We present a random matrix realization of a two-dimensional percolation model with the occupation probability $p$. We find that the behavior of the model is governed by the two first extreme eigenvalues. While the second extreme eigenvalue resides on the moving edge of the semicircle bulk distribution with an additional semicircle functionality on $p$, the first extreme exhibits a disjoint isolated Gaussian statistics which is responsible for the emergence of a rich finite-size scaling and criticality. Our extensive numerical simulations along with analytical arguments unravel the power-law divergences due to the coalescence of the first two extreme eigenvalues in the thermodynamic limit. We develop a scaling law that provides a universal framework in terms of a set of scaling exponents uncovering the full finite-size scaling behavior of the extreme eigenvalue's fluctuation. Our study may provide a simple practical approach to capture the criticality in complex systems and their inverse problems with a possible extension to the interacting systems.

In one-dimensional particle-in-cell simulations of a plasma irradiated by linearly polarized lasers from both sides of boundaries, it is found that there is an appreciable growth of the electromagnetic field in cavitons in the transverse direction perpendicular to the direction of polarization, which indicates the polarization conversion of the electromagnetic field in cavitons. This paper demonstrates the mechanism of this phenomenon based on parametric resonance induced by ponderomotive force with twice the frequency of the electromagnetic radiation in the caviton. We develop a theoretical model and verify it with simulation results. This phenomenon contributes to the heating and acceleration of particles and traps more EM energy in cavitons.

We generalize a tensor-network algorithm to study the thermodynamic properties of self-similar spin lattices constructed on a square-lattice frame with two types of couplings, $J_1^{}$ and $J_2^{}$, chosen to transform a regular square lattice ($J_1^{}=J_2^{}$) onto a fractal lattice if decreasing $J_2^{}$ to zero (the fractal fully reconstructs when $J_2^{}=0$). We modified the higher-order tensor renormalization group (HOTRG) algorithm for this purpose. Single-site measurements are performed by means of so-called impurity tensors. So far, only a single local tensor and uniform extension-contraction relations have been considered in HOTRG. We introduce 10 independent local tensors, each being extended and contracted by 15 different recursion relations. We applied the Ising model to the $J_1^{}-J_2^{}$ planar fractal whose Hausdorff dimension at $J_2^{}=0$ is $d^{\left(H\right)}=ln12/ln4\approx 1.792$. The generalized tensor-network algorithm is applicable to a wide range of fractal patterns and is suitable for models without translational invariance.

Echo chambers and polarization dynamics are, as of late, a very prominent topic in scientific communities around the world. As these phenomena directly affect our lives, seemingly more and more as our societies and communication channels evolve, it becomes ever so important for us to understand the intricacies of opinion dynamics in the modern era. Here we extend an existing echo-chamber model with activity-driven agents to a bilayer topology and study the dynamics of the polarized state as a function of interlayer couplings. Different cases of such couplings are presented: unidirectional coupling that can be reduced to a monolayer facing an external bias and symmetric and nonsymmetric couplings. We have assumed that initial conditions impose system polarization and agent opinions are different for both layers. Such a preconditioned polarized state can persist without explicit homophilic interactions provided the coupling strength between agents belonging to different layers is weak enough. For a strong unidirectional or attractive coupling between two layers a discontinuous transition to a radicalized state takes place when mean opinions in both layers are the same. When coupling constants between the layers are of different signs, the system exhibits sustained or decaying oscillations. Transitions between these states are analyzed using a mean field approximation and classified in the framework of bifurcation theory.

Solitary states emerge in oscillator networks when one oscillator separates from the fully synchronized cluster and oscillates with a different frequency. Such chimera-type patterns with an incoherent state formed by a single oscillator were observed in various oscillator networks; however, there is still a lack of understanding of how such states can stably appear. Here, we study the stability of solitary states in Kuramoto networks of identical two-dimensional phase oscillators with inertia and a phase-lagged coupling. The presence of inertia can induce rotatory dynamics of the phase difference between the solitary oscillator and the coherent cluster. We derive asymptotic stability conditions for such a solitary state as a function of inertia, network size, and phase lag that may yield either attractive or repulsive coupling. Counterintuitively, our analysis demonstrates that (1) increasing the size of the coherent cluster can promote the stability of the solitary state in the attractive coupling case and (2) the solitary state can be stable in small-size networks with all repulsive coupling. We also discuss the implications of our stability analysis for the emergence of rotatory chimeras.

The coupling of deterministic rotary motion and stochastic orientational diffusion of a self-propeller leads to a spiral trajectory of the expected displacement. We extend our former analysis of spiral diffusion [Phys. Rev. E 94, 030601(R) (2016)] in the white-noise limit to a more realistic scenario of stochastic noise with Gaussian memory and orientational fluctuations driven by an Ornstein-Uhlenbeck process. A variety of dynamical regimes including crossovers from ballistic to diffusive to ballistic in the angular dynamics are determined by the inertial timescale, orientational diffusivity, and angular speed.

Rigidity regulates the integrity and function of many physical and biological systems. This is the first of two papers on the origin of rigidity, wherein we propose that “energetic rigidity,” in which all nontrivial deformations raise the energy of a structure, is a more useful notion of rigidity in practice than two more commonly used rigidity tests: Maxwell-Calladine constraint counting (first-order rigidity) and second-order rigidity. We find that constraint counting robustly predicts energetic rigidity only when the system has no states of self-stress. When the system has states of self-stress, we show that second-order rigidity can imply energetic rigidity in systems that are not considered rigid based on constraint counting, and is even more reliable than shear modulus. We also show that there may be systems for which neither first- nor second-order rigidity imply energetic rigidity. The formalism of energetic rigidity unifies our understanding of mechanical stability and also suggests new avenues for material design.

This is the second paper devoted to energetic rigidity, in which we apply our formalism to examples in two dimensions: Underconstrained random regular spring networks, vertex models, and jammed packings of soft particles. Spring networks and vertex models are both highly underconstrained, and first-order constraint counting does not predict their rigidity, but second-order rigidity does. In contrast, spherical jammed packings are overconstrained and thus first-order rigid, meaning that constraint counting is equivalent to energetic rigidity as long as prestresses in the system are sufficiently small. Aspherical jammed packings on the other hand have been shown to be jammed at hypostaticity, which we use to argue for a modified constraint counting for systems that are energetically rigid at quartic order.

The self-consistent relaxation theory is employed to describe the collective ion dynamics in strongly coupled Yukawa classical one-component plasmas. The theory is applied to equilibrium states corresponding to intermediate screening regimes with appropriate values of the structure and coupling parameters. The information about the structure (the radial distribution function and the static structure factor) and the thermodynamics of the system are sufficient to describe collective dynamics over a wide range of spatial scales, namely, from the extended hydrodynamic to the microscopic dynamics scale. The main experimentally measurable characteristics of the equilibrium collective dynamics of ions—the spectrum of the dynamic structure factor, the dispersion parameters, the speed of sound, and the sound attenuation—are determined within the framework of the theory without using any adjustable parameters. The results demonstrate agreement with molecular dynamics simulations. Thus a direct realization is presented of the key idea of statistical mechanics: for the theoretical description of the collective particle dynamics in equilibrium fluids it is sufficient to know the interparticle interaction potential and the structural characteristics. Comparison with alternative or complementary theoretical approaches is provided.

Exponential averages that appear in integral fluctuation theorems can be recast as a sum over moments of thermodynamic observables. We use two examples to show that such moment series can exhibit nonuniform convergence in certain singular limits. The first example is a simple model of a process with measurement and feedback. In this example, the limit of interest is that of error-free measurements. The second system we study is an ideal gas particle inside an (infinitely) fast expanding piston. Both examples show qualitative similarities; the low-order moments are close to their limiting value, while high-order moments strongly deviate from their limit. As the limit is approached the transition between the two groups of moments is pushed toward higher and higher moments. Our findings highlight the importance of the ordering of limits in certain nonequilibrium-related calculations.

We apply the recently introduced cavity master equation (CME) to epidemic models and compare it to previously known approaches. We show that CME seems to be the formal way to derive (and correct) dynamic message passing (rDMP) equations that were previously introduced in an intuitive ad hoc manner. CME outperforms rDMP in all cases studied. Both approximations are nonbacktracking and this causes CME and rDMP to fail when the ecochamber mechanism is relevant, as in loopless topologies or scale free networks. However, we studied several random regular graphs and Erdős-Rényi graphs, where CME outperforms individual based mean field and a type of pair based mean field, although it is less precise than pair quenched mean field. We derive analytical results for endemic thresholds and compare them across different approximations.

During tissue development and repair, cells contract and expand in coordination with their neighbors, giving rise to tissue deformations that occur on length scales far larger than that of a single cell. The biophysical mechanisms by which the contractile forces of each cell cause deformations on multicellular length scales are not fully clear. To investigate this question, we began with the principle of force equilibrium, which dictates a balance of tensile forces between neighboring cells. Based on this principle, we hypothesized that coordinated changes in cell area result from tension transmitted across the cell layer. To test this hypothesis, spatial correlations of both contractile tension and the divergence of cell velocities were measured as readouts of coordinated contractility and collective area changes, respectively. Experiments were designed to alter the spatial correlation of contractile tension using three different methods, including disrupting cell-cell adhesions, modulating the alignment of actomyosin stress fibers between neighboring cells, and changing the size of the cell monolayer. In all experiments, the spatial correlations of both tension and divergence increased or decreased together, in agreement with our hypothesis. To relate our findings to the intracellular mechanism connecting changes in cell area to contractile tension, we disrupted activation of extracellular signal-regulated kinase (ERK), which is known to mediate the intracellular relationship between cell area and contraction. Consistent with prior knowledge, a temporal cross-correlation between cell area and tension revealed that ERK was responsible for a proportional relationship between cell area and contraction. Inhibition of ERK activation reduced the spatial correlations of the divergence of cell velocity but not of tension. Together, our findings suggest that coordination of cell contraction and expansion requires transfer of cell tension over space and ERK-mediated coordination between cell area and contraction in time.

In this work, the aerodynamic role of the artificial covert feathers (i.e., coverts) on an airfoil is experimentally studied in a wind tunnel to investigate the flow control effect on the leading-edge separation. We apply flexible featherlike devices on a high-angle-of-attack airfoil. We use a hot-wire anemometer to measure the velocity profiles and turbulent fluctuations in the downstream wake flow. As a baseline of flow separation, a two-dimensional NACA 0018 airfoil model is set at the angle of attack of 15 ° at the chord-based Reynolds number of $1.0\times {10}^5$, causing strong leading-edge and trailing-edge shear layers and a low-speed wake flow area in between as large as 0.35 chord length. When deployed on the upper wing surface, the flexible coverts adaptively flutter under the influence of the local unsteady airflow. Hot-wire measurement results show that the leading-edge coverts effectively suppress the flow separation and reduce the size of the wake flow area. The change of power spectral density shows that the predominant peaks as the fundamental and harmonic frequencies are both attenuated due to the suppression of unsteady motions of the shear layers. On the other hand, the fluttering coverts at the trailing edge modify the trailing-edge shear layer by redistributing the turbulent kinetic energy to the high-frequency components. By simultaneous double-point measurement, we find that the leading-edge and trailing-edge shear layers are drawn closer to each other, and the two shear layers show an increased peak in the coherence spectrum. Further multiscale wavelet analysis shows that the perturbations at the 60% chord length increase the large-scale amplitude modulation of small-scale turbulence and therefore they stabilize the leading-edge and trailing-edge shear layers. Meanwhile, the flow intermittency outside of the wake flow area is attenuated as well. The effective flow control effects in the present work are in good agreement with the previous direct observations of bird flight in literature that the coverts on the upper wing surface play an important role in flow separation control during high-angle-of-attack flight. These findings advance the understanding of aerodynamic contribution of the covers on bird wings and reveal the engineering potential of bioinspired coverts for flow separation control of aircrafts and unmanned air vehicles.

Research on laser-plasma interaction in the quantum-electrodynamic (QED) regime has been greatly advanced by particle-in-cell and Monte Carlo simulations (PIC-MC). While these simulations are widely used, we find that a noticeable numerical error arises due to inappropriate implementation of the quantum process accounting for hard photon emission and pair production in the PIC-MC codes. The error stems from the low resolution of the QED table used to sample photon energy, which is generated in the logarithmic scale and cannot resolve high energy photons. We propose a sampling method via sigmoid function that handles both the low energy and high energy end of the photon emission spectrum. It guarantees the accuracy of PIC-MC algorithms for hard photon radiation and other related processes in the strong-field QED regime.

Have you ever taken a disputed decision by tossing a coin and checking its landing side? This ancestral “heads or tails” practice is still widely used when facing undecided alternatives since it relies on the intuitive fairness of equiprobability. However, it critically disregards an interesting third outcome: the possibility of the coin coming at rest on its edge. Provided this evident yet elusive possibility, previous works have already focused on capturing all three landing probabilities of thick coins, but have only succeeded computationally. Hence, an exact analytical solution for the toss of bouncing objects still remains an open problem due to the strongly nonlinear processes induced at each bounce. In this Letter we combine the classical equations of collisions with a statistical-mechanics approach to derive an exact analytical solution for the outcome probabilities of the toss of a bouncing object, i.e., the coin toss with arbitrarily inelastic bouncing. We validate the theoretical prediction by comparing it to previously reported simulations and experimental data; we discuss the moderate discrepancies arising at the highly inelastic regime; we describe the differences with previous, approximate models; we propose the optimal geometry for the fair cylindrical three-sided die; and we finally discuss the impact of current results within and beyond the coin toss problem.

The random Lotka-Volterra model is widely used to describe the dynamical and thermodynamic features of ecological communities. In this work, we consider random symmetric interactions between species and analyze the strongly competitive interaction case. We investigate different scalings for the distribution of the interactions with the number of species and try to bridge the gap with previous works. Our results show two different behaviors for the mean abundance at zero and finite temperature, respectively, with a continuous crossover between the two. We confirm and extend previous results obtained for weak interactions: at zero temperature, even in the strong competitive interaction limit, the system is in a multiple-equilibria phase, whereas at finite temperature only a unique stable equilibrium can exist. Finally, we establish the qualitative phase diagrams and compare the species abundance distributions in the two cases.

Hematite at room temperature is a weak ferromagnetic material. Its permanent magnetization is three orders smaller than for magnetite. Thus, hematite colloids allow us to explore a different physical range of particle interaction parameters compared to ordinary ferromagnetic particle colloids. In this paper we investigate a colloid consisting of hematite particles with cubic shape. We search for energetically favorable structures in an external magnetic field with analytical and numerical methods and molecular dynamics simulations and analyze whether it is possible to observe them in experiments. We find that energetically favorable configurations are observable only for short chains. Longer chains usually contain kinks which are formed in the process of chain formation due to the interplay of energy and thermal fluctuations as an individual cube can be in one of two alignments with an equal probability.

We study the nonequilibrium thermodynamics of a heat engine operating between two finite-sized reservoirs with well-defined temperatures. Within the linear response regime, it is found that the uniform temperature of the two reservoirs at final time $\tau$ is bounded from below by the entropy production ${\sigma }_{\min }\propto 1/\tau$. We discover a general power-efficiency tradeoff depending on the ratio of heat capacities ($\gamma$) of the reservoirs for the engine, and a universal efficiency at maximum average power of the engine for arbitrary $\gamma$ is obtained. For practical purposes, the operation protocol of an ideal gas heat engine to achieve the optimal performance associated with ${\sigma }_{\min }$ is demonstrated. Our findings can be used to develop a general optimization scenario for thermodynamic cycles with finite-sized reservoirs in real-world circumstances.

The Ising spin-glass model on the three-dimensional $(d=3)$ hierarchical lattice with long-range ferromagnetic or spin-glass interactions is studied by the exact renormalization-group solution of the hierarchical lattice. The chaotic characteristics of the spin-glass phases are extracted in the form of our calculated, in this case continuously varying, Lyapunov exponents. Ferromagnetic long-range interactions break the usual symmetry of the spin-glass phase diagram. This phase-diagram symmetry breaking is dramatic, as it is underpinned by renormalization-group peninsular flows of the Potts multicritical type. A Berezinskii-Kosterlitz-Thouless (BKT) phase with algebraic order and a BKT-spin-glass phase transition with continuously varying critical exponents are seen. Similarly, for spin-glass long-range interactions, the Potts mechanism is also seen, by the mutual annihilation of stable and unstable fixed distributions causing the abrupt change of the phase diagram. On one side of this abrupt change, two distinct spin-glass phases, with finite (chaotic) and infinite (chaotic) coupling asymptotic behaviors are seen with a spin-glass to spin-glass phase transition.