We characterize the superdiffusive dynamics of tracer particles in an electrohydrodynamically driven emulsion of oil droplets in an immiscible oil medium, where the amplitude and frequency of an external electric field are the control parameters. In the weakly driven electrohydrodynamic regime, the droplets are trapped dielectrophoretically on a patterned electrode, and the driving is therefore spatially varying. We find excellent agreement with a $\langle x^2\rangle \sim t^{1.5}$ power law and find that this superdiffusive dynamics arises from an underlying displacement distribution that is distinctly non-Gaussian and exponential for small displacements and short times. While these results are comparable with a random-velocity field model, the tracer particle speeds are in fact spatially varying in two dimensions, arising from a spatially varying electrohydrodynamic driving force. This suggests that the important ingredient for the superdiffusive $t^{1.5}$ behavior observed is a velocity field that is isotropic in the plane and spatially correlated. Finally, we can extract, from the superdiffusive dynamics, a experimental length scale that corresponds to the lateral range of the hydrodynamic flows. This experimental length scale is non zero only above a threshold ion mobility length.

It is well known that a binary system of nonactive disks that experience driving in opposite directions exhibits jammed, phase separated, disordered, and laning states. In active matter systems, such as a crowd of pedestrians, driving in opposite directions is common and relevant, especially in conditions which are characterized by high pedestrian density and emergency. In such cases, the transition from laning to disordered states may be associated with the onset of a panic state. We simulate a laning system containing active disks that obey run-and-tumble dynamics, and we measure the drift mobility and structure as a function of run length, disk density, and drift force. The activity of each disk can be quantified based on the correlation timescale of the velocity vector. We find that in some cases, increasing the activity can increase the system mobility by breaking up jammed configurations; however, an activity level that is too high can reduce the mobility by increasing the probability of disk-disk collisions. In the laning state, the increase of activity induces a sharp transition to a disordered strongly fluctuating state with reduced mobility. We identify a novel drive-induced clustered laning state that remains stable even at densities below the activity-induced clustering transition of the undriven system. We map out the dynamic phase diagrams highlighting transitions between the different phases as a function of activity, drive, and density.

Gaseous flows inside microfluidic devices often fall in the slip-flow regime. According to this theoretical description, the Navier-Stokes model remains applicable in bulk, while at solid walls a slip velocity boundary model shall be considered. Physically, it is well established that, to properly account for the wall curvature, the wall slip velocity must be determined by the shear stress, rather than the normal component of the velocity derivative alone, as commonly applied to planar surfaces. It follows that the numerical transcription of this type of boundary condition is generally a challenging task for standard computational fluid dynamics (CFD) techniques. This paper aims to show that the realization of the slip velocity condition on arbitrarily shaped boundaries can be accomplished in a natural way with the lattice Boltzmann method (LBM). To substantiate this conclusion, this work undertakes the following three studies. First, we examine the conditions under which the generic reflection-type boundary rules used by LBM become consistent models for the slip velocity boundary condition. This effort makes use of the second-order Chapman-Enskog expansion method, where we address both planar and curved boundaries. The analysis also clarifies the capabilities and limitations behind the considered reflection-type slip schemes. Second, we revisit the family of parabolic accurate LBM slip boundary schemes, originally formulated in [Phys. Rev. E 96, 013311 (2017)] on the basis of the multireflection framework, and discuss their characteristics when operating on curved boundaries as well as the limitations of other less accurate LBM slip boundary formulations, such as the linearly accurate slip schemes and the widely popular “kinetic-based” boundary schemes. In addition, we also discuss the numerical stability of the parabolic slip schemes previously developed, providing an heuristic strategy to improve their stable range of operation. Third, we evaluate the performance of the several slip boundary schemes debated in this paper. The numerical tests correspond to two classical 2D benchmark flow problems of slip over non-planar solid surfaces, namely: (i) the velocity profile of the cylindrical Couette flow, and (ii) the permeability of a slow rarefied gas over a periodic array of circular cylindrical obstacles. The obtained numerical results confirm the competitiveness of the LBM when equipped with slip boundary schemes of parabolic accuracy as CFD tool to simulate slippage phenomena over arbitrarily non-planar surfaces. Indeed, although operating on a simple uniform mesh discretization, the LBM yields a similar, or even superior, level of accuracy compared to state-of-the-art FEM simulations conducted on hardworking body-fitted meshes. This conclusion establishes the LBM as a very appealing CFD technique for simulating microfluidic flows in the slip-flow regime, a result that deserves further exploration in future studies.

We present an iterative algorithm to count Feynman diagrams via many-body relations. The algorithm allows us to count the number of diagrams of the exact solution for the general fermionic many-body problem at each order in the interaction. Further, we apply it to different parquet-type approximations and consider spin-resolved diagrams in the Hubbard model. Low-order results and asymptotics are explicitly discussed for various vertex functions and different two-particle channels. The algorithm can easily be implemented and generalized to many-body relations of different forms and levels of approximation.

We report on specific effects of collective scattering for a cloud of heavy impurities exposed to a gas stream. Formation is presented of a common density perturbation and shock waves, both generated collectively by a system of scatterers at sudden application of the stream-inducing external field. Our results demonstrate that (i) the scattering of gas stream can be essentially amplified, due to nonlinear collective effects, upon fragmentation of a solid obstacle into a cluster of impurities (heterogeneously fractured obstacle); (ii) a cluster of disordered impurities can produce considerably stronger scattering accompanied by enhanced and accelerated shock wave, as compared to a regularly ordered cluster. We also show that the final steady-state density distribution is formed as a residual perturbation left after the shock front passage. In particular, a kinklike steady distribution profile can be formed as a result of shock front stopping effect. The possibility of the onset of solitary diffusive density waves, reminiscent of precursor solitons, is shown and briefly discussed.

The supercritical phase of fluids has long been known to feature significantly different liquidlike and gaslike regimes. However, it is textbook knowledge that the supercritical state is a homogeneous fluid phase where properties change continuously. Nevertheless, there has been an increasing amount of evidence published that suggests that there might exist a unique line that rigorously separates different regimes in supercritical phases, particularly in the case of water. Here, we use the quasiexact IAPWS95 equation of state to rigorously assess the macroscopic thermodynamic properties of supercritical water without invoking any water model or related approximations. We focus on how these properties change deep in the supercritical phase, in particular if they allow one to introduce a unique “thermodynamic separatrix.” Our rigorous thermodynamic analysis, which relies exclusively on accurate experimental data, makes clear that there is no unique separatrix in real supercritical water—such as the recently much-invoked “Widom line.” A comparison to the van der Waals equation of state reproduces qualitatively all our findings for real water, thereby suggesting that our analysis should be transferable to other fluids and critical points. Topological analysis of the H-bond network structure of supercritical water, as obtained from molecular-dynamics simulations using a standard water model, demonstrates that also the percolation line does not provide a meaningful separatrix to rigorously distinguish liquidlike from gaslike regimes.

We study the energy transfer in a classical dipole chain of $N$ interacting rigid rotating dipoles. The underlying high-dimensional potential energy landscape is analyzed in particular by determining the equilibrium points and their stability in the common plane of rotation. Starting from the minimal energy configuration, the response of the chain to excitation of a single dipole is investigated. Using both the linearized and the exact Hamiltonian of the dipole chain, we detect an approximate excitation energy threshold between a weakly and a strongly nonlinear dynamics. In the weakly nonlinear regime, the chain approaches in the course of time the expected energy equipartition among the dipoles. For excitations of higher energy, strongly localized excitations appear whose trajectories in time are either periodic or irregular, relating to the well-known discrete or chaotic breathers, respectively. The phenomenon of spontaneous formation of domains of opposite polarization and phase locking is found to commonly accompany the time evolution of the chaotic breathers. Finally, the sensitivity of the dipole chain dynamics to the initial conditions is studied as a function of the initial excitation energy by computing a fast chaos indicator. The results of this study confirm the aforementioned approximate threshold value for the initial excitation energy, below which the dynamics of the dipole chain is regular and above which it is chaotic.

We use the Fisher information to provide a lens on the transition to synchronization of the Kuramoto model of nonidentical frequencies on a variety of undirected graphs. We numerically solve the equations of motion for a $N=400$ complete graph and $N=1000$ small-world, scale-free, uniform random, and random regular graphs. For large but finite graphs of small average diameter the Fisher information $\mathcal{F}$ as a function of coupling shows a peak closely coinciding with the critical point as determined by Kuramoto's order parameter or synchronization measure $r$. However, for graphs of larger average diameter the position of the peak in $\mathcal{F}$ differs from the critical point determined by estimates of $r$. On the one hand, this is a finite-size effect even at $N=1000$; however, we show across a range of topologies that the Fisher information peak points to a transition for smaller graphs that indicates structural changes in the numbers of locally phase-synchronized clusters, often directly from metastable to stable frequency synchronization. Solving explicitly for a two-cluster ansatz subject to Gaussian noise shows that the Fisher infomation peaks at such a transition. We discuss the implications for Fisher information as an indicator for edge-of-chaos phenomena in finite-coupled oscillator systems.

We study the behavior of a generalized consensus dynamics on a temporal network of interactions, the activity-driven network with attractiveness. In this temporal network model, agents are endowed with an intrinsic activity $a$, ruling the rate at which they generate connections, and an intrinsic attractiveness $b$, modulating the rate at which they receive connections. The consensus dynamics considered is a mixed voter and Moran dynamics. Each agent, either in state 0 or 1, modifies his or her state when connecting with a peer. Thus, an active agent copies his or her state from the peer (with probability $p$) or imposes his or her state to him or her (with the complementary probability $1-p$). Applying a heterogeneous mean-field approach, we derive a differential equation for the average density of voters with activity $a$ and attractiveness $b$ in state 1, which we use to evaluate the average time to reach consensus and the exit probability, defined as the probability that a single agent with activity $a$ and attractiveness $b$ eventually imposes his or her state to a pool of initially unanimous population in the opposite state. We study a number of particular cases, finding an excellent agreement with numerical simulations of the model. Interestingly, we observe a symmetry between voter and Moran dynamics in pure activity-driven networks and their static integrated counterparts that exemplifies the strong differences that a time-varying network can impose on dynamical processes.

Biological systems are typically highly open, nonequilibrium systems that are very challenging to understand from a statistical mechanics perspective. While statistical treatments of evolutionary biological systems have a long and rich history, examination of the time-dependent nonequilibrium dynamics has been less studied. In this paper we first derive a generalized master equation in the genotype space for diploid organisms incorporating the processes of selection, mutation, recombination, and reproduction. The master equation is defined in terms of continuous time and can handle an arbitrary number of gene loci and alleles and can be defined in terms of an absolute population or probabilities. We examine and analytically solve several prototypical cases which illustrate the interplay of the various processes and discuss the timescales of their evolution. The entropy production during the evolution towards steady state is calculated and we find that it agrees with predictions from nonequilibrium statistical mechanics where it is large when the population distribution evolves towards a more viable genotype. The stability of the nonequilibrium steady state is confirmed using the Glansdorff-Prigogine criterion.

We present numerical simulations of symmetric surface-directed spinodal decomposition in thin films with varying film thickness and film composition. The simulations utilize a Cahn-Hilliard model to describe phase separation kinetics in confined film geometries. The systems consist of two phases: a wetting phase that completely wets the top and bottom surfaces, and a nonwetting phase. Three distinct morphologies emerge including a discrete nonwetting morphology, a discrete wetting morphology, as well as a unique two-dimensional bicontinuous morphology that forms for specific values of film thickness and composition. The morphologies are analyzed with a Hoshen-Kopelman algorithm to quantify the degree of continuity of the nonwetting phase, and a morphology map is presented to guide future work.

Reaction fronts described by the Kuramoto-Sivashinsky (KS) equation can exhibit complex behavior as they separate reacted from unreacted fluids. If the fluid of higher density is above a fluid of lower density, then the Rayleigh-Taylor instability can lead to fluid motion. In the reverse situation, where the lighter fluid is on top, gravitationally driven forces can stabilize a convectionless flat front inhibiting the complex front propagation described by the KS equation. In these cases, a critical density difference is required to provide stability to the flat front. A linear stability analysis shows that the transition from stable to unstable flat fronts can be oscillatory for viscous fluid motion. Once the transition takes place, the fronts exhibit oscillatory convection resulting in oscillations of the shape and speed of the front.

A theoretical study on the electrophoresis of a soft particle made up of a charged hydrophobic inner core surrounded by polyelectrolyte layer (PEL) is made. The dielectric permittivity of the PEL and aqueous solution are considered to be different, which creates the ion partitioning effect. The ion partitioning effect, which is accounted by the Born energy difference, modifies the distribution of mobile ions in the PEL and hence alters the particle electrophoresis. The combined effects of core hydrophobicity and the ion partitioning effect on the mobility are determined based on the Debye-Huckel approximation under a thin Debye layer assumption. An analytic expression for the electrophoretic mobility taking into account the core hydrophobicity and ion partitioning effect is obtained. The occurrence of zero mobility and reversal of mobility of the soft particle is illustrated.

We study the rotational dynamics of inertial disks and rods in three-dimensional, homogeneous, isotropic turbulence. In particular, we show how the alignment and the decorrelation timescales of such spheroids depend, critically, on both the level of inertia and the aspect ratio of these particles. These results illustrate the effect of inertia—which leads to a preferential sampling of the local flow geometry—on the statistics of both disks and rods in a turbulent flow. Our results are important for a variety of natural and industrial settings where the turbulent transport of asymmetric, spheroidal inertial particles is ubiquitous.

We revisit and analyze the thermodynamic efficiency of the Feynman-Smoluchowski (FS) ratchet, a classical thought experiment describing an autonomous heat-work converter. Starting from the full kinetics of the FS ratchet and deriving the exact forms of the hidden dissipations resulting from coarse graining, we restate the historical controversy over its thermodynamic efficiency. The existence of hidden entropy productions implies that the standard framework of stochastic thermodynamics applied to the coarse-grained descriptions fails in capturing the dissipative feature of the system. In response to this problem, we explore an extended framework of stochastic thermodynamics to reconstruct the hidden entropy production from the coarse-grained dynamics. The approach serves as a key example of how we can systematically address the problem of thermodynamic efficiency in a multivariable fluctuating nonequilibrium system.

When a quantity reaches a value higher (or lower) than its value at any time before, it is said to have made a record. We numerically study the statistical properties of records in the time series of order parameters in different models near their critical points. Specifically, we choose the transversely driven Edwards-Wilkinson model for interface depinning in (1+1) dimensions and the Ising model in two dimensions, as paradigmatic and simple examples of nonequilibrium and equilibrium critical behaviors, respectively. The total number of record-breaking events in the time series of the order parameters of the models show maxima when the system is near criticality. The number of record-breaking events and associated quantities, such as the distribution of the waiting time between successive record events, show power-law scaling near the critical point. The exponent values are specific to the universality classes of the respective models. Such behaviors near criticality can be used as a precursor to imminent criticality, i.e., abrupt and catastrophic changes in the system. Due to the extreme nature of the records, its measurements are relatively free of detection errors and thus provide a clear signal regarding the state of the system in which they are measured.

Quantum time evolution exhibits rich physics, attributable to the interplay between the density and phase of a wave function. However, unlike classical heat diffusion, the wave nature of quantum mechanics has not yet been extensively explored in modern data analysis. We propose that the Laplace transform of quantum transport (QT) can be used to construct an ensemble of maps from a given complex network to a circle $S^1$, such that closely related nodes on the network are grouped into sharply concentrated clusters on $S^1$. The resulting QT clustering (QTC) algorithm is as powerful as the state-of-the-art spectral clustering in discerning complex geometric patterns and more robust when clusters show strong density variations or heterogeneity in size. The observed phenomenon of QTC can be interpreted as a collective behavior of the microscopic nodes that evolve as macroscopic cluster “orbitals” in an effective tight-binding model recapitulating the network. python source code implementing the algorithm and examples are available at https://github.com/jssong-lab/QTC.

Langevin dynamics simulations of polymer translocation are performed where the polymer is stretched via two opposing forces applied on the first and last monomer before and during translocation. In this setup, polymer translocation is achieved by imposing a bias between the two pulling forces such that there is net displacement towards the trans side. Under the influence of stretching forces, the elongated polymer ensemble contains less variations in conformations compared to an unstretched ensemble. Simulations demonstrate that this reduced spread in initial conformations yields a reduced variation in translocation times relative to the mean translocation time. This effect is explored for different ratios of the amplitude of thermal fluctuations to driving forces to control for the relative influence of the thermal path sampled by the polymer. Since the variance in translocation times is due to contributions coming from sampling both thermal noise and initial conformations, our simulations offer independent control over the two main sources of noise and allow us to shed light on how they both contribute to translocation dynamics. Simulation parameter space corresponding to experimentally relevant conditions is highlighted and shown to correspond to a significant decrease in the spread of translocation times, thus indicating that stretching DNA prior to translocation could assist nanopore-based sequencing and sizing applications.

The atmosphere gains available potential energy by solar radiation and dissipates kinetic energy mainly in the atmospheric boundary layer. We analyze the fluctuations of the global mean energy cycle defined by Lorenz in a simulation with a simplified hydrostatic model. The energy current densities are well approximated by the generalized Gumbel distribution and the Generalized Extreme Value (GEV) distribution. In an attempt to assess the fluctuation relation of Evans, Cohen, and Morriss we define entropy production by the injected power and use the GEV location parameter as a reference state. The fluctuation ratio reveals a linear behavior in a finite range.

A practical search technique for finding the complex saddle points used in wave packet and coherent state propagation is developed which works for a large class of Hamiltonian dynamical systems with many degrees of freedom. The method can be applied to problems in atomic, molecular, and optical physics and other domains. A Bose-Hubbard model is used to illustrate the application to a many-body system where discrete symmetries play an important and fascinating role. For multidimensional wave packet propagation, locating the necessary saddles involves the seemingly insurmountable difficulty of solving a boundary value problem in a high-dimensional complex space, followed by determining whether each particular saddle found actually contributes. In principle, this must be done for each propagation time considered. The method derived here identifies a real search space of minimal dimension, which leads to a complete set of contributing saddles up to intermediate times much longer than the Ehrenfest timescale for the system. The analysis also gives a powerful tool for rapidly identifying the various dynamical regimes of the system.