We investigate the effects of the Péclet number (Pe) on transport of an inert chemical tracer in heterogeneous porous media. We simulate fluid flow and transport through two-dimensional pore-scale matrices with varying structural complexity. With increasing Pe, the anomalous nature of the transport becomes enhanced as the host domain becomes more heterogeneous, due to the increasingly dominant effects of the complex velocity field. The sensitivity of (anomalous) transport to Pe is shown to be controlled by the medium structure. We quantify the effects of Pe by interpreting the numerical simulations within the continuous time random walk method (CTRW) framework, and incorporating Pe within the underlying tracer transition time distribution. We then investigate transport behavior subjected to temporal variation in the velocity field magnitude, accounting for tracer propagation controlled by Pe. Because of the nonlinear influence of Pe on the transport behavior, we show that temporal variations in the velocity field can lead to an increase in the anomalous nature of the transport.

We present a model that describes the departure from equilibrium of the OH(A) rotational level distribution in collisional plasmas. In this model, the OH(A) rotational state densities are governed by a rate equation including: (i) a balanced rotational energy transfer process with the buffer gas species; (ii) unbalanced exothermic reactions, which pump rotationally excited states into the system. Based on the prior assumptions, we formally derive a model function describing the non-Boltzmann distribution. This function depends on five parameters, each of which has a physical meaning. The temperature is given as one of the model function parameters, which can be readily identified with the translational temperature of the buffer gas. The validity of the model was tested by means of the least-squares fitting of data found in literature. Based on this analysis we propose the formation processes of rotationally excited OH(A) in several discharge conditions.

Let $X_t$ be a random process starting at $x\in [0,1]$ with absorbing boundary conditions at both ends of the interval. Denote by $P_1\left(x\right)$ the probability to first exit at the upper boundary. For Brownian motion, $P_1\left(x\right)=x$, which is equivalent to $P_1^{\prime }\left(x\right)=1$. For fractional Brownian motion with Hurst exponent $H$, we establish that $P_1^{\prime }\left(x\right)=\mathcal{N}{\left[x(1-x)\right]}^{1/H-2}{e}^{\epsilon \mathcal{F}\left(x\right)+O\left({\epsilon }^2\right)}$, where $\epsilon =H-\frac{1}{2}$. The function $\mathcal{F}\left(x\right)$ is analytic and well approximated by its Taylor expansion $\mathcal{F}\left(x\right)\simeq 16(C-1){(x-\frac{1}{2})}^2+O{(x-\frac{1}{2})}^4$, where $C=0.915...$ is the Catalan constant. A similar result holds for moments of the exit time starting at $x$. We then consider the span of $X_t$, i.e., the size of the (compact) domain visited up to time $t$. For Brownian motion, we derive an analytic expression for the probability that the span reaches 1 for the first time and then generalize it to fractional Brownian motion. Using large-scale numerical simulations with system sizes up to $N=2^{24}$ and a broad range of $H$, we confirm our analytic results. There are important finite-discretization corrections which we quantify. They are most severe for small $H$, necessitating going to the large systems mentioned above.

The continuum percolation of randomly orientated overlapping polyhedral particles, including tetrahedron, cube, octahedron, dodecahedron, and icosahedron, was analyzed by Monte Carlo simulations. Two numerical strategies, (1) a Monte Carlo finite-size-scaling analysis and (2) a real-space Monte Carlo renormalization-group method, were, respectively, presented in order to determine the percolation threshold (e.g., the critical volume fraction ${\varphi }_c$ or the critical reduced number density ${\eta }_c$), percolation transition width Δ, and correlation-length exponent ν of the polyhedral particles. The results showed that ${\varphi }_c$ (or ${\eta }_c$) and Δ increase in the following order: tetrahedron < cube < octahedron < dodecahedron < icosahedron. In other words, both the percolation threshold and percolation transition width increase with the number of faces of the polyhedral particles as the shape becomes more “spherical.” We obtained the statistical values of ν for the five polyhedral shapes and analyzed possible errors resulting in the present numerical values ν deviated from the universal value of $\nu =0.88$ reported in literature. To validate the simulations, the corresponding excluded-volume bounds on the percolation threshold were obtained and compared with the numerical results. This paper has practical applications in predicting effective transport and mechanical properties of porous media and composites.

We consider a finite-time quantum Otto cycle with single- and two spin-$1/2$ systems as its working medium. To mimic adiabatic dynamics at a finite time, we employ a shortcut-to-adiabaticity technique and evaluate the performance of the engine including the cost of the shortcut. We compare our results with the true adiabatic and nonadiabatic performances of the same cycle. Our findings indicate that the use of the shortcut-to-adiabaticity scheme significantly enhances the performance of the quantum Otto engine as compared to its adiabatic and nonadiabatic counterparts for different figures of merit.

We analyze a variant of the Desai-Zwanzig model [J. Stat. Phys. 19, 1 (1978)]. In particular, we study stationary states of the mean field limit for a system of weakly interacting diffusions moving in a multiwell potential energy landscape, coupled via a Curie-Weiss type (quadratic) interaction potential. The location and depth of the local minima of the potential are either deterministic or random. We characterize the structure and nature of bifurcations and phase transitions for this system, by means of extensive numerical simulations and of analytical calculations for an explicitly solvable model. Our numerical experiments are based on Monte Carlo simulations, the numerical solution of the time-dependent nonlinear Fokker-Planck (McKean-Vlasov) equation, the minimization of the free-energy functional, and a continuation algorithm for the stationary solutions.

Behavior of mobile adsorbed species can be affected by the presence of a strong non-homogeneous electric field. Such a field exists in the proximity of a biased tip of the scanning tunneling microscope. Depending on the electronic properties of the adsorbate and the polarity of the electric field, self-assembly of ordered structures on the surface can be facilitated or prevented. We use a kinetic Monte Carlo model to investigate the effect of the electric field on the assembly of planar molecules on weakly interacting surfaces. Using phthalocyanine molecules as a model system, we study mechanisms behind the results of our previous experimental study of electric-field controlled switching of molecular arrays. The complex interplay between intermolecular and field-molecule interactions is illustrated by detailed phase diagrams at various surface coverages.

Groupthink occurs when everyone in a group starts thinking alike, as when people put unlimited faith in a leader. Avoiding this phenomenon is a ubiquitous challenge to problem-solving enterprises and typical countermeasures involve the mobility of group members. Here we use an agent-based model of imitative learning to study the influence of the mobility of the agents on the time they require to find the global maxima of NK-fitness landscapes. The agents cooperate by exchanging information on their fitness and use this information to copy the fittest agent in their influence neighborhoods, which are determined by face-to-face interaction networks. The influence neighborhoods are variable since the agents perform random walks in a two-dimensional space. We find that mobility is slightly harmful for solving easy problems, i.e., problems that do not exhibit suboptimal solutions or local maxima. For difficult problems, however, mobility can prevent the imitative search being trapped in suboptimal solutions and guarantees a better performance than the independent search for any system size.

The main point of this paper is to provide an affirmative answer through exploiting reinforcement learning (RL) in artificial intelligence (AI) for eliminating herding without any external control in complex resource allocation systems. In particular, we demonstrate that when agents are empowered with RL (e.g., the popular Q-learning algorithm in AI) in that they get familiar with the unknown game environment gradually and attempt to deliver the optimal actions to maximize the payoff, herding can effectively be eliminated. Furthermore, computations reveal the striking phenomenon that, regardless of the initial state, the system evolves persistently and relentlessly toward the optimal state in which all resources are used efficiently. However, the evolution process is not without interruptions: there are large fluctuations that occur but only intermittently in time. The statistical distribution of the time between two successive fluctuating events is found to depend on the parity of the evolution, i.e., whether the number of time steps in between is odd or even. We develop a physical analysis and derive mean-field equations to gain an understanding of these phenomena. Since AI is becoming increasingly widespread, we expect our RL empowered minority game system to have broad applications.

A 15-state kinetic model for ${\mathrm{Na}}^{+}$ channel gating that describes the coupling between three activation sensors, a two-stage fast inactivation process, and slow inactivated states may be reduced to equations for a 6-state system by application of the method of multiple scales. By expressing the occupation probabilities for closed states and the open state in terms of activation and fast inactivation variables, and assuming that activation has a faster relaxation than inactivation and that the activation sensors are mutually independent, the kinetic equations may be further reduced to rate equations for activation, and coupled fast and slow inactivation that describe spike frequency adaptation, a repetitive bursting oscillation in the neural membrane, and a cardiac action potential with a plateau oscillation. The fast inactivation rate function is, in general, dependent on the activation variable $m\left(t\right)$ but may be approximated by a voltage-dependent function, and the rate function for entry into the slow inactivated state is dependent on the fast inactivation variable.

We investigate the secular dynamics of long-range interacting particles moving on a sphere, in the limit of an axisymmetric mean-field potential. We show that this system can be described by the general kinetic equation, the inhomogeneous Balescu-Lenard equation. We use this approach to compute long-term diffusion coefficients, that are compared with direct simulations. Finally, we show how the scaling of the system's relaxation rate with the number of particles fundamentally depends on the underlying frequency profile. This clarifies why systems with a monotonic profile undergo a kinetic blocking and cannot relax as a whole under $1/N$ resonant effects. Because of its general form, this framework can describe the dynamics of globally coupled classical Heisenberg spins, long-range couplings in liquid crystals, or the orbital inclination evolution of stars in nearly Keplerian systems.

We study diffusive transport of a particle in a channel with periodically varying cross-section, occurring when the size of the particle periodically switches between two values. In such a situation, the entropy potential, which accounts for the area accessible for diffusion particle, varies both spatially (along the channel axis) and temporally. This underlies the complex interplay between different timescales of the system and leads to novel dynamic regimes. The most notable observations are: emergence of directed motion (in case of asymmetric channel) and resonant diffusion, both controlled by the switching frequency. Resonantlike behaviors of the drift velocity and the effective diffusion coefficient are shown and discussed. Based on heuristic arguments, an approximate analytical treatment of the transport process is proposed. As a comparison with the results obtained from Brownian dynamics simulations indicates, this approach provides a satisfactory way to handle the problem analytically.

We study absorbing phase transitions in systems of branching annihilating random walkers and pair contact process with diffusion on a one-dimensional ring, where the walkers hop to their nearest neighbor with a bias $\epsilon$. For $\epsilon =0$, three universality classes—directed percolation (DP), parity-conserving (PC), and pair contact process with diffusion (PCPD)—are typically observed in such systems. We find that the introduction of $\epsilon$ does not change the DP universality class but alters the other two universality classes. For nonzero $\epsilon$, the PCPD class crosses over to DP, and the PC class changes to a new universality class.

We study the roughening of $d$-dimensional directed elastic interfaces subject to quenched random forces. As in the Larkin model, random forces are considered constant in the displacement direction and uncorrelated in the perpendicular direction. The elastic energy density contains an harmonic part, proportional to ${\left({\partial }_{x}u\right)}^2$, and an anharmonic part, proportional to ${\left({\partial }_{x}u\right)}^{2n}$, where $u$ is the displacement field and $n>1$ an integer. By heuristic scaling arguments, we obtain the global roughness exponent $\zeta$, the dynamic exponent $z$, and the harmonic to anharmonic crossover length scale, for arbitrary $d$ and $n$, yielding an upper critical dimension $d_c\left(n\right)=4n$. We find a precise agreement with numerical calculations in $d=1$. For the $d=1$ case we observe, however, an anomalous “faceted” scaling, with the spectral roughness exponent ${\zeta }_s$ satisfying ${\zeta }_s>\zeta >1$ for any finite $n>1$, hence invalidating the usual single-exponent scaling for two-point correlation functions, and the small gradient approximation of the elastic energy density in the thermodynamic limit. We show that such $d=1$ case is directly related to a family of Brownian functionals parameterized by $n$, ranging from the random-acceleration model for $n=1$ to the Lévy arcsine-law problem for $n=\infty$. Our results may be experimentally relevant for describing the roughening of nonlinear elastic interfaces in a Matheron-de Marsilly type of random flow.

We investigate the effect of higher-order interactions induced by shape-dependent confinement in the modulational instability (MI) of a binary mixture of Bose-Einstein condensates. For this, we present and compute both analytically and numerically a system of coupled Gross-Pitaevskii equations with residual nonlinearity that rule the dynamics of the mixture. Using the linear stability approach, we obtain the instability criteria of the mixture and find that the MI can be excited in miscible condensates and altered in immiscible condensates due to the effect of residual nonlinearity. Direct numerical calculations are performed to support the analytical predictions, and a good agreement is found. The space-time evolution of the condensate density is displayed in both cases when the mixture is miscible and immiscible, showing the generation of bright solitons for modes predicted to be unstable.

We study and compare three characteristic times of the standard map: the Lyapunov time $t_L$, the Poincaré recurrence time $t_r$, and the stickiness (or escape) time $t_{st}$. The Lyapunov time is the inverse of the Lyapunov characteristic number ($L$) and in general is quite small. We find empirical relations for the $L$ as a function of the nonlinearity parameter $K$ and of the chaotic area $A$. We also find empirical relations for the Poincaré recurrence time $t_r$ as a function of the nonlinearity parameter $K$, of the chaotic area $A$, and of the size of the box of initial conditions $\epsilon$. As a consequence, we find relations between $t_r$ and $L$. We compare the distributions of the stickiness time and the Poincaré recurrence time. The stickiness time inside the sticky regions at the boundary of the islands of stability is orders of magnitude smaller than the Poincaré recurrence time $t_r$ and this affects the diffusion exponent $\mu$, which converges always to the value $\mu =1$. This is shown in an extreme stickiness case. The diffusion is anomalous (ballistic motion) inside the accelerator mode islands of stability with $\mu =2$ but it is normal everywhere outside the islands with $\mu =1$. In a particular case of extreme stickiness, we find the hierarchy of islands around islands.

Potts statistical models have become a popular and promising way to analyze mutational covariation in protein multiple sequence alignments (MSAs) in order to understand protein structure, function, and fitness. But the statistical limitations of these models, which can have millions of parameters and are fit to MSAs of only thousands or hundreds of effective sequences using a procedure known as inverse Ising inference, are incompletely understood. In this work we predict how model quality degrades as a function of the number of sequences $N$, sequence length $L$, amino-acid alphabet size $q$, and the degree of conservation of the MSA, in different applications of the Potts models: in “fitness” predictions of individual protein sequences, in predictions of the effects of single-point mutations, in “double mutant cycle” predictions of epistasis, and in 3D contact prediction in protein structure. We show how as MSA depth $N$ decreases an “overfitting” effect occurs such that sequences in the training MSA have overestimated fitness, and we predict the magnitude of this effect and discuss how regularization can help correct for it, using a regularization procedure motivated by statistical analysis of the effects of finite sampling. We find that as $N$ decreases the quality of point-mutation effect predictions degrade least, fitness and epistasis predictions degrade more rapidly, and contact predictions are most affected. However, overfitting becomes negligible for MSA depths of more than a few thousand effective sequences, as often used in practice, and regularization becomes less necessary. We discuss the implications of these results for users of Potts covariation analysis.

For more than half a century, the action potential (AP) has been considered a purely electrical phenomenon. However, experimental observations of membrane deformations occurring during APs have revealed that this process also involves mechanical features. This discovery has recently fuelled a controversy on the real nature of APs: whether they are mechanical or electrical. In order to examine some of the modern hypotheses regarding APs, we propose here a coupled mechanoelectrophysiological membrane finite-element model for neuronal axons. The axon is modeled as an axisymmetric thin-wall cylindrical tube. The electrophysiology of the membrane is modeled using the classic Hodgkin-Huxley (H-H) equations for the Nodes of Ranvier or unmyelinated axons and the cable theory for the internodal regions, whereas the axonal mechanics is modeled by means of viscoelasticity theory. Membrane potential changes induce a strain gradient field via reverse flexoelectricity, whereas mechanical pulses result in an electrical self-polarization field following the direct flexoelectric effect, in turn influencing the membrane potential. Moreover, membrane deformation also alters the values of membrane capacitance and resistance in the H-H equation. These three effects serve as the fundamental coupling mechanisms between the APs and mechanical pulses in the model. A series of numerical studies was systematically conducted to investigate the consequences of interaction between the APs and mechanical waves on both myelinated and unmyelinated axons. Simulation results illustrate that the AP is always accompanied by an in-phase propagating membrane displacement of $\approx 1\mathrm{nm}$, whereas mechanical pulses with enough magnitude can also trigger APs. The model demonstrates that mechanical vibrations, such as the ones arising from ultrasound stimulations, can either annihilate or enhance axonal electrophysiology depending on their respective directionality and frequency. It also shows that frequency of pulse repetition can also enhance signal propagation independently of the amplitude of the signal. This result not only reconciles the mechanical and electrical natures of the APs but also provides an explanation for the experimentally observed mechanoelectrophysiological phenomena in axons, especially in the context of ultrasound neuromodulation.

Unlike the traditionally reported Leidenfrost droplet which only floats on a thin film of vapor, we observe a prominent jump of the impinged droplets in the transition from the contact boiling to the Leidenfrost state. The vapor generation between the droplet and the substrate is vigorous enough to propel the spreading droplet pancake to an anomalous height. The maximum repellent height can be treated as an index of the total transferred energy. Counterintuitively, a stronger vaporization and a higher jump can be generated in the conditions normally considered to be unfavorable to heat transfer, such as a lower substrate temperature, a lower droplet impact velocity, a higher droplet temperature, or a lower thermal conductivity of the deposition on the substrate. Since the total transferred energy is the accumulation of the instantaneous heat flux during the droplet contacting with the substrate, it can be deduced that a longer contact time period is secured in the case of a lower instantaneous heat flux. The inference is supported by our experimental observations. Moreover, the phase diagrams describe the characteristics of the high repellency under different substrate temperatures, droplet subcooling temperatures, and Weber numbers. It allows us to manipulate the droplet jump for the relative applications.