Exact site-percolation probability on the square lattice

We present an algorithm to compute the exact probability $R_{n}(p)$ for a site percolation cluster to span an $n\times n$ square lattice at occupancy $p$. The algorithm has time and space complexity $O(\lambda^n)$ with $\lambda \approx 2.6$. It allows us to compute $R_{n}(p)$ up to $n=24$. We use the data to compute estimates for the percolation threshold $p_c$ that are several orders of magnitude more precise than estimates based on Monte-Carlo simulations.

Potential Landscape of a Probe Penetrant Particle for Fast Estimating of Silica Diffusion Properties

Successful search for optimal molecular structures of membrane materials requires efficient algorithms for assessing their diffusion properties. It is shown in this work that the potential landscape of a probe penetrating particle, a component that passes through the membrane during gas separation, is suitable for solving such problems. A number of indicators are considered that can be easily calculated from potential landscapes of specific models of silicate materials, both not related to the topology of the potential landscape (global minimum, voxel energy distribution), and depending on it (percolation cluster). A good correlation of these indicators with the corresponding diffusion coefficients is shown

Multiscale entropy and asynchronies of percolation-based price model and Chinese stock market

In recent years, the concept of entropy is widely used to measure the degree of uncertainty or complexity of dynamics system. In our work, we utilize the composite multiscale entropy (CMSE) and the composite multiscale cross-sample entropy (CMSCE) which are two modified algorithms of SampEn and Cross-SampEn by considering multiscale factors, to, respectively, investigate the multiscale complexities and asynchronies (correlations) in the Chinese stock market (SSZ, SZSE and HSI) as well as in our established financial stock price model. The price model is given based on a greatly important statistical physics system, the two-dimensional continuum percolation system. In the model, the fluctuations of stock price changes are assumed to be attributed to the market information interactions among the traders, and the percolation cluster is taken to represent the traders holding the same investment attitude. The empirical CMSE and CMSCE results display and meanwhile make comparisons of abundant complexities and correlations properties about Chinese stock indices and simulation data on both overall and the upwards, downwards trend of their returns.

Ячеистый беспорядок наноглобул желатина

The surface topology of thin polymer films obtained on glass from micellar solutions of gelatin samples in a mixture of isooctane – water – (bis-2-ethylhexyl) sodium sulfosuccinate (AOT) with a variation in the average molecular weight M of the polymer and a constant molar ratio [H2O]/[AOT] = 40, has been studied using electron microscopy. It is shown that solutions with an initial gelatin concentration corresponding to the gelation threshold form films with a characteristic structure: polymer nanoglobuls are located in the cells of the physical network of macromolecules-the internal percolation cluster of particles. At the same time, with a decrease in M, the average size of the globules decreases and the degree of their polydisperity increases. The same changes are observed for network cells in which local density – density correlations weaken. The ratio of average cell sizes to nanoglobuls is independent of M due to the universal fractal cluster structure of the films.