How robust are socioeconomic agent-based models with respect to the details of the agents' decision rule? We tackle this question by considering an occupation model in the spirit of the Sakoda-Schelling model, historically introduced to shed light on segregation dynamics among human groups. For a large class of utility functions and decision rules, we pinpoint the nonequilibrium nature of the agent dynamics, while recovering an equilibrium-like phase separation phenomenology. Within the mean-field approximation we show how the model can be mapped, to some extent, onto an active matter field description. Finally, we consider nonreciprocal interactions between two populations and show how they can lead to nonsteady macroscopic behavior. We believe our approach provides a unifying framework to further study geography-dependent agent-based models, notably paving the way for joint consideration of population and price dynamics within a field theoretic approach.

Most studies of droplet impact on liquid pools focus on droplet diameters up to the capillary length (0.27 cm). We break from convention and study extremely large water droplets (1 to 6 cm diameter) falling into a pool of water. We demonstrate that the depth and width of the cavity formed by large droplet impact is greatly influenced by the deformed shape of the droplet at impact (i.e., prolate, spherical, and oblate), and larger droplets amplify this behavior by flattening before impact. In particular, the maximum cavity depth is a function of the Froude number and axis ratio of the droplet just before impact. Further, the cavity depth is more dependent on the droplet height than width, and the maximum cavity diameter is independent of the droplet height. In general, we observe that more oblate droplets result in decreasing cavity depths for a fixed liquid volume. This is because an increase in horizontal droplet diameter results in a reduced impact energy flux and therefore reduced cavity depth.

The deceleration of a low-density beam of ions in plasma with developed ion-acoustic turbulence arising in strong electric field is described. The time and length of beam deceleration along and across the anisotropy axis of the wave number distribution of ion-acoustic waves are found. It is shown to what extent an increase in the strength of the electric field that generates turbulence is accompanied by a decrease in the time and length of braking. As the beam propagates along the anisotropy axis, its velocity decreases to approximately the velocity of ion sound, and the direction of propagation does not change. When the beam is decelerated with an initial velocity across the anisotropy axis, a velocity component appears along the anisotropy axis during deceleration, which results in the beam deflection from the initial direction. In this case, the modulus of the beam velocity at the end of deceleration is close to the ion sound velocity.

The totally asymmetric simple exclusion process with generalized update is a version of the discrete time totally asymmetric exclusion process with an additional interparticle interaction that controls the degree of particle clustering. Though the model was shown to be integrable on the ring and on the infinite lattice, on the open chain it was studied mainly numerically, while no analytic results existed even for its phase diagram. In this paper, we introduce boundary conditions associated with the infinite translation invariant stationary states of the model, which allow us to obtain the exact phase diagram analytically. We discuss the phase diagram in detail and confirm the analytic predictions by extensive numerical simulations.

Anomalous diffusion processes, characterized by their nonstandard scaling of the mean-squared displacement, pose a unique challenge in classification and characterization. In a previous study [Mangalam et al., Phys. Rev. Res. 5, 023144 (2023)], we established a comprehensive framework for understanding anomalous diffusion using multifractal formalism. The present study delves into the potential of multifractal spectral features for effectively distinguishing anomalous diffusion trajectories from five widely used models: fractional Brownian motion, scaled Brownian motion, continuous-time random walk, annealed transient time motion, and Lévy walk. We generate extensive datasets comprising ${10}^6$ trajectories from these five anomalous diffusion models and extract multiple multifractal spectra from each trajectory to accomplish this. Our investigation entails a thorough analysis of neural network performance, encompassing features derived from varying numbers of spectra. We also explore the integration of multifractal spectra into traditional feature datasets, enabling us to assess their impact comprehensively. To ensure a statistically meaningful comparison, we categorize features into concept groups and train neural networks using features from each designated group. Notably, several feature groups demonstrate similar levels of accuracy, with the highest performance observed in groups utilizing moving-window characteristics and $p$ varation features. Multifractal spectral features, particularly those derived from three spectra involving different timescales and cutoffs, closely follow, highlighting their robust discriminatory potential. Remarkably, a neural network exclusively trained on features from a single multifractal spectrum exhibits commendable performance, surpassing other feature groups. In summary, our findings underscore the diverse and potent efficacy of multifractal spectral features in enhancing the predictive capacity of machine learning to classify anomalous diffusion processes.

We study the effect of a resetting point randomly distributed around the origin on the mean first-passage time of a Brownian searcher moving in one dimension. We compare the search efficiency with that corresponding to reset to the origin and find that the mean first-passage time of the latter can be larger or smaller than the distributed case, depending on whether the resetting points are symmetrically or asymmetrically distributed. In particular, we prove the existence of an optimal reset rate that minimizes the mean first-passage time for distributed resetting to a finite interval if the target is located outside this interval. When the target position belongs to the resetting interval or it is infinite then no optimal reset rate exists, but there is an optimal resetting interval width or resetting characteristic scale which minimizes the mean first-passage time. We also show that the first-passage density averaged over the resetting points depends on its first moment only. As a consequence, there is an equivalent point such that the first-passage problem with resetting to that point is statistically equivalent to the case of distributed resetting. We end our study by analyzing the fluctuations of the first-passage times for these cases. All our analytical results are verified through numerical simulations.

We investigate steady-state current fluctuations in two models of hardcore run-and-tumble particles (RTPs) on a periodic one-dimensional lattice of $L$ sites, for arbitrary tumbling rate $\gamma ={\tau }_p^{-1}$ and density $\rho$; model I consists of standard hardcore RTPs, while model II is an analytically tractable variant of model I, called a long-ranged lattice gas (LLG). We show that, in the limit of $L$ large, the fluctuation of cumulative current $Q_i(T,L)$ across the $i\mathrm{th}$ bond in a time interval $T\gg 1/D$ grows first subdiffusively and then diffusively (linearly) with $T$: $\langle Q_i^2\rangle \sim T^{\alpha }$ with $\alpha =1/2$ for $1/D\ll T\ll L^2/D$ and $\alpha =1$ for $T\gg L^2/D$, where $D(\rho ,\gamma )$ is the collective- or bulk-diffusion coefficient; at small times $T\ll 1/D$, exponent $\alpha$ depends on the details. Remarkably, regardless of the model details, the scaled bond-current fluctuations $D\langle Q_i^2(T,L)\rangle /2\chi L\equiv \mathcal{W}\left(y\right)$ as a function of scaled variable $y=DT/L^2$ collapse onto a universal scaling curve $\mathcal{W}\left(y\right)$, where $\chi (\rho ,\gamma )$ is the collective particle mobility. In the limit of small density and tumbling rate, $\rho ,\gamma \to 0$, with $\psi =\rho /\gamma$ fixed, there exists a scaling law: The scaled mobility ${\gamma }^a\chi (\rho ,\gamma )/{\chi }^{\left(0\right)}\equiv \mathcal{H}\left(\psi \right)$ as a function of $\psi$ collapses onto a scaling curve $\mathcal{H}\left(\psi \right)$, where $a=1$ and 2 in models I and II, respectively, and ${\chi }^{\left(0\right)}$ is the mobility in the limiting case of a symmetric simple exclusion process; notably, the scaling function $\mathcal{H}\left(\psi \right)$ is model dependent. For model II (LLG), we calculate exactly, within a truncation scheme, both the scaling functions, $\mathcal{W}\left(y\right)$ and $\mathcal{H}\left(\psi \right)$. We also calculate spatial correlation functions for the current and compare our theory with simulation results of model I; for both models, the correlation functions decay exponentially, with correlation length $\xi \sim {\tau }_p^{1/2}$ diverging with persistence time ${\tau }_p\gg 1$. Overall, our theory is in excellent agreement with simulations and complements the prior findings [T. Chakraborty and P. Pradhan, Phys. Rev. E 109, 024124 (2024)].

We observe homogeneous crystallization in simulated high-dimensional $(d>3)$ liquids that follow physically realistic dynamics and have system sizes that are large enough to eliminate the possibility that crystallization was induced by the periodic boundary conditions. Supercooled four-dimensional (4D) Lennard-Jones (LJ) liquids maintained at zero pressure and constant temperatures $0.59<T<0.63$ crystallized within $\sim 2\times {10}^4\tau$, where $\tau$ is the LJ time unit. Weeks-Chandler-Andersen (WCA) liquids that were maintained at the same densities and temperatures at which their LJ counterparts nucleated did not crystallize even after $2.5\times {10}^5\tau$, showing that the presence of long-ranged attractive interactions dramatically speeds up 4D crystallization, much as it does in 3D. On the other hand, the overlap of the liquid and crystalline phases' local-bond-order distributions is smaller for LJ systems than for WCA systems, which is the opposite of the 3D trend. This implies that the widely accepted hypothesis that increasing geometrical frustration rapidly suppresses crystallization as the spatial dimension $d$ increases is only generally valid in the absence of attractive interparticle forces.

We carry out an in-depth analysis of a recently introduced vortex gas model of homogeneous and isotropic turbulence. Direct numerical simulations are used to provide a concrete physical interpretation of one of the model's constituent fields: the degree of vortex polarization. Our investigations shed light on the complexity underlying vortex interactions and reveal, furthermore, that despite some striking similarities, classical and quantum turbulence exhibit distinct structural characteristics, even at inertial range scales. Crucially, these differences arise due to correlations between the polarization and circulation intensity within vortex clusters.

Metastability in liquids is at the foundation of complex phase transformation dynamics such as nucleation and cavitation. Intermolecular interaction details, beyond the equation of state, and thermal hydrodynamic fluctuations play a crucial role. However, most numerical approaches suffer from a slow time and space convergence, thus hindering the convergence to the hydrodynamic limit. This work shows that the Shan-Chen lattice Boltzmann model has the unique capability of simulating the hydrodynamics of the metastable state. The structure factor of density fluctuations is theoretically obtained and numerically verified to a high precision, for all simulated wave vectors, reduced temperatures, and pressures, deep into the metastable region. Such remarkable agreement between the theory and simulations leverages the exact implementation at the lattice level of the mechanical equilibrium condition. The static structure factor is found to consistently diverge as the temperature approaches the critical point or the density approaches the spinodal line at a subcritical temperature. Theoretically predicted critical exponents are observed in both cases. Finally, the phase separation in the unstable branch follows the same pattern, i.e., the generation of interfaces with different topology, as observed in molecular dynamics simulations.

Heat transfer across a granular flow is comprised of two resistances in series : near the wall and within the bulk particle bed, neither of which is well understood due to the lack of experimental probes to separate their respective contribution. Here, we use a frequency modulated photothermal technique to separately quantify the thermal resistances in the near-wall and the bulk bed regions of particles in flowing states. Compared to the stationary state, the flowing leads to a higher near-wall resistance and a lower thermal conductivity of bulk beds. Coupled with discrete element method simulation, we show that the near-wall resistance can be explained by particle diffusion in granular flows.

Many manifestations of natural processes give rise to interesting morphologies; it is all too easy to cite the corrugation of the Earth's surface or of planets in general. However, limiting ourselves to 2D cases, the morphology to which crystal growth gives rise is also intriguing. In particular, it is interesting to study some characteristics of the cluster projection in 2D, namely the study of the shapes of the speckles (fractal dimension of their rims) or the distribution of their areas. Recently, for instance, it has been shown that the size cumulative distribution function (cdf) of “voids” in a corrole film on Au(111) is well described by the well known Weibull distribution. The present article focuses on the cdf of cluster areas generated by numerical simulations: the clumps (clusters) are generated by overlapping grains (disks) whose germs (disk centers) are chosen randomly in a $2000\times 2000$ square lattice. The obtained cdf of their areas is excellently fitted to the Weibull function in a given range of surface coverage. The same type of analysis is also performed for a fixed-time clump distribution in the case of Kolmogorov-Johnson-Mehl-Avrami (KJMA) kinetics. Again, a very good agreement with the Weibull function is obtained.

We consider the effect of multiple stochastic parameters on the time-average quantities of chaotic systems. We employ the recently proposed sensitivity-enhanced generalized polynomial chaos expansion, se-gPC, to quantify efficiently this effect. se-gPC is an extension of gPC expansion, enriched with the sensitivity of the time-averaged quantities with respect to the stochastic variables. To compute these sensitivities, the adjoint of the shadowing operator is derived in the frequency domain. Coupling the adjoint operator with gPC provides an efficient uncertainty quantification algorithm, which, in its simplest form, has computational cost that is independent of the number of random variables. The method is applied to the Kuramoto-Sivashinsky equation and is found to produce results that match very well with Monte Carlo simulations. The efficiency of the proposed method significantly outperforms sparse-grid approaches, such as Smolyak quadrature. These properties make the method suitable for application to other dynamical systems with many stochastic parameters.

Large language models based on self-attention mechanisms have achieved astonishing performances, not only in natural language itself, but also in a variety of tasks of different nature. However, regarding processing language, our human brain may not operate using the same principle. Then, a debate is established on the connection between brain computation and artificial self-supervision adopted in large language models. One of most influential hypotheses in brain computation is the predictive coding framework, which proposes to minimize the prediction error by local learning. However, the role of predictive coding and the associated credit assignment in language processing remains unknown. Here, we propose a mean-field learning model within the predictive coding framework, assuming that the synaptic weight of each connection follows a spike and slab distribution, and only the distribution, rather than specific weights, is trained. This meta predictive learning is successfully validated on classifying handwritten digits where pixels are input to the network in sequence, and moreover, on the toy and real language corpus. Our model reveals that most of the connections become deterministic after learning, while the output connections have a higher level of variability. The performance of the resulting network ensemble changes continuously with data load, further improving with more training data, in analogy with the emergent behavior of large language models. Therefore, our model provides a starting point to investigate the connection among brain computation, next-token prediction, and general intelligence.

All the cells of a multicellular organism are the product of cell divisions that trace out a single binary tree, the so-called cell lineage tree. Because cell divisions are accompanied by replication errors, the shape of the cell lineage tree is a key determinant of how somatic evolution, which can potentially lead to cancer, proceeds. Carcinogenesis requires the accumulation of a certain number of driver mutations. By mapping the accumulation of mutations into a graph theoretical problem, we present an exact numerical method to calculate the probability of collecting a given number of mutations and show that for low mutation rates it can be approximated with a simple analytical formula, which depends only on the distribution of the lineage lengths, and is dominated by the longest lineages. Our results are crucial in understanding how natural selection can shape the cell lineage trees of multicellular organisms and curtail somatic evolution.

This paper presents the results of numerical calculations revealing how the structural parameters (i.e., the pitch $p_{\mathrm{TB}}$, the spatial period $p_{\mathrm{SB}}$, and the tilt angle ${\theta }_{\mathrm{TB}}$ or ${\theta }_{\mathrm{SB}}$) of twist-bend nematics ($N_{\mathrm{TB}}$) and splay-bend nematics ($N_{\mathrm{SB}}$) depend on the values of elastic constants in Dozov's theory [I. Dozov, Europhys. Lett. 56, 247 (2001)]. Alternative formulas for $p_{\mathrm{TB}}$, ${\theta }_{\mathrm{TB}}$, $p_{\mathrm{SB}}$, and ${\theta }_{\mathrm{SB}}$ have been derived and it has been proved that they give more accurate results than the expressions proposed by Dozov. Although the determination of the fourth-order elastic constants $C_1$, $C_2$, and $C_3$ is not feasible in a simple way, the order of magnitude of the sum $C_1+C_2$ has been easily estimated and is equal to ${10}^{-31}\mathrm{J}\mathrm{m}$. Moreover, the numerical calculations have shown that twist-bend nematics can exist even when $K_{11}$ is smaller than $2K_{22}$ and thus Dozov's criterion $K_{11}>2K_{22}$ for the stability of the $N_{\mathrm{TB}}$ phase is not strictly satisfied.

When a voltage is applied to a uniformly aligned nematic liquid crystal, a characteristic texture designated as reverse tilt domain (RTD) appears. The RTD, surrounded by a domain wall, gradually shrinks and finally disappears. The domain wall splits into a pair of disclination lines by increase of the voltage. This work examines the energy dissipation mechanism of annihilation dynamics by ascertaining the phenomenological viscosity $\mathrm{\Gamma }$ based on experimentation. To evaluate $\mathrm{\Gamma }$, the time dependence of curvature radius $R$ is analyzed using an equation $R=A\sqrt{t_0-t}$, where $A$ is a fitting parameter. Parameter $A$ decreased linearly with increasing applied voltage and suddenly became constant. Also, $\mathrm{\Gamma }$ was evaluated from $A$ as a function of voltage. When the voltage reaches a critical value, $\mathrm{\Gamma }$ increased sharply to be one order of magnitude greater than that under low voltages. The critical voltage is consistent with the theoretically expected value at which the splitting of domain wall occurs. The transition of $\mathrm{\Gamma }$ is described clearly by localized deformation of the director field.

To find a way to control the electron-bunching process and the bunch-emitting directions when an ultraintense, linearly polarized laser pulse interacts with a nanoscale target, we explored the mechanisms for the periodical generation of relativistic attosecond electron bunches. By comparing the simulation results of three different target geometries, the results show that for nanofoil target, limiting the transverse target size to a small value and increasing the longitudinal size to a certain extent is an effective way to improve the total electron quantity in a single bunch. Then the subfemtosecond electronic dynamics when an ultrashort ultraintense laser grazing propagates along a nanofoil target was analyzed through particle-in-cell simulations and semiclassical analyses, which shows the detailed dynamics of the electron acceleration, radiation, and bunching process in the laser field. The analyses also show that the charge separation field produced by the ions plays a key role in the generation of electron bunches, which can be used to control the quantity of the corresponding attosecond radiation bunches by adjusting the length of the nanofoil target.

We consider quantum-jump trajectories of Markovian open quantum systems subject to stochastic in time resets of their state to an initial configuration. The reset events provide a partitioning of quantum trajectories into consecutive time intervals, defining sequences of random variables from the values of a trajectory observable within each of the intervals. For observables related to functions of the quantum state, we show that the probability of certain orderings in the sequences obeys a universal law. This law does not depend on the chosen observable and, in the case of Poissonian reset processes, not even on the details of the dynamics. When considering (discrete) observables associated with the counting of quantum jumps, the probabilities in general lose their universal character. Universality is only recovered in cases when the probability of observing equal outcomes in the same sequence is vanishingly small, which we can achieve in a weak-reset-rate limit. Our results extend previous findings on classical stochastic processes [N. R. Smith et al., Europhys. Lett. 142, 51002 (2023)] to the quantum domain and to state-dependent reset processes, shedding light on relevant aspects for the emergence of universal probability laws.

We employ the eigen microstates approach to explore the self-organized criticality (SOC) in two celebrated sandpile models, namely the BTW model and the Manna model. In both models, phase transitions from the absorbing state to the critical state can be understood by the emergence of dominant eigen microstates with significantly increased weights. Spatial eigen microstates of avalanches can be uniformly characterized by a linear system size rescaling. The first temporal eigen microstates reveal scaling relations in both models. Furthermore, by finite-size scaling analysis of the first eigen microstates, we numerically estimate critical exponents, i.e., $\sqrt{{\sigma }_0{w}_1}/{\tilde{v}}_1\propto L^D$ and ${\tilde{v}}_1\propto L^{D(1-{\tau }_s)/2}$. Our findings could provide profound insights into eigen microstates of the universality and phase transition in nonequilibrium complex systems governed by self-organized criticality.