Adhesion dynamics of cells is of great value to biological systems and adhesion-based biomedical applications. Although adhesion of a single cell or capsule has been widely studied, physical insights into the adhesion dynamics of aggregates containing two or more cells remain elusive. In this paper, we numerically investigate the dynamic adhesion of a deformable cell pair to a flat substrate under shear flow. Specifically, the immersed boundary–lattice Boltzmann method is utilized as the flow solver, and the stochastic receptor-ligand kinetics model is implemented to recover cell-substrate and cell-cell adhesive interactions. Special attention is paid to the roles of the cell deformability and adhesion strengths in cellular motion. Four distinct adhesion states, namely, rolling, tumbling, firm adhesion, and detachment, are identified and presented in phase diagrams as a function of the adhesion strengths for cell pairs with different deformabilities. The simulation results suggest that both the cell-cell and cell-substrate adhesion strengths act as the resistance to the rolling motion, and dominate the transition among various adhesion states. The cell deformability not only enhances the resistance effect, but also contributes to detachment or fast tumbling of the cell pair. These findings enrich the understanding of adhesion dynamics of cell aggregates, which could shed light on complex adhesion processes and provide instructions in developing adhesion-based applications.

We investigate opportunities and challenges for improving unsupervised machine learning using four common strategies with a long history in physics: divide and conquer, Occam's razor, unification, and lifelong learning. Instead of using one model to learn everything, we propose a paradigm centered around the learning and manipulation of theories, which parsimoniously predict both aspects of the future (from past observations) and the domain in which these predictions are accurate. Specifically, we propose a generalized mean loss to encourage each theory to specialize in its comparatively advantageous domain, and a differentiable description length objective to downweight bad data and “snap” learned theories into simple symbolic formulas. Theories are stored in a “theory hub,” which continuously unifies learned theories and can propose theories when encountering new environments. We test our implementation, the toy “artificial intelligence physicist” learning agent, on a suite of increasingly complex physics environments. From unsupervised observation of trajectories through worlds involving random combinations of gravity, electromagnetism, harmonic motion, and elastic bounces, our agent typically learns faster and produces mean-squared prediction errors about a billion times smaller than a standard feedforward neural net of comparable complexity, typically recovering integer and rational theory parameters exactly. Our agent successfully identifies domains with different laws of motion also for a nonlinear chaotic double pendulum in a piecewise constant force field.

In this Rapid Communication, the Rayleigh-Taylor instability (RTI) along the density interfaces of gravity current fronts is analyzed. Both the location and the spanwise wave number of the most unstable mode determined by the local dispersion relation agree with those of the strongest perturbation obtained from numerical simulations, suggesting that the original formation mechanism of lobes and clefts at the current front is RTI. Furthermore, the predictions of the semi-infinite RTI model, i.e., the original dominating spanwise wave number of the Boussinesq current substantially depends on the Prandtl number and has a 1/3 scaling law with the Grashof number, are confirmed by the three-dimensional numerical simulations.

We present a theoretical study on pattern formation occurring in miscible fluids reacting by a second-order reaction $A+B\to C$ in a vertical Hele-Shaw cell under constant gravity. We have recently reported that the concentration-dependent diffusion of species coupled with a frontal neutralization reaction can produce a multilayer system where low-density depleted zones could be embedded between the denser layers. This leads to the excitation of chemoconvective modes spatially separated from each other by a motionless fluid. In this Rapid Communication, we show that the layers can interact via a diffusion mechanism. Since diffusively coupled instabilities initially have different wavelengths, this causes a long-wave modulation of one pattern by another. We have developed a mathematical model which includes a system of reaction-diffusion-convection equations. The linear stability of a transient base state is studied by calculating the growth rate of the Lyapunov exponent for each unstable layer. Numerical simulations supported by phase portrait reconstruction and Fourier spectra calculation have revealed that nonlinear dynamics consistently passes through (i) a perfect spatially periodic system of chemoconvective cells, (ii) a quasiperiodic system of the same cells, and (iii) a disordered fingering structure. We show that in this system, the coordinate codirected to the reaction front paradoxically plays the role of time, time itself acts as a bifurcation parameter, and a complete spatial analog of the two-frequency torus breakup is observed.

This work presents a nonequilibrium statistical-thermodynamic approach to the study of a Fröhlich-Bose-Einstein condensation of magnons under radio-frequency radiation pumping. Fröhlich-Bose-Einstein condensates display a complex behavior consisting in steady-state conditions to the emergence of a synergetic dissipative structure resembling the Bose-Einstein condensation of systems in equilibrium. Then a kind of “two-fluid model” arises: the “normal” nonequilibrium structure and the Fröhlich condensate, which is shown to be an attractor to the system. In this study we analyze some aspects of the irreversible thermodynamics of this dissipative complex system. We obtained the expression for the informational entropy of the two-fluid condensate and introduced an order parameter to characterize the role of the Fröhlich interaction in ordering the system. The analysis highlights the order increase due to the Fröhlich interaction. We also study the informational entropy production of the system, considering its internal and external parts. Finally, the Glansdorff-Prigogine criteria for evolution and (in)stability are verified.

We show that the only solutions of the Thouless-Anderson-Palmer (TAP) equations for the Sherrington-Kirkpatrick model of Ising spin glasses which can be found by iteration are those whose free energy lies on the border between replica-symmetric and broken-replica-symmetric states, when the number of spins $N$ is large. Convergence to this same borderline also happens in quenches from a high-temperature initial state to a locally stable state where each spin is parallel to its local field; both are examples of self-organized criticality. At this borderline the band of eigenvalues of the Hessian associated with a solution extends to zero, so the states reached have marginal stability. We have also investigated the factors which determine the free-energy difference between a stationary solution corresponding to a saddle point and its associated minimum, which is the barrier which has to be surmounted to escape from the vicinity of a TAP minimum or pure state.

Emergence of distinct collective dynamical states in the two smallest populations of nonlinear oscillators with global coupling among them is delineated. In particular, considering four oscillators constituting two populations of two oscillators each, we show the emergence of local chimera, global chimera, and global amplitude chimera states by breaking the permutation symmetry within the populations, in addition to the local synchronized and global synchronized states. Further, the symmetry breaking facilitates the onset of local chimera accompanied by the anomalous synchronization even with an identical nonisochronicity parameter in contrast to the existing literature. Furthermore, the spread of local synchronized and local chimera states is found to increase upon increasing the frequency difference among the populations, while the spread of local chimera, global chimera, and global amplitude chimera states increases for larger values of the nonisochronicity parameter. In addition, we have also deduced the stability condition for the global synchronized state using both the amplitude and its phase model, and find that the global synchronized state attains stability even for smaller values of the coupling strength for the amplitude model when compared to its phase reduced model.

Will a large economy be stable? Building on Robert May's original argument for large ecosystems, we conjecture that evolutionary and behavioural forces conspire to drive the economy towards marginal stability. We study networks of firms in which inputs for production are not easily substitutable, as in several real-world supply chains. Relying on results from random matrix theory, we argue that such networks generically become dysfunctional when their size increases, when the heterogeneity between firms becomes too strong, or when substitutability of their production inputs is reduced. At marginal stability and for large heterogeneities, we find that the distribution of firm sizes develops a power-law tail, as observed empirically. Crises can be triggered by small idiosyncratic shocks, which lead to “avalanches” of defaults characterized by a power-law distribution of total output losses. This scenario would naturally explain the well-known “small shocks, large business cycles” puzzle, as anticipated long ago by Bak, Chen, Scheinkman, and Woodford.

The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing a general framework using a method based on topological data analysis. By considering the diffusion process at a single specified timescale in a network, we map the network nodes to a finite set of points that contains the topological information of the network at a single scale. Subsequently, we study the shape of these point sets over variable timescales that provide scale-variant topological information, to understand the varying topological scales and the complex interactions in the network. We conduct experiments on synthetic and real-world data to demonstrate the effectiveness of the proposed framework in identifying network models, classifying real-world networks, and detecting transition points in time-evolving networks. Overall, our study presents a unified analysis that can be applied to more complex network structures, as in the case of multilayer and multiplex networks.

Compared with the classical Kendall's model to analyze the steady-state peeling behavior of an infinite length film attaching to a rigid substrate, this paper establishes a model of a finite length thin film adhering on a rigid substrate and analyzes the influence of film's initial adhesion length, film stiffness, and initial cantilever length of films on the whole interface peeling behavior. Both theoretical prediction and finite element calculation are carried out. The typical relationship between the peeling force and the separation distance at the loading point is obtained as well as the morphology of deformed films. It is found that the initial adhesion length has a significant effect on the peeling behavior. Differently from the case of infinite thin films, whether the steady-state peeling process can be achieved or not depends on the film's adhesion length. If the film is long enough, the whole peeling process can be divided into an initial peeling stage, a transition stage, a steady-state stage, and an unstable peeling stage. The maximum peeling force of the interface does not necessarily occur in the steady-state stage, which is influenced by the film's initial adhesion length, film stiffness, and initial cantilever length. The results achieved in this paper can not only provide a systematic understanding of peeling behavior of a thin film on a rigid substrate, but also be helpful for the design of high-quality interface and peeling tests in practical applications.

A conservative discrete velocity method (DVM) is developed for the ellipsoidal Fokker-Planck (ES-FP) equation in prediction of nonequilibrium neutral gas flows in this paper. The ES-FP collision operator is solved in discrete velocity space in a concise and quick finite difference framework. The conservation problem of the discrete ES-FP collision operator is solved by multiplying each term in it by extra conservative coefficients whose values are very close to unity. Their differences to unity are in the same order of the numerical error in approximating the ES-FP operator in discrete velocity space. All the macroscopic conservative variables (mass, momentum, and energy) are conserved in the present modified discrete ES-FP collision operator. Since the conservation property in a discrete element of physical space is very important for the numerical scheme when discontinuity and a large gradient exist in the flow field, a finite volume framework is adopted for the transport term of the ES-FP equation. For $nD-3V$ ($n<3$) cases, a $nD$-quasi $nV$ reduction is specifically proposed for the ES-FP equation and the corresponding FP-DVM method, which can greatly reduce the computational cost. The validity and accuracy of both the ES-FP equation and FP-DVM method are examined using a series of $0D-3V$ homogenous relaxation cases and $1D-3V$ shock structure cases with different Mach numbers, in which $1D-3V$ cases are reduced to $1D$-quasi $1V$ cases. Both the predictions of $0D-3V$ and $1D-3V$ cases match well with the benchmark results such as the analytical Boltzmann solution, direct full-Boltzmann numerical solution, and DSMC result. Especially, the FP-DVM predictions match well with the DSMC results in the Mach 8.0 shock structure case, which is in high nonequilibrium, and is a challenge case of the model Boltzmann equation and the corresponding numerical methods.

We discuss effects of pairwise aligning interactions in an ensemble of central place foragers or of searchers that are connected to a common home. In a wider sense, we also consider self-moving entities that are attracted to a central place such as, for instance, the zooplankton Daphnia being attracted to a beam of light. Single foragers move with constant speed due to some propulsive mechanism. They explore at random loops the space around and return rhytmically to their home. In the ensemble, the direction of the velocity of a searcher is aligned to the motion of its neighbors. At first, we perform simulations of this ensemble and find a cooperative behavior of the entities. Above an overcritical interaction strength the trajectories of the searcher qualitatively changes and searchers start to move along circles around the home position. Thereby, all searchers rotate either clockwise or anticlockwise around the central home position as it was reported for the zooplankton Daphnia. At second, the computational findings are analytically explained by the formulation of transport equations outgoing from the nonlinear mean field Fokker-Planck equation of the considered situation. In the asymptotic stationary limit, we find expressions for the critical interaction strength, the mean radial and orbital velocities of the searchers and their velocity variances. We also obtain the marginal spatial and angular densities in the undercritical regime where the foragers behave like individuals as well as in the overcritical regime where they rotate collectively around the considered home. We additionally elaborate the overdamped Smoluchowski-limit for the ensemble.

Planar cell polarity (PCP) is a biological phenomenon where a large number of cells get polarized and coordinatedly align in a plane. PCP is an example of self-organization through local and global interactions between cells. In this work, we have used a lattice-based spin model for PCP that mimics the alignment of cells through local interactions. We have investigated the equilibrium behavior of this model. In this model, alignment of cells leads to the formation of clusters of aligned cells, and such clustering exhibits percolation transition. Even though the alignment of a cell in this model depends upon its neighbors, finite-size scaling analysis shows that this model belongs to the universality class of simple two-dimensional random percolation.

We have described a novel mechanism of the kinklike pressure $\mathcal{P}(z-vt)$ response of the microsized twisted nematic volume under the effect of externally applied electric field $\mathbf{\text{E}}$ directed parallel to the restricted surfaces and induced by a strong local disturbance of the director field $\widehat{\mathbf{\text{n}}}$. It is found that the torques acting on the director $\widehat{\mathbf{\text{n}}}$ may excite the pressure traveling wave spreading along the normal to both boundaries, whose resemblance to a kink-like wave increases with increasing the value of the applied electric field greater than some critical value $E_{cr}$.

The present work investigates paper-paper friction dynamics by pulling a slider over a substrate. It focuses on the transition between stick-slip and inertial regimes. Although the device is classical, probing solid friction with the fewest contact damage requires that the applied load should be small. This induces noise, mostly impulsive in nature, on the recorded slider motion and force signals. To address the challenging issue of describing the physics of such systems, we promote here the use of nonlinear filtering techniques relying on recent nonsmooth optimization schemes. In contrast to linear filtering, nonlinear filtering captures the slider velocity asymmetry and, thus, the creep motion before sliding. Precise estimates of the stick and slip phase durations can thus be obtained. The transition between the stick-slip and inertial regimes is continuous. Here we propose a criterion based on the probability of the system to be in the stick-slip regime to quantify this transition. A phase diagram is obtained that characterizes the dynamics of this frictional system under low confinement pressure.

Soft particles at fluid interfaces play an important role in many aspects of our daily life, such as the food industry, paints and coatings, and medical applications. Analytical methods are not capable of describing the emergent effects of the complex dynamics of suspensions of many soft particles, whereas experiments typically either only capture bulk properties or require invasive methods. Computational methods are therefore a great tool to complement experimental work. However, an efficient and versatile numerical method is needed to model dense suspensions of many soft particles. In this article we propose a method to simulate soft particles in a multicomponent fluid, both at and near fluid-fluid interfaces, based on the lattice Boltzmann method, and characterize the error stemming from the fluid-structure coupling for the particle equilibrium shape when adsorbed onto a fluid-fluid interface. Furthermore, we characterize the influence of the preferential contact angle of the particle surface and the particle softness on the vertical displacement of the center of mass relative to the fluid interface. Finally, we demonstrate the capability of our model by simulating a soft capsule adsorbing onto a fluid-fluid interface with a shear flow parallel to the interface, and the covering of a droplet suspended in another fluid by soft particles with different wettability.

We investigate the effect of sequentially disrupting the shortest path of percolation clusters at criticality by comparing it with the shortest alternative path. We measure the difference in length and the enclosed area between the two paths. The sequential approach allows us to study spatial correlations. We find the lengths of the segments of successively constant differences in length to be uncorrelated. Simultaneously, we study the distance between red bonds. We find the probability distributions for the enclosed areas $A$, the differences in length $\mathrm{\Delta }l$, and the lengths between the red bonds $l_r$ to follow power-law distributions. Using maximum likelihood estimation and extrapolation we find the exponents $\beta =1.38\pm 0.03$ for $\mathrm{\Delta }l$, $\alpha =1.186\pm 0.008$ for $A$, and $\delta =1.64\pm 0.03$ for the distribution of $l_r$.

We investigate a stochastic process where a rectangle breaks into smaller rectangles through a series of horizontal and vertical fragmentation events. We focus on the case where both the vertical size and the horizontal size of a rectangle are discrete variables. Because of this constraint, the system reaches a jammed state where all rectangles are sticks, that is, rectangles with minimal width. Sticks are frozen as they cannot break any further. The average number of sticks in the jammed state, $S$, grows as $S\simeq A/\sqrt{2\pi lnA}$ with rectangle area $A$ in the large-area limit, and remarkably, this behavior is independent of the aspect ratio. The distribution of stick length has a power-law tail, and further, its moments are characterized by a nonlinear spectrum of scaling exponents. We also study an asymmetric breakage process where vertical and horizontal fragmentation events are realized with different probabilities. In this case, there is a phase transition between a weakly asymmetric phase where the length distribution is independent of system size and a strongly asymmetric phase where this distribution depends on system size.

We investigate a one-dimensional model of active motion, which takes into account the effects of persistent self-propulsion through a memory function in a dissipative-like term of the generalized Langevin equation for particle swimming velocity. The proposed model is a generalization of the active Ornstein-Uhlenbeck model introduced by G. Szamel [Phys. Rev. E 90, 012111 (2014)]. We focus on two different kinds of memory which arise in many natural systems: an exponential decay and a power law, supplemented with additive colored noise. We provide analytical expressions for the velocity autocorrelation function and the mean-squared displacement, which are in excellent agreement with numerical simulations. For both models, damped oscillatory solutions emerge due to the competition between the memory of the system and the persistence of velocity fluctuations. In particular, for a power-law model with fractional Brownian noise, we show that long-time active subdiffusion occurs with increasing long-term memory.

We consider a realistic nonequilibrium protocol, where a quantum system in thermal equilibrium is suddenly subjected to an external force. Due to this force, the system is driven out of equilibrium and the expectation values of certain observables acquire a dependence on time. Eventually, upon switching off the external force, the system unitarily evolves under its own Hamiltonian and, as a consequence, the expectation values of observables equilibrate towards specific constant long-time values. Summarizing our main results, we show that, in systems which violate the eigenstate thermalization hypothesis (ETH), this long-time value exhibits an intriguing dependence on the strength of the external force. Specifically, for weak external forces, i.e., within the linear response regime, we show that expectation values thermalize to their original equilibrium values, despite the ETH being violated. In contrast, for stronger perturbations beyond linear response, the quantum system relaxes to some nonthermal value which depends on the previous nonequilibrium protocol. While we present theoretical arguments which underpin these results, we also numerically demonstrate our findings by studying the real-time dynamics of two low-dimensional quantum spin models.