Dynamic Percolation Research Articles

Biased random walk on dynamical percolation

Biased random walk on dynamical percolation

The crossover from a dynamical percolation class to a directed percolation class on a two dimensional lattice

The crossover from a dynamical percolation class to a directed percolation class on a two dimensional lattice

Critical speeding-up in dynamical percolation

We study the autocorrelation time of the size of the cluster at the origin in discrete-time dynamical percolation. We focus on binary trees and high-dimensional tori, and show in both cases that this autocorrelation time is linear in the volume in the subcritical regime, but strictly sublinear in the volume at criticality. This establishes rigorously that the cluster size at the origin in these models exhibits critical speeding-up. The proofs involve controlling relevant Fourier coefficients. In the case of binary trees, these Fourier coefficients are studied explicitly, while for high-dimensional tori we employ a randomised algorithm argument introduced by Schramm and Steif in the context of noise sensitivity.

Stability and chaos in dynamical last passage percolation

Many complex disordered systems in statistical mechanics are characterized by intricate energy landscapes. The ground state, the configuration with lowest energy, lies at the base of the deepest valley. In important examples, such as Gaussian polymers and spin glass models, the landscape has many valleys and the abundance of near-ground states (at the base of valleys) indicates the phenomenon of chaos, under which the ground state alters profoundly when the disorder of the model is slightly perturbed. In this article, we compute the critical exponent that governs the onset of chaos in a dynamic manifestation of a canonical model in the Kardar-Parisi-Zhang [KPZ] universality class, Brownian last passage percolation [LPP]. In this model in its static form, semidiscrete polymers advance through Brownian noise, their energy given by the integral of the white noise encountered along their journey. A ground state is a geodesic, of extremal energy given its endpoints. We perturb Brownian LPP by evolving the disorder under an Ornstein-Uhlenbeck flow. We prove that, for polymers of length n n , a sharp phase transition marking the onset of chaos is witnessed at the critical time n − 1 / 3 n^{-1/3} . Indeed, the overlap between the geodesics at times zero and t > 0 t > 0 that travel a given distance of order n n will be shown to be of order n n when t ≪ n − 1 / 3 t\ll n^{-1/3} ; and to be of smaller order when t ≫ n − 1 / 3 t\gg n^{-1/3} . We expect this exponent to be universal across a wide range of interface models. The present work thus sheds light on the dynamical aspect of the KPZ class; it builds on several recent advances. These include Chatterjee’s harmonic analytic theory [Superconcentration and related topics, Springer, Cham, 2014] of equivalence of superconcentration and chaos in Gaussian spaces; a refined understanding of the static landscape geometry of Brownian LPP developed in the companion paper (see S. Ganguly and A. Hammond [Electron. J. Probab. 28 (2023), 80 pp.]); and, underlying the latter, strong comparison estimates of the geodesic energy profile to Brownian motion (see J. Calvert, A. Hammond, and M. Hegde [Astérisque 441 (2023), pp. v+119]).

Combinatorial entropy determines the early stages of nucleation

AbstractBiomolecular phase separation, a complex phenomenon within living systems, has garnered significant interest due to its diverse roles in cellular organization and function. Despite its importance, studying phase separation dynamics experimentally, particularly in the early stages, poses challenges. Our study investigates the dynamics of biomolecular phase separation using a graph‐based simulation module, particularly emphasizing its early stages. Through a simplified model, we dissect the influences of various factors on collective behavior, highlighting the crucial role of combinatorial entropy in percolation dynamics. This study offers valuable insights into the fundamental principles governing biomolecular phase separation, with implications for understanding cellular processes and disease mechanisms.

Creep and recovery in dense suspensions of smooth and rough colloids

We report the effect of particle surface roughness on creep deformation and subsequent strain recovery in dense colloidal suspensions. The suspensions are composed of hard-spherelike poly(methyl methacrylate) smooth (S) and rough (R) colloids with particle volume fractions ϕS = 0.64 ± 0.01 and ϕR = 0.56 ± 0.01, corresponding to a distance of 3.0% and 3.4% based on their jamming volume fractions (ϕJS=0.66±0.01, ϕJR=0.58±0.01). The suspensions are subject to a range of shear stresses (0.01–0.07 Pa) above and below the yield stress values of the two suspensions (σyS=0.035Pa, σyR=0.02Pa). During creep, suspensions of rough colloids exhibit four to five times higher strain deformation compared to smooth colloids, irrespective of the applied stress. The interlocking of surface asperities in rough colloids is likely to generate a heterogeneous microstructure, favoring dynamic particle activity and percolation of strain heterogeneities, therefore resulting in higher magnitude of strain deformation and an earlier onset of steady flow. Strain recovery after the cessation of stress reveals a nonmonotonic recoverable strain for rough colloids, where the peak recoverable strain is observed near the yield stress, followed by a steep decline with increasing stress. This type of response suggests that frictional constraints between geometrically frustrated interlocking contacts can serve as particle bonds capable of higher elastic recovery but only near the yield stress. Understanding how particle roughness affects macroscopic creep and recovery is useful in designing yield stress fluids for additive manufacturing and product formulations.

Cover times for random walk on dynamical percolation

Cover times for random walk on dynamical percolation

SIR model on one dimensional small world networks

We study the nonequilibrium phase transition for the model of epidemic spreading, Susceptible–Infected–Refractory (SIR), on one dimensional small world networks. This model belongs to the universality class of dynamical percolation class (DyP) and the upper critical dimension corresponding to this class is dc=6. One dimensional case is special case of this class in which the percolation threshold goes to one (boundary value) in thermodynamic limit. This behavior resembles slightly the behavior of equilibrium phase transition in a one dimensional Ising and XY models where the critical thresholds for both models go to zero temperature (boundary value) in thermodynamic limit. By analytical arguments and numerical simulations we demonstrate that, increasing the connectivity (2k) of this model on regular one dimensional lattice does not alter the criticality of the model. However the phase transition study shows that, this model crosses from a one dimensional structure to mean field like for any finite value of the rewiring probability (p). This behavior is similar to what happened in the equilibrium phase transition for the Ising and XY models on small world networks. Thus, this model is a one of nonequilibrium models which behaves similarly to the equilibrium systems on small world networks. Unlike of many nonequilibrium systems on small world networks which have been found to display a mean field like behavior only at finite values of p or even show critical exponents depend on p. Furthermore, we calculate the critical exponents and the full critical phase space of this model on small world network. We also introduce the crossover scaling function of this model from one dimensional behavior to mean field behavior and reveal the similarity between this model and the equilibrium models on the small world networks.

Sand-fixing vegetation regulates deep percolation and soil water dynamics in semiarid sandy land: Evidence from a deep percolation recorder and in-situ test

Deep percolation (DP) determines the sustainable utilization of regional groundwater resources and provides large hydrological benefits to ecosystems in semiarid sandy regions. However, studies involving DP variability have rarely conducted in-situ tests with different vegetation coverages (VC) and vegetation types using direct measurements. This study measured soil moisture and DP for four years in five plots, with DP measured using a deep percolation recorder: mobile sand (MS) as the control group; Artemisia ordosica semifixed (AOSF) with VC of 30%–35% and Artemisia ordosica fixed (AOF) with VC of 70%–75% (AOSF and AOF stand ages: 30–40 years), representing different vegetation coverages; and Salix psammophila fixed (SPF) and Pinus sylvestrix var. Mongolica fixed (PSMF) with the same VC of 45%–50% (SPF and PSMF stand ages: 30 years), representing different vegetation types. The effects of sand-fixing vegetation on DP and soil water were evaluated using the relative extractable soil water (RESW) and soil water storage deficit metrics. DP occurrence in MS was closely related to rainfall amounts of > 10 mm and high-intensity rainfall rather than the total annual rainfall. Increases in vegetation coverages and forest selection significantly reduced DP and RESW compared with MS. DP in the shrub plot (SPF) was significantly higher than that in the forest plot (PSMF). Plants utilized water from different sources among the sandy land types: the shallow (0–80 cm) and deep layers (80–200 cm) in PSMF and AOF, and only from the shallow layer in AOSF and SPF. However, compared with MS, soil water storage deficit occurred to varying degrees in each plot. This study can provide a scientific reference for the restoration of the ecology and water cycle in sandy regions.

Tight sandstone gas accumulation mechanisms and sweet spot prediction, Triassic Xujiahe Formation, Sichuan Basin, China

The prediction of continental tight sandstone gas sweet spots is an obstacle during tight sandstone gas exploration. In this work, the classic physical fluid charging experimental equipment is improved, the combination of the gas migration and accumulation process with the pore network numerical simulation method is investigated, and application of the permeability/porosity ratio is proposed to predict the gas saturation and sweet spots of continental formations. The results show that (1) as the charging pressure increases, the permeability of the reservoir increases because more narrow pore throats are displaced in the percolation process; and (2) based on pore network numerical simulation and theoretical analysis, the natural gas migration and accumulation mechanisms are revealed. The gas saturation of tight sandstone rock is controlled by the gas charging pressure and dynamic percolation characteristics. (3) The ratio of permeability/porosity and fluid charging pressure is proposed to predict the gas saturation of the formation. The ratio is verified in a pilot and proven to be applicable and practical. This work highlights the tight sandstone gas migration and accumulation mechanisms and narrows the gap among microscale physical experiments, numerical simulation research, and field applications.

DTE-RR: Dynamic Topology Evolution-Based Reliable Routing in VANET

The dynamics of Vehicular Ad-hoc Network (VANET) brings tremendous challenges to reliable routing. In the existing topology evolution schemes, the link connectivity and the interaction between links have yet to be well investigated, resulting in the inability to accurately describe the evolution of routing topology. In this letter, we propose a Dynamic Topology Evolution (DTE) based reliable routing algorithm to improve transmission reliability. The DTE model is constructed to formulate the evolution of network topology. Especially, we analyze the network topology changes from the perspective of nodes and links. Meanwhile, the Dynamic Bond Percolation (DBP) model is extended to describe link interaction. Then, the DTE model is completed by deriving the state transition matrix of the network topology based on the link change using Markov theory. Finally, the DTE-based Reliable Routing (DTE-RR) algorithm is designed to optimize routing paths. The experimental results demonstrate that DTE-RR outperforms the existing protocols regarding packet delivery ratio and end-to-end delay.

Evidence for Bootstrap Percolation Dynamics in a Photoinduced Phase Transition.

Upon intense femtosecond photoexcitation, a many-body system can undergo a phase transition through a nonequilibrium route, but understanding these pathways remains an outstanding challenge. Here, we use time-resolved second harmonic generation to investigate a photoinduced phase transition in Ca_{3}Ru_{2}O_{7} and show that mesoscale inhomogeneity profoundly influences the transition dynamics. We observe a marked slowing down of the characteristic time τ that quantifies the transition between two structures. τ evolves nonmonotonically as a function of photoexcitation fluence, rising from below 200fs to ∼1.4 ps, then falling again to below 200fs. To account for the observed behavior, we perform a bootstrap percolation simulation that demonstrates how local structural interactions govern the transition kinetics. Our work highlights the importance of percolating mesoscale inhomogeneity in the dynamics of photoinduced phase transitions and provides a model that may be useful for understanding such transitions more broadly.

Investigating the ecotoxicity of construction product eluates as multicomponent mixtures

BackgroundThe release of hazardous compounds from construction products can harm human health and the environment. To improve the sustainability of construction materials, the leaching of substances from construction products and their potential environmental impact should be assessed. Twenty-seven construction products from different product groups were examined with a combination of standardized leaching tests (dynamic surface leaching test and percolation test) and biotests (algae, daphnia, fish egg, luminescent bacteria, umu and Ames fluctuation tests). To identify the released substances, extensive qualitative and quantitative chemical analyses were performed, including gas chromatographic and liquid chromatographic screening techniques.ResultsMany of the tested eluates caused significant ecotoxic effects. Particularly high ecotoxicities were observed for grouts (lowest ineffective dilution (LID) up to 16384) and cork granules (LID up to 24578). The results of ecotoxicity tests allow the prioritization of the eluates that should be subjected to detailed chemical analyses. Organic screening by different methods and ranking the identified substances based on recorded hazard classification is a suitable approach to identify the relevant toxic substances.ConclusionsDetermining the ecotoxicity of eluates from construction products records the summary effect of all leachable substances. This instrument is especially useful for construction products of complex and largely unknown composition. The ecotoxicological and the chemical–analytical approach complement each other in an ideal way to characterize the potential hazard of eluates from construction products and to identify the environmentally hazardous components in these eluates. Our results confirm that the proposed harmonized methods for testing eluate toxicity are an adequate and applicable procedure to move toward a more sustainable way of building and to reduce toxic effects of construction products in their use phase in the environment..

Noise sensitivity of percolation via differential inequalities

AbstractConsider critical Bernoulli percolation in the plane. We give a new proof of the sharp noise sensitivity theorem shown by Garban, Pete, and Schramm (Acta Math. 205 (2010), 19–104). Contrary to the previous approaches, we do not use any spectral tool. We rather study differential inequalities satisfied by a dynamical four‐arm event, in the spirit of Kesten's proof of scaling relations in Kesten (Comm. Math. Phys. 109 (1987), 109–156). We also obtain new results in dynamical percolation. In particular, we prove that the Hausdorff dimension of the set of times with both primal and dual percolation equals almost surely.

Contact process on a dynamical long range percolation

Contact process on a dynamical long range percolation

Discovery of Variscan orogenic peridotites in the Pelvoux Massif (Western Alps, France)

Small bodies of mantle-derived peridotites and other ultramafic rocks are commonly found in exhumed lower crustal units of collisional orogens. They provide a direct record of the complex evolution of the upper mantle before and during an orogeny, and are therefore key markers of the geodynamic evolution of an orogen. We report here the discovery of such mantle-derived peridotites, which occur as fragmented enclaves in migmatites of the high-grade Variscan lower crust exposed in the Pelvoux Massif (external Western Alps). A wide petrographic diversity has been observed, from very fertile, garnet-bearing lherzolites, to more depleted spinel/chromite-bearing harzburgites. Thermobarometric calculations on a garnet lherzolite indicate an initial stage at 3.0–4.0 GPa and 970–1140 °C, followed by exhumation to 0.8–1.3 GPa and 800–850 °C, while the harzburgites do not show any evidence of equilibration in the garnet field. Petrological observations, whole-rock geochemistry and in situ mineral compositions suggest the peridotites have undergone a complex history prior to their incorporation in the lower crust during the Variscan Orogeny. They derive from a refractory mantle, which has experienced variable degrees of melt depletion, and has then been extensively refertilized. Cryptic metasomatism is observed in all samples. It is characterized by an enrichment in large-ion lithophile elements (LILE, in particular Cs, Rb, U and Pb) relative to high field strength elements (HFSE), in particular Nb and Ta. This cryptic metasomatism is presumably related to percolation of subduction-related fluids or melts in the mantle. In addition, modal metasomatism occurred in some samples, where crystallization of phlogopite, pargasite, chromite and apatite has been observed. This modal metasomatism resulted in significant enrichment in K2O, P2O5 and Cr2O3 of the bulk rock, together with a strong enrichment in incompatible LREE relative to HREE. These geochemical characteristics are strikingly similar to that of syn-collisional, Mg–Cr–LILE rich mantle-derived (ultra)-potassic magmas such as durbachites and vaugnerites, which are ubiquitous in the Variscan metamorphic allochthons of Massif Central, external Alps, Vosges and Bohemian Massif. We therefore suggest that this metasomatism results from dynamic percolation of the peridotites by K2O–P2O5–Cr2O3-rich melts from which the durbachites and vaugnerites are primarily derived. These geochemical characteristics are in line with whole-rock Nd isotopic compositions, which indicate enrichment of the mantle by a continental crust component, presumably related to Variscan subductions. This evolution is consistent with that of other Variscan peridotites in the Eastern Alps (Ulten) and the Bohemian Massif, where multiple metasomatic episodes related to melts or fluids released in Variscan subduction zones have been documented.

Transitions for exceptional times in dynamical first-passage percolation

In first-passage percolation (FPP), we let $$(\tau _v)$$ be i.i.d. nonnegative weights on the vertices of a graph and study the weight of the minimal path between distant vertices. If F is the distribution function of $$\tau _v$$ , there are different regimes: if F(0) is small, this weight typically grows like a linear function of the distance, and when F(0) is large, the weight is typically of order one. In between these is the critical regime in which the weight can diverge, but does so sublinearly. We study a dynamical version of critical FPP on the triangular lattice where vertices resample their weights according to independent rate-one Poisson processes. We prove that if $$\sum F^{-1}(1/2+1/2^k) = \infty $$ , then a.s. there are exceptional times at which the weight grows atypically, but if $$\sum k^{7/8} F^{-1}(1/2+1/2^k) <\infty $$ , then a.s. there are no such times. Furthermore, in the former case, we compute the Hausdorff and Minkowski dimensions of the exceptional set and show that they can be but need not be equal. These results show a wider range of dynamical behavior than one sees in subcritical (usual) FPP.

Human-muscle-inspired single fibre actuator with reversible percolation

Artificial muscles are indispensable components for next-generation robotics capable of mimicking sophisticated movements of living systems. However, an optimal combination of actuation parameters, including strain, stress, energy density and high mechanical strength, is required for their practical applications. Here we report mammalian-skeletal-muscle-inspired single fibres and bundles with large and strong contractive actuation. The use of exfoliated graphene fillers within a uniaxial liquid crystalline matrix enables photothermal actuation with large work capacity and rapid response. Moreover, the reversible percolation of graphene fillers induced by the thermodynamic conformational transition of mesoscale structures can be in situ monitored by electrical switching. Such a dynamic percolation behaviour effectively strengthens the mechanical properties of the actuator fibres, particularly in the contracted actuation state, enabling mammalian-muscle-like reliable reversible actuation. Taking advantage of a mechanically compliant fibre structure, smart actuators are readily integrated into strong bundles as well as high-power soft robotics with light-driven remote control.

Direct observation of quantum percolation dynamics

Abstract Percolation, describing critical behaviors of phase transition in a geometrical context, prompts wide investigations in natural and social networks as a fundamental model. The introduction of quantum coherence and superposition brings percolation into quantum regime with more fascinating phenomena and unique features, which, however, has not been experimentally explored yet. Here we successfully map these large-scale porous structures into a photonic chip using femtosecond laser direct writing techniques and present an experimental demonstration of quantum transport in hexagonal percolation lattices, probed by coherent light. A quantum percolation threshold of 80% is observed in the prototyped laser-written lattices with up to 1,600 waveguides, which is significantly larger than the classical counterpart of 63%. We also investigate the spatial confinement by localization parameters and exhibit the transition from ballistic to diffusive propagation with the decrease of the occupation probability. Direct observation of quantum percolation may deepen the understanding of the relation among materials, quantum transport, geometric quenching, disorder and localization, and inspire applications for quantum technologies.

Two-Stage Structural and Slowing-Down Percolation Transitions in the Densifying Cancer Cell Monolayer.

We experimentally demonstrate the two-stage structural and slowing-down percolating transitions, followed by the confluent transition in the densifying cancer cell monolayers from the dilute state, and investigate their impacts on collective cell dynamics. It is found that cells aggregate into clusters at low cell density. With increasing cell number density, the structural percolation through the formation of a large cell cluster percolating through the space precedes the dynamical percolation transition of forming a percolating cluster of slow cell elements. Both percolating transitions exhibit scale-free scaling behaviors of cluster size distributions and fractal structures, similar to those of the universality class of 2D nonequilibrium systems governed by percolation theory. Dynamically, at low cell density, cell aggregation enhances cooperative motion. The structural percolation leads to slower motion, especially with stronger suppression for the high-frequency modes in the turbulent-like velocity power spectra. The following slowing-down percolation associated with the onset of cell crowding in regions occupied by cells further enhances dynamical slowing-down, and suppresses the increasing trend of dynamical heterogeneity and the steepening of the power spectrum of motion, until their reversions after the confluent transition.