Classical density functional theory is used to determine the fluid-solid surface tensions for low-index faces of crystals of hard spheres and Lennard-Jones particles. The calculations make use of the recently introduced explicitly stable fundamental measure theory model for hard spheres, and we show that this gives state-of-the-art accuracy compared to simulation. For the Lennard-Jones system, results are presented for both solid-liquid and solid-vapor interfaces, and in both cases the FCC results compare favorably with existing results from the literature. We find that the BCC crystal has significantly lower solid-liquid surface tension than the FCC structure. For the solid-vapor interface, our results indicate that the BCC phase is unstable with respect to transition to the HCP structure, in agreement with various zero-temperature results in the literature.

In three-dimensional percolation, we apply and test the critical geometry approach for bounded critical phenomena based on the fractional Yamabe equation. The method predicts the functional shape of the order parameter profile $\varphi$, which is obtained by raising the solution of the Yamabe equation to the scaling dimension ${\mathrm{\Delta }}_{\varphi }$. The latter can be fixed from outcomes of numerical simulations, from which we obtain ${\mathrm{\Delta }}_{\varphi }=0.47846\left(71\right)$ and the corresponding value of the anomalous dimension $\eta =-0.0431\left(14\right)$. The comparison with values of $\eta$ determined by using scaling relations is discussed. A test of hyperscaling is also performed.

A simple limiting factor in the intrinsic variable of the normal diffusive coupling is known to facilitate the phenomenon of reviving of oscillation [Zou et al., Nat. Commun. 6, 7709 (2015)], where the limiting factor destabilizes the stable steady states, thereby resulting in the manifestation of the stable oscillatory states. In contrast, in this work we show that the same limiting factor can indeed facilitate the manifestation of the stable steady states by destabilizing the stable oscillatory state. In particular, the limiting factor in the intrinsic variable facilitates the genesis of a nontrivial amplitude death via a saddle-node infinite-period limit (SNIPER) bifurcation and symmetry-breaking oscillation death via a saddle-node bifurcation among the coupled identical oscillators. The limiting factor facilities the onset of symmetric oscillation death among the coupled nonidentical oscillators. It is known that the nontrivial amplitude death state manifests via a subcritical pitchfork bifurcation in general. Nevertheless, here we observe the transition to the nontrivial amplitude death via a SNIPER bifurcation. The in-phase oscillatory state loses its stability via the SNIPER bifurcation, resulting in the manifestation of the nontrivial amplitude death state, whereas the out-of-phase oscillatory state loses its stability via a homoclinic bifurcation, resulting in an unstable oscillatory state. Multistabilities among the various dynamical states are also observed. We have also deduced the evolution equation for the perturbation governing the stability of the observed dynamical states and stability conditions for SNIPER and pitchfork bifurcations. The generic nature of the effect of the limiting factor is also reinforced using two distinct nonlinear oscillators.

We propose a data-driven stochastic method that allows the simulation of a complex system's long-term evolution. Given a large amount of historical data on trajectories in a multi-dimensional phase space, our method simulates the time evolution of a system based on a random selection of partial trajectories in the data without detailed knowledge of the system dynamics. We apply this method to a large data set of time evolution of approximately one million business firms for a quarter century. Accordingly, from simulations starting from arbitrary initial conditions, we obtain a stationary distribution in three-dimensional log-size phase space, which satisfies the allometric scaling laws of three variables. Furthermore, universal distributions of fluctuation around the scaling relations are consistent with the empirical data.

The diversity of mutations in human chromosomes is nowadays very well documented. The mutations characterize populations in the world as well as genetic causes of diseases. In the approach that we follow, we study the patterns of gaps between mutations by means of the rescaled range analysis and the fractal dimension estimates. The results for chromosomes 1 to 22 and X indicate the existence of the so-called Hurst phenomenon in all of them. The interpretation of this outcome entails the presence of long-range correlations and we propose an explanation based on the genomic feature dubbed linkage disequilibrium, a nonrandom association of alleles at different loci. An unexpected outcome is the noteworthy uniform reduction in the Hurst phenomenon when considering the centimorgan metric instead of base position units. By contrast, such uniform reduction is not observed with the fractal dimension values.

Partial differential equations (PDEs) have been widely used to reproduce patterns in nature and to give insight into the mechanism underlying pattern formation. Although many PDE models have been proposed, they rely on the pre-request knowledge of physical laws and symmetries, and developing a model to reproduce a given desired pattern remains difficult. We propose a method, referred to as Bayesian modeling of PDEs (BM-PDEs), to estimate the best dynamical PDE for one snapshot of a objective pattern under the stationary state without ground truth. We apply BM-PDEs to nontrivial patterns, such as quasicrystals (QCs), a double gyroid, and Frank-Kasper structures. We also generate three-dimensional dodecagonal QCs from a PDE model. This is done by using the estimated parameters for the Frank-Kasper A15 structure, which closely approximates the local structures of QCs. Our method works for noisy patterns and the pattern synthesized without the ground-truth parameters, which are required for the application toward experimental data.

We analyze the long-lasting effects of initial conditions on dynamical fluctuations in one-dimensional diffusive systems. We consider the mean-squared displacement of tracers in homogeneous systems with single-file diffusion, and current fluctuations for noninteracting diffusive particles. In each case we show analytically that the long-term memory of initial conditions is mediated by a single static quantity: a generalized compressibility that quantifies the density fluctuations of the initial state. We thereby identify a universality class of hyperuniform initial states whose dynamical variances coincide with the quenched cases studied previously, alongside a continuous family of other classes among which equilibrated (or annealed) initial conditions are but one member. We verify our predictions through extensive Monte Carlo simulations.

In the one-dimensional low-density Jaynes-Cummings Hubbard (JCH) model, we find that when the hopping strength is much smaller than the coupling strength, the average restricted energy gap ratio exhibits an abnormal statistical behavior that is neither a Poisson nor a Gaussian orthogonal ensemble. But the average half-chain entanglement entropy exhibits ergodicity, and the eigenstate thermalization hypothesis (ETH) is valid for the observable. These results are quite different from those of the standard JCH model. In addition, when the hopping and the coupling strengths are of the same order, quantum chaos still appears in the low-density JCH model, which is in contrast to the integrability of the one-dimensional hard-core bosons. Finally, the dipole-dipole interaction breaks the particle-hole symmetry and leads the abnormal statistical properties to be closer to those of the integrable system at the weak hopping strength limit, but the quantum chaos properties cannot be affected when the hopping strength is of the same order as the coupling strength. Our results demonstrate the counterintuitive behavior in the low-density JCH model and explain the physics behind them from the perspective of the energy spectrum.

An ideal equilibrium Bose–Einstein condensate (BEC) is usually considered in the grand canonical ($\mu VT$) ensemble, which implies the presence of the chemical equilibrium with the environment. However, in most experimental scenarios, the total amount of particles in BEC is determined either by the initial conditions or by the balance between dissipation and pumping. As a result, BEC may possess the thermal equilibrium but almost never the chemical equilibrium. In addition, many experimentally achievable BECs are non-ideal due to interaction between particles. In the recent work [Shiskov et al., Phys. Rev. Lett. 128, 065301 (2022)], it has been shown that invariant subspaces in the system Hilbert space appear in non-equilibrium BEC in the fast thermalization limit. In each of these subspaces, Gibbs distribution is established with a certain number of particles that makes it possible to investigate properties of non-ideal non-equilibrium BEC independently in each invariant subspace. In this work, we analyze the BEC stability due to change in dispersion curve caused by non-linearity in BEC. Generally, non-linearity leads to the redshift or blueshift of the dispersion curve and to the change in the effective mass of the particles. We show that the redshift of the dispersion curve can lead to the negative compressibility of BEC and onset of instability, whereas the change in the effective mass always makes BEC more stable. We find the explicit condition for the particle density in BEC, at which the negative compressibility appears. We show that the appearance of BEC instability is followed by the formation of stable and spatially inhomogeneous BEC.

The second law of thermodynamics imposes a fundamental asymmetry in the flow of events. The so-called thermodynamic arrow of time introduces an ordering that divides the system's state space into past, future, and incomparable regions. In this work, we analyze the structure of the resulting thermal cones, i.e., sets of states that a given state can thermodynamically evolve to (the future thermal cone) or evolve from (the past thermal cone). Specifically, for a $d$-dimensional classical state of a system interacting with a heat bath, we find explicit construction of the past thermal cone and the incomparable region. Moreover, we provide a detailed analysis of their behavior based on thermodynamic monotones given by the volumes of thermal cones. Results obtained apply also to other majorization-based resource theories (such as that of entanglement and coherence), since the partial ordering describing allowed state transformations is then the opposite of the thermodynamic order in the infinite temperature limit. Finally, we also generalize the construction of thermal cones to account for probabilistic transformations.

It is known that the quantum transport of noninteracting Bose particles across a tight-binding chain is ballistic in the sense that the current does not depend on the chain length. We address the question whether the transport of strongly interacting bosons can be ballistic as well. We find such a regime and show that, classically, it corresponds to the synchronized motion of local nonlinear oscillators. It is also argued that, unlike the case of noninteracting bosons, the transporting state responsible for the ballistic transport of interacting bosons is metastable, i.e., the current decays in the course of time. An estimate for the decay time is obtained.

We report on the effect of spatially correlated noise on the velocities of self-propelled particles. Correlations in the random forces acting on self-propelled particles can induce directed collective motion, i.e., swarming. Even with repulsive coupling in the velocity directions, which favors a disordered state, strong correlations in the fluctuations can align the velocities locally leading to a macroscopic, turbulent velocity field. On the other hand, while spatially correlated noise is aligning the velocities locally, the swarming transition to globally directed motion is inhibited when the correlation length of the noise is nonzero, but smaller than the system size. We analyze the swarming transition in $d$-dimensional space in a mean field model of globally coupled velocity vectors.

Transport coefficients are typically divergent for quantum integrable systems in one dimension, such as a Bose gas with a two-body contact interaction. However, when a one-dimensional system is realized by confining bosons into a tight matter waveguide, an effective three-body interaction inevitably arises as leading perturbation to break the integrability. This fact motivates us to study the thermal conductivity of a Bose gas in one dimension with both two-body and three-body interactions. In particular, we evaluate the Kubo formula exactly to the lowest order in perturbation by summing up all contributions that are naively higher orders in perturbation but become comparable in the zero-frequency limit due to the pinch singularity. Consequently, a self-consistent equation for a vertex function is derived, showing that the thermal conductivity in quasi-one-dimension is dominated by the three-body interaction rather than the two-body interaction. Furthermore, the resulting thermal conductivity in the weak-coupling limit proves to be identical to that computed based on the quantum Boltzmann equation and its temperature dependence is numerically determined.

We study the thermodynamic properties of the magnetic dipolar spin ice on a 2D pentagonal Cairo lattice by using the numerical Metropolis and the complete enumeration methods. We use the model of point Ising-like dipoles considering long-range interactions with up to 100 nearest neighbors and with periodic boundary conditions. There are two explicit peaks both in the temperature behavior of the heat capacity and in the magnetic susceptibility. The low-temperature peak is caused only by long-range interactions and is not present in the model where each dipole interacts only with four nearest neighbors. The height of the peak depends logarithmically on the quantity of dipoles, which indicates a phase transition. The nature of the low-temperature phase transition is related to the transformation from order to disorder in orthogonal sublattices while maintaining the spin ice state and the spin ice rule in the sublattice of crosses. The high-temperature heat capacity peak is associated with the melting of spin ice, i.e., with the crossover from spin ice to paramagnetic chaos. Its height is constant and does not depend on the quantity of dipoles. It is shown that the choice of the radius of the dipole-dipole interaction has a significant effect on the statistical properties of the model. The model may even show the appearance of the long-range order and the phase transition in the case of long-range interaction or its absence in the case of short-range interaction.

We study the dynamics of two-component vector solitons, namely, bright-bright (BB) solitons interacting with parity-time ($\mathcal{PT}$)-symmetric potentials. We employ direct numerical simulations to demonstrate the unidirectional segregation of the BB soliton. Using a modified perturbed dynamical variational Lagrangian approximation, we develop an analytical model to verify the results obtained from numerical calculations. Simplified variational equations of motion suggest that the splitting of BB solitons can be explained by considering the effective force between the two components.

In the studies of network structures, much attention has been devoted to developing approaches to reconstruct networks and predict missing links when edge-related information is given. However, such approaches are not applicable when we are only given noisy node activity data with missing values. This work presents an unsupervised learning framework to learn node vectors and construct networks from such node activity data. First, we design a scheme to generate random node sequences from node context sets, which are generated from node activity data. Then, a three-layer neural network is adopted training the node sequences to obtain node vectors, which allow us to construct networks and capture nodes with synergistic roles. Furthermore, we present an entropy-based approach to select the most meaningful neighbors for each node in the resulting network. Finally, the effectiveness of the method is validated through both synthetic and real data.

Quantifying the eigenvalue spectra of large random matrices allows one to understand the factors that contribute to the stability of dynamical systems with many interacting components. This work explores the effect that the interaction network between components has on the eigenvalue spectrum. We build on previous results, which usually only take into account the mean degree of the network, by allowing for nontrivial network degree heterogeneity. We derive closed-form expressions for the eigenvalue spectrum of the adjacency matrix of a general weighted and directed network. Using these results, which are valid for any large well-connected complex network, we then derive compact formulas for the corrections (due to nonzero network heterogeneity) to well-known results in random matrix theory. Specifically, we derive modified versions of the Wigner semicircle law, the Girko circle law, and the elliptic law and any outlier eigenvalues. We also derive a surprisingly neat analytical expression for the eigenvalue density of a directed Barabási-Albert network. We are thus able to deduce that network heterogeneity is mostly a destabilizing influence in complex dynamical systems.

Understanding the spread of diseases through complex networks is of great interest where realistic, heterogeneous contact patterns play a crucial role in the spread. Most works have focused on mean-field behavior—quantifying how contact patterns affect the emergence and stability of (meta)stable endemic states in networks. On the other hand, much less is known about longer time scale dynamics, such as disease extinction, whereby inherent process stochasticity and contact heterogeneity interact to produce large fluctuations that result in the spontaneous clearance of infection. Here we show that heterogeneity in both susceptibility and infectiousness (incoming and outgoing degree, respectively) has a nontrivial effect on extinction in directed contact networks, both speeding up and slowing down extinction rates depending on the relative proportion of such edges in a network, and on whether the heterogeneities in the incoming and outgoing degrees are correlated or anticorrelated. In particular, we show that weak anticorrelated heterogeneity can increase the disease stability, whereas strong heterogeneity gives rise to markedly different results for correlated and anticorrelated heterogeneous networks. All analytical results are corroborated through various numerical schemes including network Monte Carlo simulations.

The folding of epithelial cell sheets is a fundamental process that sculpts developing tissues and organs into their proper shapes required for normal physiological functions. In the absence of detailed biochemical regulations, the epithelial sheet folding may simply proceed through buckling due to mechanical compression arising extrinsically from the surroundings or intrinsically within the sheets. Previous studies hypothesized that the formation of an expanding supracellular actomyosin ring within epithelial sheets could result in compression that ultimately leads to epithelial folding during tracheal development in the Drosophila (fruit fly) embryo. However, the exact mechanism by which the formation of epithelial folds is coordinated by the ring expansion remains unclear. Using a vertex-based mechanical model, here I systematically study the dependence of epithelial fold formation on the physical properties of expanding supracellular contractile rings. The simulations show that depending on the contractile strength, epithelial cell sheets can undergo distinct patterns of folding during ring expansion. The formation of folds in particular is robust against fluctuations in the ring properties such as ring numbers and tensions. These findings provide a systematic view to understand how the expansion of supracellular contractile rings in epithelial sheets mediates epithelial folding morphogenesis.

The Rayleigh-Taylor instability is strongly modified in the presence of a vertical mean magnetic field. Perturbations are first stretched in the vertical direction with no mixing due to the inhibition of small-scale shear instabilities. Then smooth elongated fingers eventually break after transition to turbulence, and a strong anisotropy persists. For increasing Alfvèn velocities, the growth rate of the mixing zone in the fully turbulent regime is decreased due to the conversion of potential energy into turbulent magnetic energy. A new theoretical prediction for the growth rate based on turbulent quantities is proposed and assessed with high-resolution direct numerical simulations of the Boussinesq-Navier-Stokes equations under the magnetohydrodynamics approximation.