Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCorrelated percolation patterns in PEF damaged cellular material
65
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We present results of numerical and experimental investigation of the electric breakage of a cellular material in pulsed electric fields (PEF). The numerical model simulates the conductive properties of a cellular material by a two-dimensional array of biological cells. The application of an external field in the form of the idealised square pulse sequence with a pulse duration $t_{i}$, and a pulse repetition time $Delta t$ is assumed. The simulation model includes the known mechanisms of temporal and spatial evolution of the conductive properties of different microstructural elements in a tissue. The kinetics of breakage at different values of electric field strength $E$, $t_{i}$ and $Delta t$ was studied in experimental investigation. We propose the hypothesis for the nature of tissue properties evolution after PEF treatment and consider this phenomena as a correlated percolation, which is governed by two key processes: resealing of cells and moisture transfer processes inside the cellular structure. The breakage kinetics was shown to be very sensitive to the repetition times $Delta t$ of the PEF treatment. We observed correlated percolation patterns in a case when $Delta t$ exceeds the characteristic time of the processes of moisture transfer and random percolation patterns in other cases. The long-term mode of the pulse repetition times in PEF treatment allows us to visualize experimentally the macroscopic percolation channels in the sample.
rate research
Read More
We consider the simplified dielectric breakage model used for simulation of the kinetics of cellular material breakage under the pulsed electric field (PEF) treatment. The model is based on an effective media approximation, which includes equations with the same morphology parameters as in percolation theory. The probability of a whole cell breakage by the pulse with $t_{i}$ duration is estimated on the basis of electroporation theory. We account for the bridging effect resulting from the deviations of the local conductivity near the selected cell from the average effective media conductivity. The most important feature of the proposed model is the existence of the ``jamming behaviour occurring sometimes in experimental observations of the biological tissue breakage. The different transitions corresponding to the ``jamming steps are identified. The experimental results are obtained for thin apple slices treated with electric pulses at field strengths $E=0.2-2.2$ kV cm$^{-1}$, pulse durations $t_{i}=10-100$ $mu$s, pulse repetition times $t=10-100$ ms and the number of pulses $N=1-100000$. The model gives results consistent in general with the experimental observations. We discuss the correlation between the degree of cellular material destruction, field strength, time of PEF treatment and power consumption.
Cluster concepts have been extremely useful in elucidating many problems in physics. Percolation theory provides a generic framework to study the behavior of the cluster distribution. In most cases the theory predicts a geometrical transition at the percolation threshold, characterized in the percolative phase by the presence of a spanning cluster, which becomes infinite in the thermodynamic limit. Standard percolation usually deals with the problem when the constitutive elements of the clusters are randomly distributed. However correlations cannot always be neglected. In this case correlated percolation is the appropriate theory to study such systems. The origin of correlated percolation could be dated back to 1937 when Mayer [1] proposed a theory to describe the condensation from a gas to a liquid in terms of mathematical clusters (for a review of cluster theory in simple fluids see [2]). The location for the divergence of the size of these clusters was interpreted as the condensation transition from a gas to a liquid. One of the major drawback of the theory was that the cluster number for some values of thermodynamic parameters could become negative. As a consequence the clusters did not have any physical interpretation [3]. This theory was followed by Frenkels phenomenological model [4], in which the fluid was considered as made of non interacting physical clusters with a given free energy. This model was later improved by Fisher [3], who proposed a different free energy for the clusters, now called droplets, and consequently a different scaling form for the droplet size distribution. This distribution, which depends on two geometrical parameters, has the nice feature that the mean droplet size exhibits a divergence at the liquid-gas critical point.
We reconsider the problem of percolation on an equilibrium random network with degree-degree correlations between nearest-neighboring vertices focusing on critical singularities at a percolation threshold. We obtain criteria for degree-degree correlations to be irrelevant for critical singularities. We present examples of networks in which assortative and disassortative mixing leads to unusual percolation properties and new critical exponents.
We study the dynamics of a carrier, which performs a biased motion under the influence of an external field E, in an environment which is modeled by dynamic percolation and created by hard-core particles. The particles move randomly on a simple cubic lattice, constrained by hard-core exclusion, and they spontaneously annihilate and re-appear at some prescribed rates. Using decoupling of the third-order correlation functions into the product of the pairwise carrier-particle correlations we determine the density profiles of the environment particles, as seen from the stationary moving carrier, and calculate its terminal velocity, V_c, as the function of the applied field and other system parameters. We find that for sufficiently small driving forces the force exerted on the carrier by the environment particles shows a viscous-like behavior. An analog Stokes formula for such dynamic percolative environments and the corresponding friction coefficient are derived. We show that the density profile of the environment particles is strongly inhomogeneous: In front of the stationary moving carrier the density is higher than the average density, $rho_s$, and approaches the average value as an exponential function of the distance from the carrier. Past the carrier the local density is lower than $rho_s$ and the relaxation towards $rho_s$ may proceed differently depending on whether the particles number is or is not explicitly conserved.
We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network undergoes a percolation transition. The percolation transition is characterized by a weak singular behavior of the mean cluster size and power-law scalings of the percolation order parameter and the cluster size distribution in the entire non-percolating phase. These results suggest that the assortative degree-degree correlation generates a global structural correlation which is relevant to the percolation critical phenomena of complex networks.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
