The thermodynamic and structural properties of two-dimensional dense Yukawa liquids are studied with molecular dynamics simulations. The “exact” thermodynamic properties are simultaneously employed in an advanced scheme for the determination of an equation of state that shows an unprecedented level of accuracy for the internal energy, pressure, and isothermal compressibility. The “exact” structural properties are utilized to formulate a novel empirical correction to the hypernetted-chain approach that leads to a very high accuracy level in terms of static correlations and thermodynamics.

Power-law (PL) time-dependent infection growth has been reported in many COVID-19 statistics. In simple susceptible infected recovered (SIR) models, the number of infections grows at the outbreak as $I\left(t\right)\propto t^{d-1}$ on $d$-dimensional Euclidean lattices in the endemic phase, or it follows a slower universal PL at the critical point, until finite sizes cause immunity and a crossover to an exponential decay. Heterogeneity may alter the dynamics of spreading models, and spatially inhomogeneous infection rates can cause slower decays, posing a threat of a long recovery from a pandemic. COVID-19 statistics have also provided epidemic size distributions with PL tails in several countries. Here I investigate SIR-like models on hierarchical modular networks, embedded in $2d$ lattices with the addition of long-range links. I show that if the topological dimension of the network is finite, average degree-dependent PL growth of prevalence emerges. Supercritically, the same exponents as those of regular graphs occur, but the topological disorder alters the critical behavior. This is also true for the epidemic size distributions. Mobility of individuals does not affect the form of the scaling behavior, except for the $d=2$ lattice, but it increases the magnitude of the epidemic. The addition of a superspreader hot spot also does not change the growth exponent and the exponential decay in the herd immunity regime.

We propose a model that describes cyclic state transitions of a micromachine driven by a catalytic chemical reaction. We consider a mechanochemical coupling of variables representing the degree of a chemical reaction and the internal state of a micromachine. The total free energy consists of a tilted periodic potential and a mechanochemical coupling energy. We assume that the reaction variable obeys a deterministic stepwise dynamics characterized by two typical timescales, i.e., the mean first passage time and the mean first transition path time. To estimate the functionality of a micromachine, we focus on the quantity called “nonreciprocality” and further discuss its dependence on the properties of catalytic reaction. For example, we show that the nonreciprocality is proportional to the square of the mean first transition path time. The explicit calculation of the two timescales within the decoupling approximation model reveals that the nonreciprocality is inversely proportional to the square of the energy barrier of catalytic reaction.

An approach based on modal analysis is developed to describe the state space of a nonlinear dynamical system using finite-dimensional linear systems. This strategy provides meta-reduced-order modeling (meta-ROM) consisting of the modes, which are the linear combinations of extra-decomposed modes (meta-modes). We confirm that, in a broad range of parameter spaces, a meta-ROM can yield appropriate solutions for a simple nonlinear equation, in which the conventional ROM shows unphysical solutions. The meta-modal analysis on a manifold provides an insight into the description of the state space in low dimensional space. This interpretation leads to the description of nonlinear dynamics in terms of intrinsic geometry rather than conventional extrinsic geometry.

This work proposes a fundamental thermodynamic description of structural relaxation in glasses by establishing a link between the Prony series solution to volume relaxation derived from the principles of irreversible thermodynamics and asymmetric Lévy stable distribution of relaxation rates. Additionally, it is shown that the bulk viscosity of glass, and not the shear viscosity, is the transport coefficient governing structural relaxation. We also report the distribution of relaxation times and energy barrier heights underpinning stretched exponential relaxation. It is proposed that this framework may be used for qualitative and quantitative descriptions of the relaxation kinetics in glass.

Janus particles with different patch sizes, confined to two dimensions, generate a series of patterns of interest to the field of nanoscience. Here we observe reverse melting, where for some densities the system melts under cooling. For a broad range of hydrophobic patch sizes $({60}^{\circ }<{\theta }_0<{90}^{\circ })$, a reentrant transition from solid to liquid and then to an ordered phase emerges as temperature $\left(T\right)$ decreases due to the formation of rhombus chains at low $T$. This reentrant phase has pseudo long-range orientational order but short-range translational order, similar to a hexatic phase. Our work provides guidelines to study the melting and assembly of Janus particles in two dimensions, as well as mechanisms to generate phases with specific symmetry.

Tactoids are spindle-shaped droplets of a uniaxial nematic phase suspended in the coexisting isotropic phase. They are found in dispersions of a wide variety of elongated colloidal particles, including actin, fd virus, carbon nanotubes, vanadium peroxide, and chitin nanocrystals. Recent experiments on tactoids of chitin nanocrystals in water show that electric fields can very strongly elongate tactoids even though the dielectric properties of the coexisting isotropic and nematic phases differ only subtly. We develop a model for partially bipolar tactoids, where the degree of bipolarness of the director field is free to adjust to optimize the sum of the elastic, surface, and Coulomb energies of the system. By means of a combination of a scaling analysis and a numerical study, we investigate the elongation and director field's behavior of the tactoids as a function of their size, the strength of the electric field, the surface tension, anchoring strength, the elastic constants, and the electric susceptibility anisotropy. We find that tactoids cannot elongate significantly due to an external electric field, unless the director field is bipolar or quasibipolar and somehow frozen in the field-free configuration. Presuming that this is the case, we find reasonable agreement with experimental data.

We study experimentally the dynamics of long waves among turbulent bending waves in a thin elastic plate set into vibration by a monochromatic forcing at a frequency $f_o$. This frequency is chosen large compared with the characteristic frequencies of bending waves. As a consequence, a range of conservative scales without energy flux on average exists for frequencies $f<f_o$. Within this range, we report a flat power density spectrum for the orthogonal velocity, corresponding to energy equipartition between modes. Thus, the average energy per mode ${\beta }^{-1}$—analogous to a temperature—fully characterizes the large-scale turbulent wave field. We present an expression for $\beta$ as a function of the forcing frequency, amplitude, and of the plate characteristics.

Formation of diverse patterns in spatially extended reaction-diffusion systems is an important aspect of study that is pertinent to many chemical and biological processes. Of special interest is the peculiar phenomenon of chimera state having spatial coexistence of coherent and incoherent dynamics in a system of identically interacting individuals. In the present article, we report the emergence of various collective dynamical patterns while considering a system of prey-predator dynamics in the presence of a two-dimensional diffusive environment. Particularly, we explore the observance of four distinct categories of spatial arrangements among the species, namely, spiral wave, spiral chimera, completely synchronized oscillations, and oscillation death states in a broad region of the diffusion-driven parameter space. Emergence of amplitude-mediated spiral chimera states displaying drifted amplitudes and phases in the incoherent subpopulation is detected for parameter values beyond both Turing and Hopf bifurcations. Transition scenarios among all these distinguishable patterns are numerically demonstrated for a wide range of the diffusion coefficients which reveal that the chimera states arise during the transition from oscillatory to steady-state dynamics. Furthermore, we characterize the occurrence of each of the recognizable patterns by estimating the strength of incoherent subpopulations in the two-dimensional space.

The phenomenon of the chimera state symbolizes the coexistence of coherent and incoherent sections of a given population. This phenomenon identified in several physical and biological systems presents several variants, including the multichimera states and the traveling chimera state. Here, we numerically study the influence of a weak external electric field on the dynamics of a network of Hindmarsh-Rose (HR) neurons coupled locally by an electrical interaction and nonlocally by a chemical one. We first focus on the phenomena of traveling chimera states and multicluster oscillating breathers that appear in the electric field's absence. Then in the field's presence, we highlight the presence of a chimera state, a multichimera state, an alternating chimera state, and a multicluster traveling chimera.

Understanding of the behavior of an individual droplet suspended in a liquid and subjected to a stress is important for studying and designing more complex systems, such as emulsions. Here, we present an experimental study of the behavior of a particle-covered droplet and its particle shell under compressive stress. The stress was induced by an application of a DC electric field. We studied how the particle coverage ($\phi$), particle size ($d$), and the strength of an electric field ($E$) influence the magnitude of the droplet deformation ($D$). The experimental results indicate that adding electrically insulating particles to a droplet interface drastically changes the droplet deformation by increasing its magnitude. We also found that the magnitude of the deformation is not retraceable during the electric field sweeping, i.e., the strain-stress curves form a hysteresis loop due to the energy dissipation. The field-induced droplet deformation was accompanied by structural and morphological changes in the particle shell. We found that shells made of smaller particles were more prone to jamming and formation of arrested shells after removal of an electric stress.

The graph transformation (GT) algorithm robustly computes the mean first-passage time to an absorbing state in a finite Markov chain. Here we present a concise overview of the iterative and block formulations of the GT procedure and generalize the GT formalism to the case of any path property that is a sum of contributions from individual transitions. In particular, we examine the path action, which directly relates to the path probability, and analyze the first-passage path ensemble for a model Markov chain that is metastable and therefore numerically challenging. We compare the mean first-passage path action, obtained using GT, with the full path action probability distribution simulated efficiently using kinetic path sampling, and with values for the highest-probability paths determined by the recursive enumeration algorithm (REA). In Markov chains representing realistic dynamical processes, the probability distributions of first-passage path properties are typically fat-tailed and therefore difficult to converge by sampling, which motivates the use of exact and numerically stable approaches to compute the expectation. We find that the kinetic relevance of the set of highest-probability paths depends strongly on the metastability of the Markov chain, and so the properties of the dominant first-passage paths may be unrepresentative of the global dynamics. Use of a global measure for edge costs in the REA, based on net productive fluxes, allows the total reactive flux to be decomposed into a finite set of contributions from simple flux paths. By considering transition flux paths, a detailed quantitative analysis of the relative importance of competing dynamical processes is possible even in the metastable regime.

In a recent work [R. Shojaei et al., Phys. Rev. E 100, 022303 (2019)] the authors calculate numerically the critical temperature $T_c$ of the balanced-imbalanced phase transition in a fully connected graph. According to their findings, $T_c$ decreases with the number of nodes $N$. Here we calculate the same critical temperature using the heat-bath algorithm. We show that $T_c$ increases with $N$ as $N^{\gamma }$, with $\gamma$ close to 0.5 or 1.0. This value depends on the initial fraction of positive bonds.

Recently, we introduced a stochastic social balance model with Glauber dynamics which takes into account the role of randomness in the individual's behavior [Phys. Rev. E 100, 022303 (2019)]. One important finding of our study was a phase transition from a balance state to an imbalance state as the randomness crosses a critical value, which was shown to vanish in the thermodynamic limit. In a similar study [Malarz and Kułakowski, Phys. Rev. E 103, 066301 (2021)], it was shown that the critical randomness tends to infinity as the system size diverges. This led the authors to question the appropriateness of the results in our Monte Carlo simulations, when compared with the non-normalized form, used in their work. The normalized form of energy in our model is, in fact, a common choice when one deals with systems comprising long-range interactions. Here, we show how their probabilistic definition leads to vanishing possibility of forming negative bonds, thus leading to a frozen ordered (paradise) state for any amount of finite randomness (temperature) for large enough system size. On the other hand, in the same large system size limit, our model is unstable to thermal randomness due to global, long-range effect of changing a bond's sign. We also address the rule of different updating mechanisms (synchronous vs sequential) in the two models. We finally discuss the distinction between the balanced states reached by each model and provide arguments for social relevance of our model.

Helicity plays an important role in spectacular geophysical phenomena such as hurricanes or the generation of the terrestrial magnetic field. The present investigation shows how helicity can be created in a statistically homogeneous but anisotropic flow, driven by buoyancy. If the flow is close enough to a two-dimensional limit, spontaneous symmetry breaking leads to the generation of mean helicity. In particular, we explain these observations by identifying a simple linear mechanism, the relevance of which is illustrated by simulations of unstably stratified turbulence in a conducting fluid on which a magnetic field is imposed. Finally it is shown that the self-organized state displays dynamical reversals of the sign of the mean helicity.

It is shown that the choice of spin operator affects the form of the response tensor describing a spin-dependent electron gas. The covariant, spin-dependent response tensor for a magnetic dipole moment-polarized electron gas (statistical distribution of electrons and positrons) is evaluated. A simultaneous eigenfunction of both the magnetic-moment spin operator and the Dirac Hamiltonian is constructed, from which explicit expressions for the magnetic-moment states and the corresponding vertex functions are derived. It is shown that a gas of electrons having a preferred magnetic-moment spin has a rotatory-type response that is gyrotropic. In contrast, when the helicity is chosen as the spin operator, the response of an electron gas with a preferred helicity spin has a rotatory response that is analogous to an optically active medium. The distinction between these spin operators does not appear in conventional treatments of spin dependence in quantum plasmas.

Simulational studies of spin glasses since the early 2010s have focused on the so-called replicon exponent $\alpha$ as a means of determining whether the low-temperature phase of spin glasses is described by the replica symmetry breaking picture of Parisi or by the droplet-scaling picture. On the latter picture, it should be zero, but we shall argue that it will only be zero for systems of linear dimension $L>L^{*}$. The crossover length $L^{*}$ may be of the order of hundreds of lattice spacings in three dimensions and approach infinity in six dimensions. We use the droplet-scaling picture to show that the apparent nonzero value of $\alpha$ when $L<L^{*}$ should be $2\theta$, where $\theta$ is the domain wall energy scaling exponent. This formula is in reasonable agreement with the reported values of $\alpha$.

The dynamics of a driven, damped pendulum as used in mechanical clocks is numerically investigated. In addition to the analysis of well-known mechanisms such as chronometer escapement, the unusual properties of Harrison's grasshopper escapement are explored, giving some insights regarding the dynamics of this system. Both the steady-state operation and transient effects are discussed, indicating the optimal condition for stable long-term clock accuracy. The possibility of chaotic motion is investigated.

We consider coupled network dynamics under uncorrelated noises, but only a subset of the network and their node dynamics can be observed. The effects of hidden nodes on the dynamics of the observed nodes can be viewed as having an extra effective noise acting on the observed nodes. These effective noises possess spatial and temporal correlations whose properties are related to the hidden connections. The spatial and temporal correlations of these effective noises are analyzed analytically and the results are verified by simulations on undirected and directed weighted random networks and small-world networks. Furthermore, by exploiting the network reconstruction relation for the observed network noisy dynamics, we propose a scheme to infer information of the effects of the hidden nodes such as the total number of hidden nodes and the weighted total hidden connections on each observed node. The accuracy of these results are demonstrated by explicit simulations.

We present a generic epidemic model with stochastic parameters in which the dynamics self-organize to a critical state with suppressed exponential growth. More precisely, the dynamics evolve into a quasi-steady state, where the effective reproduction rate fluctuates close to the critical value 1 for a long period, as indeed observed for different epidemics. The main assumptions underlying the model are that the rate at which each individual becomes infected changes stochastically in time with a heavy-tailed steady state. The critical regime is characterized by an extremely long duration of the epidemic. Its stability is analyzed both numerically and analytically in different models.