We investigate the effects of Markovian resetting events on continuous time random walks where the waiting times and the jump lengths are random variables distributed according to power-law probability density functions. We prove the existence of a nonequilibrium stationary state and finite mean first arrival time. However, the existence of an optimum reset rate is conditioned to a specific relationship between the exponents of both power-law tails. We also investigate the search efficiency by finding the optimal random walk which minimizes the mean first arrival time in terms of the reset rate, the distance of the initial position to the target, and the characteristic transport exponents.

Fluid properties near rough surfaces are crucial in describing fundamental surface phenomena and modern industrial material design implementations. One of the most powerful approaches to model real rough materials is based on the surface representation in terms of random geometry. Understanding the influence of random solid geometry on the low-temperature fluid thermodynamics is a cutting-edge problem. Therefore, this work extends recent studies bypassing high-temperature expansion and small heterogeneity scale. We introduce random branching trees whose topology reflects the hierarchical properties of a random solid geometry. This mathematical representation allows us to obtain averaged free energy using a statistical model of virtual clusters interacting through random ultrametric pairwise potentials. Our results demonstrate that a significant impact to fluid-solid interface energy is induced by the hierarchical structure of random geometry at low temperature. These calculations coincide with direct Monte Carlo simulations. Due to the study's interdisciplinary nature, the developed approach can be applied to a wide range of quenched disorder systems on random graphs.

Social media has blurred the distinction between news outlets and social networks by giving everyone access to mass communication. We simulate how influencers compete for attention on a social network by spreading information. The network structure occupies an ordered metastable state where one influencer maintains dominance for a sustained period or a fragmented state that divides attention between influencers. Numerical simulations are performed to map the domain of the ordered regime on various network topologies. Mutual coexistence between a few dominating influencers occurs on a scale-free social network. Our findings suggest the perception of fake news as a pervasive problem is endemic to a society where everyone can become a news outlet.

We evaluate the thermodynamic consistency of the anisotropic mobile slip-link model for entangled flexible polymers. The level of description is that of a single chain, whose interactions with other chains are coarse grained to discrete entanglements. The dynamics of the model consist of the motion of entanglements through space and of the chain through the entanglements, as well as the creation and destruction of entanglements, which are implemented in a mean-field way. Entanglements are modeled as discrete slip links, whose spatial positions are confined by quadratic potentials. The confinement potentials move with the macroscopic velocity field, hence the entanglements fluctuate around purely affine motion. We allow for anisotropy of these fluctuations, described by a set of shape tensors. By casting the model in the form of the general equation for the nonequilibrium reversible-irreversible coupling from nonequilibrium thermodynamics, we show that (i) since the confinement potentials contribute to the chain free energy, they must also contribute to the stress tensor, (ii) these stress contributions are of two kinds: one related to the virtual springs connecting the slip links to the centers of the confinement potentials and the other related to the shape tensors, and (iii) these two kinds of stress contributions cancel each other if the confinement potentials become anisotropic in flow, according to a lower-convected evolution of the confinement strength or, equivalently, an upper-convected evolution of the shape tensors of the entanglement spatial fluctuations. In previous publications, we have shown that this cancellation is necessary for the model to obey the stress-optical rule and the Green-Kubo relation, and simultaneously to agree with plateau modulus predictions of multichain models and simulations.

We study steady-state properties of active, nonchiral and chiral Brownian particles with polar alignment and steric interactions confined within a ring-shaped confinement (annulus) in two dimensions. Exploring possible interplays between polar interparticle alignment, geometric confinement and the surface curvature, being incorporated here on minimal levels, we report a surface-population reversal effect, whereby active particles migrate from the outer concave boundary of the annulus to accumulate on its inner convex boundary. This contrasts the conventional picture, implying stronger accumulation of active particles on concave boundaries relative to the convex ones. The population reversal is caused by both particle alignment and surface curvature, disappearing when either of these factors is absent. We explore the ensuing consequences for the chirality-induced current and swim pressure of active particles and analyze possible roles of system parameters, such as the mean number density of particles and particle self-propulsion, chirality, and alignment strengths.

We show that self-driven particles coupled to a periodic obstacle array exhibit active matter commensuration effects that are absent in the Brownian limit. As the obstacle size is varied for sufficiently large activity, a series of commensuration effects appear in which the motility induced phase separation produces commensurate crystalline states, while for other obstacle sizes we find frustrated or amorphous states. The commensuration effects are associated with peaks in the amount of sixfold ordering and the maximum cluster size. When a drift force is added to the system, the mobility contains peaks and dips similar to those found in transport studies for commensuration effects in superconducting vortices and colloidal particles.

We experimentally study the propagating of an optical intensity jump discontinuity in a nonlocal stochastic Kerr focusing nematic liquid crystal cell. We show both theoretically and experimentally that nonlocality opens a route towards beam steering in our system. Indeed, the discontinuity trajectory follows a curve that bends with the injected power. Despite the stochastic nature of the medium and the constant presence of transverse instabilities, the development of a focusing shocklike dynamics is shown to survive. The distance $Z_s$ for the focusing shock to occur follows a power law with the beam power $P$ according to $Z_s\propto P^{\chi }$, with $\chi =-4/3$, as for shock dynamics in self-defocusing media.

We propose to describe the dynamics of phase transitions in terms of a nonstationary generalized Langevin equation for the order parameter. By construction, this equation is nonlocal in time, i.e., it involves memory effects whose intensity is governed by a memory kernel. In general, it is a hard task to determine the physical origin and the extent of the memory effects based on the underlying microscopic equations of motion. Therefore we propose to relate the extent of the memory kernel to quantities that are experimentally observed such as the induction time and the duration of the phase transformation process. Using a simple kinematic model, we show that the extent of the memory kernel is positively correlated with the duration of the transition, and that it is of the same order of magnitude, while the distribution of induction times does not have an effect on the memory kernel. This observation is tested at the example of several model systems, for which we have run computer simulations: a modified Potts model, a dipole gas, an anharmonic spring in a bath, and a nucleation problem. All these cases are shown to be consistent with the simple theoretical model.

We study the phase transition of the degree-weighted majority vote (DWMV) model on Erdős-Rényi networks (ERNs) and scale-free networks (SFNs). In this model, a weight parameter $\alpha$ adjusts the level of influence of each node on its connected neighbors. Through the Monte Carlo simulations and the finite-size scaling analysis, we find that the DWMV model on ERNs and SFNs with degree exponents $\lambda >5$ belongs to the mean-field Ising universality class, regardless of $\alpha$. On SFNs with $3<\lambda <5$ the model belongs to the Ising universality class only when $\alpha =0$. For $\alpha >0$ we find that the critical exponents continuously change as $\alpha$ increases from $\alpha =0$. However, on SFNs with $\lambda <3$ we find that the model undergoes a continuous transition only for $\alpha =0$, but the critical exponents significantly deviate from those for the mean-field Ising model. For $\alpha >0$ on SFNs with $\lambda <3$ the model is always in the disordered phase.

The design of small scale nonequilibrium steady states (NESS) is a challenging, open ended question. While similar equilibrium problems are tractable using standard thermodynamics, a generalized description for nonequilibrium systems is lacking, making the design problem particularly difficult. Here we show we can exploit the large-deviation behavior of a Brownian particle and design a variety of geometrically complex steady-state density distributions and flux field flows. We achieve this design target from direct knowledge of the joint large-deviation functional for the empirical density and flow, and a “relaxation” algorithm on the desired target states via adjustable force field parameters. We validate the method by replicating analytical results, and demonstrate its capacity to yield complex prescribed targets, such as rose-curve or polygonal shapes on the plane. We consider this dynamical fluctuation approach a first step towards the design of more complex NESS where general frameworks are otherwise still lacking.

We consider a generic nonlinear extension of May's 1972 model by including all higher-order terms in the expansion around the chosen fixed point (placed at the origin) with random Gaussian coefficients. The ensuing analysis reveals that as long as the origin remains stable, it is surrounded by a “resilience gap”: there are no other fixed points within a radius $r_{*}>0$ and the system is therefore expected to be resilient to a typical initial displacement small in comparison to $r_{*}$. The radius $r_{*}$ is shown to vanish at the same threshold where the origin loses local stability, revealing a mechanism by which systems close to the tipping point become less resilient. We also find that beyond the resilience radius the number of fixed points in a ball surrounding the original point of equilibrium grows exponentially with $N$, making systems dynamics highly sensitive to far enough displacements from the origin.

With the growing number of discovered exoplanets, the Gaia concept finds its second wind. The Gaia concept defines that the biosphere of an inhabited planet regulates a planetary climate through feedback loops such that the planet remains habitable. Crunching the “Gaia” puzzle has been a focus of intense empirical research. Much less attention has been paid to the mathematical realization of this concept. In this paper, we consider the stability of a planetary climate system with the dynamic biosphere by linking a conceptual climate model to a generic population dynamics model with random parameters. We first show that the dynamics of the corresponding coupled system possesses multiple timescales and hence falls into the class of slow-fast dynamics. We then investigate the properties of a general dynamical system to which our model belongs and prove that the feedbacks from the biosphere dynamics cannot break the system's stability as long as the biodiversity is sufficiently high. That may explain why the climate is apparently stable over long time intervals. Interestingly, our coupled climate-biosphere system can lose its stability if biodiversity decreases; in this case, the evolution of the biosphere under the effect of random factors can lead to a global climate change.

The zero forcing number is the minimum number of black vertices that can turn a white graph black following a single neighbor color forcing rule. The zero forcing number provides topological information about linear algebra on graphs, with applications to the controllability of quantum dynamical systems. Here, I investigate the zero forcing number of undirected graphs with a power law degree distribution $p_k\sim k^{-\gamma }$ by means of numerical simulations. For graphs generated by the preferential attachment model, with a diameter scaling logarithmically with the graph size, the zero forcing number approaches the graph size when $\gamma \to 2$. In contrast, for graphs generated by the deactivation model, with a diameter scaling linearly with the graph size, the zero forcing number is smaller than the graph size independently of $\gamma$. Therefore the scaling of the graph diameter with the graph size is another factor determining the controllability of dynamical systems. These results have implications for the controllability of quantum dynamics on energy landscapes, often characterized by a complex network of couplings between energy basins.

Mechanical waves, which are commonly employed for the noninvasive characterization of fluid-saturated porous media, tend to induce pore-scale fluid pressure gradients. The corresponding fluid pressure relaxation process is commonly referred to as squirt flow and the associated viscous dissipation can significantly affect the waves' amplitudes and velocities. This, in turn, implies that corresponding measurements contain key information about flow-related properties of the probed medium. In many natural and applied scenarios, pore fluids are effectively non-Newtonian, for which squirt flow processes have, as of yet, not been analyzed. In this work, we present a numerical approach to model the attenuation and modulus dispersion of compressional waves due to squirt flow in porous media saturated by Maxwell-type non-Newtonian fluids. In particular, we explore the effective response of a medium comprising an elastic background with interconnected cracks saturated with a Maxwell-type non-Newtonian fluid. Our results show that wave signatures strongly depend on the Deborah number, defined as the relationship between the classic Newtonian squirt flow characteristic frequency and the intrinsic relaxation frequency of the non-Newtonian Maxwell fluid. With larger Deborah numbers, attenuation increases and its maximum is shifted towards higher frequencies. Although the effective plane-wave modulus of the probed medium generally increases with increasing Deborah numbers, it may, however, also decrease within a restricted region of the frequency spectrum.

In deuterium-tritium cryogenic implosions, hot-spot x-ray self-emission is observed to begin at a larger shell radius than is predicted by a one-dimensional radiation-hydrodynamic implosion model. Laser-imprint is shown to explain the observation for a low-adiabat implosion. For more-stable implosions the data are not described by the imprint model and suggest there are additional sources of decompression of the dense fuel.

The mechanism of negative group delay (NGD) is used to understand the anticipatory capability of a retina. Experiments with retinas from bullfrogs are performed to compare with the predictions of the NGD model. In particular, whole field stochastic stimulations with various autocorrelation times are used to probe anticipatory responses from the retina. We find that the NGD model can reproduce essential features of experimental observations characterized by the cross correlations between the stimulation and the retinal responses. Experiments with dark light pulse stimulations further support the NGD mechanism, with the retina producing time-advanced pulse responses. However, no time-advanced pulse responses are produced by bright pulses. Counterintuitively, the NGD model shows that it is the delay in the system which gives rise to anticipation because of the negative feedback adaptation mechanism.

In this work we study the fractal properties of diffusion-limited aggregation (DLA) clusters grown on spherical surfaces. Diffusion-limited aggregation clusters, or DLA trees, are highly branched fractal clusters formed by the adhesion of particles. In two-dimensional media, DLA clusters have a fractal dimension $D_f=1.70$ in the continuous limit. In some physical systems, the existence of characteristic lengths leads us to model them as discrete systems. Such characteristic lengths may result also from limitations in measuring instruments, for example, the resolution of biomedical imaging systems. We simulate clusters for different particle sizes and examine the influence of discretization by exploring the systems in terms of the relationship between the particle size $r$ and the radius of the sphere $R$. We also study the effect of stereographic projection on the fractal properties of DLA clusters. Both discretization and projection alter the fractal dimension of DLA clusters grown on curved surfaces and must be considered in the interpretation of photographic biomedical images.

By controlling synaptic and neural correlations, deep learning has achieved empirical successes in improving classification performances. How synaptic correlations affect neural correlations to produce disentangled hidden representations remains elusive. Here we propose a simplified model of dimension reduction, taking into account pairwise correlations among synapses, to reveal the mechanism underlying how the synaptic correlations affect dimension reduction. Our theory determines the scaling of synaptic correlations requiring only mathematical self-consistency for both binary and continuous synapses. The theory also predicts that weakly correlated synapses encourage dimension reduction compared to their orthogonal counterparts. In addition, these synapses attenuate the decorrelation process along the network depth. These two computational roles are explained by a proposed mean-field equation. The theoretical predictions are in excellent agreement with numerical simulations, and the key features are also captured by deep learning with Hebbian rules.