Contrary to classical thermodynamics, which deals with systems in thermal equilibrium, partially ionized gases generally do not reach thermal equilibrium. Nonextensive statistical mechanics has helped extend classical thermodynamics to nonequilibrium ionized gas. However, the fundamental question on whether the statistics of non-Maxwellian electrons satisfy the laws of thermodynamics has not been resolved. Here, we verify the thermodynamic laws of reversible and adiabatic processes for a magnetically expanding ionized gas. Together with the experimental evidence of the non-Maxwellian electron distribution, the κ distribution, which measures the thermal equilibrium states, shows the Tsallis entropy to be nearly constant and the polytropic index to be close to adiabatic values along a divergent magnetic field. These results verify that the collisionless magnetic expansion of a nonequilibrium plasma is reversible and adiabatic, and an isentropic process is the origin of the high-energy tail of the energy distribution far downstream.

The interaction of electromagnetic radiation with inhomogeneous plasma formed by multiphoton ionization of inert gas atoms has been studied. In high-frequency and normal skin effects modes the field structure in plasma is described and reflection and absorption coefficients are found. It is shown that as the thickness of the plasma region, in which the photoelectron density grows linearly, increases, both the depth of field penetration and the absorption coefficient increase, too. It is found that, due to the Ramzauer-Townsend effect, there is a relative increase in the effective frequency of photoelectron collisions with atoms, which is accompanied by a significant increase in the absorption coefficient.

Recently, we considered the $g$-subdiffusion equation with a fractional Caputo time derivative with respect to another function $g$, T. Kosztołowicz et al. [Phys. Rev. E 104, 014118 (2021)]. This equation offers different possibilities for modeling diffusion such as a process in which a type of diffusion evolves continuously over time. However, the equation has not been derived from a stochastic model and the stochastic interpretation of $g$ subdiffusion is still unknown. In this Letter, we show the stochastic foundations of this process. We derive the equation by means of a modified continuous time random walk model. An interpretation of the $g$-subdiffusion process is also discussed.

We study the roughening properties of the anharmonic elastic interface in the presence of temporally correlated noise. The model can be seen as a generalization of the anharmonic Larkin model, recently introduced by Purrello, Iguain, and Kolton [Phys. Rev. E 99, 032105 (2019)], to investigate the effect of higher-order corrections to linear elasticity in the fate of interfaces. We find analytical expressions for the critical exponents as a function of the anharmonicity index $n$, the noise correlator range $\theta \in [0,1/2]$, and dimension $d$. In $d=1$ we find that the interface becomes faceted and exhibits anomalous scaling for $\theta >1/4$ for any degree of anharmonicity $n>1$. Analytical expressions for the anomalous exponents ${\alpha }_{\mathrm{loc}}$ and $\kappa$ are obtained and compared with a numerical integration of the model. Our theoretical results show that anomalous roughening cannot exist for this model in dimensions $d>1$.

Dynamic-mode decomposition (DMD) is a versatile framework for model-free analysis of time series that are generated by dynamical systems. We develop a DMD-based algorithm to investigate the formation of functional communities in networks of coupled, heterogeneous Kuramoto oscillators. In these functional communities, the oscillators in a network have similar dynamics. We consider two common random-graph models (Watts–Strogatz networks and Barabási–Albert networks) with different amounts of heterogeneities among the oscillators. In our computations, we find that membership in a functional community reflects the extent to which there is establishment and sustainment of locking between oscillators. We construct forest graphs that illustrate the complex ways in which the heterogeneous oscillators associate and disassociate with each other.

The effect of cholesterol on the bending modulus of DOPC lipid bilayers has become a controversial topic that has implications for methods of measuring the bending modulus. Recent results using neutron spin echo and nuclear magnetic resonance relaxation methods that involve linear transport properties have conflicted with earlier results from purely equilibrium experiments that do not involve linear transport properties. A general discussion indicates how one can be misled by data obtained by methods that involve linear transport properties. It is then shown specifically how the recent neutron spin echo results can be interpreted to agree with the earlier purely equilibrium experimental results, thereby resolving that conflict. Regarding the nuclear magnetic resonance relaxation method, it is noted that current interpretation of the data is unclear regarding the identity of the modulus that is involved, and an alternative interpretation is explored that does not disagree with the results of the equilibrium experiments.

We use a two-level simulation method to analyze the critical point associated with demixing of binary hard-sphere mixtures. The method exploits an accurate coarse-grained model with two- and three-body effective interactions. Using this model within the two-level methodology allows computation of properties of the full (fine-grained) mixture. The critical point is located by computing the probability distribution for the number of large particles in the grand canonical ensemble and matching to the universal form for the 3D Ising universality class. The results have a strong and unexpected dependence on the size ratio between large and small particles, which is related to three-body effective interactions and the geometry of the underlying hard-sphere packings.

We calculate exact analytic expressions for the average cluster numbers ${\langle k\rangle }_{{\mathrm{\Lambda }}_s}$ on infinite-length strips ${\mathrm{\Lambda }}_s$, with various widths, of several different lattices, as functions of the bond occupation probability $p$. It is proved that these expressions are rational functions of $p$. As special cases of our results, we obtain exact values of ${\langle k\rangle }_{{\mathrm{\Lambda }}_s}$ and derivatives of ${\langle k\rangle }_{{\mathrm{\Lambda }}_s}$ with respect to $p$, evaluated at the critical percolation probabilities $p_{c,\mathrm{\Lambda }}$ for the corresponding infinite two-dimensional lattices $\mathrm{\Lambda }$. We compare these exact results with an analytic finite-size correction formula and find excellent agreement. We also analyze how unphysical poles in ${\langle k\rangle }_{{\mathrm{\Lambda }}_s}$ determine the radii of convergence of series expansions for small $p$ and for $p$ near to unity. Our calculations are performed for infinite-length strips of the square, triangular, and honeycomb lattices with several types of transverse boundary conditions.

The small-angle neutron scattering (SANS) on HeLa nuclei demonstrates the bifractal nature of the chromatin structural organization. The border line between two fractal structures is detected as a crossover point at $Q_c\approx 4\times {10}^{-2}{\mathrm{nm}}^{-1}$ in the momentum transfer dependence $Q^{-D}$. The use of contrast variation (${\mathrm{D}}_2\mathrm{O}\text{−}{\mathrm{H}}_2\mathrm{O}$) in SANS measurements reveals clear similarity in the large scale structural organizations of nucleic acids (NA) and proteins. Both NA and protein structures have a mass fractal arrangement with the fractal dimension of $D\approx 2.5$ at scales smaller than 150 nm down to 20 nm. Both NA and proteins show a logarithmic fractal behavior with $D\approx 3$ at scales larger than 150 nm up to 6000 nm. The combined analysis of the SANS and atomic force microscopy data allows one to conclude that chromatin and its constitutes (DNA and proteins) are characterized as soft, densely packed, logarithmic fractals on the large scale and as rigid, loosely packed, mass fractals on the smaller scale. The comparison of the partial cross sections from NA and proteins with one from chromatin as a whole demonstrates spatial correlation of two chromatin's components in the range up to 900 nm. Thus chromatin in HeLa nuclei is built as the unified structure of the NA and proteins entwined through each other. Correlation between two components is lost upon scale increases toward 6000 nm. The structural features at the large scale, probably, provide nuclei with the flexibility and chromatin-free space to build supercorrelations on the distance of ${10}^3$ nm resembling cycle cell activity, such as an appearance of nucleoli and a DNA replication.

Purely pairwise interactions of the core-softened type, i.e., featuring a soft repulsion followed by a hard-core interaction at shorter distance, give rise to nontrivial equilibrium structures entirely different from the standard close packing of spheres. In particular, in a suitable low-temperature region of their phase diagram, such interactions are well known to favor a transition from a fluid to a cluster crystal. The residual mutual interaction between individual clusters can lead to the formation of patterns of their reciprocal orientations. In this work, we investigate two examples of such models in two dimensions, at the density most appropriate to the dimer phase, whereby clusters consist of just two particles, studying them with optimization techniques and Monte Carlo simulations. We focus on the dimer crystal, and unveil a second phase transition at extremely low temperature. This transition leads from a triangular dimer lattice with randomly disordered dimer orientations at high temperature to a reduced-symmetry ground state with nematic orientational order and a slightly distorted structure characterized by a centered-rectangular lattice at low temperature.

Proton radiography is a widely fielded diagnostic used to measure magnetic structures in plasma. The deflection of protons with multi-MeV kinetic energy by the magnetic fields is used to infer their path-integrated field strength. Here the use of tomographic methods is proposed for the first time to lift the degeneracy inherent in these path-integrated measurements, allowing full reconstruction of spatially resolved magnetic field structures in three dimensions. Two techniques are proposed which improve the performance of tomographic reconstruction algorithms in cases with severely limited numbers of available probe beams, as is the case in laser-plasma interaction experiments where the probes are created by short, high-power laser pulse irradiation of secondary foil targets. A new configuration allowing production of more proton beams from a single short laser pulse is also presented and proposed for use in tandem with these analytical advancements.

This Letter investigates the nature of synchronization in multilayered and multiplexed populations in which the interlayer interactions are randomly pinned. First, we show that a multilayer network constructed by setting up all-to-all interlayer connections between the two populations leads to explosive synchronization in the two populations successively, leading to the coexistence of coherent and incoherent populations forming chimera states. Second, a multiplex formation of the two populations in which only the mirror nodes are interconnected espouses explosive transitions in the two populations concurrently. The occurrence of both explosive synchronization and chimera are substantiated with rigorous theoretical mean-field analysis. The random pinning in the interlayer interactions concerns the practical problems where the impact of dynamics of one network on that of other interconnected networks remains elusive, as is the case for many real-world systems.

Chaotic oscillations of a linearly polarized single longitudinal-mode thin-slice $\mathrm{Nd}:\mathrm{GdV}{\mathrm{O}}_4$ laser placed in a self-mixing laser Doppler velocity scheme were dynamically characterized in terms of the intensity probability distribution, joint time-frequency analysis, and short-term Fourier transformation of temporal evolutions, and the degree of disorder in the amplitude and phase of the long-term temporal evolutions. The transition from chaotic relaxation oscillations (ROs) to chaotic spiking oscillations (SOs) was explored via the chaotic itinerancy (CI) regime by increasing the feedback ratio toward the laser from a rotating scattering object. The intensity probability distribution was found to change from an exponential decay in the RO regime to an inverse power law in the SO regime, which manifests itself in self-organized critical behavior, while stochastic subharmonic frequency locking among the two periodicities of RO and SO takes place in the CI regime featuring quantum-noise (spontaneous-emission)-induced order in the amplitude and phase of the spiking oscillations. All of the experimental results were reproduced by numerical simulations of a model equation of a single-mode self-mixing solid-state laser subjected to Doppler-shifted optical feedback from a rotating scattering object.

Populations composed of a collection of subpopulations (demes) with random migration between them are quite common occurrences. The emergence and sustenance of cooperation in such a population is a highly researched topic in the evolutionary game theory. If the individuals in every deme are considered to be either cooperators or defectors, the migration dilemma can be envisaged: The cooperators would not want to migrate to a defector-rich deme as they fear of facing exploitation; but without migration, cooperation cannot be established throughout the network of demes. With a view to studying the aforementioned scenario, in this paper, we set up a theoretical model consisting of a coupled map lattice of replicator maps based on two-player–two-strategy games. The replicator map considered is capable of showing a variety of evolutionary outcomes, like convergent (fixed point) outcomes and nonconvergent (periodic and chaotic) outcomes. Furthermore, this coupled network of the replicator maps undergoes the phenomenon of amplitude death leading to nonoscillatory stable synchronized states. We specifically explore the effect of (i) the nature of coupling that models migration between the maps, (ii) the heterogenous demes (in the sense that not all the demes have the same game being played by the individuals), (iii) the degree of the network, and (iv) the cost associated with the migration. In the course of investigation, we are intrigued by the effectiveness of the random migration in sustaining a uniform cooperator fraction across a population irrespective of the details of the replicator dynamics and the interaction among the demes.

The control of transport through mucus layers is a ubiquitous phenomenon in physiological systems. Mucus is often tasked with the mediation of passive, diffusive transport of small ionic species. However, questions remain regarding how mucin gel characteristics (charge density of the polymeric network, binding affinity of ions with mucus) govern the rate at which ions diffuse through mucus layers. Experimental studies measuring hydrogen diffusion through gastric mucus have provided conflicting results, and it is not clear if the rate of ionic diffusion through mucus layers is appreciably different than in aqueous environments (depending on experimental preparation). Here, we present a mathematical analysis of electrodiffussion of two ionic species (hydrogen and chloride) through a mucus layer. In addition to accounting for the chemical binding of hydrogen to the mucus network, we enforce a zero net current condition (as mucus layers in physiological systems are not generally electrogenic) and calculate the Donnan potential that occurs at the edge of the mucus layer. The model predicts the steady-state fluxes of ionic species and the induced potential across the layer. We characterize the dependence of these quantities on the chemical properties of the mucus gel, the composition of the bath solution, and the molecular mobility of the dissolved anion, and we show that the model predictions are consistent with a large portion of the experimental literature. Our analysis predicts that mucus layers generically slow the diffusive transport of hydrogen, but that chemical binding with the network attenuates this effect.

“Remote triggering” refers to the inducement of earthquakes by weak perturbations that emanate from faraway sources, typically intense earthquakes that happen at much larger distances than their nearby aftershocks, sometimes even around the globe. Here, we propose a mechanism for this phenomenon; the proposed mechanism is generic, resulting from the breaking of Hamiltonian symmetry due to the existence of friction. We allow a transition from static to dynamic friction. Linearly stable stressed systems display giant sensitivity to small perturbations of arbitrary frequency (without a need for resonance), which trigger an instability with exponential oscillatory growth. Once nonlinear effects kick in, the blow up in mean-square displacements can reach 15–20 orders of magnitude. Analytic and numerical results of the proposed model are presented and discussed.

We studied the creep motion of granular materials in a gradient potential field that is created using a slow spin-up experiment device. Natural sand confined in the acrylic box is spun up by a controlled turntable and the surface flows are captured using video-based measurements. Various spin-up accelerations were considered to understand the responses of creep motion on different accelerating paths. Convergent behaviors in the morphological change of sand surface were observed in the final steady state. To quantify the quasistatic spin-up process, we examined the net flux and the surface slope as a function of the spin rate and offset from the rotation axis. The creep motion of sand demonstrated behaviors similar to the regolith migration in numeric simulations. We have noticed the sand surface approaches criticality as the spin-up proceeding, consistent with the observation that top-shaped asteroids near limiting spin rate take on critical shapes. Comparisons to large-scale numeric simulations and analytical solutions reveal underlying similarities between the experiments and the million-year evolution of asteroid regolith under Yarkovsky-O'Keefe-Radzievskii-Paddack acceleration, which raises the possibility of studying asteroid surface processes in laboratory analog experiments.

We study a phase transition in parameter learning of hidden Markov models (HMMs). We do this by generating sequences of observed symbols from given discrete HMMs with uniformly distributed transition probabilities and a noise level encoded in the output probabilities. We apply the Baum-Welch (BW) algorithm, an expectation-maximization algorithm from the field of machine learning. By using the BW algorithm we then try to estimate the parameters of each investigated realization of an HMM. We study HMMs with $n=4,8,$ and 16 states. By changing the amount of accessible learning data and the noise level, we observe a phase-transition-like change in the performance of the learning algorithm. For bigger HMMs and more learning data, the learning behavior improves tremendously below a certain threshold in the noise strength. For a noise level above the threshold, learning is not possible. Furthermore, we use an overlap parameter applied to the results of a maximum a posteriori (Viterbi) algorithm to investigate the accuracy of the hidden state estimation around the phase transition.

We revisit the so-called folded XXZ model, which was treated earlier by two independent research groups. We argue that this spin-1/2 chain is one of the simplest quantum integrable models, yet it has quite remarkable physical properties. The particles have constant scattering lengths, which leads to a simple treatment of the exact spectrum and the dynamics of the system. The Hilbert space of the model is fragmented, leading to exponentially large degeneracies in the spectrum, such that the exponent depends on the particle content of a given state. We provide an alternative derivation of the Hamiltonian and the conserved charges of the model, including an alternative interpretation of the so-called “dual model” considered earlier. We also construct a nonlocal map that connects the model with the Maassarani-Mathieu spin chain, also known as the $SU\left(3\right)$ XX model. We consider the exact solution of the model with periodic and open boundary conditions, and also derive multiple descriptions of the exact thermodynamics of the model. We consider quantum quenches of different types. In one class of problems the dynamics can be treated relatively easily: we compute an example for the real-time dependence of a local observable. In another class of quenches the degeneracies of the model lead to the breakdown of equilibration, and we argue that they can lead to persistent oscillations. We also discuss connections with the $T\overline{T}$ and hard rod deformations known from quantum field theories.

The phase transition of epidemic spreading model on networks is one of the most important concerns of physicists to theoretical epidemiology. In this paper, we present an analytical expression of epidemic threshold for interplay between epidemic spreading and human behavior on multiplex networks. The threshold formula proposed in this paper reveals the relation between the threshold on single-layer networks and that on multiplex networks, which means that the theoretical conclusions of single-layer networks can be used to improve the threshold accuracy of multiplex networks. To verify how well our formula works in different networks, we build a network model with constant total number of edges but gradually changing the heterogeneity of the network, from scale-free network to Erdős-Rényi random network. By use of theoretical analysis and computer simulations, we find that the heterogeneity of information layer behaves as a “double-edged sword” on the epidemic threshold: The strong heterogeneity can effectively improve the epidemic threshold (which means the disease outbreak requires a higher infection probability) when the awareness probability $\alpha$ is low, while the opposite effect takes place for high $\alpha$. Meanwhile, the weak heterogeneity of the information layer is effective in suppressing the epidemic prevalence when the awareness probability is neither too high nor too low.