-correlated activity provides a more nuanced activity profile, which ultimately hinders systemic breakdowns of cooperation. To determine optimal conditions for the evolution of cooperation, we introduce an exponential decay to payoff-correlated activity that determines how fast the activity of a player returns to its default state. We show that there exists an intermediate decay rate at which the resolution of the social dilemma is optimal. This can be explained by the emerging activity patterns of players, where the inactivity of hubs is compensated effectively by the increased activity of average-degree players, who through their collective influence in the network sustain a higher level of cooperation. The sudden drops in the fraction of cooperators observed with degree-correlated activity therefore vanish, and so does the need for the lengthy spatiotemporal reorganization of compact cooperative clusters. The absence of such asymmetric dynamic instabilities thus leads to an optimal resolution of social dilemmas, especially when the conditions for the evolution of cooperation are strongly adverse.