We present a detailed derivation of the Langevin dynamics obeyed by a massive rigid body immersed in a chiral active bath. We show how the antisymmetric nature of the noise leads to an unusual relationship between the Langevin equation describing stochastic trajectories and the Fokker-Planck equation governing the time evolution of the probability density. The chirality of the bath endows the object dynamics with odd diffusivity, odd mobility, and rotational ratchet effects that depend on the object symmetries. For rotationally symmetric objects, we show that a hidden time-reversal symmetry leads to separate effective equilibrium descriptions for the translational and rotational degrees of freedom. Finally, starting from the bath dynamics, we construct a multipole expansion to quadrupolar order that allows predicting the far-field current and density modulation induced by the object on the bath.

This study explores the effects of introducing a symmetry-breaking disorder on the dynamics of a system invariant under particle permutation. The disorder forces quantum states, confined to the $N+1$-dimensional completely symmetric space to penetrate the exponentially large $2^N$-dimensional Hilbert space of $N$ particles. In particular, we focus on the quantum kicked top as a Floquet system of $N$ qubits and use linear entropy, measuring single-qubit entanglement, to investigate the changes in the timescales and values of saturation when disorder is introduced. In the near-integrable regime of the kicked top, we study the robustness of quantum revivals to disorder. We also find that a classical calculation yields the quantum single-qubit entanglement to remarkable accuracy in the disorder-free limit. The disorder, on the other hand, is modeled in the form of noise, which again fits well with the numerical calculations. We measure the extent to which the dynamics is retained within the symmetric subspace and its spreading to the full Hilbert space using different quantities. We show that increasing disorder drives the system to a chaotic phase in full Hilbert space, as also supported by the spectral statistics. We find that there is robustness to disorder in the system, and this is a function of how chaotic the kicked top is.

We study long-term evolution of radiating quasi-$Q$-balls in $1+1$ dimensional models without mass threshold. Two different models are considered, the model with a rational modification of the usual $Q$-ball sextic potential and the model of a $Q$-ball in a box with outgoing boundary conditions. We find that the outgoing boundary conditions modify the angular frequency of quasi-$Q$-balls which becomes complex-valued. The quasi-$Q$-balls decay initially very similarly but, in the last stage, quasi-$Q$-balls in a box become linear resonances, whereas in the rationally modified model, they decay according to some power law.

Hemocytes migrate within Drosophila melanogaster embryos during their morphogenesis. The spatial distribution of the hemocytes reflects the emergent anatomy of the embryos. It poses a significant challenge to statistical characterization using conventional methods, such as mean-square displacements of tracks and Ripley's $L$ function. This challenge arises from the complex heterogeneity of hemocyte dynamics and the variability of the organism's anatomy due to inherent nonlinear stochastic processes. We apply topological data analysis (TDA) to three different genotypes of Drosophila embryos: wild type, $LanB{1}^{Df}$ (extracellular matrix mutants), and $SCA{R}^{\mathrm{\Delta }37}$ (motility mutants). Computationally efficient methods are developed to characterize the embryos' topologies. Based on the Wasserstein distances, the LanB1 mutant is topologically distinct from the wild type and SCAR mutant, which are indistinguishable. Furthermore, an increase in the Betti-1 number (the number of holes in the hemocyte configurations) is observed across all samples with age, which is consistent with prior findings on cellular tiling behavior due to contact inhibition of locomotion. We also apply TDA methods to the hemocyte tracks within the embryos, allowing the wild type and SCAR mutant to be distinguished. Computational topology thus provides a robust method to quantify the emergent anatomy of embryos that is well suited to the complex heterogeneous datasets observed with hemocyte dynamics.

We investigate the impact of disturbances on forest ecosystems by examining transient population dynamics in a controlled experiment carried out in a tropical rainforest. We first model the mean species abundance with a simple consumer-resource model, which is then extended into two multispecies frameworks for community dynamics: a neutral model, which emphasises the ability of any species to recover independently of the others; and a non-neutral one, where species interactions play an important role in reconstructing ecosystem's structure and patterns. The results indicate that, while both frameworks accurately describe correlation functions and mean-variance relations, the non-neutral model more effectively captures community structure as revealed by an evenness indicator. This suggests that interspecific interactions significantly influence the ecosystem's ability to respond to disturbances, providing deeper insights into the recovery dynamics of forest ecosystems.

Acoustic pressure nodes in acoustophoretic devices are crucial for applications in tissue engineering, cell analysis, and particle trapping. Typically, a single primary node forms at the half-wavelength resonance condition, with its shape and position constrained by the channel dimensions. The generation of additional nodes, along with control over their positions and shapes, is highly desirable in biomedical applications and could significantly enhance particle manipulation capabilities. To explore this potential, we numerically demonstrate the formation of additional, complex-shaped nodes, alongside the primary one, induced by a circular scatterer within a rectangular cavity. We identify three distinct types: ring, protuberant, and crescent nodes, whose formation depends on the scatterer's size, its relative placement, and the corresponding resonant frequency. Furthermore, we analyze the impact of the scatterer on acoustic pressure, acoustic energy, and the quality factor. We show that the emergence of additional nodes come at the cost of reduced acoustic pressure and energy in the channel. This study provides foundational insight into generating complex nodes in a standing-wave acoustic cavity at the fundamental frequency, offering new opportunities for noncontact particle and fluidic manipulation in acoustofluidic devices.

The mechanical properties of DNA nanotubes (DNTs) are of great significance for studying the structure and dynamic characteristics of polymer networks. However, this information remains limited due to complex microscale interactions, multiscale structural characteristics, undefined pretension states, and characterization challenges. This paper quantifies a multiscale correlation between the bending properties of DNT and its structure- and solution-dependent pretension states. Based on existing experimental results, DNT was reduced to a multidomain structure featuring multiple parallel micrometer-sized DNA rods and periodically arranged nanoscale crossovers, and its global bending properties were characterized by extending our multiscale tensile model to incorporate the local crossover effect. The results not only reveal the mechanism in the pretension-dependent bending properties of DNT, but also lay a theoretical foundation for predicting and customizing the mechanical properties of DNT via adjusting its pretension state.

Motivated by the concept of self-organized criticality and its link with the theory of random walks, distributions of returns are studied. In particular, distributions of returns for one-dimensional random walks, defined in discrete time and space, with jumps restricted to nearest neighbors and constant transition rates, are investigated. Explicit expressions are provided for certain parameter sets, and an integral representation is developed, with the asymptotic behavior rigorously characterized across different domain regions. It is shown that, in the symmetric case, the distribution of returns exhibits a universal asymptotic power-law decay with an exponent of $-3/2$, whereas deviations from symmetry introduce exponential corrections. These results are connected with nonadditive statistical mechanics by showing that a $q$-Gaussian fit would imply a nonadditively parameter $q=7/3$. The analysis provides an expression for the distribution of returns as a Stieltjes transform as well as a framework for understanding fat-tailed distributions of returns in discrete random walk models.

Neurons display spontaneous spiking (in the absence of stimulus signals) as well as a characteristic response to time-dependent external stimuli. In a simple but important class of stochastic neuron models, the integrate-and-fire model with Gaussian current noise, both aspects can mathematically be related via fluctuation-response relations (FRRs) as has been shown recently [B. Lindner, Phys. Rev. Lett. 129, 198101 (2022)]. Here we extend the class of FRRs to include the susceptibilities of the membrane voltage and subthreshold voltage nonlinearity as well as the power spectrum of the membrane voltage. For a simple but often considered IF model, the leaky IF model with white Gaussian noise, we exploit the FRRs and derive explicit expressions for the power spectrum and susceptibility of the subthreshold membrane voltage. We also put forward a relation between the response functions of the spike train and membrane voltage, a response-response relation (RRR) that holds true for a more general setting than considered in most parts of the paper. For the generalized IF model with an adaptation current and colored Gaussian noise, we derive an FRR and an RRR. We briefly discuss useful applications of the derived FRRs and RRRs.

Gene expression is a random and complex process involving multistep biochemical reactions. This process is commonly modeled by using a delay chemical master equation (DCME), which introduces delays to simplify the intermediate reaction steps. However, such a model is difficult to achieve the stationary analytical solution because it contains one or more joint probabilities. In this paper, we investigate a two-stage gene expression, consisting of an active or inactive promoter, mRNA degradation, RNA polymerase (RNAP) transcription with a delay due to the time interval from RNAP's initialization to the production of a mature RNA. Unlike previous DCME models of gene expression, we introduce a survival probability derived from the undelayed reactions to establish a new DCME model without the joint probabilities. Through our research, the exact stationary solution of this model is obtained, and numerical simulations for it demonstrate that the delay has a remarkable impact on the probability distribution of mRNA number, as well as on the mean and Fano factor of this distribution. Our results provide valuable insights into the study of stochastic delay gene expression.

It is well established that the brain spontaneously traverses through a very large number of states. Nevertheless, despite its relevance to understanding brain function, a formal description of this phenomenon is still lacking. To this end, we introduce a machine learning-based method allowing for the determination of the probabilities of all possible states at a given coarse graining, as well as the density of states, from which all the thermodynamics can be derived. This is a challenge not unique to the brain, since similar problems are at the heart of the statistical mechanics of complex systems. This paper provides a rigorous demonstration of the linear scaling of the entropies and energies of the brain states, a behavior first conjectured by Hagedorn to be typical at the limiting temperature at which ordinary matter disintegrates into quark matter. Equivalently, this establishes the thermodynamic origin of the Zipf law scaling underlying the appearance of a wide range of brain states. Based on our estimation of the density of states for large-scale functional magnetic resonance imaging (fMRI) human brain recordings, we observe that the brain operates asymptotically at the Hagedorn temperature. The presented approach is not only relevant to brain function but should be applicable to a wide variety of complex systems.

Polar regions are covered by sea ice, which can be seen as a thin solid elastic sheet with heterogeneous mechanical properties. The dynamics of deformation of a floating solid sheet is primarily governed by gravity, water density, and the flexural modulus, which depends on its mechanical properties, namely, the thickness, the Young modulus, and the Poisson ratio. Noninvasive methods from seismology can retrieve these three parameters from sheet deformation dynamics. In this article we develop another method to extract locally the flexural modulus of a floating thin elastic sheet from the spatiotemporal deformations of the sheet. We perform laboratory experiments to test the accuracy and the robustness of this method on silicon membranes of controlled mechanical properties. Using patches of different thicknesses and shapes, we eventually draw maps of sheet thickness, with a subwavelength spatial resolution.

This study investigates the ionization and excitation processes induced by electron impact between two configurations or superconfigurations. Rate coefficients are calculated for transition arrays or supertransition arrays rather than level-to-level transitions. Special attention is given to a series of oxygenlike ions relevant to inertial confinement fusion, specifically silicon, germanium, argon, and krypton. Calculations are performed over a wide temperature range, from 50 to 3000 eV. To facilitate the determination of rates at any temperature and ion charge, the computed rates are fitted with a two-dimensional Chebyshev polynomial expansion, yielding a set of coefficients for practical applications. Additionally, an extension of the Clenshaw algorithm to two dimensions, using the Chebyshev coefficients, is proposed to address numerical challenges and enhance computational efficiency.

The paper addresses the dynamics of solitary waves in binary complex plasmas, focusing on charge diagnostics for dust particles and its relevance for plasma research, space physics, and fusion applications. The paper uses the reductive perturbation method to derive the Korteweg–de Vries equation for dust acoustic solitary waves in binary complex plasmas. The model successfully explains the phenomena observed in the experiment. Dependence of the amplitude, the width, and the speed of a solitary wave on the plasma parameters are given. Furthermore, a significant breakthrough is the development of a novel charge diagnostic method based on dust acoustic wave speed in binary complex plasmas. This method can be directly tested in a modified gaseous electronics conference plasma chamber and in the Plasmakristall-4 laboratory on the International Space Station under microgravity, providing feasible pathways for experimental validation and future applications. An extended analysis including non-Maxwellian distributions, arbitrary-amplitude solitary structures, spatial inhomogeneity, and dust charging variation further confirms the validity of the dusty plasma fluid model and its relevance to realistic plasma environments.

Many motile microorganisms and biomimetic microparticles have been successfully modeled as active rods—elongated bodies capable of self-propulsion. A hallmark of active rod dynamics under confinement is their tendency to accumulate at the walls. Unlike passive particles, which typically sediment and cease their motion at the wall, accumulated active rods continue to move along the wall, reorient, and may even escape from it. In addition to boundary accumulation, active rods also exhibit upstream swimming and a tendency to concentrate in regions of high boundary curvature. The dynamics of active rods at the wall and those away from it result in complex and nontrivial distributions. In this work, we examine how wall curvature and extruding fluid flow affect the distribution of active rods by studying elliptical perturbations of tubelike three-dimensional microchannels, that is, cylindrical confinements with circular cross-sections that are common in both natural systems and practical applications. We develop a computational model for individual active rods and, through both analytical methods and Monte Carlo simulations, investigate how their accumulation distribution depends on the background flow, rotational diffusion, and the cross-sectional aspect ratio. Additionally, we examined the role of wall torque on accumulated active rods. While it promotes escape by aligning rods tangentially along flat walls, we showed, both theoretically and numerically, that stable entrapment can occur at regions of high curvature despite this torque.

We present a numerical study, based on the lattice Boltzmann method, of nematic liquid crystals flowing in microfluidic channels. We show that disclination lines are generated by the interaction between flow and anchoring conditions of the channel walls. In particular, we observe nucleations of pairs of twist disclinations in those regions of the channel where the elastic aligning forces, resulting from the anchoring conditions, are perpendicular to the local shear plane of the flow. The newly formed disclinations either persist or annihilate, depending on the overall configuration of the director field in the channel. We study the behavior at boundaries between different anchoring conditions and describe the formation of flow-induced disclination arcs. We show that the numerical model correctly reproduces the results of an experimental study [Agha and Bahr, Soft Matter 12, 4266 (2016)], thereby validating our numerical results.

Motility-induced phase separation (MIPS) is a paradigmatic nonequilibrium transition in active matter, determined by the Péclet number and packing fraction. We investigate the single-phase and phase-separated regimes of MIPS using a complex network approach, where networks are constructed from particle interactions over finite time windows. In the single-phase (gas-like) regime, the degree distributions $P\left(k\right)$ exhibit Gaussian behavior and resemble those of random graphs. Plotting the location and height of the $P\left(k\right)$ peak reveals a universal curve across different Péclet numbers at fixed packing fraction. In the phase-separated regime, we analyze the dense and dilute phases independently. The $P\left(k\right)$ distributions unveil distinct collective dynamics, including gas-like behavior in the dense phase and the emergence of active solid-like structures at longer times. Clustering coefficients and average path lengths in both phases stabilize rapidly, indicating that short simulations are sufficient to capture essential network features. Overall, our results show that network metrics expose both universal and phase-specific aspects of active matter dynamics. Notably, we identify distinct and previously unreported topological structures arising in the dense and dilute phases within the MIPS regime.

By employing Monte Carlo simulations, we investigate the isotropic Heisenberg system model on a simple cubic lattice with short-range interactions, allowing the system to evolve toward a steady state under the influence of competition between Glauber and Kawasaki dynamics. With probability $q$, the system is in contact with a thermal reservoir at temperature $T$ and evolves toward the lower energy state through Glauber dynamics. However, with probability $1-q$, the system is subjected to an external energy flux that drives it toward the higher energy state through Kawasaki dynamics. By analyzing the phase diagram of $T$ versus $q$, our findings show: (i) second-order phase transitions at high $q$ and intermediate $T$ values and first-order phase transitions below the tricritical point at $(q_t,T_t)=(0.615\pm 0.004,0.905\pm 0.001)$, and (ii) the phenomenon of unstable self-organization in the system in which the antiferromagnetic phase is only found at $q=0$ with an initial antiferromagnetic state; however, as $q$ increases at low temperatures, the system evolves to the ordered ferromagnetic phase.

Quantum walks play a crucial role in quantum algorithms and computational problems. Many-body quantum walks can reveal and exploit quantum correlations that are unavailable for single-walker cases. Studying quantum walks under noise and dissipation, particularly in multiwalker systems, has significant implications. In this context, we use a thermodynamically consistent formalism of dissipation modeling, namely the steepest entropy ascent (SEA) formalism. We analyze two spinless fermionic continuous-time walkers on a one-dimensional graph with tunable Hubbard and extended Hubbard-like interactions. By contrasting SEA-driven dynamics with unitary evolution, we systematically investigate how interaction strengths modulate thermalization and entropy production. Our findings highlight the relevance of the SEA formalism in modeling nonlinear dissipation in many-body quantum systems and its implications for quantum thermalization.