Using the example of configurations generated with the worm algorithm for the two-dimensional Ising model, we propose renormalization group (RG) transformations, inspired by the tensor RG, that can be applied to sets of images. We relate criticality to the logarithmic divergence of the largest principal component. We discuss the changes in link occupation under the RG transformation, suggest ways to obtain data collapse, and compare with the two-state tensor RG approximation near the fixed point.

More than half of a century has passed since the free energy of classical fluids defined by second Legendre transform was derived as a functional of density-density correlation function. It is now becoming an increasingly significant issue to develop the correlation functional theory that encompasses the liquid state theory, especially for glassy systems where out of equilibrium correlation fields are to be investigated. Here, we have formulated a field theoretic perturbation theory that incorporates two-body fields (both of density-density correlation field and its dual field playing the role of two-body interaction potential) into a density functional integral representation of the Helmholtz free energy. Quadratic density fluctuations are only considered in the saddle-point approximation of two-body fields as well as the density field. We have obtained a set of self-consistent field equations with respect to these fields, which simply reads a modified mean-field equation of density field where the bare interaction potential in the thermal energy unit is replaced by minus the direct correlation function given in the mean spherical approximation. Such replacement of the interaction potential in the mean-field equation belongs to the same category as the local molecular field theory proposed by Weeks and co-workers in a series of papers [e.g., Rodgers et al., Phys. Rev. Lett. 97, 097801 (2006); Remsing et al., Proc. Natl. Acad. Sci. USA 113, 2819 (2016)]. Notably, it has been shown that even the mean-field part of the free energy functional given by the self-consistent field theory includes information on short-range correlations between fluid particles, similar to the formulation of the local molecular field theory. The advantage of our field theoretic approach is not only that the modified mean-field equation can be improved systematically, but also that fluctuations of two-body fields in nonuniform fluids may be considered, which would be relevant especially for glass-forming liquids where heterogeneous out-of-equilibrium correlations are to be investigated.

We study the number $P\left(n\right)$ of partitions of an integer $n$ into sums of distinct squares and derive an integral representation of the function $P\left(n\right)$. Using semiclassical and quantum statistical methods, we determine its asymptotic average part $P_{as}\left(n\right)$, deriving higher-order contributions to the known leading-order expression [Tran et al., Ann. Phys. (NY) 311, 204 (2004)], which yield a faster convergence to the average values of the exact $P\left(n\right)$. From the Fourier spectrum of $P\left(n\right)$ we obtain hints that integer-valued frequencies belonging to the smallest Pythagorean triples $(m,p,q)$ of integers with $m^2+p^2=q^2$ play an important role in the oscillations of $P\left(n\right)$. We analyze the oscillating part $\delta P\left(n\right)=P\left(n\right)-P_{as}\left(n\right)$ in the spirit of semiclassical periodic orbit theory [M. Brack and R. K. Bhaduri: Semiclassical Physics (Westview, Boulder, 2003)]. A semiclassical trace formula is derived which accurately reproduces the exact $\delta P\left(n\right)$ for $n\gtrsim 500$ using ten pairs of orbits. For $n\gtrsim 4000$ only two pairs of orbits with the frequencies 4 and 5, belonging to the lowest Pythagorean triple (3,4,5), are relevant and create the prominent beating pattern in the oscillations. For $n\gtrsim 100000$ the beat fades away and the oscillations are given by just one pair of orbits with frequency 4.

The abrupt changes that are ubiquitous in physical systems often are well characterized by shot noise with a state-dependent recurrence frequency and jump amplitude. For such state-dependent behavior, we derive the transition probability for both the Itô and Stratonovich jump interpretations and subsequently use the transition probability to pose a master equation for the jump process. For exponentially distributed inputs, we present a class of transient solutions, as well as a generic steady-state solution in terms of a potential function and the Pope-Ching formula. These results allow us to describe state-dependent jumps in a double-well potential for steady-state particle dynamics, as well as transient salinity dynamics forced by state-dependent jumps. Both examples showcase a stochastic description that is more general than the limiting case of Brownian motion to which the jump process defaults in the limit of infinitely frequent and small jumps. Accordingly, our analysis may be used to explore a continuum of stochastic behavior from infrequent, large jumps to frequent, small jumps approaching a diffusion process.

The spectra of empirical correlation matrices, constructed from multivariate data, are widely used in many areas of sciences, engineering, and social sciences as a tool to understand the information contained in typically large data sets. In the past two decades, random-matrix-theory-based tools such as the nearest-neighbor eigenvalue spacing and eigenvector distributions have been employed to extract the significant modes of variability present in such empirical correlations. In this work we present an alternative analysis in terms of the recently introduced spacing ratios, which does not require the cumbersome unfolding process. It is shown that the higher-order spacing ratio distributions for the Wishart ensemble of random matrices, characterized by the Dyson index $\beta$, are related to the first-order spacing ratio distribution with a modified value of codimension ${\beta }^{\prime }$. This scaling is demonstrated for the Wishart ensemble and also for the spectra of empirical correlation matrices drawn from the observed stock market and atmospheric pressure data. Using a combination of analytical and numerics, such scalings in spacing distributions are also discussed.

We investigate heat transport via a charged flexible chain in the presence of magnetic fields. We focus on the Nernst-like effect, where the average positions of particles deviate in the perpendicular direction to the heat flow. This phenomenon is induced by the nonlinear dynamics as well as nonequilibrium state. We develop a linear response formalism to derive a thermodynamic force that induces the Nernst-like effect, and we show that the phenomenon is quantitatively explained. We also discuss the inverse effect, where an external ac-driving force induces finite net heat current in the homogeneous system attached to heat baths with the same temperature.

We report a multiscale investigation of water inside graphene slitlike channels that extends from the detailed all-atom level (AA) to the cheaper particle-based coarse-grained (CG) level, and to the continuum-based level. Since water is a highly polar solvent, the detailed description of its structural and dielectric properties close to the interfaces is of paramount importance in many applications. For this purpose, we have systematically developed an extended dipole-based CG model using the relative entropy method that can accurately reproduce the radial distribution function (RDF), diffusion coefficient, and bulk dielectric permittivity of the underlying AA reference model. The extended model is simple yet complex enough to shed light on the role of dipolar interactions in polar liquids such as water. Using the CG potentials developed in this work, we show that the structure, parallel dielectric permittivity, and polarization profiles can be captured reasonably well compared to all-atom molecular dynamics simulations. Furthermore, we use the empirical potential-based quasicontinuum (EQT) framework to predict the density and polarization of water molecules inside nanoslit channels of various widths. Our continuum analyses reveal that the mean field treatment of dipolar correlations in combination with the use of CG potentials are sufficient to accurately reproduce the structural variations of water inside the confined graphene slit channels. Finally, by using coarse-grained molecular dynamics and EQT simulations, we comment on the applicability of dipolar-based CG models in reproducing the structure of water near charged interfaces.

In this paper we consider the Ising model (called the dynamical Ising model with dynamical temperature $T$) on the Ising-correlated percolation lattice. To construct this lattice, another Ising model (which is called the quenched Ising model with quench artificial temperature $T_q$) is employed to model the correlations between imperfections. We argue that for each quenched temperature, there is a particular dynamical temperature $T_c\left(T_q\right)$ for which the dynamical Ising model becomes critical. We present some finite-size arguments (based on the moments of the magnetism and the energy as well as the spanning cluster probability) to extract the critical points and also show that they are compatible with the finite-size scaling of the singular point of the magnetic susceptibility. The model is thoroughly characterized in and out of these points. We find that the critical behaviors of the model change significantly with respect to the regular Ising model as well as the Ising model on the uncorrelated percolation lattice. It is shown that for the critical lattice, $T_q=T_c^{\text{square}\text{Ising}\text{model}}\approx 2.269$, the critical temperature for the dynamical Ising model in the thermodynamic limit is $T_c(T_q=T_c^{\text{square}\text{Ising}\text{model}})=1.94\pm 0.005$, and the fractal dimension of the exterior perimeter of geometrical spin clusters is $D_f^{T=T_c(T_q=2.269)}=1.408\pm 0.002$. Many quantities, such as the dynamical critical temperatures, all local and global critical exponents, and the fractal dimension of loops $D_f$, scale with the quench temperature in a power-law fashion, with some critical exponents that are reported. Significantly we see that $D_f^{T=T_c\left(T_q\right)}-D_f^{T=T_c(T_q=2.269)}\sim \frac{1}{\sqrt{\zeta \left(T_q\right)}}$ in which $\zeta \left(T_q\right)$ is the correlation length of the quenched Ising model at temperature $T_q$.

We study the efficiency of a simple quantum dot heat engine at maximum power. In contrast to the quasistatically operated Carnot engine whose efficiency reaches the theoretical maximum, recent research on more realistic engines operated in a finite time has revealed other classes of efficiencies such as the Curzon-Ahlborn efficiency maximizing the power. Such a power-maximizing efficiency has been argued to be always half of the maximum efficiency up to the linear order near equilibrium under the tight-coupling condition between thermodynamic fluxes. We show, however, that this universality may break down for the quantum dot heat engine, depending on the constraint imposed on the engine control parameters (local optimization), even though the tight-coupling condition remains satisfied. It is shown that this deviation is critically related to the applicability of the linear irreversible thermodynamics.

Our earlier model for diffusing diffusivity [R. Jain and K. L. Sebastian, J. Phys. Chem. B 120, 3988 (2016) and Phys. Rev. E 95, 032135 (2017)], is extended to cover the case of subdiffusing diffusivity. In this, the diffusion coefficient is taken to be the square of a random process $z$, that fluctuates with a mean square variation which is proportional to ${\left(\mathit{time}\right)}^{(2\alpha -1)}$, with $1/2<\alpha \le 1$. (The previous analysis was only of the case $\alpha =1$.) We model the diffusivity as the square of the position coordinate of a fractional Brownian oscillator. As in our earlier papers, the probability distribution of the displacement of a particle with diffusing diffusivity is given as the Fourier transform of the survival probability of the fractional oscillator, in the presence of an absorbing term that depends quadratically on its position. To derive the expression for the survival probability, we use phase-space path integration, which is surprisingly easy to use. An easy numerical method is used to calculate the survival probability. Also, we find analytical expressions for the short time and long time survival probabilities for arbitrary $\alpha$. Long time survival probability is found to be exponential in time. Using these to analyze the problem of diffusing diffusivity, we find that the results are similar to those obtained in our earlier model of diffusivity, i.e., $\alpha =1$ case. The short time probability distribution of the particle can be found exactly, and is non-Gaussian, while the long time result is Gaussian. Finally, exact numerical results are presented for probability distributions for different values of $\alpha$ and the time $T$.

We explore the emergence of complete synchronization under advection in a linear array of chaotic maps. The couplings decay algebraically with the distance between maps, covering from nearest-neighbor to infinite-range interactions, while the update protocol allows us to scan continuously from nondelayed to one-time-delayed dynamics. When the couplings are symmetric (diffusive) and the update is nondelayed, it is well known that chaotic orbits can synchronize if the range of interactions is long enough, while the inclusion of delays allows complete synchronization of a variety of other trajectories besides chaotic ones. Now we investigate through numerical simulations and theoretical analysis how the inclusion of antisymmetric couplings (advection) affects this scenario, showing the interplay among advection, the range of the interactions, and delay. In general, advection reduces the region in parameter space where completely synchronized states are stable, without affecting the nature of the orbits. The presence of delay can lessen the destabilizing effect of advection, such that synchronization is still possible even when couplings are short-range, for a suitable contribution of the delay, but globally coupled lattices are also affected when delayed responses predominate.

This paper presents a numerical description of amplitude death in delay-coupled thermoacoustic oscillators. An oscillator is a gas-filled resonance tube with a temperature gradient. Delay coupling is introduced by hollow tubes that connect the oscillators. Thermoacoustic oscillators and their connecting tubes are modeled by linear acoustic equations. For them, two coupling methods are tested: single-tube and double-tube coupling. For single-tube coupling, amplitude death occurs when the connecting tube length is one-quarter or three-quarters of the wavelength of the oscillation frequency and when the tube diameter is greater than 62.5% of the resonance tube diameter. For double-tube coupling, amplitude death occurs with specific combinations of the tube lengths given by integer multiples of the half-wavelength. The required tube diameter is as small as 7.5% of the resonance tube diameter. Death regions for the double-tube coupling are verified from the experimentally obtained results. Comparison with the delay-coupled van der Pol oscillators highlights acoustic aspects of the double-tube coupling.

We consider a large network of globally coupled quadratic integrate-and-fire neurons, which are canonical representatives for class I neurons near the spiking threshold. The model includes two heterogeneous parameters. One of them characterizes the state of isolated neurons and subdivides them into excitable and spiking units. The other heterogeneous parameter is the interaction delay time. In the infinite-size limit, we reduce the model to a simple system of ordinary differential equations. By bifurcation analysis of these equations, we identify the regions in the parameter space where the network exhibits macroscopic self-oscillations. The robustness of the oscillations against aging damage, which transforms spiking neurons into nonspiking neurons, is analyzed. We found an interesting counterintuitive effect when an increase in the proportion of nonspiking neurons induces macroscopic oscillations. The validity of the reduced equations is confirmed by comparing their solutions with the solutions of microscopic equations for a finite-size network. The solutions are compared not only for the periodic oscillation modes but also for the collective chaos regime.

Collective behavior is ubiquitous in living systems such as human crowds, microbial communities, insect swarms, and bird flocks. It is widely reported that simple, local, temporal interactions between individuals may lead to the emergence of collective behavior. In large-scale flocks, however, the global information transfer in dynamical models with time-varying neighborhoods is not normally instantaneous. Here, we present an information transfer network in which interactions last for a certain period of time. We then combine this network with a dynamic model of self-propelled particles. We observe that the resulting model that uses a stable information transfer network creates a bird flock with a more robust performance. We further show that the time of information transfer in a flock grows logarithmically with its size and is proportional to the average response time of the birds. Moreover, we find that the ranking curves displaying the order in which birds first perceive an external stimulus have similar shapes across different flocks. Our results demonstrate that, beyond the traditional local, temporal interactions, our stable information transfer network serves as an efficient mechanism to model the emergence of large-scale collective behavior.

Soft random geometric graphs (SRGGs) have been widely applied to various models including those of wireless sensors, communication, and social and neural networks. SRGGs are constructed by randomly placing nodes in some space and making pairwise links probabilistically using a connection function that is system specific and usually decays with distance. In this paper we focus on the application of SRGGs to wireless communication networks where information is relayed in a multihop fashion, although the analysis is more general and can be applied elsewhere by using different distributions of nodes and/or connection functions. We adopt a general nonuniform density which can model the stationary distribution of different mobility models, with the interesting case being when the density goes to zero along the boundaries. The global connectivity properties of these nonuniform networks are likely to be determined by highly isolated nodes, where isolation can be caused by the spatial distribution or the local geometry (boundaries). We extend the analysis to temporal-spatial networks where we fix the underlying nonuniform distribution of points and the dynamics are caused by the temporal variations in the link set, and we explore the probability that a node near the corner is isolated at time $T$. This work allows for insight into how nonuniformity (caused by mobility) and boundaries impact the connectivity features of temporal-spatial networks. We provide a simple method for approximating these probabilities for a range of different connection functions and verify them against simulations. Boundary nodes are numerically shown to dominate the connectivity properties of these finite networks with nonuniform measure.

The origin of entrapment of microswimmers near a solid surface is investigated experimentally. We report observations on cell entrapment of pusher, puller, and bimodal Vibrio alginolyticus near a glass surface in a custom made microchannel. We find that all the investigated bacterial strains can be entrapped near surface, regardless of their swimming modes. Furthermore, the near-surface cell concentration of pushers is reduced, while more significant entrapment was observed for pullers as the swimming speed increases. Interestingly, for the bimodal bacterial strain that could switch from pusher to puller through a reversed rotation of the flagellum, the near-surface entrapment appears to have no dependence on swimming speed. We propose a qualitative explanation to the observation, based on forces balance between steric, near-field, and dipolar-field hydrodynamic interactions.

Computing reactive trajectories and free-energy landscapes associated with rare-event kinetics is key to understanding the dynamics of complex systems. The analysis of the free-energy landscape on which the underlying dynamics takes place has become central to compute transition rates. In the overdamped limit, most often encountered in biophysics and soft condensed matter, the Kramers theory and its multidimensional extension derived by Langer have proved to be quite successful in recovering correct kinetics. However, the additional calculation to obtain rate constants in complex systems where configurational entropy is competing with energy is still challenging conceptually and computationally. Building on the Kramers theory and the metadynamics framework, we propose an expression for the rate in terms of the height of the free-energy barrier measured along the minimum free-energy path and an auxiliary measure of the configurational entropy in terms of the joint probability distribution of the reactive and nonreactive coordinates representing the slow modes of the system. We apply the formalism to three different problems where our approach shows good agreement with simulations and experiments and can present significant improvement over the Kramers-Langer's framework when slow entropic contribution, such as configurational entropy, predominates over enthalpic contribution.

Oscillatory behavior in tissue biology is ubiquitous and may be observed in the form of either chemical or mechanical signals. We present here and solve a mechanical cell model that exhibits oscillations emerging from delayed viscoelastic rheological laws. These include a time delay between the mechanical response and the rest-length changes, which evolve proportionally to the delayed cell deformation and use a remodeling rate parameter. We show that different regimes (no oscillatory response, sustained oscillations, and unstable oscillations) are obtained for different values of the delay or the remodeling rate. The results are analytically demonstrated in a one-dimensional problem with one and two cells that are represented by simple line elements. Oscillations of the cell deformations are obtained whenever different delays coexist, or when the delay is size-dependent. We also extend our results to a multicellular two-dimensional vertex model that includes the same rheological law, and which inherits the presence of critical values of the delay or remodeling rate. We numerically show that indeed the size-dependent rest-length changes induce oscillations in the cell shapes and areas.

Cell contractile forces deform and reorganize the surrounding matrix, but the relationship between the forces and the resulting displacements is complicated by the fact that the fibrous structure brings about a complex set of mechanical properties. Many studies have quantified nonlinear and time-dependent properties at macroscopic scales, but it is unclear whether macroscopic properties apply to the scale of a cell, where the matrix is composed of a heterogeneous network of fibers. To address this question, we mimicked the contraction of a cell embedded within a fibrous collagen matrix and quantified the resulting displacements. The data revealed displacements that were heterogeneous and nonaffine. The heterogeneity was reproducible during cyclic loading, and it decreased with decreasing fiber length. Both the experiments and a fiber network model showed that the heterogeneous displacements decayed over distance at a rate no faster than the average displacement field, indicating no transition to homogeneous continuum behavior. Experiments with cells fully embedded in collagen matrices revealed the presence of heterogeneous displacements as well, exposing the dramatic heterogeneity in matrix reorganization that is induced by cells at different positions within the same fibrous matrix.

Recent experimental studies, both in vivo and in vitro, have revealed that membrane components that bind to the cortical actomyosin meshwork are driven by active fluctuations, whereas membrane components that do not bind to cortical actin are not. Here we study the statistics of density fluctuations and dynamics of particles advected in an active quasi-two-dimensional medium comprising self-propelled filaments with no net orientational order, using a combination of agent-based Brownian dynamics simulations and analytical calculations. The particles interact with each other and with the self-propelled active filaments via steric interactions. We find that the particles show a tendency to cluster and their density fluctuations reflect their binding to and driving by the active filaments. The late-time dynamics of tagged particles is diffusive, with an active diffusion coefficient that is independent of (or at most weakly dependent on) temperature at low temperatures. Our results are in qualitative agreement with the experiments mentioned above. In addition, we make predictions that can be tested in future experiments.