We suggest a simple model to describe polyamorphism in single-component fluids using a maximum-valence approach. The model contains three types of interactions: (i) Atoms attract each other by van der Waals forces that generate a liquid-gas transition at low pressures, (ii) atoms may form covalent bonds that induce association, and (iii) atoms with maximal valence attract or repel each other stronger than other atoms, thus generating liquid-liquid separation. As an example, we qualitatively compare this model with the behavior of liquid sulfur and show that condition (iii) generates a liquid-liquid phase transition in addition to the liquid-gas phase transition.

Biochemical clocks are essential for virtually all living systems. A biochemical clock that is isolated from an external periodic signal and subjected to fluctuations can oscillate coherently only for a finite number of oscillations. Furthermore, such an autonomous clock can oscillate only if it consumes free energy. What is the minimum amount of free-energy consumption required for a certain number of coherent oscillations? We conjecture a universal bound that answers this question. A system that oscillates coherently for $\mathcal{N}$ oscillations has a minimal free-energy cost per oscillation of $4{\pi }^2\mathcal{N}{k}_{B}T$. Our bound is valid for general finite Markov processes, is conjectured based on extensive numerical evidence, is illustrated with numerical simulations of a known model for a biochemical oscillator, and applies to existing experimental data.

The rich ground-state phase diagram of the mixed spin-(1,1/2) Heisenberg octahedral chain was previously elaborated from effective mixed-spin Heisenberg chains, which were derived by employing a local conservation of a total spin on square plaquettes of an octahedral chain. Here we present a comprehensive analysis of the thermodynamic properties of this model. In the highly frustrated parameter region the lowest-energy eigenstates of the mixed-spin Heisenberg octahedral chain belong to flat bands, which allow a precise description of low-temperature magnetic properties within the localized-magnon approach exploiting a classical lattice-gas model of hard-core monomers. The present article provides a more comprehensive version of the localized-magnon approach, which extends the range of its validity down to a less frustrated parameter region involving the Haldane and cluster-based Haldane ground states. A comparison between results of the developed localized-magnon theory and accurate numerical methods such as full exact diagonalization and finite-temperature Lanczos technique convincingly evidence that the low-temperature magnetic properties above the Haldane and the cluster-based Haldane ground states can be extracted from a classical lattice-gas model of hard-core monomers and dimers, which is additionally supplemented by a hard-core particle spanned over the whole lattice representing the gapped Haldane phase.

We study the contact process on layered networks in which each layer is unidirectionally coupled to the next layer. Each layer has elements sitting on (i) an Erdös-Réyni network, and (ii) a $d$-dimensional lattice. The top layer is not connected to any layer and undergoes an absorbing transition in the directed percolation class for the corresponding topology. The critical infection probability $p_c$ for the transition is the same for all layers. For an Erdös-Réyni network the order parameter decays as $t^{-{\delta }_l}$ at $p_c$ for the $l\text{th}$ layer with ${\delta }_l\sim 2^{1-l}$. This can be explained with a hierarchy of differential equations in the mean-field approximation. The dynamic exponent $z=0.5$ for all layers and ${\nu }_{\parallel }\to 2$ for larger $l$. For a $d$-dimensional lattice, we observe a stretched exponential decay of the order parameter for all but the top layer at $p_c$.

We investigate analytically and numerically the determining factors of the slip front propagation (SFP) velocity. The slip front has two forms characterized by an intruding or extruding front. We assume a one-dimensional viscoelastic medium on a rigid and fixed substrate, and we employ the friction law depending on the slip and slip velocity. Despite this dependency potentially being nonlinear, we use the linear marginal stability hypothesis, which linearizes the governing equation for the slip, to investigate the intruding and extruding front velocities. The analytically obtained velocities are found to be consistent with the numerical computation where we assume the friction law depends nonlinearly on both the slip and slip velocity. This implies that the linearized friction law is sufficient to capture the dominant features of SFP behavior.

We present a thorough investigation of the particles on demand kinetic model. After a brief introduction of the method, an appropriate multiscale analysis is carried out to derive the hydrodynamic limit of the model. In this analysis, the effect of the time-space dependent comoving reference frames are taken into account. This could be regarded as a generalization of the conventional Chapman-Enskog analysis applied to the lattice Boltzmann models which feature global constant reference frames. Further simulations of target benchmarks provide numerical evidence confirming the theoretical predictions.

We study the classical two-dimensional ${\mathrm{RP}}^2$ and Heisenberg models, using the tensor-network renormalization (TNR) method. The determination of the phase diagram of these models has been challenging and controversial due to the very large correlation lengths at low temperatures. The finite-size spectrum of the transfer matrix obtained by TNR is useful in identifying the conformal field theory describing a possible critical point. Our results indicate that the ultraviolet fixed point for the Heisenberg model and the ferromagnetic ${\mathrm{RP}}^2$ model in the zero-temperature limit corresponds to a conformal field theory with central charge $c=2$, in agreement with two independent would-be Nambu-Goldstone modes. On the other hand, the ultraviolet fixed point in the zero-temperature limit for the antiferromagnetic Lebwohl-Lasher model, which is a variant of the ${\mathrm{RP}}^2$ model, seems to have a larger central charge. This is consistent with $c=4$ expected from the effective SO(5) symmetry. At $T>0$, the convergence of the spectrum is not good in both the Heisenberg and ferromagnetic ${\mathrm{RP}}^2$ models. Moreover, there seems to be no appropriate candidate of conformal field theory matching the spectrum, which shows the effective central charge $c\sim 1.9$. These suggest that both models have a single disordered phase at finite temperatures, although the ferromagnetic ${\mathrm{RP}}^2$ model exhibits a strong crossover at the temperature where the dissociation of ${\mathbb{Z}}_2$ vortices has been reported.

We revisit the field-free Ising model on a square lattice with up to third-neighbor (NNNN) interactions, also known as the $J_1\text{−}{J}_2\text{−}{J}_3$ model, in the mean-field approximation. Using a systematic enumeration procedure, we show that the region of phase space in which the high-temperature disordered phase is stable against all modes representing periodic magnetization patterns up to a given size is a convex polytope that can be obtained by solving a standard vertex enumeration problem. Each face of this polytope corresponds to a set of coupling constants for which a single set of modes, equivalent up to a symmetry of the lattice, bifurcates from the disordered solution. While the structure of this polytope is simple in the half-space $J_3>0$, where the NNNN interaction is ferromagnetic, it becomes increasingly complex in the half-space $J_3<0$, where the antiferromagnetic NNNN interaction induces strong frustration. We then pass to the limit $N\to \infty$ giving a closed-form description of the order-disorder surface in the thermodynamic limit, which shows that for $J_3<0$, the emergent ordered phases will have a “devil's surface”-like mode structure. Finally, using Monte Carlo simulations, we show that for small periodic systems, the mean-field analysis correctly predicts the dominant modes of the ordered phases that develop for coupling constants associated with the centroid of the faces of the disorder polytope.

In this article we experimentally demonstrate an efficient scheme to regulate the behavior of coupled nonlinear oscillators through dynamic control of their interaction. It is observed that introducing intermittency in the interaction term as a function of time or the system state predictably alters the dynamics of the constituent oscillators. Choosing the nature of the interaction, attractive or repulsive, allows for either suppression of oscillations or stimulation of activity. Two parameters $\mathrm{\Delta }$ and $\tau$, that reign the extent of interaction among subsystems, are introduced. They serve as a harness to access the entire range of possible behaviors from fixed points to chaos. For fixed values of system parameters and coupling strength, changing $\mathrm{\Delta }$ and $\tau$ offers fine control over the dynamics of coupled subsystems. We show this experimentally using coupled Chua's circuits and elucidate their behavior for a range of coupling parameters through detailed numerical simulations.

We propose a method for estimating the asymptotic phase and amplitude functions of limit-cycle oscillators using observed time series data without prior knowledge of their dynamical equations. The estimation is performed by polynomial regression and can be solved as a convex optimization problem. The validity of the proposed method is numerically illustrated by using two-dimensional limit-cycle oscillators as examples. As an application, we demonstrate data-driven fast entrainment with amplitude suppression using the optimal periodic input derived from the estimated phase and amplitude functions.

The motility of cilia and flagella plays important physiological roles, and there has been a great deal of research on the mechanisms underlying the motility of molecular motors. Although recent molecular structural analyses have revealed the components of the ciliary axoneme, the mechanisms involved in the regulation of dynein activity are still unknown, and how multiple dyneins coordinate their movements remains unclear. In particular, the mode of binding for axonemal dynein has not been elucidated. In this study, we constructed a thermodynamic stochastic model of microtubule-dynein coupling and reproduced the experiments of Aoyama and Kamiya on the minimal component of axonemal microtubule-dynein. We then identified the binding mode of axonemal dynein and clarified the relationship between dynein activity distribution and axonemal movement. Based on our numerical results, the slip-bond mechanism agrees quantitatively with the experimental results in terms of amplitude, frequency, and propagation velocity, implying that axial microtubule-dynein coupling may follow a slip-bond mechanism. Moreover, the frequency and propagation velocity decayed in proportion to the fourth power of microtubule length, and the critical load of the trigger for the oscillation agreed well with Euler's critical load.

The main aim of our work is to explore the effect of particle shape heterogeneity on the dynamics of an intruder moving through a two-dimensional mixture of dumbbells and disks. In spite of similar physical conditions (the mass of the dumbbell is the same as that of the disk) and the same area fraction, we noticed a significant difference in the drag experienced by the intruder as the mixture concentration varies. The propagation of stress from the intruder to the granular grains manifests in the form of force chains, and interestingly these force chains can vary significantly depending on the shape of the grains. These differences, however, appear to be suppressed in the frictionless case where the force chains cannot extend very far from the initial point of contact. Apart from particle shape, the effect of the area fraction of the system and the size of the intruder have also been explored. As the area fraction increases, the drag force on the intruder increases owing to the increase in the contact forces. Finally, we present the velocity and stress fields at different dumbbell fractions and for various intruder diameters to show the effect of the moving intruder on its surrounding particles.

Amorphous solids under mechanical strains are prone to plastic responses. Recent work showed that in amorphous granular systems these plastic events, that are typically quadrupolar in nature, can screen the elastic response. When the density of the quadrupoles is high, the gradients of the quadrupole field act as emergent dipole sources, leading to qualitative changes in the mechanical response, as seen for example in the displacement field. In this paper we examine the effect of screening in classical glass formers. These are made of point particles that interact via binary forces. Both inverse power law forces and Lennard-Jones interactions are examined, and it is shown that in both cases the elastic response can be strongly screened, in agreement with the novel theory. The degree of deviation from classical elasticity theory is parametrized by a proposed measure that is shown to have a functional dependence on the amount of energy lost to plastic responses.

To improve the numerical stability of the lattice Boltzmann method, Karlin et al. [Phys. Rev. E 90, 031302(R) (2014)] proposed the entropic multiple relaxation time (EMRT) collision model. The idea behind EMRT is to construct an optimal postcollision state by maximizing its local entropy value. The critical step of the EMRT model is to solve the entropy maximization problem under certain constraints, which is often computationally expensive and even not feasible. In this paper, we propose to employ perturbation theory and obtain an asymptotic solution to the maximum entropy state. With mathematical analysis of particular cases under relaxed constraints, we obtain the unperturbed form of the original problem and derive the asymptotic solution. We show that the asymptotic solution well approximates the optimal states; thus, our approach provides an efficient way to solve the constrained maximum entropy problem in the EMRT model. Also, we use the same idea of the EMRT model for the initial condition of the distribution function and propose to leave the entropy function to determine the missing information at the initial nodes. Finally, we numerically verify that the simulation results of the EMRT model obtained via the perturbation theory agree well with the exact solution to the Taylor-Green vortex problem. Furthermore, we also demonstrate that the EMRT model exhibits excellent stability performance for under-resolved simulations in the doubly periodic shear layer flow problem.

We show that confining extensile nematics in three-dimensional (3D) channels leads to the emergence of two self-organized flow states with nonzero helicity. The first is a pair of braided antiparallel streams—this double helix occurs when the activity is moderate, anchoring negligible, and reduced temperature high. The second consists of axially aligned counter-rotating vortices—this grinder train arises between spontaneous axial streaming and the vortex lattice. These two unanticipated helical flow states illustrate the potential of active fluids to break symmetries and form complex but organized spatiotemporal structures in 3D fluidic devices.

Indentation is a common experimental technique to study the mechanics of polymeric materials. The main advantage of using indentation is this provides a direct correlation between the microstructure and the small-scale mechanical response, which is otherwise difficult within the standard tensile testing. The majority of studies have investigated hydrogels, microgels, elastomers, and even soft biomaterials. However, a less investigated system is the indentation in highly cross-linked polymer (HCP) networks, where the complex network structure plays a key role in dictating their physical properties. In this work, we investigate the structure-property relationship in HCP networks using the computational indentation of a generic model. We establish a correlation between the local bond breaking, network rearrangement, and small-scale mechanics. The results are compared with the elastic-plastic deformation model. HCPs harden upon indentation.

Injecting artificial noise into a feedforward threshold neural network allows it to become trainable by gradient-based methods and also enlarges the parameter space as well as the range of synaptic weights. This configuration constitutes a stochastic-resonance-based threshold neural network, where the noise level can adaptively converge to a nonzero optimal value for finding a local minimum of the loss criterion. We prove theoretically that the injected noise plays the role of a generalized Tikhonov regularizer for training the designed threshold network. Experiments on regression and classification problems demonstrate that the generalization of the stochastic-resonance-based threshold network is improved by the injection of noise. The feasibility of injecting noise into the threshold neural network opens up the potential for adaptive stochastic resonance in machine learning.

Analytical understanding of how low-dimensional latent features reveal themselves in large-dimensional data is still lacking. We study this by defining a probabilistic linear latent features model with additive noise and by analytically and numerically computing the statistical distributions of pairwise correlations and eigenvalues of the data correlation matrix. This allows us to resolve the latent feature structure across a wide range of data regimes set by the number of recorded variables, observations, latent features, and the signal-to-noise ratio. We find a characteristic imprint of latent features in the distribution of correlations and eigenvalues and provide an analytic estimate for the boundary between signal and noise, even in the absence of a spectral gap.

Characterization of composite materials, whose properties vary in space over microscopic scales, has become a problem of broad interdisciplinary interest. In particular, estimation of the inhomogeneous transport coefficients, e.g., the diffusion coefficient or the heat conductivity, which shape important processes in biology and engineering, is a challenging task. The analysis of such systems is further complicated because two alternative formulations of the inhomogeneous transport equations exist in the literature—the Smoluchowski and Fokker-Planck equations, which are also related to the so-called Ito-Stratonovich dilemma. Using the theory of statistical physics, we show that the two formulations, usually regarded as distinct models, are physically equivalent. From this result we develop efficient estimates for the transverse space-dependent diffusion coefficient in fluids near a phase boundary. Our method requires only measurements of escape probabilities and mean exit times of molecules leaving a narrow spatial region. We test our estimates in three case studies: (i) a Langevin model of a Büttikker-Landauer ratchet; atomistic molecular-dynamics simulations of liquid-water molecules in contact with (ii) vapor, and (iii) soap (surfactant) film which has promising applications in physical chemistry. Our analysis reveals that near the surfactant monolayer the mobility of water molecules is slowed down almost twice with respect to the bulk liquid. Moreover, the diffusion coefficient of water correlates with the transition from hydrophilic to hydrophobic parts of the film.