The inherent structure landscape for a system of hard spheres confined to a hard cylindrical channel, such that spheres can only contact their first and second neighbors, is studied using an analytical model that extends previous results [Phys. Rev. Lett. 115, 025702 (2015)] to provide a comprehensive picture of jammed packings over a range of packing densities. In the model, a packing is described as an arrangement of $k$ helical sections, separated by defects, that have alternating helical twist directions and where all spheres satisfy local jamming constraints. The structure of each helical section is determined by a single helical twist angle, and a jammed packing is obtained by minimizing the length of the channel per particle with respect to the $k$ helical section angles. An analysis of a small system of $N=20$ spheres shows that the basins on the inherent structure landscape associated with these helical arrangements split into a number of distinct jammed states separated by low barriers giving rise to a degree of hierarchical organization. The model accurately predicts the geometric properties of packings generated using the Lubachevsky and Stillinger compression scheme $(N={10}^4)$ and provides insight into the nature of the probability distribution of helical section lengths.

We employ Langevin-dynamics simulations to unveil non-Brownian and non-Gaussian center-of-mass self-diffusion of massive flexible dumbbell-shaped particles in crowded two-dimensional solutions. We study the intradumbbell dynamics of the relative motion of the two constituent elastically coupled disks. Our main focus is on effects of the crowding fraction $\varphi$ and of the particle structure on the diffusion characteristics. We evaluate the time-averaged mean-squared displacement (TAMSD), the displacement probability-density function (PDF), and the displacement autocorrelation function (ACF) of the dimers. For the TAMSD at highly crowded conditions of dumbbells, e.g., we observe a transition from the short-time ballistic behavior, via an intermediate subdiffusive regime, to long-time Brownian-like spreading dynamics. The crowded system of dimers exhibits two distinct diffusion regimes distinguished by the scaling exponent of the TAMSD, the dependence of the diffusivity on $\varphi ,$ and the features of the displacement-ACF. We attribute these regimes to a crowding-induced transition from viscous to viscoelastic diffusion upon growing $\varphi$. We also analyze the relative motion in the dimers, finding that larger $\varphi$ suppress their vibrations and yield strongly non-Gaussian PDFs of rotational displacements. For the diffusion coefficients $D\left(\varphi \right)$ of translational and rotational motion of the dumbbells an exponential decay with $\varphi$ for weak and a power-law variation $D\left(\varphi \right)\propto {(\varphi -{\varphi }^{★})}^{2.4}$ for strong crowding is found. A comparison of simulation results with theoretical predictions for $D\left(\varphi \right)$ is discussed and some relevant experimental systems are overviewed.

We study numerically how multiple deformable capsules squeeze into a constriction. This situation is largely encountered in microfluidic chips designed to manipulate living cells, which are soft entities. We use fully three-dimensional simulations based on the lattice Boltzmann method to compute the flow of the suspending fluid and on the immersed boundary method to achieve the two-way fluid-structure interaction. The mechanics of the capsule membrane elasticity is computed with the finite-element method. We obtain two main states: continuous passage of the particles and their blockage that leads to clogging the constriction. The transition from one state to another is dictated by the ratio between the size of the capsules and the constriction width and by the capsule membrane deformability. The latter is found to enhance particle passage through narrower constrictions, where rigid particles with similar diameter are blocked and lead to clogging.

A nonequilibrium molecular dynamics method is proposed to produce nonequilibrium states flexibly. In this method, virtual points are set in a simulation box, and coarse-grained physical quantities at these points are constrained using Gauss's principle of least constraint. The coarse-grained physical quantities are evaluated by averaging microscopic quantities with an appropriate weight. To obtain the weight to evaluate the coarse-grained physical quantities, a shape function matrix is initially constructed from the particle configuration. This matrix expresses an interpolation of the physical quantities at particle positions from the coarse-grained quantities at the virtual points. Then, a matrix form of the weight is calculated as the Moore-Penrose pseudoinverse matrix for the shape function matrix. This method is applied to constrain the coarse-grained kinetic energy and produce a nonuniform temperature field in the system. The temperature profile at a nonequilibrium steady state depends on the method for constructing the shape function matrix. In particular, a local temperature coincides with the coarse-grained temperature when the shape function matrix is constructed based on a higher-order interpolation.

In the last few years the derivative expansion of the nonperturbative renormalization group has proven to be a very efficient tool for the precise computation of critical quantities. In particular, recent progress in the understanding of its convergence properties allowed for an estimate of the error bars as well as the precise computation of many critical quantities. In this work we extend previous studies to the computation of several universal amplitude ratios for the critical regime of O($N$) models using the derivative expansion of the nonperturbative renormalization group at order $\mathcal{O}\left({\partial }^4\right)$ for three-dimensional systems.

The perceived risk and reward for a given situation can vary depending on resource availability, accumulated wealth, and other extrinsic factors such as individual backgrounds. Based on this general aspect of everyday life, here we use evolutionary game theory to model a scenario with randomly perturbed payoffs in a prisoner's dilemma game. The perception diversity is modeled by adding a zero-average random noise in the payoff entries and a Monte Carlo simulation is used to obtain the population dynamics. This payoff heterogeneity can promote and maintain cooperation in a competitive scenario where only defectors would survive otherwise. In this work, we give a step further, understanding the role of heterogeneity by investigating the effects of quenched disorder in the critical properties of random games. We observe that payoff fluctuations induce a very slow dynamic, making the cooperation decay behave as power laws with varying exponents, instead of the usual exponential decay after the critical point, showing the emergence of a Griffiths phase. We also find a symmetric Griffiths phase near the defector's extinction point when fluctuations are present, indicating that Griffiths phases may be frequent in evolutionary game dynamics and play a role in the coexistence of different strategies.

Partition function zeros play a central role in the study of phase transitions. Recently, energy probability distribution (EPD) zeros were proposed as an alternative approach that solves some of the implementation issues present in the Fisher zeros method by allowing drastic reduction of the polynomial. Here, a formulation based on the EPD zeros that can reduce even more the polynomial degree while maintaining its accuracy is presented. This method has shown to be computationally cheaper than the EPD zeros, allowing the study of systems by using partition function zeros that would be unfeasible otherwise. In addition, the method can be easily extended to study phase transitions in external fields while maintaining all of its improvements.

Discrete breathers (DBs) in nonlinear lattices have attracted much attention in the past decades. In this work, we focus on the formation of DBs and their induced energy localization in the nonlinear honeycomb lattice derived from graphene. The key step is to construct a reduced system (RS) with only a few degrees of freedom, which contains one central site and its three nearest neighbors. The fixed points and periodic orbits of the RS can be obtained from the Poincaré section of the dynamics. Our main finding is that the long-running DB solution of the full honeycomb system corresponds to the periodic orbit given by one of the fixed points of RS, where the central site and its nearest neighbors vibrate inversely. When the initial condition deviates from this fixed point, the local vibration is attracted to it after a short transient process. When the initial condition is assigned to other fixed points of the RS, the initial excitation energy flows to the other part of the full system quickly, resulting in a delocalized wave propagation. Another main finding is that the long-lived DB solutions emerge only when the initial excitation energy is larger than a threshold value, above which the frequency of the DB exceeds the phonon band edge. The excitation energy generally dissipates from the local region due to the interactions between the DB and phonons near the $\mathrm{\Gamma }$ point in the dispersion relation. These results provide a holistic physical picture for the DB solutions in two-dimensional nonlinear lattices with complex potentials, which will be crucial to the understanding of energy localization in the realistic two-dimensional materials.

We study the breaking of time-reversal invariance (TRI) by the application of a magnetic field in the quantum kicked rotor (QKR), using Izrailev's finite-dimensional model. There is a continuous crossover from TRI to time-reversal noninvariance (TRNI) in the spectral and eigenvector fluctuations of the QKR. We show that the properties of this TRI to TRNI transition depend on ${\alpha }^2/N$, where $\alpha$ is the chaos parameter of the QKR and $N$ is the dimensionality of the evolution operator matrix. For ${\alpha }^2/N\gtrsim N$, the transition coincides with that in random matrix theory. For ${\alpha }^2/N<N$, the transition shows a marked deviation from random matrix theory. Further, the speed of this transition as a function of the magnetic field is significantly enhanced as ${\alpha }^2/N$ decreases.

In contrast to the common assumption in epidemic models that the rate of infection between individuals is constant, in reality, an individual's viral load determines their infectiousness. We compare the average and individual reproductive numbers and epidemic dynamics for a model incorporating time-dependent infectiousness and a standard SIR (susceptible-infected-recovered) model for both fully mixed and category-mixed populations. We find that the reproductive number depends only on the total infectious exposure and the largest eigenvalue of the mixing matrix and that these two effects are independent of each other. When we compare our time-dependent mean-field model to the SIR model with equivalent rates, the epidemic peak is advanced, and modifying the infection rate function has a strong effect on the time dynamics of the epidemic. We also observe behavior akin to a traveling wave as individuals transition through infectious states.

Gastric cancer (GC) is the most common digestive system malignant cancer, and gastric cancer cells (GCC) can migrate in normal solid tissue and lymphatic fluid. Previously, much research has focused on the migration process when the cells are in the solid condition, such as migration through tissue, adhesion, and invasion processes, while little is known about the migration process of GCC in lymphatic fluid. In the current study, we investigate the migration of GCC in a fluid condition in an in vitro environment. We find that the cells diffuse mainly because of their cell viability. Therefore, despite the fact that lymph fluid is almost quiescent, GCCs can migrate around easily. The dynamics of cells also demonstrate a collective glassy dynamic similar to ordinary inactive glassy materials. As density of the cells increases, the movement of the cells becomes slower, and the collective dynamic becomes heterogeneous, which is similar to the dynamically heterogeneous behavior in glassy materials. The results will help us gain a better knowledge of the characteristics of GCC dynamics in the liquid phase which is crucial for the understanding of the mechanism for lymphatic metastasis. This can also potentially help early diagnosis of lymph node metastasis in GC and provide new insights for future clinical treatment.

We analyze the statistical physics of self-propelled particles from a general theoretical framework that properly describes the most salient characteristic of active motion, persistence, in arbitrary spatial dimensions. Such a framework allows the development of a Smoluchowski-like equation for the probability density of finding a particle at a given position and time, without assuming an explicit orientational dynamics of the self-propelling velocity as Langevin-like equation-based models do. Also, the Brownian motion due to thermal fluctuations and the active one due to a general intrinsic persistent motion of the particle are taken into consideration on an equal footing. The persistence of motion is introduced in our formalism in the form of a two-time memory function, $K(t,t^{\prime })$. We focus on the consequences when $K(t,t^{\prime })\sim {(t/t^{\prime })}^{-\eta }exp[-\mathrm{\Gamma }(t-t^{\prime })], \mathrm{\Gamma }$ being the characteristic persistence time, and show that it precisely describes a variety of active motion patterns characterized by $\eta$. We find analytical expressions for the experimentally obtainable intermediate scattering function, the time dependence of the mean-squared displacement, and the kurtosis.

Icing affects many technical systems, like aircraft or high-voltage power transmission and distribution in cold regions. Ice accretion is often initiated by ice nucleation in sessile supercooled water droplets and is influenced by several influencing factors, of which the impact of electric fields on ice nucleation is still not completely understood. Especially the influence of transient electric fields is rarely or not at all investigated, even though it is of great interest, e.g., for high-voltage transmission lines or for the food industry. In the present study the impact of transient electric fields on ice nucleation in supercooled sessile water droplets is experimentally investigated under well-defined conditions. A set of droplets is cooled down to a certain temperature and is subsequently exposed to electric fields generated from standard lightning or standard switching impulse voltages, which are commonly used for testing of high-voltage equipment. The nucleation behavior of individual droplets is captured using a high-speed camera and the effect of the transient electric field on ice nucleation is analyzed by considering both the singular and the stochastic nature of nucleation. While the singular nature of nucleation is referred to during analysis of the relative number of droplets remaining liquid long times after the impulse voltage, its stochastic nature is accounted for in the analysis of the temporal evolution of the relative number of frozen droplets. It is shown that low electric field strengths ($\widehat{E}\le 6.52\mathrm{kV}$/cm) only have a negligible impact on ice nucleation, independent of the supercooling. In contrast, high electric field strengths ($\widehat{E}\ge 9.78\mathrm{kV}$/cm) promote significantly ice nucleation. It is also shown that depending on the supercooling, the freezing delay of the different droplets in the ensemble may vary over several magnitudes for the same conditions. It is demonstrated that the electric field appears to indirectly affect the nucleation rate by generating droplet oscillations, finally promoting ice nucleation. The experiments clearly demonstrate the possibility to actively force ice nucleation by applying transient electric fields. These results improve the understanding of ice accretion on high-voltage insulators and may also lend insight into freezing processes in food industry. We expect that these results will be a valuable contribution in formulating and/or validating new nucleation models.

Life threatening cardiac arrhythmias result from abnormal propagation of nonlinear electrical excitation waves in the heart. Finding the locations of the sources of these waves remains a challenging problem. This is mainly due to the low spatial resolution of electrode recordings of these waves. Also, these recordings are subjected to noise. In this paper, we develop a different approach: the AFV-DT method based on an averaged flow velocity (AFV) technique adopted from the analysis of optical flows and the determinant-trace (DT) method used for vector field analysis of dynamical systems. This method can find the location and determine all important types of sources found in excitable media such as focal activity, spiral waves, and waves rotating around obstacles. We test this method on in silico data of various wave excitation patterns obtained using the Luo-Rudy model for cardiac tissue. We show that the method works well for data with low spatial resolutions (up to $8\times 8$) and is stable against noise. Finally, we apply it to two clinical cases and show that it can correctly identify the arrhythmia type and location. We discuss further steps on the development and improvement of this approach.

We present the fractional extensions of the porous media equation (PME) with an emphasis on the applications in stock markets. Three kinds of “fractionalization” are considered: local, where the fractional derivatives for both space and time are local; nonlocal, where both space and time fractional derivatives are nonlocal; and mixed, where one derivative is local, and another is nonlocal. Our study shows that these fractional equations admit solutions in terms of generalized $q$-Gaussian functions. Each solution of these fractional formulations contains a certain number of free parameters that can be fitted with experimental data. Our focus is to analyze stock market data and determine the model that better describes the time evolution of the probability distribution of the price return. We proposed a generalized PME motivated by recent observations showing that $q$-Gaussian distributions can model the evolution of the probability distribution. Various phases (weak, strong super diffusion, and normal diffusion) were observed on the time evolution of the probability distribution of the price return separated by different fitting parameters [Phys. Rev. E 99, 062313 (2019)]. After testing the obtained solutions for the S&P500 price return, we found that the local and nonlocal schemes fit the data better than the classic porous media equation.

The buckling of thin elastic sheets is a classic mechanical instability that occurs over a wide range of scales. In the extreme limit of atomically thin membranes like graphene, thermal fluctuations can dramatically modify such mechanical instabilities. We investigate here the delicate interplay of boundary conditions, nonlinear mechanics, and thermal fluctuations in controlling buckling of confined thin sheets under isotropic compression. We identify two inequivalent mechanical ensembles based on the boundaries at constant strain (isometric) or at constant stress (isotensional) conditions. Remarkably, in the isometric ensemble, boundary conditions induce a novel long-ranged nonlinear interaction between the local tilt of the surface at distant points. This interaction combined with a spontaneously generated thermal tension leads to a renormalization group description of two distinct universality classes for thermalized buckling, realizing a mechanical variant of Fisher-renormalized critical exponents. We formulate a complete scaling theory of buckling as an unusual phase transition with a size-dependent critical point, and we discuss experimental ramifications for the mechanical manipulation of ultrathin nanomaterials.

An analysis of the direct correlation functions $c_{ij}\left(r\right)$ of binary additive hard-sphere mixtures of diameters ${\sigma }_s$ and ${\sigma }_b$ (where the subscripts $s$ and $b$ refer to the “small” and “big” spheres, respectively), as obtained with the rational-function approximation method and the WM scheme introduced in previous work [S. Pieprzyk et al., Phys. Rev. E 101, 012117 (2020)], is performed. The results indicate that the functions $c_{ss}(r<{\sigma }_s)$ and $c_{bb}(r<{\sigma }_b)$ in both approaches are monotonic and can be well represented by a low-order polynomial, while the function $c_{sb}(r<\frac{1}{2}({\sigma }_b+{\sigma }_s))$ is not monotonic and exhibits a well-defined minimum near $r=\frac{1}{2}({\sigma }_b-{\sigma }_s)$, whose properties are studied in detail. Additionally, we show that the second derivative $c_{sb}^{\prime \prime }\left(r\right)$ presents a jump discontinuity at $r=\frac{1}{2}({\sigma }_b-{\sigma }_s)$ whose magnitude satisfies the same relationship with the contact values of the radial distribution function as in the Percus-Yevick theory.

Lévy flight superdiffusion consists of random walks characterized by very long jumps that dominate the transport. However, the finite size of real samples introduces truncation of long jumps and modifies the transport properties. We measure typical Levy flight parameters for photon diffusion in atomic vapor characterized by a Voigt absorption profile. We observe the change of Lévy parameter as a function of truncation length. We associate this variation with size-dependent contributions from different spectral regions of the emission profile with the Doppler core dominating the transport for thin samples and Lorentz wings for thick samples. Monte Carlo simulations are implemented to support the interpretation of results.

It recently has been found that methods of the statistical theories of spectra can be a useful tool in the analysis of spectra far from levels of Hamiltonian systems. The purpose of the present study is to deepen this kind of approach by performing a more comprehensive spectral analysis that measures both the local- and long-range statistics. We have found that, as a common feature, spectra of this kind can exhibit a situation in which local statistics are relatively quenched while the long-range ones show large fluctuations. By combining three extensions of the standard random matrix theory (RMT) and considering long spectra, we demonstrate that this phenomenon occurs when disorder and level incompleteness are introduced in an RMT spectrum. Consequently, the long-range statistics follow Taylor's law, suggesting the presence of a fluctuation scaling (FS) mechanism in this kind of spectra. Applications of the combined ensemble are then presented for spectra originate from several very diverse areas, including complex networks, COVID-19 time series, and quantitative linguistics, which demonstrate that short- and long-range statistics reflect the rigid and elastic characteristics of a given spectrum, respectively. These observations may shed some light on spectral data classification.