One class of random walks with infinite memory, so-called elephant random walks, are simple models describing anomalous diffusion. We present a surprising connection between these models and bond percolation on random recursive trees. We use a coupling between the two models to translate results from elephant random walks to the percolation process. We calculate, besides other quantities, exact expressions for the first and the second moment of the root cluster size and of the number of nodes in child clusters of the first generation. We further introduce another model, the skew elephant random walk, and calculate the first and second moment of this process.

We start from a continuous extension of a mean field approach of the quorum percolation model, accounting for the response of in vitro neuronal cultures, to carry out a normal form analysis of the critical behavior. We highlight the effects of nonlinearities associated with this mean field approach even in the close vicinity of the critical point. Statistical properties of random networks with Gaussian in-degree are related to the outcoming links distribution. Finite size analysis of explicit Monte Carlo simulations enables us to confirm the relevance of the mean field approach on such networks and to show that the order parameter is weakly self-averaging; dynamical relaxation is investigated. Furthermore we derive a mean field equation taking into account the effect of inhibitory neurons and discuss the equivalence with a purely excitatory network.

We examine the transport of extended and localized excitations in one-dimensional linear chains populated by linear and nonlinear symmetric identical $n$-mers (with $n=3$, 4, 5, and 6), randomly distributed. First, we examine the transmission of plane waves across a single linear $n$-mer, paying attention to its resonances, and looking for parameters that allow resonances to merge. Within this parameter regime we examine the transmission of plane waves through a disordered and nonlinear segment composed by $n$-mers randomly placed inside a linear chain. It is observed that nonlinearity tends to inhibit the transmission, which decays as a power law at long segment lengths. This behavior still holds when the $n$-mer parameters do not obey the resonance condition. On the other hand, the mean square displacement exponent of an initially localized excitation does not depend on nonlinearity at long propagation distances $z$, and shows a superdiffusive behavior $\sim z^{1.8}$ for all $n$-mers, when parameters obey the resonance merging condition; otherwise the exponent reverts back to the random dimer model value $\sim z^{1.5}$.

We numerically investigate the frequency bandwidth and the autocorrelation characteristics of chaotic temporal wave forms in unidirectionally coupled semiconductor lasers with time-delayed optical feedback. We evaluate the complexity of the chaotic temporal wave forms by using Lyapunov exponents. We found that larger maximum Lyapunov exponents can be obtained for smaller peak values of the autocorrelation function at the delay time of the optical feedback. On the contrary, the maximum Lyapunov exponent is independent from the frequency bandwidth of the chaotic temporal wave forms.

A theory is developed for the nanoscale patterns formed when the (001) surface of a crystalline binary material with fourfold rotational symmetry is subjected to normal-incidence ion bombardment. The deterministic nonlinear continuum equations account for the Ehrlich-Schwoebel barrier, which produces uphill atomic currents on the crystal surface. We demonstrate that highly ordered square arrays of nanopyramids can form in a certain region of parameter space. An Ehrlich-Schwoebel barrier is required for patterns of this kind to develop. For another range of parameters, a disordered square array of nanodots forms and the pattern coarsens over time.

Characterization of spatiotemporal dynamics of coupled oscillatory systems can be done by computing the Lyapunov exponents. We study the spatiotemporal dynamics of randomly coupled network of Kuramoto oscillators and find that the spectral statistics obtained from the Lyapunov exponent spectrum show interesting sensitivity to the coupling matrix. Our results indicate that in the weak coupling limit the gap distribution of the Lyapunov spectrum is Poissonian, while in the limit of strong coupling the gap distribution shows level repulsion. Moreover, the oscillators settle to an inhomogeneous oscillatory state, and it is also possible to infer the random network properties from the Lyapunov exponent spectrum.

We consider a reaction-diffusion system in a homogeneous stable steady state. On perturbation by a time-dependent sinusoidal forcing of a suitable scaling parameter the system exhibits parametric spatiotemporal instability beyond a critical threshold frequency. We have formulated a general scheme to calculate the threshold condition for oscillation and the range of unstable spatial modes lying within a V-shaped region reminiscent of Arnold's tongue. Full numerical simulations show that depending on the specificity of nonlinearity of the models, the instability may result in time-periodic stationary patterns in the form of standing clusters or spatially localized breathing patterns with characteristic wavelengths. Our theoretical analysis of the parametric oscillation in reaction-diffusion system is corroborated by full numerical simulation of two well-known chemical dynamical models: chlorite-iodine-malonic acid and Briggs-Rauscher reactions.

The spatial distribution of people exhibits clustering across a wide range of scales, from household $\left(\sim {10}^{-2}\text{km}\right)$ to continental $\left(\sim {10}^4\text{km}\right)$ scales. Empirical data indicate simple power-law scalings for the size distribution of cities (known as Zipf's law) and the population density fluctuations as a function of scale. Using techniques from random field theory and statistical physics, we show that these power laws are fundamentally a consequence of the scale-free spatial clustering of human populations and the fact that humans inhabit a two-dimensional surface. In this sense, the symmetries of scale invariance in two spatial dimensions are intimately connected to urban sociology. We test our theory by empirically measuring the power spectrum of population density fluctuations and show that the logarithmic slope $\alpha =2.04\pm 0.09$, in excellent agreement with our theoretical prediction $\alpha =2$. The model enables the analytic computation of many new predictions by importing the mathematical formalism of random fields.

The formation of coherent patterns in swarms of interacting self-propelled autonomous agents is a subject of great interest in a wide range of application areas, ranging from engineering and physics to biology. In this paper, we model and experimentally realize a mixed-reality large-scale swarm of delay-coupled agents. The coupling term is modeled as a delayed communication relay of position. Our analyses, assuming agents communicating over an Erdös-Renyi network, demonstrate the existence of stable coherent patterns that can be achieved only with delay coupling and that are robust to decreasing network connectivity and heterogeneity in agent dynamics. We also show how the bifurcation structure for emergence of different patterns changes with heterogeneity in agent acceleration capabilities and limited connectivity in the network as a function of coupling strength and delay. Our results are verified through simulation as well as preliminary experimental results of delay-induced pattern formation in a mixed-reality swarm.

Nuclear magnetic resonance (NMR) diffusion experiments are widely employed as they yield information about structures hindering the diffusion process, e.g., about cell membranes. While it has been shown in recent articles that these experiments can be used to determine the shape of closed pores averaged over a volume of interest, it is still an open question how much information can be gained in open well-connected systems. In this theoretical work, it is shown that the full structure information of connected periodic systems is accessible. To this end, the so-called “SEquential Rephasing by Pulsed field-gradient Encoding N Time intervals” (SERPENT) sequence is used, which employs several diffusion encoding gradient pulses with different amplitudes. Two two-dimensional solid matrices that are surrounded by an NMR-visible medium are considered: a hexagonal lattice of cylinders and a rectangular lattice of isosceles triangles.

The dynamics of complex networks, a current hot topic in many scientific fields, is often coded through the corresponding Laplacian matrix. The spectrum of this matrix carries the main features of the networks' dynamics. Here we consider the deterministic networks which can be viewed as “comb-of-comb” iterative structures. For their Laplacian spectra we find analytical equations involving Chebyshev polynomials whose properties allow one to analyze the spectra in deep. Here, in particular, we find that in the infinite size limit the corresponding spectral dimension goes as $d_s\to 2$. The $d_s$ leaves its fingerprint on many dynamical processes, as we exemplarily show by considering the dynamical properties of polymer networks, including single monomer displacement under a constant force, mechanical relaxation, and fluorescence depolarization.

A biological system consists of a variety of polymers that are synthesized from monomers by catalysis, which exists only for some long polymers. It is important to elucidate the emergence and sustenance of such autocatalytic polymerization. We analyze here the stochastic polymerization reaction dynamics to investigate the transition time from a state with almost no catalysts to a state with sufficient catalysts. We found an optimal volume that minimizes this transition time, which agrees with the inverse of the catalyst concentration at the unstable fixed point that separates the two states, as is theoretically explained. Relevance to the origin of life is also discussed.

Multilayer core-shell structures are frequently formed in polymers and alloys when temperature and concentration fields are well symmetrical spatially. Here we report that two- to five-layer core-shell microstructures were the dominant structural morphology of a binary $\mathrm{F}{\mathrm{e}}_{50}\mathrm{S}{\mathrm{n}}_{50}$ immiscible alloy solidified under the containerless and microgravity states within a drop tube. Three dimensional phase field simulation reveals that both the uniformly dispersive structure and the multilayer core-shells are the various metastable and transitional states of the liquid phase separation process. Only the two-layer core-shell is the most stable microstructure with the lowest chemical potential. Because of the suppression of Stokes motion, solutal Marangoni migration becomes important to drive the evolution of core-shell structures.

Photoinduced order-increasing phase transitions can occur in dye-liquid crystal mixtures when the photoproduct of the excitation of the dye molecules is more compatible with the liquid crystalline medium than the initial dye species. A detailed investigation of the photoinduced changes of the phase behavior and optical properties of mixtures of liquid crystals with naphthopyran guests upon exposure to light at 365 nm is presented here. In these guest-host systems, the nematic-to-isotropic phase transition temperature is increased upon irradiation. We show that the nematic range can be extended up to 2.9 °C by illumination in 5CB ($4-n$-pentyl-4′-cyanobiphenyl) liquid crystal mixtures. The order parameter is significantly increased by illumination at all temperatures within the nematic range and the changes are larger at higher concentrations of the guests. In particular, the illuminated guest-host mixtures exhibit order parameters close to those of the neat liquid crystal host at the same temperature relative to the clearing point. An improved understanding of the photophysical processes taking place at the molecular level in these material systems can inform the design of photoresponsive materials and enhance their potential utility in optical or photonic devices.

Internal fluid pressure often plays an important role in the rupture of brittle materials. This is a major concern for many engineering applications and for natural hazards. More specifically, the mechanisms through which fluid pressure, applied at a microscale, can enhance the failure at a macroscale and accelerate damage dynamics leading to failure remains unclear. Here we revisit the fiber bundle model by accounting for the effect of fluid under pressure that contributes to the global load supported by the fiber bundle. Fluid pressure is applied on the broken fibers, following Biot's theory. The statistical properties of damage avalanches and their evolution toward macrofailure are analyzed for a wide range of fluid pressures. The macroscopic strength of the new model appears to be strongly controlled by the action of the fluid, particularly when the fluid pressure becomes comparable with the fiber strength. The behavior remains consistent with continuous transition, i.e., second order, including for large pressure. The main change concerns the damage acceleration toward the failure that is well modeled by the concept of sweeping of an instability. When pressure is increased, the exponent $\beta$ characterizing the power-law distribution avalanche sizes significantly decreases and the exponent $\gamma$ characterizing the cutoff divergence when failure is approached significantly increases. This proves that fluid pressure plays a key role in failure process acting as destabilization factor. This indicates that macrofailure occurs more readily under fluid pressure, with a behavior that becomes progressively unstable as fluid pressure increases. This may have considerable consequences on our ability to forecast failure when fluid pressure is acting.

One-dimensional (1D) models are widely employed to simplify the analysis of axisymmetric capillary jets. These models postulate that, for slender deformations of the free surface, the radial profile of the axial velocity can be approximated as uniform (viscous slice, averaged, and Cosserat models) or parabolic (parabolic model). In classical works on spatial stability analysis with 1D models, considerable misinterpretation was generated about the modes yielded by each model. The already existing physical analysis of three-dimensional (3D) axisymmetric spatial modes enables us to relate these 1D spatial modes to the exact 3D counterparts. To do so, we address the surface stimulation problem, which can be treated as linear, by considering the effect of normal and tangential stresses to perturb the jet. A Green's function for a spatially local stimulation having a harmonic time dependence provides the general formalism to describe any time-periodic stimulation. The Green's function of this signaling problem is known to be a superposition of the spatial modes, but in fact these modes are of fundamental nature, i.e., not restricted to the surface stimulation problem. The smallness of the wave number associated with each mode is the criterion to validate or invalidate the 1D approaches. The proposed axial-velocity profiles (planar or parabolic) also have a remarkable influence on the outcomes of each 1D model. We also compare with the classical 3D results for (i) conditions for absolute instability, and (ii) the amplitude of the unstable mode resulting from both normal and tangential surface stress stimulation. Incidentally, as a previous task, we need to re-deduce 1D models in order to include eventual stresses of various possible origins (electrohydrodynamic, thermocapillary, etc.) applied on the free surface, which were not considered in the previous general formulations.

Controlled breakup of droplets using heat or acoustics is pivotal in applications such as pharmaceutics, nanoparticle production, and combustion. In the current work we have identified distinct thermal acoustics–induced deformation regimes (ligaments and bubbles) and breakup dynamics in externally heated acoustically levitated bicomponent (benzene-dodecane) droplets with a wide variation in volatility of the two components (benzene is significantly more volatile than dodecane). We showcase the physical mechanism and universal behavior of droplet surface caving in leading to the inception and growth of ligaments. The caving of the top surface is governed by a balance between the acoustic pressure field and the restrictive surface tension of the droplet. The universal collapse of caving profiles for different benzene concentration ($<70\%$ by volume) is shown by using an appropriate time scale obtained from force balance. Continuous caving leads to the formation of a liquid membrane–type structure which undergoes radial extension due to inertia gained during the precursor phase. The membrane subsequently closes at the rim and the kinetic energy leads to ligament formation and growth. Subsequent ligament breakup is primarily Rayleigh-Plateau type. The breakup mode shifts to diffusional entrapment–induced boiling with an increase in concentration of the volatile component (benzene $>70\%$ by volume). The findings are portable to any similar bicomponent systems with differential volatility.

We discuss the structure and geometrical characteristics of coherent vortices appearing as a result of the inverse cascade in two-dimensional turbulence in a finite box. We demonstrate that the universal velocity profile, established by J. Laurie et al. [Phys. Rev. Lett. 113, 254503 (2014)], corresponds to the passive regime of flow fluctuations. We find the vortex core radius and the vortex size, and we argue that the amount of vortices generated in the box depends on the system parameters.

The authors suggest a model to simulate the dynamics of ions in a supersonic plasma jet. The model relies on experimental argon ion, ${\mathrm{Ar}}^{+}$, energy distribution functions measured by a quadrupole mass spectrometer at different positions along the central axis of a supersonic argon plasma jet. The latter is generated by the pressure difference between two vacuum chambers connected through a converging nozzle: a high-pressure chamber ($P\simeq 3.20$ Pa), where an inductively coupled argon plasma discharge is maintained, and a lower-pressure one ($P\simeq 0.11$ Pa), where the plasma jet expands. The model is based on the integration of the equations of motion of a single ${\mathrm{Ar}}^{+}$, moving along the supersonic jet in a reference system in which neutral species are at rest. ${\mathrm{Ar}}^{+}$-Ar induced dipole interactions are treated using a 12-4 Lennard-Jones potential. The resulting collisions are considered to be purely elastic, and in addition to them, we allow for charge transfer processes. The energy and position of $1000 {\mathrm{Ar}}^{+}$ were calculated, using an integration time step of 10 ps for ion trajectories ranging from 5 mm to 20 mm from the nozzle, well inside the spatial extension of the supersonic jet. The numerically obtained ion energy distribution functions agree remarkably well with the experimental measurements. From our calculations we can draw conclusions about the energy loss and the mean free paths along the jet. In particular, we can distinguish between processes with and without charge transfer, allowing us to determine the effect of charge exchange phenomena in which the ion changes its nature. The calculated mean free paths were used to evaluate the effective cross sections for momentum transfer and charge transfer collisions, valid for ion energies in the range (0.5–10) eV, in very good agreement with those reported in the literature.

For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, and lattice quantum chromodynamics calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied on to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple subareas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a “bridge link” to the imaginary-time path integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling.