Prediction in complex systems at criticality is believed to be very difficult, if not impossible. Of particular interest is whether earthquakes, whose distribution follows a power-law (Gutenberg-Richter) distribution, are in principle unpredictable. We study the predictability of event sizes in the Olmai-Feder-Christensen model at different proximities to criticality using a convolutional neural network. The distribution of event sizes satisfies a power law with a cutoff for large events. We find that predictability decreases as criticality is approached and that prediction is possible only for large, nonscaling events. Our results suggest that earthquake faults that satisfy Gutenberg-Richter scaling are difficult to forecast.

We show that the Olami-Feder-Christensen model exhibits an effective ergodicity breaking transition as the noise is varied. Above the critical noise, the system is effectively ergodic because the time-averaged stress on each site converges to the global spatial average. In contrast, below the critical noise, the stress on individual sites becomes trapped in different limit cycles, and the system is not ergodic. To characterize this transition, we use ideas from the study of dynamical systems and compute recurrence plots and the recurrence rate. The order parameter is identified as the recurrence rate averaged over all sites and exhibits a jump at the critical noise. We also use ideas from percolation theory and analyze the clusters of failed sites to find numerical evidence that the transition, when approached from above, can be characterized by exponents that are consistent with hyperscaling.

We revisit the problem of excluded volume deposition of rigid rods of length $k$ unit cells over square lattices. Two new features are introduced: (a) two new short-distance complementary order parameters, called $\mathrm{\Pi }$ and $\mathrm{\Sigma }$, are defined, calculated, and discussed to deal with the phases present as coverage increases; (b) the interpretation is now done beginning at the high-coverage ordered phase which allows us to interpret the low-coverage nematic phase as an ergodicity breakdown present only when $k\ge 7$. In addition the data analysis invokes both mutability (dynamical information theory method) and Shannon entropy (static distribution analysis) to further characterize the phases of the system. Moreover, mutability and Shannon entropy are compared, and we report the advantages and disadvantages they present for their use in this problem.

We propose a kinetic gelation model of polymer growth with two monomeric types that have distinct functionalities (reaction sites), and can polymerize using different reaction types. The heterotypic aggregation of two monomer types is modeled using a moment generating function approach by tracking the temporal evolution of a closed system of moment equations up until gelation. We investigate several scenarios of polymerization with two distinct monomers that differ in the types of reactions that can occur. We determine numerical and analytical conditions for finite time blow-up (the emergence of an oligomer of infinite size) that depend on initial conditions, reaction rates, and number of reaction sites per monomer.

We investigate the transport of active matter in the presence of a disordered square lattice of asymmetric obstacles, which is built by removing a fraction of them from the initial full lattice. We obtain a spontaneous inversion of the net particle current, compared to the usual sense of such a current as a function of the fraction of removed obstacles and particle density. We observed that the negative current regime is the consequence of trapping of particles among the obstacles which favors that more particles move in the negative current direction. The same reasoning applies to the positive current regime as well. We show a calculation that partially reproduces our numerical results, based on the argument that the mean current is given by the product of the mean speed and the mean number of travelers in each direction; the breakdown of this assumption is responsible for the failure of our calculation to reproduce the initial negative current regime.

The interaction of drops and electric fields occurs in many applications like electrowetting, electrospinning, atomization, but also causes unwanted effects like the aging of high-voltage composite insulators. Water drops are influenced by electric fields due to the polar properties of the water molecules. The behavior of the drops depends on several parameters like the orientation and strength of the electric field, drop volume, and frequency of the applied field. In addition, electric charges can influence the behavior of drops significantly. However, the impact of electric charges, including the interaction with the drop as well as the electric field strength, is far from being well understood. In this work, the impact of electric charges on the behavior of single sessile drops is investigated experimentally under well-defined conditions. The effects of the drop volume, electric field strength, field frequency, and electric charge of the drop are studied. The necessary amount of charge to change the behavior of drops, depending on the applied electric field and drop volume, is determined and different drop behavior regimes are identified. Depending on the boundary conditions, the drop oscillates with the same or double the frequency of the applied voltage. The different regimes are investigated for the first three oscillation modes. The obtained results will help to improve the understanding and to manipulate the behavior of uncharged and charged drops in strong electric fields.

The effective one-component plasma (EOCP) model has provided an efficient approach to obtaining many important thermophysical parameters of hot dense matter [J. Clérouin, et al., Phys. Rev. Lett. 116, 115003 (2016)]. In this paper, we perform extensive quantum molecular dynamics (QMD) simulations to determine the equations of state, ionic structures, and ionic transport properties of neon and krypton within the warm dense matter (WDM) regime where the density ( $\rho$ ) is up to 12 $\mathrm{g}/{\mathrm{cm}}^3$ and the temperature ($T$) is up to 100 kK. The simulated data are then used as a benchmark to explicitly evaluate the EOCP and Yukawa models. It is found that, within present $\rho$-T regime, the EOCP model can excellently reproduce the diffusion and viscosity coefficients of neon and krypton due to the fact that this model defines a system which nearly reproduces the actual physical states of WDM. Therefore, the EOCP model may be a promising alternative approach to reasonably predicting the transport behaviors of matter in WDM regime at lower QMD computational cost. The evaluation of Yukawa model shows that the consideration of the energy level broadening effect in the average atom model is necessary. Finally, with the help of EOCP model, the Stokes-Einstein relationships about neon and krypton are discussed, and fruitful plasma parameters as well as a practical $\rho$-T-dependent formula of the effective coupling parameter are obtained. These results not only provide valuable information for future theoretical and experimental studies on dense neon and krypton but also reveal the applicability of the EOCP model and the limitation of the Yukawa model in WDM regime and further support the continuing search for a unified description of ionic transport in dense plasma.

Control of generically scale-invariant systems, i.e., targeting specific cooperative features in nonlinear stochastic interacting systems with many degrees of freedom subject to strong fluctuations and correlations that are characterized by power laws, remains an important open problem. We study the control of surface roughness during a growth process described by the Kardar-Parisi-Zhang (KPZ) equation in $(1+1)$ dimensions. We achieve the saturation of the mean surface roughness to a prescribed value using nonlinear feedback control. Numerical integration is performed by means of the pseudospectral method, and the results are used to investigate the coupling effects of controlled (linear) and uncontrolled (nonlinear) KPZ dynamics during the control process. While the intermediate time kinetics is governed by KPZ scaling, at later times a linear regime prevails, namely the relaxation toward the desired surface roughness. The temporal crossover region between these two distinct regimes displays intriguing scaling behavior that is characterized by nontrivial exponents and involves the number of controlled Fourier modes. Due to the control, the height probability distribution becomes negatively skewed, which affects the value of the saturation width.

The statistics of the scattering of waves inside single ray-chaotic enclosures have been successfully described by the random coupling model (RCM). We expand the RCM to systems consisting of multiple complex ray-chaotic enclosures with various coupling scenarios. The statistical properties of the model-generated quantities are tested against measured data of electrically large multicavity systems of various designs. The statistics of model-generated transimpedance and induced voltages on a load impedance agree well with the experimental results. The RCM coupled chaotic enclosure model is general and can be applied to other physical systems, including coupled quantum dots, disordered nanowires, and short-wavelength electromagnetic and acoustic propagation through rooms in buildings, aircraft, and ships.

Weak turbulence has been investigated in nonlinear-nonequilibrium physics to understand universal characteristics near the transition point of ordered and disordered states. Here the one-dimensional Nikolaevskii turbulence, which is a mathematical model of weak turbulence, is studied theoretically. We calculate the velocity field of the Nikolaevskii turbulence assuming a convective structure and carry out tagged-particle simulations in the flow to clarify the Nikolaevskii turbulence from the Lagrangian description. The tagged particle diffuses in the disturbed flow and the diffusion is superdiffusive in an intermediate timescale between ballistic and normal-diffusive scale. The diffusion of the slow structure is characterized by the power law for the control parameter near the transition point of the Nikolaevskii turbulence, suggesting that the diffusive characteristics of the slow structure remain scale invariant. We propose a simplified model, named two-scale Brownian motion, which reveals a hierarchy in the Nikolaevskii turbulence.

Spreading processes are conventionally monitored on a macroscopic level by counting the number of incidences over time. The spreading process can then be modeled either on the microscopic level, assuming an underlying interaction network, or directly on the macroscopic level, assuming that microscopic contributions are negligible. The macroscopic characteristics of both descriptions are commonly assumed to be identical. In this work we show that these characteristics of microscopic and macroscopic descriptions can be different due to coalescence, i.e., a node being activated at the same time by multiple sources. In particular, we consider a (microscopic) branching network (probabilistic cellular automaton) with annealed connectivity disorder, record the macroscopic activity, and then approximate this activity by a (macroscopic) branching process. In this framework we analytically calculate the effect of coalescence on the collective dynamics. We show that coalescence leads to a universal nonlinear scaling function for the conditional expectation value of successive network activity. This allows us to quantify the difference between the microscopic model parameter and established estimates of the macroscopic branching parameter. To overcome this difference, we propose a nonlinear estimator that correctly infers the microscopic model parameter for all system sizes.

Recent experiments support the adder model for E. coli division control. This model posits that bacteria grow, on average, a fixed size before division. It also predicts decorrelation between the noise in the added size and the size at birth. Here we develop a theory based on stochastic hybrid systems which could explain the main division strategies, including not only the adder strategy but the whole range from sizer to timer. We use experiments to explore the division control of E. coli growing with glycerol as carbon source. In this medium, the division strategy is sizerlike, which means that the added size decreases with the size at birth. We found, as our theory predicts, that in a sizerlike strategy the mean added size decreases with the size at birth while the noise in added size increases. We discuss possible molecular mechanisms underlying this strategy and propose a general model that encompasses the different division strategies.

We present a numerical investigation of the effects of gas rarefaction on the energy dynamics of resonating planar nonlinear acoustic waves. The problem setup is a gas-filled, adiabatic tube, excited from one end by a piston oscillating at the fundamental resonant frequency of the tube and closed at the other end; nonlinear wave steepening occurs until a limit cycle is reached, resulting in shock formation for sufficiently high densities. The Knudsen number, defined here as the ratio of the characteristic molecular collision timescale to the resonance period, is varied in the range $\mathrm{Kn}={10}^{-1}–{10}^{-5}$, from rarefied to dense regime, by changing the base density of the gas. The working fluid is Argon. A numerical solution of the Boltzmann equation, closed with the Bhatnagar-Gross-Krook model, is used to simulate cases for $\mathrm{Kn}\ge 0.01$. The fully compressible one-dimensional Navier-Stokes equations are used for $\mathrm{Kn}<0.01$ with adaptive mesh refinement to resolve the resonating weak shocks, reaching wave Mach numbers up to 1.01. Nonlinear wave steepening and shock formation are associated with spectral broadening of the acoustic energy in the wavenumber-frequency domain; the latter is defined based on the exact energy corollary for second-order nonlinear acoustics derived by Gupta and Scalo [Phys. Rev. E 98, 033117 (2018)], representing the Lyapunov function of the system. At the limit cycle, the acoustic energy spectra exhibit an equilibrium energy cascade with a $-2$ slope in the inertial range, also observed in freely decaying nonlinear acoustic waves by the same authors. In the present system, energy is introduced externally via a piston at low wavenumbers or frequencies and balanced by thermoviscous dissipation at high wavenumbers or frequencies, responsible for the base temperature increase in the system. The thermoviscous dissipation rate is shown to scale as ${\mathrm{Kn}}^2$ for fixed Reynolds number based on the maximum velocity amplitude, i.e., increasing with the degree of flow rarefaction; consistently, the smallest length scale of the steepened waves at the limit cycle, corresponding to the thickness of the shock (when present) also increases with $\mathrm{Kn}$. For a given fixed piston velocity amplitude, the bandwidth of the inertial range of the spectral energy cascade decreases with increasing Knudsen numbers, resulting in a reduced resonant response of the system. By exploiting dimensionless scaling laws borrowed by Kolmogorov's theory of hydrodynamic turbulence, it is shown that an inertial range for spectral energy transfer can be expected for acoustic Reynolds numbers ${\mathrm{Re}}_{{\mathit{U}}_{\max }}>100$, based on the maximum acoustic velocity amplitude in the domain.

The generalized Schrödinger-Newton system of equations with both local and nonlocal nonlinearities is widely used to describe light propagating in nonlinear media under the paraxial approximation. However, its use is not limited to optical systems and can be found to describe a plethora of different physical phenomena, for example, dark matter or alternative theories for gravity. Thus, the numerical solvers developed for studying light propagating under this model can be adapted to address these other phenomena. Indeed, in this work we report the development of a solver for the HiLight simulations platform based on GPGPU supercomputing and the required adaptations for this solver to be used to test the impact of new extensions of the Theory of General Relativity in the dynamics of the systems. In this work we shall analyze theories with nonminimal coupling between curvature and matter. This approach in the study of these new models offers a quick way to validate them since their analytical analysis is difficult. The simulation module, its performance, and some preliminary tests are presented in this paper.

It is widely believed that mean-field theory is exact for a wide range of classical long-range interacting systems. Is this also true once quantum fluctuations have been accounted for? As a test case we study the Hamiltonian mean-field (HMF) model for a system of bosons which is predicted (according to mean-field theory) to undergo a second-order quantum phase transition at zero temperature. The ordered phase is characterized by a spontaneously broken $\text{O}\left(2\right)$ symmetry, which, despite occurring in a one-dimensional model, is not ruled out by the Mermin-Wagner theorem due to the presence of long-range interactions. Nevertheless, a spontaneously broken symmetry implies gapless Goldstone modes whose large fluctuations can restore broken symmetries. In this work we study the influence of quantum fluctuations by projecting the Hamiltonian onto the continuous subspace of symmetry-breaking mean-field states. We find that the energetic cost of gradients in the center-of-mass wave function inhibits the breaking of the $\text{O}\left(2\right)$ symmetry, but that the energetic cost is very small, scaling as $O(1/N^2)$. Nevertheless, for any finite $N$, no matter how large, this implies that the ground state has a restored $\text{O}\left(2\right)$ symmetry. Implications for the finite-temperature phases, as well as the classical limit, of the HMF model are discussed.

We study the planar motion of telegraphic processes. We derive the two-dimensional telegrapher's equation for isotropic and uniform motions starting from a random walk model which is the two-dimensional version of the multistate random walk with a continuum number of states representing the spatial directions. We generalize the isotropic model and the telegrapher's equation to include planar fractional motions. Earlier, we worked with the one-dimensional version [Masoliver, Phys. Rev. E 93, 052107 (2016)] and derived the three-dimensional version [Masoliver, Phys. Rev. E 96, 022101 (2017)]. An important lesson is that we cannot obtain the two-dimensional version from the three-dimensional or the one-dimensional one from the two-dimensional result. Each dimension must be approached starting from an appropriate random walk model for that dimension.

We study the phase dynamics in power grids in response to small disturbances and how this depends on the grid topology. To this end, we consider the swing equations in linear order in phase disturbances and solve the resulting linear wave equation, deriving the eigenmodes of the weighted graph Laplacian. A linear response expression for the deviation of frequency is given in terms of these eigenvalues and eigenvectors, which it is argued to be the basis for future power system stabilizers and other control measures in power systems. As an example, we present results for random networks based on the Watts-Strogatz model, where we observe a transition to localized eigenstates as the randomness in the degree distribution grows. Moreover, it is found that localization leads to faster decay rates. Thereby, disturbances are found to remain localized on a few nodes where they decay faster. Finally, we also consider the German transmission grid topology, where the eigenstate of the lowest eigenfrequency, the Fiedler vector, is found to be extended, with large intensities at the northwestern and southern boundaries.

We show that a non-Markovian behavior can appear in a type of Markovian multimeric channel. Such a channel consists of $N$ independent subunits, and each subunit has at least one open state and more than one closed state. Suppose the open state of the channel is defined as $M$ out of $N$ subunits in the open state with $N>M>0$. We show that, although the gating dynamics for each subunit between open and closed states is Markovian, the channel can show a memory behavior of weak anti-cross-correlation between the adjacent open and closed durations. Our study indicates that a non-Markovian binary time series can be obtained from a linear superposition of some independent channel subunits with Markovian gating dynamics.

As a unique subset of functional polymers, many biopolymers have a set of well-defined three-dimensional (3D) structural characteristics that can be described by spatial contacts between monomers. Statistical analysis of the contacts has been extremely productive in characterizing the biopolymer structural ensemble, such as for 3D chromosome structures. Often, native contacts and compartment structures are the focus of the studies, while the generic polymer aspect, such as the overall decaying of contacts with increasing sequence distance, is analyzed separately or preemptively removed. Here, we explore insights that can be gained by performing “compartment analysis” that keeps the distance decay, which we believe is particularly useful for characterizing the structure transformation of biopolymers. We tested contact analysis on several such transformations under physical perturbation or biological processes, including (1) unfolding of proteins induced by thermal denaturation, (2) chromosome conformation transition during the cell cycle, and (3) chromosome unpacking by physicochemical perturbations. Useful score functions were developed to further quantitatively characterize the transformation judging from the contact analysis. We also find that the sinusoidal undertone of eigenvector patterns (the “unwanted,” low frequency signal, in contrast to the detailed A/B compartment) that had previously been attributed to biological effects of centromere proximal and distal interactions may in fact reflect a universal feature of polymers that have relatively weaker long-range contacts.

Integrin receptor (IR) clustering is an example of pattern self-organization in biological systems. This paper describes a model for receptor activation whose content is guided by two major principles in cellular signal transduction: (i) Proteins cycle between different conformational states; (ii) the dynamics of their conformational dynamics is environment dependent. Based on a simple activation pathway where these two hypotheses are formulated in a self-consistent way, this paper focuses mainly on stochastic simulations valid in the limit of a small number of molecules. It is shown that coherent clustering can lead to digital signaling and receptor competition in biochemical systems where the model gives a recruitment mechanism for the reinforcement of the mechanical linkage with the extracellular matrix. Together with previous works, this paper provides a workable model for cell integrin adhesive structures when feedback mediated by membrane diffusing signals is dominant. Consequences are discussed in the framework of published data concerning the local production of a key phospholipid for cell signaling (${\mathrm{PIP}}_2$).