Bacterial chemotaxis for the case of Escherichia coli is controlled by methylation of chemoreceptors, which in a biochemical pathway regulates the concentration of the CheY-P protein that finally controls the tumbling rate. As a consequence, the tumbling rate adjusts to changes in the concentration of relevant chemicals, such as to produce a biased random walk toward chemoattractants or against the repellers. Methylation is a slow process, implying that the internal concentration of CheY-P is not instantaneously adapted to the environment, and therefore the tumbling rate presents a memory. This implies that the Keller–Segel equations used to describe chemotaxis at the macroscopic scale, which assume a local relation between the bacterial flux and the chemical gradient, cannot be fully valid as memory and the associated nonlocal response are not taken into account. To derive the new equations that replace the Keller–Segel ones, we use a kinetic approach, in which a kinetic equation for the bacterial transport is written considering the dynamics of the protein concentration. When memory is large, the protein concentration field must be considered a relevant variable on equal foot as the bacterial density. Working out in detail the Chapman–Enskog method, the dynamical equations for these fields are obtained, which have the form of reaction-diffusion equations with flux and source terms depending on the gradients on the chemical signal. Also, the transport coefficients are obtained entirely in terms o the microscopic dynamics, showing important symmetry properties and giving their values of the case of E. coli. Solving the equations for an inhomogeneous signal it is shown that the response is nonlocal, with a smoothing length as large as $170\mu \mathrm{m}$ for E. coli. The homogeneous response and the relaxational dynamics are also studied in detail. For completeness, the case of small memory is also studied, in which case the Chapman–Enskog method reproduces the Keller–Segel equations, with explicit expressions for the transport coefficients.

We conducted a numerical study of the effects of the modulation amplitude and period of a temporally modulated laser pulse on instabilities at an ablation front. The physical features of the oscillatory acceleration and ablation velocity in unperturbed ablative flows display periodic oscillations. As the modulation amplitude or period is increased, the asymmetry of the oscillatory acceleration and ablation velocity becomes more evident, and the peak values of these quantities increase. The numerical solution of the Mathieu equation [R. Betti et al., Phys. Rev. Lett. 71, 3131 (1993)] with a fitted acceleration was used to evaluate the behaviors of the oscillatory acceleration. The spatial structure and interfacial evolution of a single-mode ablative Rayleigh-Taylor instability (ARTI) were analyzed for the modulated laser pulses with different modulation amplitudes and periods. It was also observed in a previous work [K. G. Zhao et al., Phys. Rev. E 109, 025213 (2024)] that the modulated laser exerts a stabilizing influence on the growth of the ARTI in the intermediate- and long-wavelength regions. We found that increasing either the modulation amplitude or period enhances the dynamic stabilization of the ARTI while simultaneously inducing a characteristic destabilization of the parametric instability, which may excite the short-wavelength perturbations through the parametric resonance [G. H. Wolf, Phys. Rev. Lett. 24, 444 (1970)].

Initial value problems—a system of ordinary differential equations and corresponding initial conditions—can be used to describe many physical phenomena including those arise in classical mechanics. We have developed an approach to solve physics-based initial value problems using unsupervised machine learning. We propose a deep learning framework that models the dynamics of a variety of mechanical systems through neural networks. Our framework is flexible, allowing us to solve nonlinear, coupled, and chaotic dynamical systems. We demonstrate the effectiveness of our approach on systems including a free particle, a particle in a gravitational field, a classical pendulum, and the Hénon-Heiles system (a pair of coupled harmonic oscillators with a nonlinear perturbation, used in celestial mechanics). Our results show that deep neural networks can successfully approximate solutions to these problems, producing trajectories which conserve physical properties such as energy and those with stationary action. We note that probabilistic activation functions, as defined in this paper, are required to learn any solutions of initial value problems in their strictest sense, and we introduce coupled neural networks to learn solutions of coupled systems.

Strategies for trapping and manipulating chiral active matter are crucial in fields ranging from nonequilibrium physics to chemical engineering and biology. While various methods for controlling active matter have been developed, achieving spontaneous trapping and collective manipulation in complex, variable, noisy environments remains an open challenge. In this paper, we investigate the self-trapping effect and collective motion patterns of chiral active particles induced by a noisy geometric environment in the chiral Vicsek-like model (CVLM). The heterogeneous environment relies on designing the topography by varying the spatial noise intensity, featuring a finite noiseless circular region with radius $R_0$. We identify two key conditions for self-trapping behavior: (i) sufficient interaction radius ($r$) to break symmetry and enable collective motion, and (ii) chirality ($\omega$) that satisfies the geometric constraints, where stable and effective trapping occurs only if $\omega >{\omega }_c$, with ${\omega }_c\simeq v/R_0$. We also analyze how different system parameters influence the fraction of trapped particles (FTP). Furthermore, our system reveals a variety of phase transitions driven by the interplay between $\omega$ and $r$. Interestingly, varying $\omega$ uncovers additional phases, such as self-reverting vortices, orbital polarization, and vibrational polarization. Additionally, changes in particle interaction $r$ result in three regimes of particle motion: homogeneous disorder, multiple flocks, and single flocks. These findings may inspire innovative strategies for achieving spontaneous trapping and regulating chiral particles in complex environments.

In this study, we identify an intricate class of periodic behavior, coined as “fishbone,” within the chaotic dynamics induced by external periodic disturbances in a neuronal system. Alongside this structure, we observe well-known patterns such as shrimps and cockroaches, revealing the system's sensitivity to external perturbations. Notably, our work highlights the significant impact of altering biophysical parameters, showing that changes in the ionic conductance of neurons can lead to the cohesion or detachment of complex periodic structures from the primary fishbone-shaped structure. This finding underscores the role of ionic channels in shaping neuronal responses, which is relevant given their involvement in various neuronal disorders. Furthermore, our study provides insights into how external perturbations influence neuron signal processing.

Chemotaxis in bacteria such as Escherichia coli is controlled by the slow methylation of chemoreceptors. As a consequence, intrinsic time and length scales of tens of seconds and hundreds of micrometers emerge, making the Keller–Segel equations invalid when the chemical signal changes on these scales, as occurs in several natural environments. Using a kinetic approach, we show that chemotaxis is described using the concentration field of the protein that controls tumbling in addition to bacterial density. The macroscopic equations for these fields are derived, which describe the nonlocal response.

This paper introduces two techniques for computing the distribution of the absorption or first passage time of the drifted Wiener diffusion subject to Poisson resetting times to an upper hard wall barrier and to a lower absorbing barrier. The first method, which we call the Padé-partial fraction approximation, starts with the Padé approximation to the Laplace transform of the first passage time distribution, which is then exactly inverted by means of the partial fraction decomposition. The second method, which we call the multiresolution algorithm, is a Monte Carlo technique that exploits the properties of the Wiener process to generate Brownian bridges at increasing levels of resolution. Our numerical study reveals that the multiresolution algorithm has higher efficiency than standard Monte Carlo, whereas the faster Padé-partial fraction method is accurate in various circumstances and provides an analytical formula. Also, a closed-form exact expression for the expected first passage time is derived.

We study the emergence of typicality in classical systems with a large number of binary state variables. We show analytically that for sufficiently large subsets of the complete state space, state functions which can be associated with macroscopic observables, such as density or energy, are sharply concentrated around a typical value, i.e., the vast majority of microscopic states show the same macroscopic behavior. From this static typicality result we obtain the dynamical counterpart, which states that if two initial conditions are drawn from a sufficiently large subset of the state space, the dynamical trajectories of the macroscopic observables would be approximately the same, provided that the dynamics does not abruptly compress the size of sets of states under evolution. The ensuing dynamical typicality phenomenon is very similar to what was recently found in the context of the dynamics of isolated quantum systems. We illustrate and apply our analytical results by analyzing one-dimensional cellular automata.

We examine the dynamics of a two-dimensional stripe, bubble, and crystal forming system interacting with a periodic one-dimensional substrate under an applied drive that is rotated with respect to the substrate periodicity direction $x$. We find that the stripes remain strongly directionally locked to the $x$ direction for an extended range of drives before undergoing motion parallel to the drive. In some cases, the stripes break apart at the unlocking transition, but they can dynamically reform into stripes aligned perpendicular to the $x$ direction, producing hysteresis in the directional locking and unlocking transitions. In contrast, moving anisotropic crystal and bubble phases exhibit weaker directional locking and reduced or no hysteresis. The hysteresis occurs in regimes where the particle rearrangements occur and is most pronounced near the stripe phase. We also show that for varied substrate strength, substrate spacing, and particle density, a number of novel dynamical patterns can form that include a combination of stripe, bubble, and crystal morphologies.

The nonequilibrium behavior of many bio-materials under classical jump experiments, in which the system is subject to an instantaneous increase of controlled intensive variables, is poorly studied. Here, we study the response to such jumps of a short DNA hairpin, that possesses a bubble-generating block, in which we assume an initially equilibrated DNA. In particular, we impose temperature-jump (T-jump) and force-jump (F-jump) at various strengths and follow the DNA denaturation in time. We show how partial opening states, which can be also detected in equilibrium at various temperatures and forces, are transiently populated during the equilibration process. In combined large T- and F-jumps, we demonstrate an overshoot in the opening process, in which the middle bubble re-closes transiently after its initial opening, before opening up again permanently. Such an oscillatory behavior has been previously observed in soft-matter systems, but not in DNA, and can have consequences on the intracellular opening processes of DNA.

In the recent literature, the $g$-diffusion equation involving Caputo fractional derivative with respect to another function has been proposed to describe subdiffusion in a medium having an evolving structure. In this case, a continuous transition between different subdiffusive regimes may occur. To study the underlying process of the $g$-diffusion equation, we propose a Langevin equation coupled with a subordinator involving two time-changing mechanisms to describe the microscopic motion of the $g$-diffusion process, on which we derive the same Fokker-Planck equation containing the Caputo fractional derivative with respect to another function. We further develop the theories of evaluating the common quantities in the framework of a Langevin equation, such as ensemble-averaged mean-squared displacement, time-averaged mean-squared displacement (TAMSD), scatter of TAMSD, and ergodicity breaking parameter. The proposed Langevin equation and the new subordinator provide a new perspective for studying the $g$-diffusion process and further improve the theory of the anomalous diffusion phenomena in a complex nonstatic environment.

In the previous work [Takahashi and Ikeda, Phys. Rev. E 109, 044203 (2024)], we found that tunneling probabilities for a periodically perturbed rounded rectangular potential form a sawtoothlike structure as a function of either the Planck constant $\hslash$ or the angular frequency of the perturbation $\omega$ owing to multiquanta absorption tunneling. The replacement of the dominant harmonic channel with the change of either $\hslash$ or $\omega$ occurs in every transition region of the sawtooth structure, which causes a sudden change in the tunneling probability. The tunneling probability in the potential region forms a resonance peak reflecting the fundamental resonance scattering state at each edge of the sawtooth structure. In this paper, we explore the underlying mechanism of the sawtooth structure in terms of semiclassics. The semiclassical method reproduces the sawtooth structure except for narrow transition regions accompanied by resonance peaks. The sawtooth structure is constructed by superpositioning a sufficiently large number of complex branches as an analogy of the Fourier decomposition of a sawtoothlike wave. The baseline of tunneling probability, i.e., the average line of the sawtooth structure, is well reproduced by the Melnikov method, i.e., the semiclassical weight estimated based on the theory of stable-unstable manifold guided tunneling. When $\hslash$ and $\omega$ are fixed, the average line changes as exponentiation with the base $\epsilon$, i.e., $\propto {\epsilon }^{\alpha }$, where $\alpha$ is roughly estimated as $\sim c/\hslash \omega$.

Fairness plays a key role in collective decision-making such as international trade, burden sharing in global climate change, and prey allocation after hunting. The two-player ultimatum game has facilitated a large body of research on fair behavior. But multiplayer group interactions, group decision rules, and their effects on the evolution of fair behavior remain largely unexplored. We aim to study the evolutionary dynamics of collective resource allocation interactions, and recently advanced hypergraphs can efficiently describe the group interaction relationships. Each hyperlink represents a group and the members participate in multiplayer ultimatum games. Each member acts as proposer one time, and accordingly, all other members act as responders. For one game, when all responders agree upon the proposer's scheme, the scheme succeeds and all members accrue payoffs; otherwise, the scheme fails and no payoff is produced. First, we use adaptive dynamics to demonstrate that the strategy evolves toward rational and unfair solutions for uniform random hypergraphs. However, by incorporating empathy into decision-making, the population is stabilized with fair allocation schemes. Increasing the order of uniform random hypergraphs generally promotes group fairness as long as the group size is not too large. This enhancing effect is further reinforced on heterogeneous hypergraphs, where individuals with higher degrees play a leading role in strategy propagation and thus hold sway over the population dynamics. Our work enriches the literature on the evolutionary dynamics of multiplayer ultimatum games in structured populations.

A new analytic model of isothermal evaporation of a sessile droplet in the form of a spherical cap is presented. This model is based on the rigorous theory of diffusion mass transfer and takes into account the intrinsic kinetics of the evaporation process. Due to its rigor, the presented model does not include the contact angle correction parameter $f\left(\theta \right)$ that is used in other models. An analysis of the presented model was conducted showing that a sessile droplet can evaporate in the diffusion-kinetic, diffusion, or kinetic regime. Each of these cases was considered separately. The case of sessile droplet evaporation in the constant contact radius mode (pinning) and the case of sessile droplet evaporation in the constant contact angle mode were also considered separately. A comparison of the calculated data obtained within the framework of the presented model with available experimental data on the evaporation kinetics of sessile droplets of ethanol and water into air was carried out. This comparison demonstrated that the presented model perfectly describes experimental data. In addition, this comparison demonstrated that to obtain correct results, a sessile droplet along with its surrounding gas must be isolated from the ambient atmosphere when an experiment to study the evaporation kinetics of the droplet is conducted.

Self-sustained order can emerge in complex systems due to internal feedback between coupled subsystems. Here, we present our discovery of a nonmonotonic emergence of order amidst chaos in a turbulent thermoacoustic fluid system. Fluctuations play a vital role in determining the dynamical state and transitions in a system. In this work, we use complex networks to encode jumps in amplitude scales owing to fluctuations as links between nodes representing amplitude bins. The number of possible amplitude transitions at a fixed timescale reflects the complexity of dynamics at that timescale. The network entropy quantifies the number of and uncertainty associated with such transitions. Using network entropy, we show that the uncertainty in fluctuations first increases and then decreases as the system transitions from chaos via intermittency to order. The competition between turbulence and nonlinear interactions leads to such nonmonotonic emergence of order amidst chaos in turbulent thermoacoustic fluid systems.

The current study examines, using a nonextensive statistical framework satisfying the H-theorem constraint $0\le q\le 2$, the dynamics of dust-acoustic shock waves in complex plasmas under the influence of both gravity and microgravity within adiabatic and nonadiabatic fluctuating charge. The results highlight the significant role of gravity in enhancing dissipation and breaking potential symmetry, while microgravity allows for sustained oscillations and more stable electrostatic structures. The impact of the nonextensive parameter $q$ reveals that higher values lead to stronger electrostatic interactions and prolonged wave propagation. Additionally, variations in dust grain size, charge relaxation time, and electron density influence wave stability and dissipation. The findings provide valuable insights into plasma behavior, with implications for both laboratory experiments and microgravity environments such as the PK-3 Plus laboratory on the International Space Station.

We study the first-passage-time (FPT) properties of active Brownian particles to reach an absorbing wall in two dimensions. Employing a perturbation approach, we obtain exact analytical predictions for the survival and FPT distributions for small Péclet numbers, measuring the importance of self-propulsion relative to diffusion. While randomly oriented active agents reach the wall faster than their passive counterpart, their initial orientation plays a crucial role in the FPT statistics. Using the median as a metric, we quantify this anisotropy and find that it becomes more pronounced at distances where persistent active motion starts to dominate diffusion.

The thermodynamic parameter space is flat for an ideal classical gas with noninteracting particles. In contrast, for an ideal quantum Bose (Fermi) gas, the thermodynamic curvature is positive (negative), indicating intrinsic attractive (repulsive) interactions. We generalize the classical Maxwell-Boltzmann distribution by employing a generalized form of the exponential function, proposing the Mittag-Leffler Maxwell-Boltzmann distribution within the framework of superstatistics. We demonstrate that the generalization parameter, $\alpha$, quantifies the statistical interaction. When $\alpha =1$, the distribution coincides with the standard classical Maxwell-Boltzmann distribution, where no statistical interaction is present. For $0<\alpha <1$ ($\alpha >1$), the statistical interaction is repulsive (attractive), corresponding to a negative (positive) thermodynamic curvature of the system.