The cylindrical wall boundary layer of a closed cylinder split in two halves at the equator is studied experimentally. When these two parts rotate in exact corotation the internal flow is essentially in solid-body rotation at the angular velocity of both halves. When a slight difference between the rotation frequencies is established a secondary flow is created due to the differential rotation between both sides and restricted to the boundary layer. This behavior of the boundary layer is compared with theoretical and numerical results finding the “sandwich” structure of a Stewartson boundary layer. Time-dependent waves are observed near the cylindrical wall. Their behavior for different values of the control parameters are presented. Finally, a global recirculation mode is also found due to a symmetry-breaking induced between sides that appears because of a slight misalignment of the experimental setup, whose characteristics are compatible with the behavior of a precessing cylinder.

The phenomena of diffusion in multicomponent (more than two components) mixtures are universal in both science and engineering, and from the mathematical point of view, they are usually described by the Maxwell-Stefan (MS)-theory-based diffusion equations where the molar average velocity is assumed to be zero. In this paper, we propose a multiple-relaxation-time lattice Boltzmann (LB) model for the mass diffusion in multicomponent mixtures and also perform a Chapman-Enskog analysis to show that the MS continuum equations can be correctly recovered from the developed LB model. In addition, considering the fact that the MS-theory-based diffusion equations are just a diffusion type of partial differential equations, we can also adopt much simpler lattice structures to reduce the computational cost of present LB model. We then conduct some simulations to test this model and find that the results are in good agreement with the previous work. Besides, the reverse diffusion, osmotic diffusion, and diffusion barrier phenomena are also captured. Finally, compared to the kinetic-theory-based LB models for multicomponent gas diffusion, the present model does not include any complicated interpolations, and its collision process can still be implemented locally. Therefore, the advantages of single-component LB method can also be preserved in present LB model.

A class of variational schemes for the hydrodynamic-electrodynamic model of lossless free-electron gas in a quasineutral background is developed for high-quality simulations of surface plasmon polaritons. The Lagrangian density of lossless free-electron gas with a self-consistent electromagnetic field is established, and the dynamical equations with the associated constraints are obtained via a variational principle. Based on discrete exterior calculus, the action functional of this system is discretized and minimized to obtain the discrete dynamics. Newton-Raphson iteration and the biconjugate gradient stabilized method are equipped as a hybrid nonlinear-linear algebraic solver. Instead of discretizing the partial differential equations, the variational schemes have better numerical properties in secular simulations, as they preserve the discrete Lagrangian symplectic structure, gauge symmetry, and general energy-momentum density. Two numerical experiments were performed. The numerical results reproduce characteristic dispersion relations of bulk plasmons and surface plasmon polaritons, and the numerical errors of conserved quantities in all experiments are bounded by a small value after long-term simulations.

When three species compete cyclically in a well-mixed, stochastic system of $N$ individuals, extinction is known to typically occur at times scaling as the system size $N$. This happens, for example, in rock-paper-scissors games or conserved Lotka-Volterra models in which every pair of individuals can interact on a complete graph. Here we show that if the competing individuals also have a “social temperament” to be either introverted or extroverted, leading them to cut or add links, respectively, then long-living states in which all species coexist can occur. These nonequilibrium quasisteady states only occur when both introverts and extroverts are present, thus showing that diversity can lead to stability in complex systems. In this case, it enables a subtle balance between species competition and network dynamics to be maintained.

Avalanches in coal and sandstone samples under common uniaxial stress serve as a model for mixing of avalanche exponents in ceramics, multiferroics, and alloys. The two media are sandwiched together and subjected to common uniaxial stress using high- and low-stress compression. Each medium collapses individually through avalanches that often coincide with secondary avalanches into the other medium. The total avalanche time sequence allows a detailed investigation of the mixing by superposition and delayed coincidence. Correlations can be described by an inter-media Båth's law.

The fundamental problem in modeling complex phenomena such as human perception using probabilistic methods is that of deducing a stochastic model of interactions between the constituents of a system from observed configurations. Even in this era of big data, the complexity of the systems being modeled implies that inference methods must be effective in the difficult regimes of small sample sizes and large coupling variability. Thus, model inference by means of minimization of a cost function requires additional assumptions such as sparsity of interactions to avoid overfitting. In this paper, we completely divorce iterative model updates from the value of a cost function quantifying goodness of fit. This separation enables the use of goodness of fit as a natural rationale for terminating model updates, thereby avoiding overfitting. We do this within the mathematical formalism of statistical physics by defining a formal free energy of observations from a partition function with an energy function chosen precisely to enable an iterative model update. Minimizing this free energy, we demonstrate coupling strength inference in nonequilibrium kinetic Ising models, and show that our method outperforms other existing methods in the regimes of interest. Our method has no tunable learning rate, scales to large system sizes, and has a systematic expansion to obtain higher-order interactions. As applications, we infer a functional connectivity network in the salamander retina and a currency exchange rate network from time-series data of neuronal spiking and currency exchange rates, respectively. Accurate small sample size inference is critical for devising a profitable currency hedging strategy.

Aspects related to driven nonequilibrium systems considered in Beck-Cohen superstatistics (BCS) formalism and, in addition, the unbiased maximum entropy density estimation, show the pertinence of considering the three-parameter Burr-type-XII distribution as a suitable way to describe stationary states of complex and nonequilibrium systems. The above is shown following a variant to the procedure presented in the formulation of BCS, which consists of the incorporation of an expanded Boltzmann factor through the Mittag-Leffler function. On the other hand, maximization of Shannon-Boltzmann-Gibbs entropy and other generalized forms of entropy show that the Burr-type-XII distribution may emerge as the least informative distribution for the mentioned systems.

We analyze the statistical properties of complex systems with specific conservation laws and symmetry conditions which lead to various constraints and thereby structures in their matrix representation. An increase of constraints leads to a variation of the spectral statistics from Wigner-Dyson to Poisson limits, but the eigenfunction statistics remains weakly multifractal in the bulk. For some constraints, the statistics not only lies between the two limits but is size-independent too, thus indicating a critical point. Our results also reveal an important trend: While the spectral statistics is strongly sensitive to the number of independent matrix elements, the eigenfunction statistics seems to be affected mainly by their relative strengths. This is contrary to a previously held belief of a one-to-one relation between the statistics of the eigenfunctions and eigenvalues (e.g., associating Poisson statistics to the localized eigenfunctions and Wigner-Dyson statistics to delocalized ones). This also indicates the existence of new universality classes based on the matrix constraints (different from the 10 already-known symmetry-based classes).

The spread of infectious diseases, rumors, fashions, and innovations are complex contagion processes, embedded in network and spatial contexts. While the studies in the former context are intensively expanded, the latter remains largely unexplored. In this paper, we investigate the pattern formation of an interacting contagion, where two infections, A and B, interact with each other and diffuse simultaneously in space. The contagion process for each follows the classical susceptible-infected-susceptible kinetics, and their interaction introduces a potential change in the secondary infection propensity compared to the baseline reproduction number $R_0$. We show that the nontrivial spatial infection patterns arise when the susceptible individuals move faster than the infected and the interaction between the two infections is neither too competitive nor too cooperative. Interestingly, the system exhibits pattern hysteresis phenomena, i.e., quite different parameter regions for patterns exist in the direction of increasing or decreasing $R_0$. Decreasing $R_0$ reveals remarkable enhancement in contagion prevalence, meaning that the eradication becomes difficult compared to the single-infection or coinfection without space. Linearization analysis supports our observations, and we have identified the required elements and dynamical mechanism, which suggests that these patterns are essentially Turing patterns. Our work thus reveals new complexities in interacting contagions and paves the way for further investigation because of its relevance to both biological and social contexts.

The subject of the present theoretical study is the dynamics of bubble-bubble interactions in a viscoelastic medium. First, new equations for calculating the viscoelastic drag exerted on bubbles during their translational motion in a viscoelastic medium are derived. The drag equations are incorporated in the bubble-bubble interaction model in which, thereby, both the translational and radial motions of the bubbles are affected by the viscoelastic features of the medium. Second, the derived equations are applied to investigate how the viscoelastic properties of the medium can affect the dynamics of multiple bubbles, as well as how the bubbles can affect each other. It was discovered that the bubble-bubble interaction can significantly influence the dynamics of a single bubble. As the distance between the bubbles increases, their effect on each other decreases, and at a distance of several millimeters, this effect can be neglected. Moreover, it was concluded that with increasing elasticity and viscosity of the medium, as well with decreasing relaxation time, the effects of other bubbles on the current bubble's radial motion can become negligible. The translational motion of the bubbles was investigated for different viscoelastic models. The elasticity resists the motion of bubbles in space, resulting in a dynamical steady state of the distance between the bubbles at high elasticity values. The relaxation time of the medium was also found to be important in terms of the bubbles' translational movement.

We report an experimental observation of rotating depression soliton sets on the inner surface of a viscous liquid ring, carrying background waves. These occur within a rotating shallow layer of oil inside a stationary cylindrical container. The solitons are organized either in single, two, or regular polygonal (triangle and hexagon) clusters; they travel in unison at a higher speed than the background traveling waves. The spectral power density reveals a possible energy exchange between the soliton clusters and the background mixed radial-azimuthal modulations through wave radiation.

A hybrid numerical method which couples the immersed-boundary lattice Boltzmann method with the smoothed point interpolation method (S-PIM) is presented in this paper for the fluid-structure interaction problems involving large solid deformation. In the method, the lattice Boltzmann method is adopted for its advantages in modeling complex fluid flow, the S-PIM is coupled for its robustness in dealing with large solid deformation, and the immersed-boundary method is used for its efficiency in handling the interaction of fluid and solid. In the fluid-solid coupling procedure, a force correction technique based direct-forcing scheme is introduced to enforce nonslip boundary condition with high accuracy, and an averaged dual time stepping scheme is proposed to get stronger robustness of the present method. Numerical experiments are carefully carried out from benchmark problems such as cylinder Couette flow and a beam in a fluid tunnel to more challenging problems such as a flexible beam in the wake of a cylinder and the swimming of a two-dimensional fishlike body. Comparisons of the numerical results with the referenced solutions show that all desirable features of these coupled methods are inherited in the present coupling scheme, and the efficiency of the present method to model such complex problems is verified.

We report on a nonequilibrium phase of matter, the minimally disordered crystal phase, which we find exists between the maximally amorphous glasses and the ideal crystal. Even though these near crystals appear highly ordered, they display glassy and jamming features akin to those observed in amorphous solids. Structurally, they exhibit a power-law scaling in their probability distribution of weak forces and small interparticle gaps as well as a flat density of vibrational states. Dynamically, they display anomalous aging above a characteristic pressure. Quantitatively, this disordered crystal phase has much in common with the Gardner-like phase seen in maximally disordered solids. Near crystals should be amenable to experimental realizations in commercially available particulate systems and are to be indispensable in verifying the theory of amorphous materials.

It is often regarded that the dwell time (or residence time, escape time, trapping duration) of trapped Brownian particles is described by the multiplication of two separate factors, i.e., the diffusive traveling time of the trapping domain size without taking into account the trapping force, and the stochastic event of overcoming the trapping energy by thermal one instantaneously. However, we show that the ratio of dwell time to the typical traveling time for the trapping domain size depends on the shape of the force field. The shape of the trapping potential affects this ratio even if the trapping energy gap is the same and the smooth potential has a single minimum. Our finding suggests the possible application of the potential shape to realize the desired trapping characteristics.

Scale dependence of electrostatic and magnetostatic properties is investigated in the setting of spatially random linear lossless materials with statistically homogeneous and spatially ergodic random microstructures. First, from the Hill-Mandel homogenization conditions adapted to electric and magnetic fields, uniform boundary conditions are formulated for a statistical volume element (SVE). From these conditions, there follow upper and lower mesoscale bounds on the macroscale (effective) electrical permittivity and magnetic permeability. Using computational electromagnetics methods, these bounds are obtained through numerical simulations for composites of two types: (i) two-dimensional (2D) random checkerboard (two-phase) microstructures and (ii) analogous 3D random (two-phase) media. The simulation results demonstrate a scale-dependent trend of these bounds toward the properties of a representative volume element (RVE). This transition from SVE to RVE is described using a scaling function dependent on the mesoscale $\delta$, the volume fraction $v_f$, and the property contrast $k$ between two phases. The scaling function is calibrated through fitting the data obtained from extensive simulations ($\sim 10000$) conducted over the aforementioned parameter space. The RVE size of a given microstructure can be estimated down to within any desired accuracy using this scaling function as parametrized by the contrast and the volume fraction of two phases.

The energetically favored icosahedral structure has been seen as the central figure for describing the local structure of simple liquids and glasses. Although regular icosahedral structures are rarely found, it is accepted that distorted icosahedral structures occur in simple liquids and glasses. However, which local structure dominates and why it is more frequent than the others remain unanswered questions. In this study, by using a recently developed structure descriptor, we show that docosahedral structures are the most favored not only in models of simple liquids and glasses but also in an experimental colloid glass. We also show that the the predominance of docosahedral structures is entropy-driven. Our findings represent a significant milestone towards comprehending mysterious phenomena such as supercooling, glass transition, and crystallization, where local structures play a key role.

Superdiffusion, characterized by a spreading rate $t^{1/\alpha }$ of the probability density function $p(x,t)=t^{-1/\alpha }p\left(t^{-1/\alpha }x,1\right)$, where $t$ is time, may be modeled by space-fractional diffusion equations with order $1<\alpha <2$. Some applications in biophysics (calcium spark diffusion), image processing, and computational fluid dynamics utilize integer-order and fractional-order exponents beyond this range ($\alpha >2$), known as high-order diffusion or hyperdiffusion. Recently, space-time duality, motivated by Zolotarev's duality law for stable densities, established a link between time-fractional and space-fractional diffusion for $1<\alpha \le 2$. This paper extends space-time duality to fractional exponents $1<\alpha \le 3$, and several applications are presented. In particular, it will be shown that space-fractional diffusion equations with order $2<\alpha \le 3$ model subdiffusion and have a stochastic interpretation. A space-time duality for tempered fractional equations, which models transient anomalous diffusion, is also developed.

We discuss the effects that fractal coupling induces on chimera states in a network of leaky integrate-and-fire (LIF) oscillators arranged in a two-dimensional toroidal geometry. We provide evidence that the introduction of a hierarchical coupling topology in the form of a Sierpinski carpet gives rise to complex spatial structures such as multiple spots, stripe-and-grid chimeras, as well as traveling waves and subthreshold oscillations. Unlike in the case of typical nonlocal connectivity, when tuning the coupling strength to small positive values a spot chimera is formed with internal structure reminiscent of the fractal connectivity scheme. This is in line with previous results for one-dimensional networks, where hierarchical connectivity also induces chimeras with stratified spatial arrangements. In the case of negative coupling, cooperative effects produce subthreshold oscillating regions with traveling active islands crossing through them. Subthreshold oscillations and traveling waves are frequently reported in biological neural network experiments.

We study theoretically and computationally the behavior of the classical and quantum parametrically periodically driven linear oscillator. As a basic paradigm of such a Floquet system we consider the case of the harmonic oscillation of the oscillator frequency, which is convenient to handle theoretically and computationally, while keeping the general features. We derive an explicit analytic formula for the quantum propagator in terms of the classical propagator. Using this, we derive the explicit exact formula for the evolution of the expectation value of the energy starting from an arbitrary normalizable initial state. In the case of the starting pure stationary eigenstate the evolution is exactly the same as for the classical microcanonical ensemble of initial conditions of the same starting energy. We perform a rather complete computational analysis of the system's behavior inside the instability regions (lacunae), where the energy of the oscillator increases exponentially, as well as in the stability regions, and in particular in the vicinity of the (in)stability borders. We confirm also numerically with absolute certainty that the borders of (in)stability regions classically and quantally coincide exactly, in accordance with the theory, which is an important check of the numerical accuracy of computations, and we find a number of important empirical results, especially an equation of the elliptic type describing the rate of exponential energy growth inside the lacunae in terms of other systems' quantities. We believe that our approach and findings are of generic linear type, i.e., applicable in most such linear Floquet systems, and we present a strong motivation for a general theory, classically and quantally.