We study theoretically the stability of a trapless dipolar Bose-Einstein condensate (BEC) with temporal modulation of the short-range contact interaction. For this aim, through both analytical and numerical methods, we solve a Gross-Pitaevskii equation with both constant and oscillatory forms of the short-range contact interaction along with long-range, nonlocal, dipole-dipole interaction terms. By using the variational method, we discuss the stability of the trapless dipolar BEC with the presence and absence of both constant and oscillatory contact interactions. We show that the oscillatory contact interaction prevents the collapse of the trapless dipolar BEC. We confirm the analytical prediction through numerical simulations. We also study the collective excitations in the system induced by the effective potential due to the oscillating interaction.

Several schemes are proposed to accelerate the recently designed variational approach for finding periodic orbits in a nonlinear system with chaotic dynamics, especially those close to a singularity or with long period. An effective equation is derived to implement an automatic allocation of lattice points to capture local fine orbit structures while keeping the exponential convergence of the variational approach. Utilizing the special structure of the matrix involved in the homotopy evolution, the lower–upper (LU) decomposition could be done with much greater efficiency and much less memory, which considerably facilitates the search for long cycles. Three examples are used to demonstrate the validity of the accelerated algorithm. For Hamiltonian systems, an interesting scheme is designed to remove the neutral direction associated with the conservation law while keeping the dynamics on the desired energy surface.

In this paper we address the evolution of finite and structured populations including two types of species. The evolutionary dynamics of the system is governed by the Moran process with constant fitnesses in the presence of mutation. We obtain the stationary distribution in a number of topologies. We also approximate the mixing time, i.e., the time that the system needs to reach its stationary distribution. It is observed that the mean frequency of a species in the stationary distribution is approximately independent of the population structure, and the mixing time has a power law behavior with respect to the population size whose exponent is closely related to the population structure. The obtained results indicate that more heterogeneity leads to longer mixing times.

Effect of forced convection on the lamellar eutectic growth was investigated by combining a modified Jackson-Hunt theory and a phase-field lattice-Boltzmann approach. Under the consideration of the asymmetrical tilting pattern and curvature effect, the classical eutectic Jackson-Hunt theory [Jackson and Hunt, Trans. Metall. Soc. AIME 236, 1129 (1966)] was modified to better understand the physical mechanism driving the eutectic growth with convection. Results showed that the eutectic growth velocity increased linearly with increasing undercooling and exhibited a parabola trend versus the inverse of initial lamellar spacing. The flow induced by a horizontal external force tilted the eutectic lamellae by altering the solute distribution near the interface. Under weak convection, the phase-field lattice-Boltzmann simulation results agreed well with those predicted by the modified Jackson-Hunt theory. But under strong convection, the consistency of the two results was largely dependent on the alloy parameters and convection intensity.

We propose a functional integral framework for the derivation of hierarchies of Landau-Lifshitz-Bloch (LLB) equations that describe the flow toward equilibrium of the first and second moments of the magnetization. The short-scale description is defined by the stochastic Landau-Lifshitz-Gilbert equation, under both Markovian or non-Markovian noise, and takes into account interaction terms that are of practical relevance. Depending on the interactions, different hierarchies on the moments are obtained in the corresponding LLB equations. Two closure Ansätze are discussed and tested by numerical methods that are adapted to the symmetries of the problem. Our formalism provides a rigorous bridge between the atomistic spin dynamics simulations at short scales and micromagnetic descriptions at larger scales.

This paper proposes a totally asymmetric simple exclusion process on a traveling lane, which is equipped with a queueing system and functions of site assignments along the parking lane. In the proposed system, new particles arrive at the rear of the queue existing at the leftmost site of the system. A particle at the head of the queue selects one of the empty sites in the parking lane and reserves it for stopping at once during its travel. The arriving time and staying time in the parking sites follow half-normal distributions. The random selections of empty sites are controlled by the bias of the exponential function. Our simulation results show the unique shape of site usage distributions. In addition, the number of reserved sites is found to increase with an S-shape curve as the bias to the rightmost site increases. To describe this phenomena, we propose an approximation model, which is derived from the birth-death process and extreme order statistics. A queueing model that takes the effect of distance from the leftmost site of the traveling lane into consideration is further proposed. Our approximation model properly describes the distributions of site usage, and the proposed queueing model shows good agreement with the simulation results.

The self-consistent method, first introduced by Kuramoto, is a powerful tool for the analysis of the steady states of coupled oscillator networks. For second-order oscillator networks, complications to the application of the self-consistent method arise because of the bistable behavior due to the co-existence of a stable fixed point and a stable limit cycle and the resulting complicated boundary between the corresponding basins of attraction. In this paper, we report on a self-consistent analysis of second-order oscillators which is simpler compared to previous approaches while giving more accurate results in the small inertia regime and close to incoherence. We apply the method to analyze the steady states of coupled second-order oscillators and we introduce the concepts of margin region and scaled inertia. The improved accuracy of the self-consistent method close to incoherence leads to an accurate estimate of the critical coupling corresponding to transitions from incoherence.

Cooperative search games are collective tasks where all agents share the same goal of reaching a target in the shortest time while limiting energy expenditure and avoiding collisions. Here we show that the equations that characterize the optimal strategy are identical to a long-known phenomenological model of chemotaxis, the directed motion of microorganisms guided by chemical cues. Within this analogy, the substance to which searchers respond acts as the memory over which agents share information about the environment. The actions of writing, erasing, and forgetting are equivalent to production, consumption, and degradation of chemoattractant. The rates at which these biochemical processes take place are tightly related to the parameters that characterize the decision-making problem, such as learning rate, costs for time, control, collisions and their tradeoffs, as well as the attitude of agents toward risk. We establish a dictionary that maps notions from decision-making theory to biophysical observables in chemotaxis, and vice versa. Our results offer a fundamental explanation of why search algorithms that mimic microbial chemotaxis can be very effective and suggest how to optimize their performance.

The interplay of elastic anisotropy and disorder dictates many of the properties of ferroic materials, specifically martensites. We use a phase-field model for ferroelastic athermal materials to study their response to an increasing external stress that couples to the strain order parameter. We show that these systems evolve through avalanches and study the avalanche-size distribution for ferroelastic systems (large anisotropy and/or small disorder) and for the strain glass (small anisotropy and/or large disorder) using various statistical analysis techniques, including the maximum likelihood method. The model predicts that in the former case the distribution is subcritical or power law (in agreement with experimental observations), whereas in the latter case it becomes supercritical. Our results are consistent with experiments on martensitic materials, and we predict specific avalanche behavior that can be tested and used as an alternative means to characterize strain glasses.

We use zero-temperature Glauber dynamics to study hysteresis in the random-field Ising model on directed random graphs. The critical behavior of the model depends on the connectivity $z$ of the graph rather differently from that on undirected graphs. Directed graphs and zero-temperature dynamics are relevant to a wide class of social phenomena including opinion dynamics. We discuss the efficacy of increasing external influence in inducing a first-order phase transition in opinion dynamics. The numerical results are supported by an analytic solution of the model.

Consider a stochastic interface $h(x,t)$, described by the $1+1$ Kardar-Parisi-Zhang (KPZ) equation on the half line $x\ge 0$. The interface is initially flat, $h(x,t=0)=0$, and driven by a Neumann boundary condition ${\partial }_{x}h(x=0,t)=A$ and by the noise. We study the short-time probability distribution $\mathcal{P}\left(H,A,t\right)$ of the one-point height $H=h(x=0,t)$. Using the optimal fluctuation method, we show that $-ln\mathcal{P}\left(H,A,t\right)$ scales as $t^{-1/2}s\left(H,A{t}^{1/2}\right)$. For small and moderate $\left|A\right|$ this more general scaling reduces to the familiar simple scaling $-ln\mathcal{P}\left(H,A,t\right)\simeq t^{-1/2}s\left(H\right)$, where $s$ is independent of $A$ and time and equal to one half of the corresponding large-deviation function for the full-line problem. For large $\left|A\right|$ we uncover two asymptotic regimes. At very short time the simple scaling is restored, whereas at intermediate times the scaling remains more general and $A$-dependent. The distribution tails, however, always exhibit the simple scaling in the leading order.

We experimentally test the validity of the Crooks fluctuation theorem (CFT) in the force ensemble by pulling DNA hairpins, first with magnetic tweezers, next with optical tweezers using force feedback. The CFT holds when using the definition of work $W_f=-\int xdf$, where $x$ is the molecular extension and $f$ is the force. In contrast, it does not hold when using the usual definition, appropriate for the constant extension ensemble, $W_x=\int fdx$, showing the importance of the contribution of boundary terms to the full entropy production in a clear example of statistical ensemble inequivalence in small systems. We also evaluate the differences in the average dissipated work in the force ensemble as compared to the extension ensemble, highlighting ensemble inequivalence also at the level of molecular kinetics.

We investigate the impact of a common external system, which we call a common environment, on the oscillator death (OD) states of a group of Stuart-Landau oscillators. The group of oscillators yield a completely symmetric OD state when uncoupled to the external system, i.e., the two OD states occur with equal probability. However, remarkably, when coupled to a common external system this symmetry is significantly broken. For exponentially decaying external systems, the symmetry breaking is very pronounced for low environmental damping and strong oscillator-environment coupling. This is evident through the sharp transition from the symmetric to asymmetric state occurring at a critical oscillator-environment coupling strength and environmental damping rate. Further, we consider time-varying connections to the common external environment, with a fraction of oscillator-environment links switching on and off. Interestingly, we find that the asymmetry induced by environmental coupling decreases as a power law with increase in fraction of such on-off connections. This suggests that blinking oscillator-environment links can restore the symmetry of the OD state. Last, we demonstrate the generality of our results for a constant external drive and find marked breaking of symmetry in the OD states there as well. When the constant environmental drive is large, the asymmetry in the OD states is very large, and the transition between the symmetric and asymmetric state with increasing oscillator-environment coupling is very sharp. So our results demonstrate an environmental coupling-induced mechanism for the prevalence of certain OD states in a system of oscillators and suggests an underlying process for obtaining certain states preferentially in ensembles of oscillators with environment-mediated coupling.

Pedestrians are active agents that undergo a repeated decision-making process while walking. These anisotropic, interactive, and feedback-oriented agents observe their surroundings, anticipate the future state of the network, and decide on their next movements accordingly, while ensuring a collision-free path toward their destination. Aiming at capturing these behavioral characteristics of human agents while walking, the present study puts forward a learning-based game theoretical approach for modeling pedestrian motion in dynamic environments. The proposed game structure provides a technical foundation to analyze optimal decision-making by pedestrians where the outcome of the game for each player's choice depends primarily on the strategies played by other players. This, in turn, ensures the frequently observed collision avoidance behavior of pedestrians while walking. The influence of nearby pedestrians on one's decision-making process and the feedback-oriented behavior of human agents are also captured via incorporating a learning structure. Optimum moving strategies are selected based on Nash equilibria calculations, where everyone is playing optimally given what all other players are playing. The validation results using real-world trajectories of pedestrians provide evidence of the model's capability in describing pedestrian motion and walking behaviors at microscopic as well as macroscopic levels.

We study epidemic processes using a metapopulation approach on the line featuring random transport rates between arbitrarily distant sites. An average transport network is found using a recently developed variant of the effective medium approximation (EMA) that is capable of dealing with these long-range connections. Using a Feynman-Kac argument in the effective medium, we derive an estimate on the size of the infected domain, and reproduce the known result of its exponential growth in time. We hereby demonstrate the applicability of long-range EMA to dynamical processes on networks more intricate than simple diffusion.

Lattice-based stochastic simulators are commonly used to study biological reaction-diffusion processes. Some of these schemes that are based on the reaction-diffusion master equation (RDME) can simulate for extended spatial and temporal scales but cannot directly account for the microscopic effects in the cell such as volume exclusion and diffusion-influenced reactions. Nonetheless, schemes based on the high-resolution microscopic lattice method (MLM) can directly simulate these effects by representing each finite-sized molecule explicitly as a random walker on fine lattice voxels. The theory and consistency of MLM in simulating diffusion-influenced reactions have not been clarified in detail. Here, we examine MLM in solving diffusion-influenced reactions in three-dimensional space by employing the spatiocyte simulation scheme. Applying the random walk theory, we construct the general theoretical framework underlying the method and obtain analytical expressions for the total rebinding probability and the effective reaction rate. By matching Collins-Kimball and lattice-based rate constants, we obtained the exact expressions to determine the reaction acceptance probability and voxel size. We found that the size of voxel should be about $2\%$ larger than the molecule. The theoretical framework of MLM is validated by numerical simulations, showing good agreement with the off-lattice particle-based method, enhanced Green's function reaction dynamics (egfrd). MLM run time is more than an order of magnitude faster than egfrd when diffusing macromolecules with typical concentrations observed in the cell. MLM also showed good agreements with egfrd and mean-field models in case studies of two basic motifs of intracellular signaling, the protein production-degradation process and the dual phosphorylation-dephosphorylation cycle. In addition, when a reaction compartment is populated with volume-excluding obstacles, MLM captures the nonclassical reaction kinetics caused by anomalous diffusion of reacting molecules.

Equilibrium clusters of protein lysozyme are at the center of an ongoing scientific debate. Previous attempts to provide a microscopic description of the clusters that is consistent with all experimental evidence have not been fully successful. The primary reason is the use of model potentials that have a predefined shape. In this paper we derive a model-free interprotein potential directly from experimental structure factor. The derived potential is globally repulsive but has a local minimum at short distances. The minimum is essential for the correct behavior of the structure factor with protein concentration, in particular the shifting pattern of the signature maximum at short wave vectors. Equilibrium clusters are observed throughout the entire range of concentrations, but their nature differs in the low and high concentration limits. At low concentrations, the clusters are extended in shape. As the concentration is increased, small clusters collapse while large clusters are assembled from the small ones. Hydrodynamic interactions drive a kinetic slowdown at high concentrations, where a transition into a fluid of permanent clusters of specific size is observed. In good agreement with the available experimental data, our simulations shed light on the microscopic nature of protein clusters.

A large number of smectic phases can have the same energy when short-range interlayer interactions (interaction of nearest layers and frustrating next-nearest layer interaction) are taken into account. In this situation even weak long-range interactions become important. They lift the degeneracy and lead to the appearance of a manifold of polar structures with multilayer periodicity. We analyze the reasons for the appearance of six-layer structures observed in experiments. Due to specific symmetry of interlayer interactions each antiferroelectric structure corresponds to a ferrielectric one in which synclinic orientations of molecules in nearest layers are replaced by anticlinic and vice versa. It is shown how different long-range interlayer interactions transform the degeneracy and induce different stable and metastable structures.

We compare all-atom simulations of nanoscale water droplets of spherical and cylindrical morphologies on flat surfaces with tunable polarities. We find that for both morphologies, the contact angle depends, albeit differently, on the droplet size, which can be well described by the modified Young equation with an apparent line tension as a fitting parameter. In order to quantify the origin of the apparent line tension, we invoke a continuum-level description of the droplets for both morphologies. This enables us to decompose the apparent line tension into individual components that stem from a contact-angle dependent line tension and the Tolman correction to the surface tension.

The present study describes a way to control the dispersion of an impulse in a two-dimensional square granular crystal with tapered beads. The control is through the redirection of the characteristic load transfer path by controlling the shape of the scattering of wavefront. The main goal is to contribute to the development of appropriately designed granular media to mitigate impacts. The crystal is constituted of spherical granules with a wide range of radii. Interstitial particles are strategically positioned to allow a large number of collisions per unit area. The waves are produced by a striker that collides against the crystal. We analyze how material combinations, number of layers, tapering parameter, and disorder affect the decay of the wave amplitude. Our studies suggest that $\sim 90\%$ impulse attenuation can be accomplished using a system thickness of 5 grains.