In this paper, we employ the persistent homology (PH) technique to examine the topological properties of fractional Gaussian noise (fGn). We develop the weighted natural visibility graph algorithm, and the associated simplicial complexes through the filtration process are quantified by PH. The evolution of the homology group dimension represented by Betti numbers demonstrates a strong dependency on the Hurst exponent ($H$). The coefficients of the birth and death curves of the $k$-dimensional topological holes ($k$-holes) at a given threshold depend on $H$ which is almost not affected by finite sample size. We show that the distribution function of a lifetime for $k$-holes decays exponentially and the corresponding slope is an increasing function versus $H$ and, more interestingly, the sample size effect completely disappears in this quantity. The persistence entropy logarithmically grows with the size of the visibility graph of a system with almost $H$-dependent prefactors. On the contrary, the local statistical features are not able to determine the corresponding Hurst exponent of fGn data, while the moments of eigenvalue distribution ($M_n$) for $n\ge 1$ reveal a dependency on $H$, containing the sample size effect. Finally, the PH shows the correlated behavior of electroencephalography for both healthy and schizophrenic samples.

The thermodynamic length, though providing a lower bound for the excess work required in a finite-time thermodynamic process, is determined by the properties of the equilibrium states reached by the quasistatic process and is thus beyond the direct experimental measurement. We propose an experimental strategy to measure the thermodynamic length of an open classical or quantum system by extrapolating finite-time measurements. The current proposal enables the measurement of the thermodynamic length for a single control parameter without requiring extra effort to find the optimal control scheme, and is illustrated with examples of the quantum harmonic oscillator with tuning frequency and the classical ideal gas with changing volume. Such a strategy shall shed light on the experimental design of the lacking platforms to measure the thermodynamic length.

We consider the long-term weakly nonlinear evolution governed by the two-dimensional nonlinear Schrödinger (NLS) equation with an isotropic harmonic oscillator potential. The dynamics in this regime is dominated by resonant interactions between quartets of linear normal modes, accurately captured by the corresponding resonant approximation. Within this approximation, we identify Fermi-Pasta-Ulam–like recurrence phenomena, whereby the normal-mode spectrum passes in close proximity of the initial configuration, and two-mode states with time-independent mode amplitude spectra that translate into long-lived breathers of the original NLS equation. We comment on possible implications of these findings for nonlinear optics and matter-wave dynamics in Bose-Einstein condensates.

Statistical physics has proved essential to analyze multiagent environments. Motivated by the empirical observation of various nonequilibrium features in Barro Colorado and other ecological systems, we analyze a plant-species abundance model of neutral competition, presenting analytical evidence of scale-invariant plant clusters and nontrivial emergent modular correlations. Such first theoretical confirmation of a scale-invariant region, based on percolation processes, reproduces the key features in natural rainforest ecosystems and can confer the most stable equilibrium for ecosystems with vast biodiversity.

Buzz pollination is described using a mathematical model considering a billiard approach. Applications to a rough morphology of a typical poricidal anther of a tomato flower (Solanum lycopersicum) experiencing vibrations applied by a bumblebee (Bombus terrestris) are made. The anther is described by a rectangular billiard with a pore on its tip while the borders are perturbed by specific oscillations according to the vibrational properties of the bumblebee. Pollen grains are considered as noninteracting particles that can escape through the pore. Our results not only recover some observed data but also provide a possible answer to an open problem involving buzz pollination.

Studies have shown significant discrepancies between the recent experiment [Berg et al., Phys. Rev. Lett. 120, 055002 (2018)] and current theoretical calculations on the electron-impact ionization cross section of ions in warm dense magnesium. Here, we present a systematic study the effects of the ionic correlations and free-electron screening on the electron-impact ionization of ions in warm dense matter. The ionic correlation and the free-electron screening effects yield additional Hermitian terms to the calculation of the ionic central-force-field potential, which significantly change the electronic structure compared with that of the isolated ion. In calculating the electron-impact ionization, we describe the impact and ionized electrons using a damped-distorted wave function, which considers the momentum relaxation of free electrons due to collisions with other free electrons and ions. We reproduce the electron-impact ionization process for ${\mathrm{Mg}}^{7+}$ in the solid-density plasma and increase the ionization cross section by one order of magnitude compared with that of the isolated ion, which excellently agrees with the experimental result of Berg et al.

We investigate experimentally the dynamic phase transition from compressed to buckled phases for thin sheets of rubber. We find that the rubber strips enter a highly compressed, metastable state when compression speed is high. During the compressed phase, higher modes grow, followed by mode coarsening. Mode growth is accompanied by an expansion of length while the system is still being compressed. We measure the forces and length of the sheet to confirm this, and we develop a mechanism for how modes grow and coarsen during dynamical buckling. The influence of crucial control parameters in the experiments, such as the material cross section and compression speed, on the buckling dynamics, are explained theoretically.

We study the heat statistics of a multilevel $N$-dimensional quantum system monitored by a sequence of projective measurements. The late-time, asymptotic properties of the heat characteristic function are analyzed in the thermodynamic limit of a high, ideally infinite, number $M$ of measurements $(M\to \infty )$. In this context, the conditions allowing for an infinite-temperature thermalization (ITT), induced by the repeated monitoring of the quantum system, are discussed. We show that ITT is identified by the fixed point of a symmetric random matrix that models the stochastic process originated by the sequence of measurements. Such fixed point is independent on the nonequilibrium evolution of the system and its initial state. Exceptions to ITT, which we refer to as partial thermalization, take place when the observable of the intermediate measurements is commuting (or quasicommuting) with the Hamiltonian of the quantum system or when the time interval between measurements is smaller or comparable with the system energy scale (quantum Zeno regime). Results on the limit of infinite-dimensional Hilbert spaces ($N\to \infty$), describing continuous systems with a discrete spectrum, are also presented. We show that the order of the limits $M\to \infty$ and $N\to \infty$ matters: When $N$ is fixed and $M$ diverges, then ITT occurs. In the opposite case, the system becomes classical, so that the measurements are no longer effective in changing the state of the system. A nontrivial result is obtained fixing $M/N^2$ where instead partial ITT occurs. Finally, an example of partial thermalization applicable to rotating two-dimensional gases is presented.

There is extensive literature on how to determine the work involving a Brownian particle interacting with an external field and submerged in a thermal reservoir. However, the information supplied is essentially theoretical without specific calculations to show how this property changes with the system parameters and initial conditions. In this article, we provide explicit calculations of the optimal work considering the particle is under the influence of a time-dependent off-centered moving harmonic potential. It is done for all physical values of the friction coefficient. The system is modeled through a more general version of the Langevin equation which encompasses its classical and quasiclassical version. From the equation that defines the work, the external protocol is found through a fairly current extended version of the Euler-Lagrange equation that unifies the local and nonlocal contributions in a simple expression. The protocol is linear and, unlike previous work, not only changes the initial velocity of the particle but also its acceleration. Calculations were done for friction constants $\gamma$ spanning all possible values. The periodic $\gamma =1$ shows discontinuities in the optimal work of the interplay of concentration and diffusion processes acting periodically in the dynamics. For higher values work appears to be as a smooth function of time, while the truly overdamped, where the inertial effect can be discarded, agrees with the analytical result up to a time where the numerical overdamped algorithm provides a different solution due to its inability to discard entirely the inertial effect.

Rotobreathers in the chain of coupled linearly elastic rotators are analyzed. Each rotator is a particle connected by a massless elastic rod with a frictionless pivot; it has two degrees of freedom, length and angle of rotation. The rods of the rotators and the elastic bonds between the nearest rotators are linearly elastic, and the nonlinearity of the system is of a purely geometric nature. It is shown that long-lived rotobreathers can exist if the stiffness of the rods is high enough to create a relatively wide gap in the phonon spectrum of the chain. The frequency of angular rotation of the rotobreather cannot be above the optical band of the phonon spectrum and is in the spectrum gap. Generally speaking, the rotation of the rotobreather is accompanied by radial oscillations; however, one can choose such initial conditions so that the radial oscillations are minimal. Some parameters of rotobreathers with minimal radial vibrations are presented on the basis of numerical simulations. The results obtained qualitatively describe the behavior of physical systems with coupled rotators.

We study the ensembles of direct product of $m$ random unitary matrices of size $N$ drawn from a given circular ensemble. We calculate the statistical measures, viz. number variance and spacing distribution to investigate the level correlations and fluctuation properties of the eigenangle spectrum. Similar to the random unitary matrices, the level statistics is stationary for the ensemble constructed by their direct product. We find that the eigenangles are uncorrelated in the small spectral intervals. While, in large spectral intervals, the spectrum is rigid due to strong long-range correlations between the eigenangles. The analytical and numerical results are in good agreement. We also test our findings on the multipartite system of quantum kicked rotors.

We study the energy distribution during the emergence of a quasiequilibrium (QE) state in the course of relaxation to equipartition in slow-fast Hamiltonian systems. A bead-spring model where beads (masses) are connected by springs is considered. The QE lasts for a long time because the energy exchange between the high-frequency vibrational and other motions is prevented when springs in the molecule become stiff. We numerically calculated the time-averaged kinetic energy and found that the kinetic energy of the solvent particles was always higher than that of the bead in a molecule. This is explained by adopting the equipartition theorem in QE, and it agrees well with the numerical results. The energy difference can help determine how far the system is from achieving equilibrium, and it can be used as an indicator of the number of frozen or inactive degrees existing in the molecule.

Some characteristics of complex networks need to be derived from global knowledge of the network topologies, which challenges the practice for studying many large-scale real-world networks. Recently, the geometric renormalization technique has provided a good approximation framework to significantly reduce the size and complexity of a network while retaining its “slow” degrees of freedom. However, due to the finite-size effect of real networks, excessive renormalization iterations will eventually cause these important “slow” degrees of freedom to be filtered out. In this paper, we systematically investigate the finite-size scaling of structural and dynamical observables in geometric renormalization flows of both synthetic and real evolutionary networks. Our results show that these observables can be well characterized by a certain scaling function. Specifically, we show that the critical exponent implied by the scaling function is independent of these observables but depends only on the structural properties of the network. To a certain extent, the results of this paper are of great significance for predicting the observable quantities of large-scale real systems and further suggest that the potential scale invariance of many real-world networks is often masked by finite-size effects.

Identifying the mechanism of intercellular feedback regulation is critical for the basic understanding of tissue growth control in organisms. In this paper, we analyze a tissue growth model consisting of a single lineage of two cell types regulated by negative feedback signaling molecules that undergo spatial diffusion. By deriving the fixed points for the uniform steady states and carrying out linear stability analysis, phase diagrams are obtained analytically for arbitrary parameters of the model. Two different generic growth modes are found: blow-up growth and final-state controlled growth which are governed by the nontrivial fixed point and the trivial fixed point, respectively, and can be sensitively switched by varying the negative feedback regulation on the proliferation of the stem cells. Analytic expressions for the characteristic timescales for these two growth modes are also derived. Remarkably, the trivial and nontrivial uniform steady states can coexist and a sharp transition occurs in the bistable regime as the relevant parameters are varied. Furthermore, the bistable growth properties allows for the external control to switch between these two growth modes. In addition, the condition for an early accelerated growth followed by a retarded growth can be derived. These analytical results are further verified by numerical simulations and provide insights on the growth behavior of the tissue. Our results are also discussed in the light of possible realistic biological experiments and tissue growth control strategy. Furthermore, by external feedback control of the concentration of regulatory molecules, it is possible to achieve a desired growth mode, as demonstrated with an analysis of boosted growth, catch-up growth and the design for the target of a linear growth dynamic.

Chronological skin aging is a complex process that is controlled by numerous intrinsic and extrinsic factors. One major factor is the gradual degradation of the dermal collagen fiber network. As a step toward understanding the mechanistic importance of dermal tissue in the process of aging, this study employs analytical and multiscale computational models to elucidate the effect of collagen fiber bundle disintegration on the mechanical properties and topography of skin. Here, human skin is modeled as a soft composite with an anisotropic dermal layer. The anisotropy of the tissue is governed by collagen fiber bundles with varying densities, average fiber alignments, and normalized alignment distributions. In all finite element models examined, collagen fiber bundle degradation results in progressive decreases in dermal and full-thickness composite stiffness. This reduction is more profound when collagen bundles align with the compression axis. Aged skin models with low collagen fiber bundle densities under compression exhibit notably smaller critical wrinkling strains and larger critical wavelengths than younger skin models, in agreement with in vivo wrinkling behavior with age. The propensity for skin wrinkling can be directly attributable to the degradation of collagen fiber bundles, a relationship that has previously been assumed but unsubstantiated. While linear-elastic analytical models fail to capture the postbuckling behavior in skin, nonlinear finite element models can predict the complex bifurcations of the compressed skin with different densities of collagen bundles.

For system coupled to heat baths, typical nonequilibrated processes, e.g., induced by varying an external parameter without waiting for equilibration in between, are very different from the corresponding equilibrium infinitely slow processes. Nevertheless, there are connections between equilibrium and nonequilibrated behaviors, e.g., the theorems of Jarzynski and Crooks, which relate the distribution $P\left(W\right)$ of nonequilibrium work to the free energy differences $\mathrm{\Delta }F$. Here we study the naturally arising question, whether those relevant but rare trajectories, which exhibit these work values, show a higher degree of similarity to equilibrium. For convenience, we have chosen a simple model of RNA secondary structures (or single-stranded DNA), here modeling a medium-size hairpin structure, under influence of a varying external force. This allows us to measure the work $W$ during the resulting fast unfolding and refolding processes within Monte Carlo simulations, i.e., in nonequilibrium. Also we sample numerically efficiently directly in exact equilibrium, for comparison. Using a sophisticated large-deviation algorithm, we are able to measure work distributions with high precision down to probabilities as small as ${10}^{-46}$, enabling us to verify the Crooks and Jarzynski theorems. Furthermore, we analyze force-extension curves and the configurations of the secondary structures during unfolding and refolding for typical equilibrium processes and nonequilibrated processes. We find that the nonequilibrated processes where the work values are close to those which are most relevant for applying Crooks and Jarzynski theorems, respectively, but which occur with exponential small probabilities, are most and quite similar to the equilibrium processes.

Nonlinear waves of electrical excitation initiate cardiac contraction. Abnormal wave propagation in the heart, e.g., spiral waves, can lead to sudden cardiac arrest. This study analyzed the dynamics of spiral waves under the influence of an instability called negative filament tension, and examined how the spiral waves can be eliminated through high-frequency pacing. A generic anatomical model of the left ventricle of the human heart and the Aliev–Panfilov model for cardiac tissue were used. The study showed that the source of such arrhythmia is elongated filaments with lengths that can be 10–20 times greater than the characteristic thickness of the heart wall. In anisotropic tissue, the filament elongated before it was annihilated at the base of the heart. The spiral waves were eliminated through overdrive pacing with stimulation periods from 0.8 to 0.95 relative to the spiral wave period. The minimum time for the expulsion was about 10 s.

The transport coefficients for dilute granular gases of inelastic and rough hard disks or spheres with constant coefficients of normal ($\alpha$) and tangential ($\beta$) restitution are obtained in a unified framework as functions of the number of translational ($d_t$) and rotational ($d_r$) degrees of freedom. The derivation is carried out by means of the Chapman–Enskog method with a Sonine-like approximation in which, in contrast to previous approaches, the reference distribution function for angular velocities does not need to be specified. The well-known case of purely smooth $d$-dimensional particles is recovered by setting $d_t=d$ and formally taking the limit $d_r\to 0$. In addition, previous results [G. M. Kremer, A. Santos, and V. Garzó, Phys. Rev. E 90, 022205 (2014)] for hard spheres are reobtained by taking $d_t=d_r=3$, while novel results for hard-disk gases are derived with the choice $d_t=2, d_r=1$. The singular quasismooth limit ($\beta \to -1$) and the conservative Pidduck's gas ($\alpha =\beta =1$) are also obtained and discussed.

Conditions for the stability under linear perturbations around the homogeneous cooling state are studied for dilute granular gases of inelastic and rough hard disks or spheres with constant coefficients of normal ($\alpha$) and tangential ($\beta$) restitution. After a formally exact linear stability analysis of the Navier–Stokes–Fourier hydrodynamic equations in terms of the translational ($d_t$) and rotational ($d_r$) degrees of freedom, the transport coefficients derived in the companion paper [A. Megías and A. Santos, “Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. I. Transport coefficients” Phys. Rev. E 104, 034901 (2021)] are employed. Known results for hard spheres [Garzó, Santos, and Kremer, Phys. Rev. E 97, 052901 (2018)] are recovered by setting $d_t=d_r=3$, while novel results for hard disks ($d_t=2, d_r=1$) are obtained. In the latter case, a high-inelasticity peculiar region in the $(\alpha ,\beta )$ parameter space is found, inside which the critical wave number associated with the longitudinal modes diverges. Comparison with event-driven molecular dynamics simulations for dilute systems of hard disks at $\alpha =0.2$ shows that this theoretical region of absolute instability may be an artifact of the extrapolation to high inelasticity of the approximations made in the derivation of the transport coefficients, although it signals a shrinking of the conditions for stability. In the case of moderate inelasticity ($\alpha =0.7$), however, a good agreement between the theoretical predictions and the simulation results is found.

We investigate the operator growth dynamics of the transverse field Ising spin chain in one dimension as varying the strength of the longitudinal field. An operator in the Heisenberg picture spreads in the extended Hilbert space. Recently, it has been proposed that the spreading dynamics has a universal feature signaling chaoticity of underlying quantum dynamics. We demonstrate numerically that the operator growth dynamics in the presence of the longitudinal field follows the universal scaling law for one-dimensional chaotic systems. We also find that the operator growth dynamics satisfies a crossover scaling law when the longitudinal field is weak. The crossover scaling confirms that the uniform longitudinal field makes the system chaotic at any nonzero value. We also discuss the implication of the crossover scaling on the thermalization dynamics and the effect of a nonuniform local longitudinal field.