It is crucial to understand the scaling behaviors of acoustic emissions (AEs) preceding damage localization in order to predict failures of brittle solids under compression. Yet, the effect of length scale on the complex interplay between the initiation, propagation, and coalescence of pre-existing fracture networks and corresponding AE behaviors is poorly understood. In this study, we perform laboratory compressional experiments on naturally fractured rocks at four sample sizes from 50 to 300 mm whose strength generally exhibits a finite-size effect. We analyze the time history of AE energy distribution and accelerated seismic release (ASR) until catastrophic failures of the specimens. We find their time evolution towards failure resembles the observations from specimens containing a single fault and highly microstructurally disordered materials. We observe clear evidence that a size effect exists at small AE magnitude, where larger specimens tend to produce a higher proportion of smaller microcracks. However, the AE energy distribution is scale-independent at high energies. Near to failure, the power-law component of the AE energy population is almost stationary. The temporal evolution of the AE activity rate is independent of sample size; instead, there exist fast and slow periods of the AE activity rate that could be attributed to the stress heterogeneities around the fracture network. ASRs are exclusively observed in the AE activity rate and are more general in the lack of criticality. Our interpretation of observed foreshock activities at varying sample sizes in fractured media may have significance for understanding and predicting failures from natural hazards and engineering instabilities.

Biological sequences do not come at random. Instead, they appear with particular frequencies that reflect properties of the associated system or phenomenon. Knowing how biological sequences are distributed in sequence space is thus a natural first step toward understanding the underlying mechanisms. Here we propose a method for inferring the probability distribution from which a sample of biological sequences were drawn for the case where the sequences are composed of elements that admit a natural ordering. Our method is based on Bayesian field theory, a physics-based machine learning approach, and can be regarded as a nonparametric extension of the traditional maximum entropy estimate. As an example, we use it to analyze the aneuploidy data pertaining to gliomas from The Cancer Genome Atlas project. In addition, we demonstrate two follow-up analyses that can be performed with the resulting probability distribution. One of them is to investigate the associations among the sequence sites. This provides a way to infer the governing biological grammar. The other is to study the global geometry of the probability landscape, which allows us to look at the problem from an evolutionary point of view. It can be seen that this methodology enables us to learn from a sample of sequences about how a biological system or phenomenon in the real world works.

The pursuit of achieving the maximum output power in microscopic heat engines has gained increasing attention in the field of stochastic thermodynamics. We employ the optimal control theory to study Brownian heat engines and determine the optimal heat-engine cycles in a generic damped situation, which were previously known only in the overdamped and the underdamped limits. These optimal cycles include two isothermal processes, two adiabatic processes, and an extra isochoric relaxation process at the high stiffness constraint. Our results determine the maximum output power under realistic control constraints, and also bridge the gap of the optimal cycles between the overdamped and the underdamped limits. Hence, we solve an outstanding problem in the studies of heat engines by employing the optimal control theory to stochastic thermodynamics. These findings bring valuable insights for the design of high-performance Brownian heat engines in experimental setups.

The behavior of nonspherical particles in a shear flow is of significant practical and theoretical interest. These systems have been the object of numerous investigations since the pioneering work of Jeffery a century ago. His eponymous orbits describe the deterministic motion of an isolated, rodlike particle in a shear flow. Subsequently, the effect of adding noise was investigated. The theory has been applied to colloidal particles, macromolecules, anisometric granular particles, and most recently to microswimmers, for example, bacteria. We study the Jeffery orbits of elongated (uniaxial, prolate) particles subject to noise using Langevin simulations and a Fokker-Planck equation. We extend the analytical solution for infinitely thin needles ($\beta =1$) obtained by Doi and Edwards to particles with arbitrary shape factor ($0\le \beta \le 1$) and validate the theory by comparing it with simulations. We examine the rotation of the particle around the vorticity axis and study the orientational order matrix. We use the latter to obtain scalar order parameters $s$ and $r$ describing nematic ordering and biaxiality from the orientational distribution function. The value of $s$ (nematic ordering) increases monotonically with increasing Péclet number, while $r$ (measure of biaxiality) displays a maximum value. From perturbation theory, we obtain simple expressions that provide accurate descriptions at low noise (or large Péclet numbers). We also examine the orientational distribution in the v-grad $v$ plane and in the perpendicular direction. Finally, we present the solution of the Fokker-Planck equation for a strictly two-dimensional (2D) system. For the same noise amplitude, the average rotation speed of the particle in 3D is larger than in 2D.

Transport of an inertial Brownian particle in an oscillating potential is numerically investigated in the presence of an external constant force. The oscillating potential can break thermodynamic equilibrium. Within appropriate parameter regimes, the particle moves in a direction opposite to the constant force, which means that the system can exhibit the phenomenon of absolute negative mobility (ANM). Furthermore, it may be inferred from the bifurcation diagrams that ANM originates from chaotic-periodic transitions, where the particle subjected to a constant force performs reverse periodic motion due to continuous reverse driving by the oscillating potential. Based on GPU acceleration techniques, we present the distribution of ANM in the parameter space and analyze how the ANM depends on the system parameters. These results are robust in a wide range of parameters and may pave the way to the experimental realization of ANM.

Understanding actual transport mechanisms of self-propelled particles (SPPs) in complex elastic gels—such as in the cell cytoplasm, in in vitro networks of chromatin or of F-actin fibers, or in mucus gels—has far-reaching consequences. Implications beyond biology/biophysics are in engineering and medicine, with a particular focus on microrheology and on targeted drug delivery. Here, we examine via extensive computer simulations the dynamics of SPPs in deformable gellike structures responsive to thermal fluctuations. We treat tracer particles comparable to and larger than the mesh size of the gel. We observe distinct trapping events of active tracers at relatively short times, leading to subdiffusion; it is followed by an escape from meshwork-induced traps due to the flexibility of the network, resulting in superdiffusion. We thus find crossovers between different transport regimes. We also find pronounced nonergodicity in the dynamics of SPPs and non-Gaussianity at intermediate times. The distributions of trapping times of the tracers escaping from “cages” in our quasiperiodic gel often reveal the existence of two distinct timescales in the dynamics. At high activity of the tracers these timescales become comparable. Furthermore, we find that the mean waiting time exhibits a power-law dependence on the activity of SPPs (in terms of their Péclet number). Our results additionally showcase both exponential and nonexponential trapping events at high activities. Extensions of this setup are possible, with the factors such as anisotropy of the particles, different topologies of the gel network, and various interactions between the particles (also of a nonlocal nature) to be considered.

For statistical mechanical systems with continuous phase transitions, there are two closely related but subtly different mean-field treatments, the Gaussian fixed point (GFP) in the renormalization group framework and the Landau mean-field theory or the complete-graph (CG) asymptotics. By large-scale Monte Carlo simulations, we systematically study the interplay of the GFP and CG effects to the finite-size scaling of percolation above the upper critical dimension $d_c=6$ with periodic and cylindrical boundary conditions. Our results suggest that, with periodic boundaries, the unwrapped correlation length scales as $L^{d/6}$ at the critical point, diverging faster than $L$ above $d_c$. As a consequence, the scaling behaviors of macroscopic quantities with respect to the linear system size $L$ follow the CG asymptotics. The distance-dependent properties, such as the short-distance behavior of the two-point correlation function and the Fourier transformed quantities with nonzero modes, are still controlled by the GFP. With cylindrical boundaries, due to the interplay of the GFP and CG effects, the correlation length along the axial direction of the cylinder scales as ${\xi }_L\sim L^{(d-1)/5}$ within the critical window of size $O\left(L^{-2(d-1)/5}\right)$, distinct from periodic boundary. A field-theoretical calculation for deriving the scaling of ${\xi }_L$ is also presented. Moreover, the one-point surface correlation function along the axial direction of the cylinder is observed to scale as ${\tau }^{(1-d)/2}$ when the distance $\tau$ is short, but then enter a plateau of order $L^{-3(d-1)/5}$ before it decays significantly fast.

We investigate dynamics of a small quantum system open to a bath with thermostat. We introduce another bath, called a superbath, weakly coupled with the bath to provide it with a thermostat, which has either the Lindblad or Redfield type. We treat the interaction between the system and bath via a rigorous perturbation theory. Due to the thermostat, the bath behaves dissipative and stochastic, for which the usual Born-Markov assumption is not needed. We consider a specific example of a harmonic oscillator system of interest and a photonic bath in a large container, and a superbath of the Caldeira-Legget oscillators distributed on the inner surface of the container. After taking the trace over the superbath states, we use the $P$ representation for the total harmonic system of the system and bath. We derive the reduced time-evolution equation for the system by explicitly finding the correlation between the system and bath beyond the product state that was not obtainable in the previous theory for the system and bath isolated from environment, and marginalizing bath degrees of freedom. Remarkably, the associated dynamic equation for the system density matrix is of the same form as the Redfield master equation with different coefficients depending on thermostat used. We find the steady state does not depend on the thermostat but the time-dependent state does, which agrees with common expectation. We expect to apply our theory to general systems. Unlike the usual quantum master equations, our reduced dynamics allows investigation for time-dependent protocols, and nonequilibrium quantum stochastic dynamics will be investigated in the future.

We introduce a deep least action method (DLAM) rooted in the principle of least action to solve the trajectory of an evolution problem. DLAM offers an efficient unsupervised solution and can be applied once the action or Lagrangian of the concerned physical system is clear, totally avoiding the differential equations. As required by the least action principle, we incorporate a normalized deep neural network to exactly satisfy the initial-terminal value conditions; thus the evolution problem is transformed into an unconstrained optimization problem. We conduct systematic investigations, initially focusing on Newtonian dynamics modeled by ordinary differential equations. Subsequently, we move on to the wave dynamics modeled by partial differential equations, covering nonlinear, high-order, and high-dimensional cases in detail. Our results showcase the effectiveness of DLAM and illustrate its efficiency and accuracy.

The double distribution function approach is an efficient route toward an extension of kinetic solvers to compressible flows. With a number of realizations available, an overview and comparative study in the context of high-speed compressible flows is presented. We discuss the different variants of the energy partition, analyses of hydrodynamic limits, and a numerical study of accuracy and performance with the particles on demand realization. Out of three considered energy partition strategies, it is shown that the nontranslational energy split requires a higher-order quadrature for proper recovery of the Navier-Stokes-Fourier equations. The internal energy split, on the other hand, while recovering the correct hydrodynamic limit with fourth-order quadrature, comes with a nonlocal—both in space and time—source term that contributes to higher computational cost and memory overhead. Based on our analysis, the total energy split demonstrates the optimal overall performance.

This work delves into studying the synchronization in two realistic neuron models using Hodgkin-Huxley dynamics. Unlike simplistic pointlike models, excitatory synapses are here randomly distributed along the dendrites, introducing strong stochastic contributions into their signal propagation. To focus on the role of different synaptic locations, we use two copies of the same neuron whose synapses are located at different distances from the soma and activated by identical Poisson distributed pulses. The synchronization is investigated through a specifically defined spiking correlation function, and its behavior is analyzed as a function of several parameters: inhibition weight, distance from the soma of one synaptic group, weight and decay time constants of the excitatory synapses.

Processes under reset, where realizations are interrupted according to some stochastic rule and restarted from the initial state, find broad application in modeling physical, chemical, and biological phenomena and in designing search strategies. While a wealth of theoretical results has been recently obtained, current derivations tend to focus on specific processes, obscuring the general principles and preventing broad applicability. We present a unified approach to those observables of stochastic processes under reset that take the form of averages of functionals depending on the most recent renewal period. We derive general solutions, and determine the conditions for existence and equality of stationary values with and without reset. For intermittent (i.e., broadly distributed) reset times, we derive exact asymptotic expressions for observables that vary asymptotically as a power of time. We illustrate the general approach with results for occupation densities and moments of subdiffusive processes. We focus on subdiffusion-decay processes with microscopic dependence between transport and decay, where the probability of a random walker to be removed and subsequently restarted depends on the local transit times. In contrast to the uncoupled case, restarting the particle upon decay does not produce a probability current associated with restart equal to the decay rate, but instead drastically alters the time dependence of the decay rate and the resulting current due to memory effects associated with ageing. Our framework shows that such effects are independent of the specific microscopic details, uncovering the general impact of restart on occupation densities, spatial moments, and other quantities.

I study effects of $q$-order antinematic (${\mathrm{AN}}_q$) interactions on the critical behavior of the antiferromagnetic (AF) $XY$ model on a square lattice. It is found that the evolution of the phase diagram topology of such $\mathrm{AF}\text{−}{\mathrm{AN}}_q$ models with the parameter $q$ does not follow the same line as for the corresponding $\mathrm{FM}\text{−}{\mathrm{N}}_q$ models with the ferromagnetic (FM) and $q$-order nematic (${\mathrm{N}}_q$) interactions. Their phase diagrams are similar only for odd values of the parameter $q$. In such cases the respective phases reported in the $\mathrm{FM}\text{−}{\mathrm{N}}_q$ models are observed in the $\mathrm{AF}\text{−}{\mathrm{AN}}_q$ models on each of the two AF-coupled sublattices and the corresponding phase transitions are concluded to be of the same kind. On the other hand, for even values of $q$ the phase diagrams of the $\mathrm{AF}\text{−}{\mathrm{AN}}_q$ models are different from the $\mathrm{FM}\text{−}{\mathrm{N}}_q$ models and their topology does not change with $q$. Besides the pure AF and ${\mathrm{AN}}_q$ phases, observed at higher temperatures in the regions of the dominant respective couplings, at low temperatures there is a new canted (C)AF phase, which results from the competition between the AF and ${\mathrm{AN}}_q$ ordering tendencies and has no counterpart in the $\mathrm{FM}\text{−}{\mathrm{N}}_q$ model. The phase transitions to the CAF phase from both AF and ${\mathrm{AN}}_q$ phases appear to be of the Berezinskii-Kosterlitz-Thouless nature.