We numerically study the anisotropic Turing patterns (TPs) of an activator-inhibitor system described by the reaction-diffusion (RD) equation of Turing, focusing on anisotropic diffusion using the Finsler geometry (FG) modeling technique. In FG modeling, the diffusion coefficients are dynamically generated to be direction dependent owing to an internal degree of freedom (IDOF) and its interaction with the activator and inhibitor. Because of this dynamical diffusion coefficient, FG modeling of the RD equation sharply contrasts with the standard numerical technique in which direction-dependent coefficients are manually assumed. To find the solution of the RD equations in FG modeling, we use a hybrid numerical technique combining the Metropolis Monte Carlo method for IDOF updates and discrete RD equations for steady-state configurations of the activator-inhibitor variables. We find that the newly introduced IDOF and its interaction are a possible origin of spontaneously emergent anisotropic patterns of living organisms, such as zebra and fishes. Moreover, the IDOF makes TPs controllable by external conditions if the IDOF is identified with the direction of cell diffusion accompanied by thermal fluctuations.

Biological tissue consists of various molecules. Instead of focusing on a particular molecule, we consider the Shannon entropy which is calculated from the abundance of different molecules at each spot in the tissue. The spatial distribution of the Shannon entropy is of interest. In this paper, we first obtain the heat map of perplexity, whose logarithm is the entropy. To characterize the spatial variety of molecules, we propose a scalar $k$ that is concerned with the coarse-graining of the perplexity heat map. To verify the usefulness of the number, experiments with mass spectrometry imaging were performed for mouse kidneys. We found that $k$ has large values in the renal pelvis area, cortex area, veins, and arteries in the mouse kidney, whereas fractal dimensions fail to distinguish those regions.

In the present work, the force term is first derived in the spectral multiple-relaxation-time high-order lattice Boltzmann model. The force term in the Boltzmann equation is expanded in the Hermite temperature rescaled central moment space (RCM), instead of the Hermite raw moment space (RM). The contribution of nonequilibrium RCM moments beyond second order are neglected. For the collision operator in the RCM space, each order of the force term can be incorporated directly. Through the transformation between the RCM space and the RM space, the force term for practical numerical implementation in the RM space can be derived. It can be demonstrated that the present force scheme is self-consistent for the isothermal flow and compressible thermal flow with adjustable Prandtl number via the numerical experiments.

In order to effectively manage infectious diseases, it is crucial to understand the interplay between disease dynamics and human conduct. Various factors can impact the control of an epidemic, including social interventions, adherence to health protocols, mask-wearing, and vaccination. This article presents the development of an innovative hybrid model, known as the Combined Dynamic-Learning Model, that integrates classical recurrent dynamic models with four different learning methods. The model is composed of two approaches: The first approach introduces a traditional dynamic model that focuses on analyzing the impact of vaccination on the occurrence of an epidemic, and the second approach employs various learning methods to forecast the potential outcomes of an epidemic. Furthermore, our numerical results offer an interesting comparison between the traditional approach and modern learning techniques. Our classic dynamic model is a compartmental model that aims to analyze and forecast the diffusion of epidemics. The model we propose has a recurrent structure with piecewise constant parameters and includes compartments for susceptible, exposed, vaccinated, infected, and recovered individuals. This model can accurately mirror the dynamics of infectious diseases, which enables us to evaluate the impact of restrictive measures on the spread of diseases. We conduct a comprehensive dynamic analysis of our model. Additionally, we suggest an optimal numerical design to determine the parameters of the system. Also, we use regression tree learning, bidirectional long short-term memory, gated recurrent unit, and a combined deep learning method for training and evaluation of an epidemic. In the final section of our paper, we apply these methods to recently published data on COVID-19 in Austria, Brazil, and China from 26 February 2021 to 4 August 2021, which is when vaccination efforts began. To evaluate the numerical results, we utilized various metrics such as RMSE and R-squared. Our findings suggest that the dynamic model is ideal for long-term analysis, data fitting, and identifying parameters that impact epidemics. However, it is not as effective as the supervised learning method for making long-term forecasts. On the other hand, supervised learning techniques, compared to dynamic models, are more effective for predicting the spread of diseases, but not for analyzing the behavior of epidemics.

Electrified sessile droplets on solid surfaces are ubiquitous in nature as well as in several practical applications. Although the influence of electric field on pinned sessile droplets and soap bubbles has been investigated experimentally, the theoretical understanding of the stability limit of generic droplets remains largely elusive. By conducting a theoretical analysis in the framework of lubrication approximation, we show that the stability limit of a sessile droplet on a lyophilic substrate in the presence of an electric field exhibits a universal power-law scaling behavior. The power-law exponent between the critical electric field and the droplet volume is found to be $-1$. The existence of this scaling law is further explained by virtue of minimization of the total free energy of the electrified droplet.

Predicting the ice melting point using molecular dynamics (MD) simulations is nontrivial due to uncertainty associated with the stochastic nature of the simulation and effect of finite domain sizes on the simulated ice-water phase transition. We developed a method based on the percolation theory to make use of the finite size effects to allow determination of a unique critical phase transition temperature as the melting point. The method involves construction of melting/freezing probability curves from multiple simulations with varying temperatures for different domain sizes. While the domain sizes affect the apparent melting/freezing probability and hence generate different curves with a wider probability distribution for a smaller size, the intersection of these curves is unique and locates the melting point. Based on MD simulations using the Tip4p/Ice water model, we tested and demonstrated the effectiveness of this method in locating the critical ice-water phase transition at a melting temperature of 268.78 K. Our analysis also showed that the apparent melting probability at this critical point is ∼0.69, not 0.5 assumed in the ad hoc method used previously. Our method, making no assumption about the system size, may provide a generic framework for analyzing phase transitions influenced by the finite size effects in MD simulations.

Non-Kolmogorov-Arnold-Moser (KAM) systems, when perturbed by weak time-dependent fields, offer a fast route to classical chaos through an abrupt breaking of invariant phase-space tori. In this work, we employ out-of-time-order correlators (OTOCs) to study the dynamical sensitivity of a perturbed non-KAM system in the quantum limit as the parameter that characterizes the resonance condition is slowly varied. For this purpose, we consider a quantized kicked harmonic oscillator (KHO) model, which displays stochastic webs resembling Arnold's diffusion that facilitate large-scale diffusion in the phase space. Although the Lyapunov exponent of the KHO at resonances remains close to zero in the weak perturbative regime, making the system weakly chaotic in the conventional sense, the classical phase space undergoes significant structural changes. Motivated by this, we study the OTOCs when the system is in resonance and contrast the results with the nonresonant case. At resonances, we observe that the long-time dynamics of the OTOCs are sensitive to these structural changes, where they grow quadratically as opposed to linear or stagnant growth at nonresonances. On the other hand, our findings suggest that the short-time dynamics remain relatively more stable and show the exponential growth found in the literature for unstable fixed points. The numerical results are backed by analytical expressions derived for a few special cases. We will then extend our findings concerning the nonresonant cases to a broad class of near-integrable KAM systems.

Statistical field theories provide powerful tools to study complex dynamical systems. In this work those tools are used to analyze the dynamics of a kinetic energy harvester, which is modeled by a system of coupled stochastic nonlinear differential equations and driven by colored noise. Using the Martin-Siggia-Rose response fields we analytically approach the problem through path integrals in the phase space and represent the moments that correspond to physical observables through Feynman diagrams. This analysis method is tested by comparing the solution to the linear case with previous analytical results. Through a perturbative expansion it is calculated how the nonlinearity affects, to the first order, the energy harvest supporting the results through numerical simulations.

Experimental evidence of vibrational resonance (VR) in the optoelectronic artificial spiking neuron based on a single photon avalanche diode and a vertical cavity laser driven by two periodic signals with low and high frequencies is reported. It is shown that a very weak subthreshold low-frequency (LF) periodic signal can be greatly amplified by the additional high-frequency (HF) signal. The phenomenon shows up as a nonmonotonic resonant dependence of the LF response on the amplitude of the HF signal. Simultaneously, a strong resonant rise of the signal-to-noise ratio is also observed. In addition, for the characterization of VR an area under the first LF period in the probability density function of interspike intervals for the LF signal and the maximal amplitude in this area were used, both of which also demonstrate a resonant behavior depending on the amplitude of the HF signal.

In an extended star with peripheral defects and a core occupied by a trap, it has been shown that exciton-mediated energy transport from the periphery to the core can be optimized [S. Yalouz et al., Phys. Rev. E 106, 064313 (2022)]. If the defects are judiciously chosen, then the exciton dynamics is isomorphic to that of an asymmetric chain and a speedup of the excitonic propagation is observed. Here we extend this previous work by considering that the exciton in both an extended star and an asymmetric chain is perturbed by the presence of a dephasing environment. Simulating the dynamics using a Lindblad master equation, two questions are addressed: How does the environment affect the energy transport on these two networks? and Do the two systems still behave equivalently in the presence of dephasing? Our results reveal that the timescale for the exciton dynamics strongly depends on the nature of the network. But quite surprisingly, the two networks behave similarly regarding the survival of their optimization law. In both cases, the energy transport can be improved using the same original optimal tuning of energy defects as long as the dephasing remains weak. However, for moderate or strong dephasing, the optimization law is lost due to quantum Zeno effect.

Within a tight-binding framework, we examine conformation-dependent charge transport properties of the DNA double-helix, including helical symmetry and the possibility of multiple charge conduction pathways. Using techniques based on the Green's function method, we inspect changes in the localization properties of DNA in the presence of long-range hopping, with varying disorder strength. We study three characteristic DNA sequences, two periodic and one random. We observe that, in all cases, due to disorder-induced delocalization, the localization length variation is similar. We also investigate the effect of backbone energetics on current-voltage ($I\text{−}V$) responses, using the Landauer-Büttiker formalism. We find that, in the presence of helical symmetry and long-range hopping, due to environmental effects, DNA can undergo a phase transition from semiconductor to insulator.

Active nematics are an important new paradigm in soft condensed matter systems. They consist of rodlike components with an internal driving force pushing them out of equilibrium. The resulting fluid motion exhibits chaotic advection, in which a small patch of fluid is stretched exponentially in length. Using simulation, this paper shows that this system can exhibit stable periodic motion when confined to a sufficiently small square with periodic boundary conditions. Moreover, employing tools from braid theory, we show that this motion is maximally mixing, in that it optimizes the (dimensionless) “topological entropy”—the exponential stretching rate of a material line advected by the fluid. That is, this periodic motion of the defects, counterintuitively, produces more chaotic mixing than chaotic motion of the defects. We also explore the stability of the periodic state. Importantly, we show how to stabilize this orbit into a larger periodic tiling, a critical necessity for it to be seen in future experiments.

A significant amount of attention was dedicated in recent years to the phenomenon of jamming of athermal amorphous solids by increasing the volume fraction of the microscopic constituents. At a critical value of the volume fraction, pressure shoots up from zero to finite values with a host of critical exponents discovered and discussed. In this paper, we advance evidence for the existence of a second transition, within the jammed state of two-dimensional granular systems, that separates two regimes of different mechanical responses. Explicitly, highly packed systems are quasielastic with quadrupole screening, and more loosely jammed systems exhibit anomalous mechanics with dipole screening. Evidence is given for a clear transition between these two regimes, reminiscent of the intermediate hexatic phase of crystal melting in two-dimensional crystals. Theoretical estimates of the screening parameters and the pressure where transition takes place are provided.

Analytic relations that describe crack growth are vital for modeling experiments and building a theoretical understanding of fracture. Upon constructing an idealized model system for the crack and applying the principles of statistical thermodynamics, it is possible to formulate the rate of thermally activated crack growth as a function of load, but the result is analytically intractable. Here, an asymptotically correct theory is used to obtain analytic approximations of the crack growth rate from the fundamental theoretical formulation. These crack growth rate relations are compared to those that exist in the literature and are validated with respect to Monte Carlo calculations and experiments. The success of this approach is encouraging for future modeling endeavors that might consider more complicated fracture mechanisms, such as inhomogeneity or a reactive environment.

We investigate the finite-size origin of the coherence time (or equivalently of its inverse, the emission linewidth) of a spatially extended, one-dimensional nonequilibrium condensate. We show that the well-known Schawlow-Townes scaling of laser theory, possibly including the Henry broadening factor, only holds for small system sizes, while in larger systems the linewidth displays a novel scaling determined by Kardar-Parisi-Zhang physics. This is shown to lead to an opposite dependence of the coherence time on the optical nonlinearity in the two cases. We then study how subuniversal properties of the phase dynamics such as the higher moments of the phase-phase correlator are affected by the finite size and discuss the relation between the field coherence and the exponential of the phase-phase correlator. We finally identify a configuration with enhanced open boundary conditions, which supports a spatially uniform steady state and facilitates experimental studies of the coherence time scaling.

We introduce a Brownian $p$-state clock model in two dimensions and investigate the nature of phase transitions numerically. As a nonequilibrium extension of the equilibrium lattice model, the Brownian $p$-state clock model allows spins to diffuse randomly in the two-dimensional space of area $L^2$ under periodic boundary conditions. We find three distinct phases for $p>4$: a disordered paramagnetic phase, a quasi-long-range-ordered critical phase, and an ordered ferromagnetic phase. In the intermediate critical phase, the magnetization order parameter follows a power-law scaling $m\sim L^{-\tilde{\beta }}$, where the finite-size scaling exponent $\tilde{\beta }$ varies continuously. These critical behaviors are reminiscent of the double Berezinskii-Kosterlitz-Thouless (BKT) transition picture of the equilibrium system. At the transition to the disordered phase, the exponent takes the universal value $\tilde{\beta }=1/8$, which coincides with that of the equilibrium system. This result indicates that the BKT transition driven by the unbinding of topological excitations is robust against the particle diffusion. On the contrary, the exponent at the symmetry-breaking transition to the ordered phase deviates from the universal value $\tilde{\beta }=2/p^2$ of the equilibrium system. The deviation is attributed to a nonequilibrium effect from the particle diffusion.

A martingale is a stochastic process that encodes a kind of fairness or unbiasedness, which is associated with a reference process. Here we show that, if the reference process $x_t$ evolves according to the Langevin equation with drift $a\left(x\right)$ and if $a\left(x_t\right)$ is a martingale, then its amplitude is the Langevin function, which originally described the canonical response of a single classical Heisenberg spin under static field. Furthermore, the asymptotic limit of $x_t/t$ obeys the ensemble statistics of such a Heisenberg spin.

One of the main issues that real energy converters present, when they produce effective work, is the inevitable entropy production. Within the context of nonequilibrium thermodynamics, entropy production tends to energetically degrade human-made or living systems. On the other hand, it is not useful to think about designing an energy converter that works in the so-called minimum entropy production regime since the effective power output and efficiency are zero. In this paper we establish some energy conversion theorems similar to Prigogine's theorem with constrained forces. The purpose of these theorems is to reveal trade-offs between design and the so-called operation modes for $(2\times 2)$-linear isothermal energy converters. The objective functions that give rise to those thermodynamic constraints show stability. A two-mesh electric circuit was built as an example to demonstrate the theorems' validity. Likewise, we reveal a type of energetic hierarchy for power output, efficiency, and dissipation function when the circuit is tuned to any of the operating regimes studied here. These are maximum power output (MPO), maximum efficient power $\left(\mathrm{MP}\eta \right)$, maximum omega function $\left(\mathrm{M}\mathrm{\Omega }\right)$, maximum ecological function (MEF), maximum efficiency $\left(\mathrm{M}\eta \right)$, and minimum dissipation function (mdf).