1-alkanols are well known to have anesthetic and penetration properties, though the mode of operation remains enigmatic. We perform extensive atomistic molecular dynamics simulation to study the penetration of 1-alkanols of different chain lengths in the dioleoyl-phosphatidylcholine (DOPC) bilayer model membrane. Our simulations show that the depth of penetration of 1-alkanol increases with chain length, $n$, and the deuterium order of the DOPC tail decreases with the chain length of the acyl-chain of the 1-alkanol. We find a cutoff value for the length of the acyl-chain of 1-alkanol, $n=12$, where 1-alkanol with a chain length greater than the cutoff value takes longer to penetrate the membrane. Our simulation study also demonstrates that the membrane exhibits clusters of 1-alkanols with acyl chains longer than the cutoff value, whereas 1-alkanols with acyl-chain shorter than the cutoff value are distributed homogeneously in the membrane and penetrate the membrane in a shorter time than longer-acyl-chain 1-alkanols. These findings add to our understanding of the anomalies in anesthetic molecule partitioning in the cell membrane and may have implications for general anesthesia.

The vertex model with homogeneous cell properties is known to exhibit a parameter degeneracy in which the system's dynamics is independent of the target area. Here, we show, for the heterogeneous vertex model where cells differ in size and stiffness, that degeneracy is also present with the average product of target areas and stiffness becoming dynamically irrelevant. Fixing this quantity is equivalent to fixing the global internal tissue pressure. Unless properly treated, this degeneracy undermines the physical relevance of key observables' numerical values, such as cell target shape index, cell pressure, and cell stress tensor. We present methods to resolve the degeneracy and to correctly set the gauge pressure via symmetry transformations applied to the cells' target areas. We further demonstrate that the degeneracy is removed under certain boundary conditions and partially lifted when spherical tissues are modeled using a locally planar approximation, leading to numerical consequences when fitting model parameters to experimental data. The approach extends beyond vertex models and provides a framework for testing whether the parameter spaces of other physical models are free from degeneracy.

The sorting of cell mixtures is fundamental to biological processes such as embryonic development, wound healing, and cancer metastasis. Previous studies have overlooked the unique nonmotile activities of cells, such as self-pulsating. In a 2D bidisperse confluent biological tissue lacking heterogeneous tension, whether the difference in self-pulsation activity alone can drive cell spontaneous separation, remains an open question. We numerically investigated this issue using a Voronoi-based model and observed robust large-scale demixing within appropriate parameter ranges. The essence is that the self-pulsation intensity disparity leads to differences in cell rigidity, which in turn results in single selectivity at the interpenetrating interface between heterogeneous cells. As the self-pulsation intensity disparity increases, the degree of demixing first increases and then stabilizes. Moderate fluidity, self-pulsation frequency, and thermal fluctuations are also important conditions for large-scale demixing. Our study contributes to a deeper understanding of the inducing factors and core mechanisms of cell sorting in confluent tissues and provides theoretical support for subsequent experiments.

Bacteria benefit from cellular heterogeneity: cells differentiate into diverse gene expression states. As colonies grow, cellular phenotypes arrange into spatial patterns. To uncover the functional role of these emergent patterns, we must understand how they arise from cellular growth and mechanical interactions. Here we present a simple, agent-based model to predict patterns of motile and extracellular matrix-producing cells in biofilms of Bacillus subtilis. By incorporating phenotypic inheritance, mechanical interactions, and peripheral motile cell dispersal, our model predicts the emergence of a pattern: matrix cells surround a fractal-like interior motile population. We find that, while some properties of the motile-matrix interface depend on initial conditions, the motile distribution at large radii depends solely on the model's growth mechanism. The phenotypic interface exhibits a fractal dimension that increases as biofilms grow but reaches a maximum as the peripheral layer of matrix cells exceeds the capacity of the inner cells to push it out of the way. By varying parameters, we find correlations between the interface fractal dimension and expansion of motile cells. We validate findings using experiments on B. subtilis biofilms in microfluidics. Our model demonstrates the emergence of colony-level phenotypes from single cell-level interactions and cells modifying their own environment.

Active particles are nonequilibrium entities that uptake energy and convert it into self-propulsion. A dynamically rich class of inertial active particles having features of wave-particle coupling and wave memory are walking/superwalking droplets. Such classical, active wave-particle entities (WPEs) have previously been shown to exhibit hydrodynamic analogs of many single-particle quantum systems. Inspired by the rich dynamics of strongly interacting superwalking droplets in experiments, we numerically investigate the dynamics of WPE clusters using a stroboscopic model. We find that several interacting WPEs self-organize into a stable bound cluster, reminiscent of an atomic nucleus. This active cluster exhibits a rich spectrum of collective excitations, including shape oscillations and chiral rotating modes, akin to vibrational and rotational modes of nuclear excitations, as the spatial extent of the waves and their temporal decay rate (memory) are varied. Dynamically distinct excitation modes create a common time-averaged collective wave field potential, bearing qualitative similarities with the nuclear shell model and the bag model of hadrons. For high memory and rapid spatial decay of waves, the active cluster becomes unstable and disintegrates; however, within a narrow regime of the parameter space, the cluster ejects single particles whose decay statistics follow exponential laws, reminiscent of radioactive nuclear decay. Our study uncovers a rich spectrum of dynamical behaviors in clusters of active particles, opening new avenues for exploring hydrodynamic quantum analogs in active matter systems.

We use the Kac-Rice formula and results from random matrix theory to obtain the average number of critical points of a family of high-dimensional empirical loss functions, where the data are correlated $d$-dimensional Gaussian vectors, whose number has a fixed ratio with their dimension. The correlations are introduced to model the existence of structure in the data, as is common in current machine learning systems. Under a technical hypothesis, our results are exact in the large-$d$ limit, and characterize the annealed landscape complexity, namely the logarithm of the expected number of critical points at a given value of the loss. We first address in detail the landscape of the loss function of a single perceptron and then generalize it to the case where two competing datasets with different covariance matrices are present, with the perceptron seeking to discriminate between them. The latter model can be applied to understand the interplay between adversity and nontrivial data structures. For completeness, we also treat the case of a loss function used in training generalized linear models in the presence of correlated input data.

In the high persistence regime of noninertial active Brownian particles (ABPs), polarization becomes a relevant dynamical field. Based on a recently proposed kinetic description for ABPs, we derive Navier-Stokes-like equations for the density and polarization fields in this regime. Using the Chapman–Enskog method, all transport coefficients in the equations are obtained entirely in terms of the microscopic dynamics. A linear stability analysis of the homogeneous and isotropic state shows that the derived equations correctly describe the density instability associated to the motility induced phase separation. Numerical solutions of the equations in one spatial dimension show the need for an additional regularizing pressure term to saturate the system at high densities. With the inclusion of this term, the solutions illustrate the clustering dynamics in detail, with the formation of polarized regions at the interfaces, and the subsequent coarsening of domains, as well as particle accumulation in presence of gravity. Finally, the derived equations imply that, as an effect of the coupling with the polarization, damped density wave modes appear in the system, which were verified with numerical simulations.

Why are human societies unstable? Theories based on the observation of recurring patterns in historical data indicate that economic inequality, as well as social factors, are key drivers. So far, models of this phenomenon are more macroscopic in nature. However, basic mechanisms at work could be accessible to minimal mathematical models. Here, we combine a simple mechanism for economic growth with a mechanism for the spreading of social dissatisfaction. Broad wealth distributions generated by the economic mechanism eventually trigger social unrest and the destruction of wealth, leading to an emerging pattern of boom and bust. We find that the model time scales compare well with empirical data. The model emphasizes the role of broad (power law) wealth distributions for dynamical social phenomena.

In eukaryotic cells, the nucleolus is a pivotal subnuclear organelle, instrumental in ribosomal RNA synthesis and nuclear organization. Although the unique viscoelastic properties of the nucleolus are associated with transient interactions between chromatin and regulatory proteins, the specific mechanistic details driving nucleolar phase separation and mechanical responses have remained largely undefined. In this study, we employ a computational approach to elucidate chromatin-protein interactions within the nucleolus of budding yeast, using a sophisticated bead-spring polymer model. This model integrates DNA and nucleolar architectures with dynamic simulations of interactions involving chromosomal structural maintenance proteins and rDNA transcriptional regulators through systematically varied cross-linking kinetics. Our findings reveal that modulations in protein-DNA interactions critically dictate the phase behavior, relaxation dynamics, and viscoelastic properties of the nucleolus, underscoring a complex but precise regulatory mechanism at play. Notably, protein-mediated bridging emerges as a critical factor enhancing nucleolar condensation and modulating stress relaxation, highlighting the transformative role of transient cross-linking in nuclear mechanics regulation. These insights not only deepen our understanding of nucleolar function but also open avenues for interventions in genetic engineering and disease therapeutics.

Disordered network materials abound in both nature and synthetic situations while rigorous analysis of their nonlinear mechanical behaviors remains challenging. The purpose of this paper is to connect the mathematical framework of the sweeping process originally proposed by Moreau to the generic class of lattice spring models that incorporate plasticity. We derive the equations of quasistatic evolution of an elastic–perfectly plastic lattice and relate them to concepts from rigidity theory and structural mechanics. Then we explicitly construct a sweeping process and provide numerical schemes to find the evolution of stresses in the model. In particular, we develop a highly efficient “leapfrog” computational framework that allows us to rigorously track the progression of plastic events in the system based on the sweeping process theory. The utility of our framework is demonstrated by analyzing the elastoplastic stresses in a novel class of disordered network materials exhibiting the property of hyperuniformity, in which the (normalized) infinite-wavelength density fluctuations associated with the distribution of network nodes are completely suppressed. We find enhanced mechanical properties such as increasing stiffness, yield strength, and tensile strength as the degree of hyperuniformity of the material system increases. Our results have implications for optimal network material design and our event-based framework can be readily generalized to nonlinear stress analysis of other heterogeneous material systems.

To probe the limits of dynamic thermalization, we numerically investigate the stability of exceptional periodic classical trajectories in chaotic many-spin systems and explore a possible connection between these trajectories and exceptional nonthermal quantum eigenstates known as “quantum many-body scars.” The systems considered are chaotic spin chains with short-range interactions, both classical and quantum. On the classical side, the chosen periodic trajectories are such that all spins instantaneously point in the same direction, which evolves as a function of time. We find that the largest Lyapunov exponents characterizing the stability of these trajectories have surprisingly strong and nontrivial dependencies on the interaction constants and chain lengths. In particular, we identify rather long spin chains, where the above periodic trajectories are Lyapunov stable on many-body energy shells overwhelmingly dominated by chaotic motion. We show that the above phenomenology can be quantitatively described by connecting Lyapunov instabilities of translationally invariant periodic trajectories to irreducible representations of the translational symmetry group with well-defined wave vectors. We also find that instabilities around periodic trajectories in modestly large spin chains develop into a transient nearly quasiperiodic nonergodic regime. In some cases, the lifetime of this regime is extremely long, which we interpret as a manifestation of Arnold diffusion in the vicinity of integrable dynamics. On the quantum side, we numerically investigate the dynamics of quantum states starting with all spins initially pointing in the same direction: These are the quantum counterparts of the initial conditions for the above periodic classical trajectories. Our investigation reveals the existence of quantum many-body scars for numerically accessible finite chains of spins-3/2 and higher. No evidence of quantum scars was observed for spin-1/2 chains, while spin-1 chains were found to be transitional in this respect. The dynamic thermalization process dominated by quantum scars is shown to exhibit a slowdown in comparison with generic thermalization at the same energy. Finally, we identify quantum signatures of the proximity to a classical separatrix of the periodic motion.

In this work, we study a prototypical, experimentally accessible scenario that enables the systematic generation of so-called high-order rogue waves in atomic Bose-Einstein condensates. These waveforms lead to significantly and controllably more extreme focusing events than the famous Peregrine soliton. In one spatial dimension, we showcase conclusive numerical evidence that our scheme generates the focusing behavior associated with the first four rogue waves from the relevant hierarchy. We then extend considerations to anisotropic two-dimensional and even three-dimensional settings, establishing that the scheme can generate second-order rogue waves despite the well-known limitation of finite-time blow up of focusing nonlinear Schrödinger equations.

The kicked rotor (KR) is perhaps the simplest physical model to illuminate the transition from regular to chaotic motion in classical mechanics. It is also widely applied as a model of light-matter interactions. In the conventional treatment, the infinitesimal width of each kick allows an immediate integration of the equations of motion. This in turn allows a full description of the dynamics via a discrete mapping, the standard map, if one looks at the dynamics only stroboscopically. In this work, we present a generalized kicked rotor (GKR) model with finite-width periodic forcing. We derive a family of maps that depend on the parameter shift $\tau$, valid for small to intermediate kick strength $K$ and width $\mathrm{\Delta }$, that allows one to capture the motion in both the driven and kicked regimes. The fixed points and symmetry of the mapping are shown analytically to depend on the value of the shift parameter, but the structure of regular vs chaotic motion is unaffected. We then formulate a series of higher-order corrections (HGKR) that extends the mapping to large $K$ and $\mathrm{\Delta }$. The HGKR mapping is in excellent agreement with full numerical results. We observe momentum localization for sufficiently large $K$ and $\mathrm{\Delta }$, an effect whose physical origin can be understood from the analytic structure of the mapping equations.

We study the susceptible-infected-susceptible (SIS) model on directed complex networks within the quenched mean-field approximation. Combining results from random matrix theory with an analytic approach to the distribution of fixed-point infection probabilities, we derive the phase diagram and show that the model exhibits a nonequilibrium phase transition between the absorbing and endemic phases for $c\ge {\lambda }^{-1}$, where $c$ is the mean degree and $\lambda$ is the average infection rate. Interestingly, the critical line is independent of the degree distribution but is highly sensitive to the form of the infection-rate distribution. We further show that the inverse participation ratio of infection probabilities diverges near the epidemic threshold, indicating that the disease may become localized on a small fraction of nodes. These results provide a systematic characterization of how network heterogeneities shape epidemic spreading on directed contact networks within the quenched mean-field approximation.

Swarms, such as schools of fish or drone formations, are prevalent in both natural and engineered systems. While previous works have focused on the social interactions within swarms, the role of external perturbations–such as environmental changes, predators, or communication breakdowns–in affecting swarm stability is not fully understood. Our study addresses this gap by modeling swarms as graphs and applying graph signal processing techniques to analyze perturbations as signals on these graphs. By examining predation, we uncover a detectability-durability trade-off, demonstrating a tension between a swarm's ability to evade detection and its resilience to predation, once detected. We provide theoretical and empirical evidence for this trade-off, explicitly tying it to properties of the swarm's spatial configuration. Toward task-specific optimized swarms, we introduce SwaGen, a graph neural network-based generative model. We apply SwaGen to resilient swarm generation by defining a task-specific loss function, optimizing the contradicting trade-off terms simultaneously. With this, SwaGen reveals unique spatial configurations, optimizing the trade-off at both ends. Applying the model can guide the design of robust artificial swarms and deepen our understanding of natural swarm dynamics.

The study of bubble dynamics in gas-liquid two-phase flow plays an important role in such fields as chemical engineering, hydraulic engineering, and aerospace. In this research, we consider the multibubble coalescence behaviors in still water, based on a machine learning approach combining data with physical constraints, namely, physics-informed neural networks (PINNs). Given the significant changes of different physical quantities including the velocity, pressure, and volume fraction during coaxial bubble coalescence, we develop a modified PINNs framework with multistage augmented Lagrangian terms (MSAL-PINNs) to capture the process of bubble rising, merging, and breaking. We first consider the corresponding penalty terms in different stages to improve the prediction accuracy of the model. We simulate the scenario of double-bubble coalescence. We further extend the cases to the breakup, different radii, and multibubble interactions. Finally, we explore the performance of the model to extrapolate in the parameter domain ($\sigma$) as well as the time domain. The results show that the MSAL-PINNs perform well in both aspects. The proposed framework in solving bubble dynamics is validated at both qualitative and quantitative levels, through comparing with computational fluid dynamics and related PINN methods. Our results provide new insights for the intelligent exploration of complex bubble dynamics in gas-liquid two-phase flow.

We conduct standard dimensional analysis (Vaschy-Buckingham $\mathrm{\Pi }$ theorem) for the mean avalanche size $\langle s\rangle$ when particles flow through, and clog at, a small orifice on the base of a flat-bottomed silo. We consider the effect of particle diameter $d$, orifice diameter $D$, particle density $\rho$, particle Young's modulus $E$, and acceleration of gravity $g$. We both perform discrete element method simulations and compile available data in the literature in order to sample the parameter space. We find that our simulations and data across many experiments and simulations of frictional grains are consistent with the scaling equation $ln(\langle s\rangle +1)=A_{\alpha }[{(D/d)}^{\alpha }-1]+B_{\alpha }\sqrt{\frac{\rho gd}{E}\phantom{{}^1}}$, where $A_{\alpha }$ and $B_{\alpha }$ are empirical constants and $\alpha$ is the dimensionality of the system ($\alpha =2$ and $\alpha =3$ for two dimensions and three dimensions, respectively). This expression successfully synthesizes the clogging behavior of a number of related clogging systems and motivates future extensions to more complex configurations involving, for example, very low friction particles or external vibrations.