Dynamic Percolation Research Articles

Water/PEG Mixtures: Phase Behavior, Dynamics and Soft Confinement

Abstract Polyethylene glycol is water soluble and forms an eutectic system with water. The eutectic temperature is −19 °C for M=1500 g mol−1 and increases with molecular weight. The dielectric relaxation spectrum of the mixtures exhibits a strong loss maximum in ϵ″ (ω) similar to pure water. Relaxation time increases with the addition of PEG. Activation energies exhibit a maximum of 0.35 eV at molar fraction χp ≈0.2. This compares well with results on ethanol water mixtures. Adding PEG molecules to nanoscopic water droplets of inverse microemulsions has only small impact on the bending modulus κ of a non-ionic microemulsion. In AOT based microemulsions an increase or decrease of κ is found in dependence on the size of the droplets. This is in accordance with the variation of the dynamic percolation transition in the same systems.

Functionality and performance evaluation of directly compressible co-processed excipients based on dynamic compaction analysis and percolation theory

In the present work functional properties of new, co-processed excipients, Pharmaburst® 500, Parteck® ODT, Ludiflash® and Disintequik™ ODT, intended for direct compression of orally disintegrating tablets (ODTs), were investigated based on dynamic compaction analysis and percolation theory. Tablet disintegration time and mechanical properties have been recognized as critical quality attributes (CQAs) which should be optimized through pharmaceutical development. According to the obtained results, in order to achieve adequate mechanical resistance, excipients exhibiting high compactibility and tabletability are required, while, on the contrary, high porosity excipients with higher extent of elastic deformations, average tabletability and compactibility are necessary to obtain fast tablet disintegration. The results obtained in this study indicate that the most important excipient properties affecting tablet CQAs are porosity, mechanism of consolidation, compactibility and tabletability. Pharmaburst® 500, excipient with the highest elastic recovery, the lowest relative density, average compactibility and tabletability, and remarkably high dilution capacity (69.6% w/w of caffeine or 49.1% w/w of ibuprofen) exhibited favourable performance for ODT direct compression. Dynamic compaction analysis and percolation theory proved to be useful tools which can contribute to identification of the most important excipient functional properties influencing critical quality attributes of the prepared ODTs.

Exceptional times for percolation under exclusion dynamics

We analyse in this paper a conservative analogue of the celebrated model of dynamical percolation introduced by H\aggstr\om, Peres and Steif in [HPS97]. It is simply defined as follows: start with an initial percolation configuration $\omega(t=0)$. Let this configuration evolve in time according to a simple exclusion process with symmetric kernel $K(x,y)$. We start with a general investigation (following [HPS97]) of this dynamical process $t \mapsto \omega_K(t)$ which we call $K$-exclusion dynamical percolation. We then proceed with a detailed analysis of the planar case at the critical point (both for the triangular grid and the square lattice $Z^2$) where we consider the power-law kernels $K^\alpha$ \[ K^{\alpha}(x,y) \propto \frac 1 {\|x-y\|_2^{2+\alpha}} \, . \] We prove that if $\alpha > 0$ is chosen small enough, there exist exceptional times $t$ for which an infinite cluster appears in $\omega_{K^{\alpha}}(t)$. (On the triangular grid, we prove that it holds for all $\alpha < \alpha_0 = \frac {217}{816}$.) The existence of such exceptional times for standard i.i.d. dynamical percolation (where sites evolve according to independent Poisson point processes) goes back to the work by Schramm-Steif in [SS10]. In order to handle such a $K$-exclusion dynamics, we push further the spectral analysis of exclusion noise sensitivity which had been initiated in [BGS13]. (The latter paper can be viewed as a conservative analogue of the seminal paper by Benjamini-Kalai-Schramm [BKS99] on i.i.d. noise sensitivity.) The case of a nearest-neighbour simple exclusion process, corresponding to the limiting case $\alpha = +\infty$, is left widely open.

Quantum walks of two interacting particles on percolation graphs

We address the dynamics of two indistinguishable interacting particles moving on a dynamical percolation graph, i.e., a graph where the edges are independent random telegraph processes whose values jump between 0 and 1, thus mimicking percolation. The interplay between the particle interaction strength, initial state and the percolation rate determine different dynamical regimes for the walkers. We show that, whenever the walkers are initially localised within the interaction range, fast noise enhances the particle spread compared to the noiseless case.

Matrix tacticity controlled tuning of microstructure, constitutive behavior and rheological percolation effect of melt‐mixed amino‐functionalized MWCNT/PP nanocomposites

Amino‐functionalized multi walled nanotube (MWCNT‐NH2) filled isotactic PP and isotactic‐syndiotactic (70:30) mixed PP based melt‐mixed nanocomposites have been comparatively evaluated with regard to morphological, rheological and thermo‐mechanical properties. The ratio of mean free space lengths (Lf) to infiltrated mean free space lengths (Linf) between nanotubes in isotactic‐syndiotactic (70:30) blended matrix based nanocomposites increased relatively indicating a dispersed‐morphology. The rheological percolation threshold increased up to a higher extent of MWCNT‐NH2 loading (from øc ∼ 2.3 × 10−4 in isotactic to øc ∼ 11 × 10−4 in iso‐syndio blend) accompanied with the formation of a mechanically responsive network structure. van‐GurpPalmen plot showed a transition in the rheological response as a consequence of network morphology getting shifted to higher concentration of MWCNT‐NH2 in the isotactic‐syndiotactic mixed PP based nanocomposites than in the isotactic based one. Constitutive modeling of complex viscosity response of the nanocomposites led to functional correlation between the percolation and relaxation dynamics of polymer chains. POLYM. ENG. SCI., 58:1115–1126, 2018. © 2017 Society of Plastics Engineers

Optimization and control of dynamic percolationin nanostructured silicon oils

The addition of carbonaceous fillers in polymers allows the conception of composites with optimized electrical properties. The conductivity of such material depends of the fillers structuration in matrix, especially the presence of percolated network. The objective of this paper is to understand the main aggregation mechanisms of carbon nanotubes in different media. The structuration of these filler network is probed by the use of electrical and dielectrical measurements. The innovative part of our work lies in the use of liquid matrices, especially silicon oils, to overcome mechanical constraints present in polymers on the one hand and to simplify processing on the other hand. Our work has revealed a filler aggregation over time, well known as dynamic percolation. Conductivity has been modeled as a function of time and filler content from Kirkpatrick equation. The further use of an electrical field led to conductivity enhancement as well as a decrease in percolation threshold. Finally, a study of intrinsic parameters of matrix has shown a strong effect of viscosity and surface tension on nanotubes aggregation.

Application of vadose-zone monitoring system for real-time characterization of leachate percolation in and under a municipal landfill

Leachates from solid-waste landfills are considered a severe threat to groundwater quality. The fate of pollutants in the waste and underlying unsaturated zone is crucial for evaluating environmental risks and selecting a restoration strategy. In this study, a vadose-zone monitoring system (VMS) installed in a municipal landfill was used, for the first time, to continuously track leachates percolation dynamics and assess their chemical transformation across the entire thickness of the waste body (15m) and underlying unsaturated zone (16m) to the water table. Winter rains were found to quickly infiltrate through the waste and underlying vadose zone despite a clay cover that was implemented as part of a restoration and leachate-prevention strategy. Within the waste body, the flow pattern was controlled by preferential flow paths, which changed frequently. It is hypothesized that ongoing decomposition of the waste creates dynamic variations in the waste’s physical structure and flow pattern. Water samples collected from the waste layer indicated the formation of highly polluted leachates. The chemical composition in the waste body showed extreme variability between sampling points with respect to DOC (407–31,464mg/L), BOD/COD ratios (0.07–0.55), Fe2+ (6.8–1154mg/L), ammonium (68–2924mg/L) and heavy metal concentrations. Environmental hot spots creating concentrated, aggressive, “acid-phase” leachates still exist in the waste more than 13years after closing the landfill. However, continuous changes in the flow pattern and moisture distribution affected the creation and decay of such environments. In the underlying sandy vadose zone, some sections repeatedly exhibited stronger and faster flow characteristics than others. These local fluxes of concentrated leachates rapidly transported heavy contaminant loads toward the groundwater. However results showed evidence of continual attenuation processes in the deep vadose zone, with the anaerobic digestion of organic matter, as well as the significant retention of heavy metals.

Synergistic effects of filler size on thermal annealing-induced percolation in polylactic acid (PLA)/graphite nanoplatelet (GNP) nanocomposites

Two graphene-based nanofillers of different sizes were melt mixed with polylactide acid (PLA). Composite films based on graphite nanoplatelets (GNPs) with the largest lateral size showed superior electrical conductivity and a lower percolation threshold after melt-compounding and hot-pressing at room temperature. However, upon annealing in the melt, composites based on GNPs with the smallest lateral size displayed significantly improved electrical conductivity and a decrease in percolation threshold as a result of dynamic percolation while composites based on large GNPs showed hardly any change in conductivity and percolation threshold. Hybrid filler systems based on 5 wt% GNP with variable small/large GNP filler ratios displayed synergistic effects in the formation of a conductive network during thermal annealing, and an optimum filler ratio of 50/50 was found to achieve the highest conductivity after annealing. This annealing-induced increase in particle connectivity for composites based on 5 wt.% hybrid small/large GNPs was also reflected in rheological measurements by the manifestation of a plateau in the storage modulus at low frequencies after annealing while such phenomenon was not observed for nanocomposites solely based on either small or large GNPs at similar loadings.

Percolation analysis for constructing a robust modular topology based on a binary-dynamics model

In the context of Internet of Things, virtualization of wireless sensor networks is a crucial technology for sharing sensors as infrastructure. In our previous work, we proposed a brain-inspired method for constructing a robust and adaptive virtual wireless sensor network topology and showed that the method of constructing links between modules has crucial effect on robustness and adaptivity of the constructed virtual wireless sensor network topology. However, the best way of constructing a robust and adaptive virtual wireless sensor network topology is still unclear. Therefore, in this article, we use an analytical approach and propose a method for clarifying robustness of a topology according to the method of constructing links between modules. We add a new tool to a binary-dynamics model which is an analytical method for investigating percolation dynamics on a modular network. Evaluation by simulation showed that graphs in which the number of nodes selected as endpoint nodes of inter-module links and the degrees of the endpoint nodes before the link addition are large have robust connectivity in terms of the point of fragmentation of the network into modules when we fix the degree of the endpoint nodes after the link addition. After the point, the internal structure of modules may matter more. We additionally investigate an applicable range of our proposed method.

Multiscale volatility duration characteristics on financial multi-continuum percolation dynamics

A random stock price model based on the multi-continuum percolation system is developed to investigate the nonlinear dynamics of stock price volatility duration, in an attempt to explain various statistical facts found in financial data, and have a deeper understanding of mechanisms in the financial market. The continuum percolation system is usually referred to be a random coverage process or a Boolean model, it is a member of a class of statistical physics systems. In this paper, the multi-continuum percolation (with different values of radius) is employed to model and reproduce the dispersal of information among the investors. To testify the rationality of the proposed model, the nonlinear analyses of return volatility duration series are preformed by multifractal detrending moving average analysis and Zipf analysis. The comparison empirical results indicate the similar nonlinear behaviors for the proposed model and the actual Chinese stock market.

Cinematic Operation of the Cerebral Cortex Interpreted via Critical Transitions in Self-Organized Dynamic Systems.

Measurements of local field potentials over the cortical surface and the scalp of animals and human subjects reveal intermittent bursts of beta and gamma oscillations. During the bursts, narrow-band metastable amplitude modulation (AM) patters emerge for a fraction of a second and ultimately dissolve to the broad-band random background activity. The burst process depends on previously learnt conditioned stimuli (CS), thus different AM patterns may emerge in response to different CS. This observation leads to our cinematic theory of cognition when perception happens in discrete steps manifested in the sequence of AM patterns. Our article summarizes findings in the past decades on experimental evidence of cinematic theory of cognition and relevant mathematical models. We treat cortices as dissipative systems that self-organize themselves near a critical level of activity that is a non-equilibrium metastable state. Criticality is arguably a key aspect of brains in their rapid adaptation, reconfiguration, high storage capacity, and sensitive response to external stimuli. Self-organized criticality (SOC) became an important concept to describe neural systems. We argue that transitions from one AM pattern to the other require the concept of phase transitions, extending beyond the dynamics described by SOC. We employ random graph theory (RGT) and percolation dynamics as fundamental mathematical approaches to model fluctuations in the cortical tissue. Our results indicate that perceptions are formed through a phase transition from a disorganized (high entropy) to a well-organized (low entropy) state, which explains the swiftness of the emergence of the perceptual experience in response to learned stimuli.

Simple unified view of branching process statistics: Random walks in balanced logarithmic potentials.

We revisit the problem of deriving the mean-field values of avalanche exponents in systems with absorbing states. These are well known to coincide with those of unbiased branching processes. Here we show that for at least four different universality classes (directed percolation, dynamical percolation, the voter model or compact directed percolation class, and the Manna class of stochastic sandpiles) this common result can be obtained by mapping the corresponding Langevin equations describing each of them into a random walker confined to the origin by a logarithmic potential. We report on the emergence of nonuniversal continuously varying exponent values stemming from the presence of small external driving - that might induce avalanche merging - that, to the best of our knowledge, has not been noticed in the past. Many of the other results derived here appear in the literature as independently derived for individual universality classes or for the branching process itself. Still, we believe that a simple and unified perspective as the one presented here can help (1) clarify the overall picture, (2) underline the superuniversality of the behavior as well as the dependence on external driving, and (3) avoid the common existing confusion between unbiased branching processes (equivalent to a random walker in a balanced logarithmic potential) and standard (unconfined) random walkers.

Propagation control of data forwarding in opportunistic underwater sensor networks

Opportunistic underwater sensor networks (OUSNs) are developed for a set of underwater applications, including the tracking of underwater creatures and tactical surveillance. The data forwarding objectives of OUSNs differ significantly from those of wireless sensor networks or delay-tolerant networks due to their large energy consumption and large propagation delay underwater. This paper begins with a description of the underwater movement, which consists of the regular movement impelled by external force and the autonomous movement controlled by nodes. Then, a topology determined model is provided to generate a power-law distribution structure, where the communication links that are overlong or are close to the space boundary can be avoided. Finally, a proactive opportunistic forwarding mechanism (POFM) is proposed to minimize the energy consumption from data forwarding. In POFM, at the start of each time slot, each node without data decides whether to request for data or not independently. In particular, the probabilities of nodes requesting for data are calculated according to a dynamic percolation analysis, which suggests the nodes with larger degrees or at earlier time slots should be given larger probabilities. The performance of POFM is analyzed through simulation experiments that produce preferable tradeoff results, indicating that POFM has a minor energy consumption with a guaranteed delivery ratio and a limited propagation delay.

Modeling the dynamic percolation of carbon nanotubes and revisiting critical exponents

In this paper, dynamic percolation of carbon nanotubes in silicone oil was probed by means of electrical measurements. Carbon nanotubes were first dispersed in silicone oils with ultrasounds. The obtained suspension was then slowly diluted. After each dilution, the changes in electrical properties was monitored over time. This procedure enabled to collect a large number volume fraction and define both the percolation threshold and the critical exponents with unmatched accuracy. The percolation threshold was found to decrease with time as a consequence of the already described aggregation of conductive nanoparticles. More surprisingly, the critical exponent also largely varied over time. This changes were correlated to the quality of the dispersion of carbon nanotubes within the host matrix. Finally, statistic percolation model was adapted into one that take into account for conductivity changes as a function of time and filler content.

Properties of distribution and entanglement in discrete-time quantum walk with percolation

We investigate one-dimensional discrete-time quantum walk on the line where the links between neighboring sites are randomly broken. Two link-broken ways, static percolation and dynamical percolation, are considered. The former means that the broken links are fixed in position space at each time step, while the latter is that broken links are varied with time step. Our attention focuses on the effects of these disorders on two physical quantities, the probability distribution and the entanglement between the coin degree of freedom and position degree of freedom. Choosing Hadamard coin operator and assuming the walker to start from the position eigenstate|0〉and attach itself to a coherent coin state 1/√2 (|↑〉+ i|↓〉), we give the statistical average results after making numerical calculations many times. The choices of coin operator and initial state, resulting in a symmetric probability distribution about origin in the ideal case, is helpful in comparing with different cases in different disorder strengths. It is shown that the probability distribution of static percolation quantum walk can change from a coherent behavior at short time to Anderson localization at longer time, while the dynamical percolation quantum walk can change to a classical diffusive behavior. With the decrease of the percolation probability, these transitions become faster. The entanglement for ideal case without disorder reaches a constant value after a short time evolution. The static percolation makes the entanglement less than that of ideal case and fluctuate irregularly around a certain value. The situation is very different for the dynamical percolation:the entanglement increases smoothly with the time step and can exceed the constant value in the ideal case at some time. Both of entanglements for two types of percolations decrease with reducing percolation probability. As a striking characteristic, the entanglement in dynamical case can tend to maximum regardless of percolation probability in long time limit, while the static case cannot. In the model for our study, the randomized unitary operations, induced by the static and dynamical percolations, can lead to some noticeable effects on the transport and entanglement of discrete time quantum walk. The results about the interplay between disorder and entanglement not only assist quantum information processing, but also give more options to further explore and understand disorder physical processes in nature.

Metal removal by pine bark compost using a permeable reactive barrier device at laboratory scale

Environmental contextPermeable reactive barriers are a developing technology to clean up contaminated groundwater. The contaminant plume moves through a reactive material placed below ground that retains or degrades the pollutants. This study shows that pine bark compost strongly adsorbs and retains metals, mostly by interaction with the organic matter of the compost, and thereby serves as a suitable reactive filler material to clean up contaminated groundwater. AbstractPermeable reactive barriers (PRBs) are in situ systems for groundwater remediation, consisting of a screen perpendicular to the flow of contaminated groundwater filled with a material capable of retaining or degrading pollutants. The use of waste materials as reactive substrates in PRBs is of particular interest owing to the possibility of their reutilisation and their generally lower cost. With this aim, the sorption capacity for copper, nickel and zinc of pine bark compost (PBC) was evaluated in competitive batch experiments that showed that metal adsorption is a rapid process and that adsorption capacities followed the sequence Cu&gt;Ni&gt;Zn, with maximum adsorption capacities of 0.157mmolg–1 for Cu2+, 0.052mmolg–1 for Ni2+, 0.046mmolg–1 for Zn2+ and 0.259mmolg–1 for the sum of the three metals. Subsequently, a dynamic percolation experiment was carried out with a multi-metal solution prepared with 50mgL–1 of Cu, Ni and Zn in 0.01M KNO3 as saline background, using an experimental device that reproduced a PRB at laboratory scale. Metal retention ranged from 92 to 99% (Cu&gt;Ni&gt;Zn). The metals were strongly retained by the filling material because low desorption was detected by subsequent leaching with 0.01M KNO3 (0.3, 1.8 and 4.1% of the previously adsorbed metal for Cu, Ni and Zn respectively). The results show that PBC is a potential candidate as a filler material for the retention of cationic metals in permeable reactive barriers.

Susceptible–infected–recovered model with recurrent infection

We analyze a stochastic lattice model describing the spreading of a disease among a community composed by susceptible, infected and removed individuals. A susceptible individual becomes infected catalytically. An infected individual may, spontaneously, either become recovered, that is, acquire a permanent immunization, or become again susceptible. The critical properties including the phase diagram is obtained by means of mean-field theories as well as numerical simulations. The model is found to belong to the universality class of dynamic percolation except when the recovering rate vanishes in which case the model belongs to the directed percolation universality class.

Aging and percolation dynamics in a Non-Poissonian temporal network model.

We present an exhaustive mathematical analysis of the recently proposed Non-Poissonian Activity Driven (NoPAD) model [Moinet et al., Phys. Rev. Lett. 114, 108701 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.108701], a temporal network model incorporating the empirically observed bursty nature of social interactions. We focus on the aging effects emerging from the non-Poissonian dynamics of link activation, and on their effects on the topological properties of time-integrated networks, such as the degree distribution. Analytic expressions for the degree distribution of integrated networks as a function of time are derived, exploring both limits of vanishing and strong aging. We also address the percolation process occurring on these temporal networks, by computing the threshold for the emergence of a giant connected component, highlighting the aging dependence. Our analytic predictions are checked by means of extensive numerical simulations of the NoPAD model.

Dynamic Percolation and Swollen Behavior of Nanodroplets in 1-Ethyl-3-methylimidazolium Trifluoromethanesulfonate/Triton X-100/Cyclohexane Microemulsions.

Microemulsions comprising an ionic liquid (IL), 1-ethyl-3-methylimidazolium trifluoromethanesulfonate ([emim][OTf]), as the polar component, Triton X-100 as a surfactant, and cyclohexane as the nonpolar medium were prepared and characterized. Conductivity and dynamic viscosity data were critically analyzed to confirm dynamic percolation among the droplets that are in continuous motion, aggregation, and fission. The transition from oil-continuous phase to bicontinuous phase was observed at the conductance and viscosity percolation thresholds and sharp changes in the values of conductivity and dynamic viscosity could be identified. Dynamic light scattering measurements revealed swelling of the droplets, which varied within the hydrodynamic diameter range of 10-100 nm. Diffusivity of the droplets suggested less Brownian movement with increased amount of the IL. Moreover, changes in the droplet sizes and diffusivity with increase in IL content supported dynamic percolation within the systems.

Critical behavior in a stochastic model of vector mediated epidemics.

The extreme vulnerability of humans to new and old pathogens is constantly highlighted by unbound outbreaks of epidemics. This vulnerability is both direct, producing illness in humans (dengue, malaria), and also indirect, affecting its supplies (bird and swine flu, Pierce disease, and olive quick decline syndrome). In most cases, the pathogens responsible for an illness spread through vectors. In general, disease evolution may be an uncontrollable propagation or a transient outbreak with limited diffusion. This depends on the physiological parameters of hosts and vectors (susceptibility to the illness, virulence, chronicity of the disease, lifetime of the vectors, etc.). In this perspective and with these motivations, we analyzed a stochastic lattice model able to capture the critical behavior of such epidemics over a limited time horizon and with a finite amount of resources. The model exhibits a critical line of transition that separates spreading and non-spreading phases. The critical line is studied with new analytical methods and direct simulations. Critical exponents are found to be the same as those of dynamical percolation.