Thermal Percolation Behavior in Thermal Conductivity of Polymer Nanocomposite with Lateral Size of Graphene Nanoplatelet

In this study, the thermal percolation behavior for the thermal conductivity of nanocomposites according to the lateral size of graphene nanoplatelets (GNPs) was studied. When the amount of GNPs reached the critical concentration, a rapid increase in thermal conductivity and thermal percolation behavior of the nanocomposites were induced by the GNP network. Interestingly, as the size of GNPs increased, higher thermal conductivity and a lower percolation threshold were observed. The in-plane thermal conductivity of the nanocomposite containing 30 wt.% M25 GNP (the largest size) was 8.094 W/m·K, and it was improved by 1518.8% compared to the polymer matrix. These experimentally obtained thermal conductivity results for below and above the critical content were theoretically explained by applying Nan’s model and the percolation model, respectively, in relation to the GNP size. The thermal percolation behavior according to the GNP size identified in this study can provide insight into the design of nanocomposite materials with excellent heat dissipation properties.

Yeast-derived nanoparticles remodel the immunosuppressive microenvironment in tumor and tumor-draining lymph nodes to suppress tumor growth

Microbe-based cancer immunotherapy has recently emerged as a hot topic for cancer treatment. However, serious limitations remain including infection associated side-effect and unsatisfactory outcomes in clinic trials. Here, we fabricate different sizes of nano-formulations derived from yeast cell wall (YCW NPs) by differential centrifugation. The induction of anticancer immunity of our formulations appears to inversely correlate with their size due to the ability to accumulate in tumor-draining lymph node (TDLN). Moreover, we use a percolation model to explain their distribution behavior toward TDLN. The abundance and functional orientation of each effector component are significantly improved not only in the microenvironment in tumor but also in the TDLN following small size YCW NPs treatment. In combination with programmed death-ligand 1 (PD-L1) blockade, we demonstrate anticancer efficiency in melanoma-challenged mice. We delineate potential strategy to target immunosuppressive microenvironment by microbe-based nanoparticles and highlight the role of size effect in microbe-based immune therapeutics.

The percolation model of relative conductivities and phase permeabilities

The universal mathematical model of relative conductivities of percolation clusters and phase permeabilities of oil-water-saturated rocks is presented. It is obtained on the basis of percolation theory, porous body physics and statistics. The model takes into account the influence of change in pore space surface properties and the nature of fluid flow on the studied characteristics and may be applied for comprehensive analysis and modeling of technological processes of oil production.

Higher-Dimensional Stick Percolation

We consider two cases of the so-called stick percolation model with sticks of length L. In the first case, the orientation is chosen independently and uniformly, while in the second all sticks are oriented along the same direction. We study their respective critical values $$\lambda _c(L)$$ λ c ( L ) of the percolation phase transition, and in particular we investigate the asymptotic behavior of $$\lambda _c(L)$$ λ c ( L ) as $$L\rightarrow \infty $$ L → ∞ for both of these cases. In the first case we prove that $$\lambda _c(L)\sim L^{-2}$$ λ c ( L ) ∼ L - 2 for any $$d\ge 2,$$ d ≥ 2 , while in the second we prove that $$\lambda _c(L)\sim L^{-1}$$ λ c ( L ) ∼ L - 1 for any $$d\ge 2.$$ d ≥ 2 .

Highlighting the impact of social relationships on the propagation of respiratory viruses using percolation theory

We develop a site-bond percolation model, called PERCOVID, in order to describe the time evolution of all epidemics propagating through respiratory tract or by skin contacts in human populations. This model is based on a network of social relationships representing interconnected households experiencing governmental non-pharmaceutical interventions. As a very first testing ground, we apply our model to the understanding of the dynamics of the COVID-19 pandemic in France from December 2019 up to December 2021. Our model shows the impact of lockdowns and curfews, as well as the influence of the progressive vaccination campaign in order to keep COVID-19 pandemic under the percolation threshold. We illustrate the role played by social interactions by comparing two typical scenarios with low or high strengths of social relationships as compared to France during the first wave in March 2020. We investigate finally the role played by the α and δ variants in the evolution of the epidemic in France till autumn 2021, paying particular attention to the essential role played by the vaccination. Our model predicts that the rise of the epidemic observed in July and August 2021 would not result in a new major epidemic wave in France.

Correlation length critical exponent as a function of the percolation radius for one-dimensional chains in bond problems

A one-dimensional lattice percolation model is constructed for the problem of constraints flowing along non-nearest neighbors. In this work, we calculated the critical exponent of the correlation length in the one-dimensional bond problem for a percolation radius of up to 6. In the calculations, we used a method without constructing a covering lattice or an adjacency matrix (to find the percolation threshold). The values of the critical exponent of the correlation length were obtained in the one-dimensional bond problem depending on the size of the system and at different percolation radii. Based on original algorithms that operate on a computer faster than standard ones (associated with the construction of a covering lattice), these results are obtained with corresponding errors.

Sharpness of the Phase Transition for the Orthant Model

The orthant model is a directed percolation model on $\mathbb {Z}^{d}$ ℤ d , in which all clusters are infinite. We prove a sharp threshold result for this model: if p is larger than the critical value above which the cluster of 0 is contained in a cone, then the shift from 0 that is required to contain the cluster of 0 in that cone is exponentially small. As a consequence, above this critical threshold, a shape theorem holds for the cluster of 0, as well as ballisticity of the random walk on this cluster.