This paper considers a simplified model of football in which passes are made according to a Markov chain. The authors focus on the time evolution of the ball-passing network. The theoretical formula for the number of different passes based on the Markov chain is derived, and its results are compared with real ball-passing data. The authors conclude that the Markov chain is a fairly good approximation even during the game.

We investigate the phenomenon of first-order transition [explosive synchronization (ES)] in an adaptively coupled phase-frustrated bilayer multiplex network. We consider Sakaguchi-Kuramoto dynamics over the top of multiplex networks and we establish that ES can emerge in all layers of a multiplex network even when one of the layers may not exhibit ES in the absence of the interlayer connections. We clearly identify the regions of the parameter space in which the multiplexity wins over the frustration parameter and network structure for the emergence of ES. Based on the mean-field analysis around the coherent state and a perturbative approach around the incoherent state we analytically derive the synchronization transition points (backward and forward) of all layers of the multiplex network as well as its monolayer counterpart satisfying a close agreement with the numerical results.

We presently propose a modified basal ganglia–corticothalamic (MBGCT) mean-field network of neural populations by incorporating the autaptic connection to subthalamic nucleus (STN) (termed ACS). The network connection is through the pulse field generated by the incoming pulse rate from the prepopulation, which is functioned into postpopulation. And then, we study the control effect of STN deep brain stimulation (DBS) on epileptic absence seizures characterized by 2–4 Hz spike and wave discharges (SWD) as the modulation of ACS is applied. For the slow dynamical effect of STN on cortical seizure activity, DBS electrodes are employed to generate sustaining input pulse of electrical potential field. In particular, the continuous symmetrical and asymmetrical charge-balanced biphasic pulse DBS with interphase gap, i.e., S-CBBP-IPGx and AS-CBBP-IPGx stimulations, are used due to their less charge and multiply adjustable stimulation parameters, to evaluate their effect on the suppression of SWD occurrence. Based on the percentage of control for the SWD number, it is shown that strong ACS directly contributes to the abatement of SWD. In contrast, weak ACS can significantly improve the control effects of CBBP DBS, which are particularly dependent on the stimulation shapes; i.e., (i) AS-CBBP-$\mathrm{IPG}x$ is less beneficial than S-CBBP-$\mathrm{IPG}x$, (ii) CBBP DBS in frequency-dependent manner can bidirectionally modulate the SWD occurrence, and (iii) CBBP DBS with moderate interphase gap (IPG) is more effective to suppress the SWD occurrence than that with no or large IPGs. These results are basically consistent with the experimental findings, which computationally supports the involvement of STN in the control mechanism of epileptic absence seizures.

The minimal ingredient to generate a biaxial liquid-crystalline order is usually considered to be a strong biaxiality either in the molecular shape or in the molecular interactions. Although there is no fundamental reason to forbid a spontaneous biaxial liquid-crystalline ordering of pure uniaxial origin, a robust demonstration of such phenomenon has been a challenging problem. We report here off-lattice Monte Carlo simulations of some new model systems of polar achiral rodlike ellipsoids which spontaneously form biaxial smectic phases of pure uniaxial origin. The phases also exhibit fascinating ferroelectric or striped ordering of the dipolar ellipsoids. We demonstrate that suitably tuned dipolar interactions can play major roles in generating biaxial phases of uniaxial origin for a wide variety of molecular length-to-width ratios.

Zipf's law is a hallmark of several complex systems with a modular structure, such as books composed by words or genomes composed by genes. In these component systems, Zipf's law describes the empirical power-law distribution of component frequencies. Stochastic processes based on a sample-space-reducing (SSR) mechanism, in which the number of accessible states reduces as the system evolves, have been recently proposed as a simple explanation for the ubiquitous emergence of this law. However, many complex component systems are characterized by other statistical patterns beyond Zipf's law, such as a sublinear growth of the component vocabulary with the system size, known as Heap's law, and a specific statistics of shared components. This work shows, with analytical calculations and simulations, that these statistical properties can emerge jointly from a SSR mechanism, thus making it an appropriate parameter-poor representation for component systems. Several alternative (and equally simple) models, for example, based on the preferential attachment mechanism, can also reproduce Heaps' and Zipf's laws, suggesting that additional statistical properties should be taken into account to select the most-likely generative process for a specific system. Along this line, we will show that the temporal component distribution predicted by the SSR model is markedly different from the one emerging from the popular rich-gets-richer mechanism. A comparison with empirical data from natural language indicates that the SSR process can be chosen as a better candidate model for text generation based on this statistical property. Finally, a limitation of the SSR model in reproducing the empirical “burstiness” of word appearances in texts will be pointed out, thus indicating a possible direction for extensions of the basic SSR process.

We study the effect of disorder on work exchange associated with quantum Hamiltonian processes by considering an Ising spin chain in which the strength of coupling between spins are randomly drawn from either Normal or Gamma distributions. The chain is subjected to a quench of the external transverse field, which induces this exchange of work. In particular, we study the irreversible work incurred by a quench as a function of the initial temperature, field strength, and magnitude of the disorder. While presence of weak disorder generally increases the irreversible work generated, disorder of sufficient strength can instead reduce it, giving rise to a disorder-induced lubrication effect. This reduction of irreversible work depends on the nature of the distribution considered and can either arise from acquiring the behavior of an effectively smaller quench for the Normal-distributed spin couplings or that of effectively single spin dynamics in the case of Gamma-distributed couplings.

Four on-lattice and six off-lattice models for active matter are studied numerically, showing that in contact with a wall, they display universal wetting transitions between three distinctive phases. The particles, which interact via exclusion volume only, move persistently and, depending on the model, change their direction either via tumble processes or rotational diffusion. When increasing the turning rate ${\nu }_T$, the systems transit from total wetting to partial wetting and dewetted phases. In the first phase, a wetting film covers the wall, with increasing heights while decreasing ${\nu }_T$. The second phase is characterized by wetting droplets on the wall. And, finally, the wall dries with few particles in contact with it. These phases present two continuous nonequilibrium transitions. For the first transition, from partial to total wetting, the fraction of dry sites vanishes continuously when decreasing ${\nu }_T$, with a power law of exponent 1. And, for the second transition, an order parameter proportional to the excess mass in droplets decreases continuously with a power law of exponent 3 when approaching a critical value of ${\nu }_T$. The critical exponents are the same for all the models studied.

Motivated by the realization of a magnetic monopole of Berry curvature by the energy crossing point, we study theoretically the effect of a magnetic monopole under a uniform electric field in semiclassical wave-packet dynamics, which is relevant to many physical situations such as relaxation through the diabolic point. We found that the competition between backward scattering by a monopole magnetic field and acceleration by an electric field leads to a bound state, i.e., capture of a particle near the monopole. Furthermore, the nonlinearity induced by the magnetic monopole leads to chaotic behavior in transient dynamics, i.e., transient chaos. We computed the characteristic quantities of the strange saddle, which gives rise to transient chaos, and we verified that the abrupt bifurcation occurs as we tune the system parameter toward the parameter region in which the system is solvable.

In the field of nonlinear dynamics, many methods have been proposed to tackle the issue of optimally setting embedding dimension and lag in order to analyze sampled scalar signals. However, intrinsic statistical uncertainties due to the finiteness of input sequences severely hinder a general solution to the problem. A more achievable approach consists of assessing sets of dimension and lag pairs that are equivalently suitable to embed a time series. Here we present a method to identify these sets of embedding pairs, under the hypothesis that the time series of interest is generated by a chaotic, finite-dimensional dynamical system. We first introduce a “distance gauge transformation” based on the analytical forms of correlation integrals corresponding to a Gaussian white noise source. We show that in this new distance gauge, correlation integrals generated by chaotic, finite-dimensional systems are characterized by distinctive features, whose absence is a marker of the unsuitability of the underlying embedding choice. By means of a new estimator of the correlation dimension that relies on the new distance gauge, sets of suitable embedding pairs are finally identified by looking at the uniformity of the estimation. The method is completely automatic and was successfully tested on both synthetic and experimental time series. It also provides a tool to estimate the redundance and irrelevance timescales of the system that underlie the time series as well as a lower constraint to the sampling rate. The method is suitable for applications in research fields where a chaotic behavior has to be identified, such as neuroscience, geophysics, and economics.

Clique is a mesoscale measurement of system and widely exists in various real-world networks. The roles of cliques on information spreading dynamics have not been systematically investigated. We here propose an information spreading model on networks with cliques, where an informed node makes all nodes in the same clique be infected simultaneously. We exactly solve the critical behavior of the proposed information spreading dynamics and find that there is a double transition when the homogeneous or weak heterogeneous network has a relatively small fraction of nodes belonging to the clique and a relatively large clique size. The first transition exhibits a continuous phase transition and the critical exponent is the same as that of the information spreading on networks without cliques. However, the second transition is not a continuous phase transition in the classic sense. For strong heterogeneous networks, the system always has one continuous phase transition. The present work provides an explanation of the cliques on critical phenomena of information spread dynamics, which is markedly different from the results of cascading-failure dynamics.

The understanding of epidemics on networks has greatly benefited from the recent application of message-passing approaches, which allow us to derive exact results for irreversible spreading (i.e., diseases with permanent acquired immunity) in locally treelike topologies. This success has suggested the application of the same approach to recurrent-state epidemics, for which an individual can contract the epidemic and recover repeatedly. The underlying assumption is that backtracking paths (i.e., an individual is reinfected by a neighbor he or she previously infected) do not play a relevant role. In this paper we show that this is not the case for recurrent-state epidemics since the neglect of backtracking paths leads to a formula for the epidemic threshold that is qualitatively incorrect in the large size limit. Moreover, we define a modified recurrent-state dynamics which explicitly forbids direct backtracking events and show that this modification completely upsets the phenomenology.

In suspensions of microorganisms, pattern formation can arise from the interplay of chemotaxis and the fluid flows collectively generated by the organisms themselves. Here we investigate the resulting pattern formation in square and elongated domains in the context of two distinct models of locomotion in which the chemoattractant dynamics is fully coupled to the fluid flows and swimmer motion. Analyses for both models reveal an aggregative instability due to chemotaxis, independent of swimmer shape and type, and a hydrodynamic instability for “pusher” swimmers. We discuss the similarities and differences between the models. Simulations reveal a critical length scale of the swimmer aggregates and this feature can be utilized to stabilize swimmer concentration patterns into quasi-one-dimensional bands by varying the domain size. These concentration bands transition to traveling pulses under an external chemoattractant gradient, as observed in experiments with chemotactic bacteria.

Kinesins transport a variety of cargo along microtubules (MTs) in the cytoplasm. Although much is known about the walking of a kinesin along a single MT, the effects of the spatial distribution of MTs on kinesin-mediated transport cannot be sufficiently understood and quantified using existing models. In this study, we present a stochastic model to study the dynamics of a kinesin in the presence of two MTs. Our model can predict the Brownian motion of the cargo, mechanochemical cycle of kinesin walking, and the unbinding and rebinding of kinesin on neighboring MTs. Specifically, a stress-influenced chemical kinetics was considered to describe changes in the walking and unbinding of a kinesin along one MT due to the neighboring MT. In addition, the effects of the neighboring MT on the rebinding of a kinesin to MTs were calibrated using a spatial marching method. By integrating these dynamics, our model predicted a significant disturbance in the transport of kinesin when the distance between two intersected MTs is close to the radius of the cargo and the two MTs have antiparallel orientations. Moreover, shorter kinesins (i.e., kinesins with a short cargo linker) are more likely to stop the transport near the intersection than longer kinesins.

Bacteria such as Escherichia coli exhibit biased motion if kept in a spatially nonuniform chemical environment. Here, we bring out unique time-dependent characteristics of bacterial chemotaxis, in response to a diffusing spatial step ligand profile. Experimentally obtained temporal characteristics of the drift velocity are compared with the theoretical and Monte Carlo simulation-based estimates, and excellent agreements can be obtained. These results bring insights to the time-responsive facets of bacterial drift, bearing far-reaching implications in understanding their migratory dynamics in the quest of finding foods by swimming toward the highest concentration of food molecules, or for fleeing from poisons, as well as toward the better understanding of therapeutic response characteristics for certain infectious diseases.

Short pitch deformed helix ferroelectric liquid crystals have numerous applications as active materials in displays, optical telemetry, and biomedical devices. In this paper, we derive convenient analytical formulas to calculate the effective dielectric tensor of these materials beyond the space average approximation. By comparison with exact numerical calculations, we show that our formulas are remarkably accurate in predicting optical properties in virtually all practical situations, including the important case of large tilt angles, where the space average approximation breaks down. We also present a comparison between the two complementary approaches of expanding the mesoscopic dielectric tensor versus the mesoscopic transfer matrix, by deriving an expression for the effective transfer matrix as an infinite expansion and explicitly calculating the corresponding effective dielectric tensor for the first time. Our results demonstrate that both methods give accurate predictions when two-photon scattering terms are taken into account.

A model for shear band width as a function of applied strain is proposed that describes shear bands as pulled fronts which propagate into an unsteady state. The evolving structural state of material ahead of and behind the front is defined according to effective temperature shear-transformation-zone theory. The model is compared to another that is based on dimensional analysis and assumes shear band dynamics is governed by the strain rate within the shear band. These models are evaluated on three material systems: a two-dimensional binary Lennard-Jones glass, a ${\mathrm{Cu}}_{64}{\mathrm{Zr}}_{36}$ glass modeled using an embedded atom method potential, and a Si glass modeled using the Stillinger-Weber potential. Shear bands form in all systems across a variety of quench rates and appear to either broaden to the system size or saturate to a finite width, remaining contained within the simulation cell. The dimensional analysis-based model appears to apply only when band growth is uncontained, indicating the dominance of a single timescale in the early stages of shear band development. The front propagation model, which reduces to the dimensional analysis model, applies to both contained and uncontained band growth. This result suggests that competition between the rate of shear-induced configurational disordering and thermal relaxation sets a maximum width for shear bands in a variety of material systems.

We investigate how clogging affects the transfer properties of a generic class of materials featuring a hydraulic network embedded in a matrix. We consider the flow of a liquid through fully saturated hydraulic networks which transfer heat (or mass) by advection and diffusion, and a matrix in which only diffusion operates. Networks are subjected to different clogging scenarios (or attacks), changing their microstructure and flow field. A series of canonical cooling tests are simulated using a tracer method prior to and following attack. Results quantify the threat posed by different types and degrees of attack to a system's transfer properties. An analytical framework is introduced to predict this vulnerability to attacks and rationalize it in terms of permeability evolution and population dynamics of island size.

An improved preconditioned multiple-relaxation-time lattice Boltzmann equation model for incompressible flow (IPMRT-LBE) in porous media is proposed. Motivated by previous LBE models [Guo et al., Phys. Rev. E 70, 066706 (2004); Premnath et al., J. Comput. Phys. 228, 746 (2009); Guo et al., J. Comput. Phys. 165, 288 (2000)], the current model is demonstrated to have the advantages of accurate implementation of the no-slip boundary condition, reducing the compressible effect as well as fast convergence rate compared with standard LBE models. To validate the IPMRT-LBE model, flows in two- and three-dimensional synthetic porous media (square array of cylinders and body-centered cubic array of spheres) are simulated. The results show that the current model can predict the macroscopic property (such as permeability) accurately with significantly accelerated convergence rate. Furthermore, simulations of flow through a three-dimensional sandpack confirm the applicability and advantages of the IPMRT-LBE model.

We unveil the basic mechanisms and general conditions for the emergence of Bellerophon states, which are higher order coherent states appearing in globally coupled phase oscillators. The critical points for the involved phase transitions are determined analytically. The significant feature of Bellerophon states is that the oscillators' effective frequencies are locked to quantized plateaus, a point which is fully clarified on the basis of circle map theory. Each quantized plateau corresponds to a harmonic frequency of the Fourier decomposition of the order parameter. Our approach exploits the fact that the order parameter is always real, due to a special symmetry of the system which furthermore prevents the formation of even integer multiple plateaus of effective frequencies.

Architected structures have aroused widespread research interest because they possess unique properties in mechanics. However, a fundamental theory describing their thermal properties has not been established. Here, we present a theoretical framework in thermotics to predict thermal properties of architected structures. Then, by experiment and simulation, we show its applications in the field of heat management. By assembling two radically different materials, we design two types of Janus structures. The different rotation degrees of the Janus structures can flexibly control the switch between different functions, such as from partial concentration to uniform concentration and from rotation to concentration. These functions are realized in a structure made of a heterogeneous core plus a homogeneous shell, which is in contrast to the existing structures made of a homogeneous core plus a heterogeneous shell designed according to the theory of transformation thermotics. This work lays a theoretical foundation in thermotics for further research on heterogeneously architected structures, and it proposes the concept of thermal Janus structures for flexible heat control, which may open an avenue for intelligent thermal metamaterials.