We present a general method of utilizing bioelectric recordings from a spatially sparse electrode grid to compute a dynamic vector field describing the underlying propagation of electrical activity. This vector field, termed the wave-front flow field, permits quantitative analysis of the magnitude of rotational activity (vorticity) and focal activity (divergence) at each spatial point. We apply this method to signals recorded during arrhythmias in human atria and ventricles using a multipolar contact catheter and show that the flow fields correlate with corresponding activation maps. Further, regions of elevated vorticity and divergence correspond to sites identified as clinically significant rotors and focal sources where therapeutic intervention can be effective. These flow fields can provide quantitative insights into the dynamics of normal and abnormal conduction in humans and could potentially be used to enhance therapies for cardiac arrhythmias.

We propose an innovative type of ergostats and thermostats for molecular dynamics simulations. A general class of active particle swarm models is considered, where any specific total energy (alternatively any specific temperature) can be provided at a fixed point of the evolution of the swarm. We identify the extended system feedback force of the Nosé-Hoover thermostat with the “internal energy” variable of active Brownian motion.

A turn on of a quantum dot (QD) semiconductor laser simultaneously operating at the ground state (GS) and excited state (ES) is investigated both experimentally and theoretically. We find experimentally that the slow passage through the two successive laser thresholds may lead to significant delays in the GS and ES turn ons. The difference between the turn-on times is measured as a function of the pump rate of change $\varepsilon$ and reveals no clear power law. This has motivated a detailed analysis of rate equations appropriate for two-state lasing QD lasers. We find that the effective time of the GS turn on follows an ${\varepsilon }^{-1/2}$ power law provided that the rate of change is not too small. The effective time of the ES transition follows an ${\varepsilon }^{-1}$ power law, but its first order correction in $ln\left(\varepsilon \right)$ is numerically significant. The two turn ons result from different physical mechanisms. The delay of the GS transition strongly depends on the slow growth of the dot population, whereas the ES transition only depends on the time needed to leave a repellent steady state.

In the present study, we analyzed field measurement data obtained for a Japanese expressway and used it as a data set for the validation of microscopic simulation models. Consequently, in accordance with previous studies, we confirmed the common features depicted by the fundamental diagram (flux vs density relation) and lane-usage ratio vs density diagram. We found two things regarding lane-changing behavior: (1) a lane change occurs asymmetrically, where a lane change from a slow to a fast lane differs from that from a fast to a slow lane; and (2) the so-called incentive criterion in the case of small gaps between the preceding vehicles in both slow and fast lanes refers to the velocities and /or the relative velocities with respect to the preceding vehicles, whereas that for relatively large gaps refers to the distances to the preceding vehicles is cast into the above incentive criterion in addition to the two factors mentioned above.

A computationally quick and conceptually simple method to recover time delay of the chaotic system from scalar time series is developed in this paper. We show that the orbits in the incomplete two-dimensional reconstructed phase-space will show local clustering phenomenon after the component reordering procedure proposed in this work. We find that information captured by the incomplete two-dimensional reconstructed phase-space is related to the time delay ${\tau }_0$ present in the system, and will be transferred to the reordered component by the procedure of component reordering. We then propose the segmented mean variance (SMV) from the reordered component to identify the time delay ${\tau }_0$ of the system. The proposed SMV shows clear maximum when the embedding delay $\tau$ of the incomplete reconstruction matches the time delay ${\tau }_0$ of the chaotic system. Numerical data generated by a time-delay system based on the Mackey-Glass equation operating in the chaotic regime are used to illustrate the effectiveness of the proposed SMV. Experimental results show that the proposed SMV is robust to additive observational noise and is able to recover the time delay of the chaotic system even though the amount of data is relatively small and the feedback strength is weak. Moreover, the time complexity of the proposed method is quite low.

Populations of oscillators can display a variety of synchronization patterns depending on the oscillators' intrinsic coupling and the coupling between them. We consider two coupled symmetric (sub)populations with unimodal frequency distributions. If internal and external coupling strengths are identical, a change of variables transforms the system into a single population of oscillators whose natural frequencies are bimodally distributed. Otherwise an additional bifurcation parameter $\kappa$ enters the dynamics. By using the Ott-Antonsen ansatz, we rigorously prove that $\kappa$ does not lead to new bifurcations, but that a symmetric two-coupled-population network and a network with a symmetric bimodal frequency distribution are topologically equivalent. Seeking for generalizations, we further analyze a symmetric trimodal network vis-à-vis three coupled symmetric unimodal populations. Here, however, the equivalence with respect to stability, dynamics, and bifurcations of the two systems no longer holds.

In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we analyzed in a previous study, we herein consider a primal-dual problem in which the investment risk minimization problem with budget and expected return constraints is regarded as the primal problem, and the expected return maximization problem with budget and investment risk constraints is regarded as the dual problem. With respect to these optimal problems, we analyze a quenched disordered system involving both of these optimization problems using the approach developed in statistical mechanical informatics and confirm that both optimal portfolios can possess the primal-dual structure. Finally, the results of numerical simulations are shown to validate the effectiveness of the proposed method.

Based on a detailed crossbridge model for individual myosin II motors, we systematically study the influence of mechanical load and adenosine triphosphate (ATP) concentration on small myosin II ensembles made from different isoforms. For skeletal and smooth muscle myosin II, which are often used in actomyosin gels that reconstitute cell contractility, fast forward movement is restricted to a small region of phase space with low mechanical load and high ATP concentration, which is also characterized by frequent ensemble detachment. At high load, these ensembles are stalled or move backwards, but forward motion can be restored by decreasing ATP concentration. In contrast, small ensembles of nonmuscle myosin II isoforms, which are found in the cytoskeleton of nonmuscle cells, are hardly affected by ATP concentration due to the slow kinetics of the bound states. For all isoforms, the thermodynamic efficiency of ensemble movement increases with decreasing ATP concentration, but this effect is weaker for the nonmuscle myosin II isoforms.

An experimental approach utilizing a Hele-Shaw cell for the investigation of the solidification of a supercooled liquid in contact with a solid wall is presented. The setup is based on an idea presented by Marín et al. [A. G. Marín et al., Phys. Rev. Lett. 113, 054301 (2014)], who investigated the planar freezing of a sessile drop without supercooling. This apparatus overcomes optical distortions present when observing the freezing of sessile drops, arising due to reflections and refraction of light on the drop surface. The facility is used to investigate the freezing process of water drops, supercooled down to $-{20}^{\circ }\mathrm{C}$, and to qualitatively demonstrate that the growth behavior is uninfluenced by the use of the Hele-Shaw cell. Different features during freezing, which are known for sessile water drops, are also observed with the Hele-Shaw cell. The growth morphology within the first phase of solidification is categorized according to the initial drop supercooling. Furthermore, freezing velocities within this phase are related to data available in the literature for the growth of single ice dendrites.

We have run a total of 311 direct numerical simulations (DNSs) of decaying three-dimensional Navier-Stokes turbulence in a periodic box with values of the Taylor length-based Reynolds number up to about 300 and an energy spectrum with a wide wave-number range of close to $-5/3$ power-law dependence at the higher Reynolds numbers. On the basis of these runs, we have found a critical time when (i) the rate of change of the square of the integral length scale turns from increasing to decreasing, (ii) the ratio of interscale energy flux to high-pass filtered turbulence dissipation changes from decreasing to very slowly increasing in the inertial range, (iii) the signature of large-scale coherent structures disappears in the energy spectrum, and (iv) the scaling of the turbulence dissipation changes from the one recently discovered in DNSs of forced unsteady turbulence and in wind tunnel experiments of turbulent wakes and grid-generated turbulence to the classical scaling proposed by G. I. Taylor [Proc. R. Soc. London, Ser. A 151, 421 (1935)] and A. N. Kolmogorov [Dokl. Akad. Nauk SSSR 31, 538 (1941)]. Even though the customary theoretical basis for this Taylor-Kolmogorov scaling is a statistically stationary cascade where large-scale energy flux balances dissipation, this is not the case throughout the entire time range of integration in all our DNS runs. The recently discovered dissipation scaling can be reformulated physically as a situation in which the dissipation rates of the small and large scales evolve together. We advance two hypotheses that may form the basis of a theoretical approach to unsteady turbulence cascades in the presence of large-scale coherent structures.

For certain classes of relativistic plasma problems, performing numerical calculations in a Lorentz boosted frame can be even more advantageous for gridded momentum-space-time (e.g., Vlasov) problems than has been demonstrated for position space-time problems and result in a potential reduction in the number of calculations needed by a factor $\sim {\gamma }_b^6$. In this study, the Lorentz boosted frame technique was applied to the problem of warm wave-breaking limits of plasma waves with relativistic phase velocity. The numerical results are consistent with analytic conclusions. By appropriate normalization and for sufficiently warm plasma, the dynamics for the Vlasov equation in different Lorentz frames were found to be independent of ${\gamma }_p$.

The head-on collision of two dust acoustic solitons (DASs) in a nonextensive plasma with positive or negative dust grains fluid including the effect of dust size distribution (DSD) is studied. The phase shifts for the two solitons due to the collision are derived by applying the extended Poincaré-Lighthill-Kuo (PLK) method. The influences of the power law DSD and the nonextensivity of plasma particles on the characteristic properties of the head-on collision of DASs are analyzed. It is found that the phase shifts can vanish, only for the case of positive dust grains, for certain values and ranges of the dust grain radius and the entropic index of ions $\left(q_i\right)$. Also, they undergo a cutoff in the range of $q_i>1$ for the subextensive distribution. A brief discussion of possible applications in laboratory and space plasmas is included.

The efficiency for minimally nonlinear irreversible heat engines at any arbitrary power has been systematically evaluated, and general lower and upper efficiency bounds under the tight coupling condition for different operating regions have been proposed, which can be seen as the generalization of the bounds $[{\eta }_C/2<{\eta }_{maxP}<{\eta }_C/(2-{\eta }_C)]$ on efficiency at maximum power $\left({\eta }_{maxP}\right)$, where ${\eta }_C$ means the Carnot efficiency. We have also calculated the universal bounds of the maximum gain in efficiency in different operating regions to give further insight into the efficiency gain with the power away from the maximum power. In the region of higher loads (higher than the load which corresponds to the maximum power), a small power loss away from the maximum power induces a much larger gain in efficiency. As actual heat engines may not work at the maximum power condition, this paper may contribute to operating actual heat engines more efficiently.

I propose a random network model governed by a Gaussian weight corresponding to Ising link antiferromagnetism as a model for emergent quantum space-time. In this model, discrete space is fundamental, not a regularization; its spectral dimension $d_s$ is not a model input but is, rather, completely determined by the antiferromagnetic coupling constant. Perturbative terms suppressing triangles and favoring squares lead to locally Euclidean ground states that are Ricci flat “large worlds” with power-law extension. I then consider the quenched graphs of lowest energy for $d_s=2$ and $d_s=3$, and I show how quenching leads to the spontaneous emergence of embedding spaces of Hausdorff dimension $d_H=4$ and $d_H=5$, respectively. One of the additional, spontaneous dimensions can be interpreted as time, causality being an emergent property that arises in the large $N$ limit (with $N$ the number of vertices). For $d_s=2$, the quenched graphs constitute a discrete version of a 5D-space-filling surface with a number of fundamental degrees of freedom scaling like $N^{2/5}$, a graph version of the holographic principle. These holographic degrees of freedom can be identified with the squares of the quenched graphs, which, being triangle-free, are the fundamental area (or loop) quanta.

We study the mutual percolation of two interdependent lattice networks ranging from two to seven dimensions, denoted as $D$. We impose that the length (measured as chemical distance) of interdependency links connecting nodes in the two lattices be less than or equal to a certain value, $r$. For each value of $D$ and $r$, we find the mutual percolation threshold, $p_c[D,r]$, below which the system completely collapses through a cascade of failures following an initial destruction of a fraction $(1-p)$ of the nodes in one of the lattices. We find that for each dimension, $D<6$, there is a value of $r=r_I>1$ such that for $r\ge r_I$ the cascading failures occur as a discontinuous first-order transition, while for $r<r_I$ the system undergoes a continuous second-order transition, as in the classical percolation theory. Remarkably, for $D=6, r_I=1$, which is the same as in random regular graphs with the same degree (coordination number) of nodes. We also find that in all dimensions, the interdependent lattices reach maximal vulnerability (maximal $p_c[D,r]$) at a distance $r=r_{\text{max}}>r_I$, and for $r>r_{\text{max}}$ the vulnerability starts to decrease as $r\to \infty$. However, the decrease becomes less significant as $D$ increases, and $p_c[D,r_{\text{max}}]-p_c[D,\infty ]$ decreases exponentially with $D$. We also investigate the dependence of $p_c[D,r]$ on the system size as well as how the nature of the transition changes as the number of lattice sites, $N\to \infty$.

It is said that complexity lies between order and disorder. In the case of brain activity and physiology in general, complexity issues are being considered with increased emphasis. We sought to identify features of brain organization that are optimal for sensory processing, and that may guide the emergence of cognition and consciousness, by analyzing neurophysiological recordings in conscious and unconscious states. We find a surprisingly simple result: Normal wakeful states are characterized by the greatest number of possible configurations of interactions between brain networks, representing highest entropy values. Therefore, the information content is larger in the network associated to conscious states, suggesting that consciousness could be the result of an optimization of information processing. These findings help to guide in a more formal sense inquiry into how consciousness arises from the organization of matter.

A kind of inverse stochastic resonance (ISR) observed in ac-driven electroconvection (EC) in a nematic liquid crystal is presented. In successive pattern evolutions by increasing noise intensity $V_{\mathrm{N}}$, a typical EC (with a normalized amplitude ${\mathit{A}}_0=1$ at $V_{\mathrm{N}}=0$) disappears $({\mathit{A}}_0\to 0)$, and then the rest state (${\mathit{A}}_0=0$) reenters into the EC (${\mathit{A}}_0=1$); eventually, it develops into complicated $\mathrm{EC}({\mathit{A}}_0>1)$. The reversed bell-shaped behavior of ${\mathit{A}}_0\left(V_{\mathrm{N}}\right)$ is evidence of ISR. The present ISR may be explained by taking into account colored noise characterized by its intensity and correlation time.

The effect of thermal fluctuations near a contact line of a liquid interface partially wetting an impenetrable substrate is studied analytically and numerically. Promoting both the interface profile and the contact line position to random variables, we explore the equilibrium properties of the corresponding fluctuating contact line problem based on an interfacial Hamiltonian involving a “contact” binding potential. To facilitate an analytical treatment, we consider the case of a one-dimensional interface. The effective boundary condition at the contact line is determined by a dimensionless parameter that encodes the relative importance of thermal energy and substrate energy at the microscopic scale. We find that this parameter controls the transition from a partial wetting to a pseudopartial wetting state, the latter being characterized by a thin prewetting film of fixed thickness. In the partial wetting regime, instead, the profile typically approaches the substrate via an exponentially thinning prewetting film. We show that, independently of the physics at the microscopic scale, Young's angle is recovered sufficiently far from the substrate. The fluctuations of the interface and of the contact line give rise to an effective disjoining pressure, exponentially decreasing with height. Fluctuations therefore provide a regularization of the singular contact forces occurring in the corresponding deterministic problem.

We derive expressions for the rates of erosion and deposition at the interface between a dense, dry, inclined granular flow and an erodible bed. In obtaining these, we assume that the interface between the flowing grains and the bed moves with the speed of a pressure wave in the flow, for deposition, or with the speed of a disturbance through the contacting particles in the bed, for erosion. We employ the expressions for the rates of erosion and deposition to show that after an abrupt change in the angle of inclination of the bed the characteristic time for the motion of the interface is much shorter than the characteristic time of the flow. This eliminates the need for introducing models of erosion and deposition rate in the mass balance; and the instantaneous value of the particle flux is the same function of the instantaneous value of the flow depth as in a steady, uniform flow.