We consider active Brownian particles that intermittently switch between active and inactive states. Such behavior is ubiquitous at all scales, from bacteria to animals and in artificial active systems. We derive exact expressions for key transport properties, including velocity autocorrelations and diffusion coefficients, and demonstrate that particle dispersion is highly sensitive to minute details, such as whether the memory of active orientation is retained across a stop event. Extending the stop-and-go model to include minimal metabolic dynamics, we show that the average survival time of an intermittently moving particle is maximized at (i) an optimal stopping frequency and (ii) a nontrivial optimal diffusivity, which itself depends on the stopping frequency.

The emergence of high-amplitude periodic oscillations is observed in various complex systems in nature and engineering. Thermoacoustic oscillations in systems comprising turbulent reactive flow exemplify such complexity in the engineering context, where the emergence of oscillatory dynamics is undesirable. Turbulent reactive flow systems undergo a transition from low-amplitude aperiodic fluctuations (disorder) to high-amplitude periodic oscillations (order) of acoustic pressure, with varying fuel-to-air ratio, represented by the global equivalence ratio as a bifurcation parameter. In this study, we perform experiments to investigate how the nature of this transition from disorder to order changes under the influence of a secondary parameter in a turbulent reactive flow in a backward-facing step combustor. In our system, we vary either the thermal power input or the flame stabilizer position from the backward-facing step as a secondary parameter and obtain two different sets of transitions. Our findings reveal five qualitatively distinct types of transitions to periodic oscillations. Of these, two types of transitions exhibit a continuous nature. Two other types of transitions consist of both continuous and discontinuous bifurcations. The last type of transition is characterized by a discontinuous bifurcation to high-amplitude periodic oscillations. We show that order can emerge through a variety of routes. The change in the nature of the transition from disorder to order is intricate and undergoes a metamorphosis from continuous to discontinuous in a complex turbulent reactive flow system. We anticipate that such metamorphosis of transition is a universal phenomenon that can also occur in other complex systems involving turbulent thermo-fluid flows.

Antimicrobial resistance is a threat to public health with millions of deaths linked to drug-resistant infections every year. To mitigate resistance, common strategies that are used are combination therapies and therapy switching. However, the stochastic nature of pathogenic mutation makes the optimization of these strategies challenging. Here, we propose a two-scale stochastic model that considers the effective evolution of therapies in a multidimensional efficacy space, where each dimension represents the efficacy of a specific drug in the therapy. The diffusion of therapies within this space is subject to stochastic resets, representing therapy switches. The boundaries of the space, inferred from coarser pathogen-host dynamics, can be either reflecting or absorbing. Reflecting boundaries impede full recovery of the host, while absorbing boundaries represent the development of antimicrobial resistance, leading to therapy failure. We derive analytical expressions for the average absorption times, accounting for both continuous and discrete genomic changes using the frameworks of Langevin and master equations, respectively. These expressions allow us to evaluate the relevance of times between drug switches and the number of simultaneous drugs in relation to typical timescales for drug resistance development. To study realistic therapy scenarios, we impose constraints on the number of administered therapies and/or their costs, which reveals nontrivial optimal drug-switching protocols that maximize the time before antimicrobial resistance develops while reducing therapy costs. Finally, we extend the model to consider single-cell heterogeneity to accurately capture the effects of individual mutations that result in drug resistance.

When an external force is present, the particle distribution as well as the local velocity and momentum are continuously accelerated from the view of the Boltzmann equation. The continuous acceleration, even within a time step, causes the conventional lattice Boltzmann equation for nonideal fluids to lack the time consistency, leading to its evolution being inconsistent with the macroscopic system and its theoretical analysis being contradictive to the numerical simulation. This paper presents a time-consistent lattice Boltzmann equation that uses the mean effects to depict the continuous acceleration and the integral characteristic. It abides Boltzmann's assumption of the independence between particle collisions and external forces and resolves the contradiction between theoretical analyses and the numercial simulations. The time-consistent equation can recover the exact Navier-Stokes equations by the Chapman-Enskog analysis. It can simulate the liquid-gas coexistence densities and saturation properties, which are in perfect agreement with the theoretical predictions of the Maxwell equal-area law and the Kelvin equation, respectively. Finally, an improved scheme enables the time-consistent multiphase model to adjust the surface tension independently by the surface tension coefficient.

In this work, an improved discrete unified gas kinetic scheme (DUGKS) is proposed. Like the original DUGKS and the optimized DUGKS, the improved DUGKS uses trapezoidal rule for the integration of the collision term, and introduces two auxiliary distribution functions with the inclusion of collision effect. Different from the original DUGKS and the optimized DUGKS, the improved DUGKS uses rectangular rule to implicitly integrate the convection term, and adopts trapezoidal rule and Taylor expansion to introduce the distribution function at the node to evaluate the interface flux at the next time step, which can be considered as a new version of the optimized DUGKS with implicit treatment. Combining the benefits of the choice of integration method, the design of implicit scheme, and the construction of interface flux, numerical results demonstrate that the improved DUGKS has a much better numerical stability than the original DUGKS and the optimized DUGKS while still maintaining better accuracy and higher efficiency. In terms of computational efficiency, the improved DUGKS improves the efficiency by fast convergence and reducing the number of auxiliary points. Among the three kinds of DUGKS, the improved DUGKS requires the fewest iteration steps and the least calculation time to reach convergence. Moreover, with the increase of the number of grids, the iteration steps and computation time decrease more. In terms of accuracy, the improved DUGKS has some improvements. Numerical tests of Couette flow and Taylor-Green vortex flow show that the error between the results obtained by the improved DUGKS and the analytical solution is the least. In terms of numerical stability, the significant improvement of the improved DUGKS is shown. In numerical tests of Couette flow, Poiseuille flow, and lid-driven cavity flow, the original DUGKS and the optimized DUGKS do not converge with a low-resolution mesh and high Re number, but the improved DUGKS can still reach convergence while still maintaining good accuracy. The ratio of time step to relaxation time is about $8\times {10}^6$ times larger than that of the original DUGKS and the optimized DUGKS, which greatly enlarges the stability region.

Constraints in the form of rigid bonds between neighboring particles are introduced at the point of calculating the instantaneous normal modes of a supercooled liquid. The effect of rigid bond constraints on the restraint exhibited by a configuration is similar to that exerted by pinned particles after adjusting for the relative number of constrained degrees of freedom. Both forms of constraint shift the liquid configurations towards a restraint similar to that of silica, a canonical strong liquid. We show that the constraints act to increase configurational stiffness, as measured by the restraint, by decreasing the amplitude of the unstable modes.

We mimic the mechanical response of touch mechanoreceptors by that of a gas cavity embedded in an elastic semicylinder, as a fingertip analog. Using tribological experiments combined with optical imaging, we measure the dynamics and deformation of the cavity as the semicylinder is put in static contact or slid against model rough surfaces at constant normal force and velocity. We propose an elastic model to predict the cavity deformation under normal load showing that membrane mechanical stresses are anisotropic and we discuss its possible biological consequences. In friction experiments, we show that the cavity shape fluctuations allow for texture discriminations.

Isolated micro-targets are a promising avenue to high-performance laser-driven proton and ion accelerators due to their ability to confine the coupled laser energy to a small volume and small number of particles. Experimental results on proton emission from levitated plastic micro-spheres with an initial diameter of 1 µm are presented. For a laser with only 0.4 J contained within the central spot, proton energies of up to 27 MeV were observed with micro-spheres pre-expanded to near-critical density. Three-dimensional PIC simulations reveal that the combination of a ponderomotively driven process similar to radiation pressure ‘hole-boring’ generates a dense plasma bunch propagating at 0.1 c with the subsequent expansion of the moving bunch driven by hot electrons boosting the maximum proton energy ${\mathrm{E}}_{\max }$ considerably. Simulations agree well with the observed experimental results and suggest a scaling of $54\mathrm{MeV}/{\mathrm{J}}^{1/2}$, predicting that 100 MeV protons are possible with only 4 J in a Gaussian spot.

We report in this work the current filamentation instability of laser-produced proton beams in a regime where the plasma collision frequency is much smaller than the plasma oscillation frequency but larger than the growth rate of the instability. In this regime, the plasma electron temperature increases significantly due to collisional Ohmic heating during the linear phase of the instability, which leads to a two-stage linear filamentation growth shown in this work. Compared to the collisionless plasma case, a reduced instability growth rate due to plasma collisions is found in the first stage, followed by a second stage with a comparable growth rate. Furthermore, an enhanced magnitude of magnetic fields and wavelength of beam filamentation are observed after instability saturation. The two-stage linear filamentation growth shows agreement with the dispersion relation of the instability and supported by detailed particle-in-cell simulations.

Defects in inherent structures are reduced by approximately $80\%$ compared to their equilibrium counterparts during two-dimensional melting. We numerically investigate the properties of inherent defects and their role in determining system states in two systems known to undergo continuous melting transitions. Despite being minor compared to virtual defects, which disappear during minimization, inherent defects alone can dictate the system's state. This is evidenced by the similar decay exponents of translational and bond-orientational correlation functions in thermal and minimized configurations, as well as the growth of isolated dislocations and disclinations among inherent defects in the hexatic and liquid phases, respectively. Inherent defects are primarily located in plastic regions during minimization and tend to cluster in the liquid phase, while the anti-correlated plastic and elastic behaviors of inherent structures transition in the hexatic phase. These findings highlight the critical role of inherent defects in two-dimensional melting.

Through the development of a microscopic deterministic model in the framework of three-phase traffic theory, microscopic features of vehicle overacceleration, which determines the occurrence of the metastability of free traffic flow at a bottleneck, have been revealed: (i) The greater the impact of vehicle overacceleration on free traffic flow at a bottleneck, the higher the maximum flow rate at which free flow can persist at the bottleneck, i.e., the better traffic breakdown can be avoided. (ii) There is vehicle overacceleration in a road lane caused by safety acceleration at the bottleneck. (iii) Overacceleration in a road lane can occur without explicitly introducing it in the model. (iv) Through a microscopic analysis of spatiotemporal competition between speed adaptation and vehicle acceleration behaviors, traffic conditions have been found at which safety acceleration in a road lane and/or vehicle acceleration due to lane-changing on a multilane road become overacceleration. (v) There is spatiotemporal cooperation of different overacceleration mechanisms. (vi) The stronger the overacceleration cooperation, the stronger the maintenance of free flow at the bottleneck due to overacceleration. (vii) On a two-lane road, both speed adaptation and overacceleration in a road lane can affect qualitatively the overacceleration mechanism caused by lane-changing. The microscopic features of the effect of vehicle overacceleration on traffic breakdown are related to traffic flow consisting of human-driving vehicles and/or of automated-driving vehicles.

Spherically averaged periodic pair potentials offer the enticing promise to provide accurate results at a drastically reduced computational cost compared to the traditional Ewald sum. In this work, we employ the pair potential by Yakub and Ronchi [J. Chem. Phys. 119, 11556 (2003)] in ab initio path integral Monte Carlo (PIMC) simulations of the warm dense uniform electron gas. Overall, we find very accurate results with respect to Ewald reference data for integrated properties such as the kinetic and potential energy, whereas wavenumber-resolved properties such as the static structure factor $S\left(\mathbf{q}\right)$, the static linear density response $\chi \left(\mathbf{q}\right)$, and the static quadratic density response ${\chi }^{\left(2\right)}(\mathbf{q},0)$ fluctuate for small $q$. In addition, we perform an analytic continuation to compute the dynamic structure factor $S(\mathbf{q},\omega )$ from PIMC results of the imaginary-time density-density correlation function $F(\mathbf{q},\tau )$ for both pair potentials. Our results have important implications for future PIMC calculations, which can be sped up significantly using the Yakub and Ronchi potential for the estimation of equation-of-state properties or $q$-resolved observables in the noncollective regime, whereas a full Ewald treatment is mandatory to accurately resolve physical effects manifesting for smaller $q$, including the evaluation of compressibility sum rules, the interpretation of x-ray scattering experiments at small scattering angles, and the estimation of optical and transport properties.

We focus on the intermittent bistable stall dynamics of an airfoil under varying angle of attack. We propose a one-dimensional Langevin equation where the stochastic forcing depends on the state of the system—high-lift attached flow or low-lift detached flow—and where the deterministic potential depends continuously on the angle of attack. The model, identified based on the flow statistics and dynamics, reproduces the S-shaped lift curve, as well as the flow dynamics. It also predicts the nature of the bifurcations that the flow undergoes as the angle of attack varies.

Krylov complexity, a quantum complexity measure which uniquely characterizes the spread of a quantum state or an operator, has recently been studied in the context of quantum chaos. However, the definitiveness of this measure as a chaos quantifier is in question in light of its strong dependence on the initial condition. This article clarifies the connection between the Krylov complexity dynamics and the initial operator or state. We find that the saturation value of Krylov complexity depends monotonically on the inverse participation ratio (IPR) of the initial condition in the eigenbasis of the Hamiltonian. We explain the reversal of the complexity saturation levels observed in [Phys. Rev. E 107, 024217 (2023)] using the initial spread of the operator in the Hamiltonian eigenbasis. IPR dependence is present even in the fully chaotic regime, where popular quantifiers of chaos, such as out-of-time-ordered correlators and entanglement generation, show similar behavior regardless of the initial condition. Krylov complexity averaged over many initial conditions still does not characterize chaos.

Resetting plays a pivotal role in optimizing the completion time of complex first-passage processes with single or multiple outcomes and exit possibilities. While it is well established that the coefficient of variation—a statistical dispersion defined as a ratio of the fluctuations over the mean of the first-passage time—must be larger than unity for resetting to be beneficial for any outcome averaged over all the possibilities, the same cannot be said while conditioned on a particular outcome. The purpose of this article is to derive a universal condition that reveals that two statistical metrics—the mean and coefficient of variation of the conditional times—come together to determine when resetting can expedite the completion of a selective outcome, and furthermore can govern the biasing between preferential and nonpreferential outcomes. The universality of this result is demonstrated for a one-dimensional diffusion process subjected to resetting with two absorbing boundaries.

We study the spreading dynamics of an initially localized wave packet of finite norm in one-dimensional nonlinear Schrödinger lattices with random potential. The problem has gained considerable interest in the literature, and it continues to attract attention due to its connection with the general properties of behavior of systems with competition between nonlinearity, nonlocality, and randomness. It is shown that adding small dielectric coupling to the ambient random medium leads to asymptotic localization of the nonlinear field regardless of the Kerr nonlinearity strength. If the electric susceptibility is zero, then the nonlinear field undergoes sharp localization-delocalization transition above a certain critical value of the nonlinearity parameter. The nonlinear localization length is found to be ${\mathrm{\Lambda }}_{\mathrm{loc}}\simeq exp[(\pi /{\varepsilon }_{r}tan\delta )ln\beta ]$, where $tan\delta$ is the dielectric loss tangent, ${\varepsilon }_r$ is the relative permeability of the medium, and $\beta$ characterizes the Kerr nonlinearity. The model predicts a possibility of self-induced localization when the “medium” to which the wave field is dielectrically coupled is the wave function itself. The mathematical methods, stipulated here, pave the way towards understanding the wave processes in complex media with competition between randomness, dispersiveness, and nonlinearity, such as Anderson localization of a wave packet interacting with the environment.

Cooperation is an important driver of resource regeneration and ecological maintenance, and a favorable environment enables the evolution of cooperation. In order to explore the dynamic relationship among environmental fluctuations and individual behaviors in biological systems, this paper designs an evolutionary game model in dynamic populations to examine the interactions between resources and cooperative evolution. The results suggest that the sustainable evolution of populations ensures that the initial population size is within the environmental carrying capacity, otherwise the system may be at risk of collapse. The strength of environmental feedbacks and synergistic factors together determine the expansion or contraction of populations and cooperation. Theoretical predictions agree with numerical simulations, thus elucidating the conditions in which cooperative behavior could be sustained in a system with limited resources. There hope that this work provides new theoretical support for the evolution of cooperation in dynamical systems and for the construction of more adaptive evolutionary models.