Sharp change properties heterogeny systems

Greetings, dear researcher!

You have visited the page of a group of Russian scientists who study the "geometric phase transition" - the formation of clusters, percolation structures and the influence of dimensional effects on the properties of real systems. Numerous works by prominent scientists have been devoted to the study of the properties of clusters and percolation structures: - Mandelbrot, Kirkpatrick, Abrikosov, Stauffer, Aharony, Shklovsky, Efros and many others. The fundamental and applied aspects of percolation theory have numerous applications in various fields of science, from physics to psychology.

In our opinion, the number of phenomena in which percolation problems exist is much higher. And often x researchers don't even suspect that they are dealing with percolation processes.

We believe that many threshold phenomena can be considered as a "geometric phase transition", in the sense that at a certain concentration in the matrix of regions with a different nature, a new macroscopic property appears in the system as a whole. It is possible to conduct an experimental study of such changes, determine the control parameters, and even construct a formula that will describe the observed effects.

However, in order to understand and the possibility of managing them, it is necessary to describe "in numbers" the process of formation and the parameters of the cluster (domain, regions) structure in the matrix. Such regions can be both embedded particles and matrix domains, the properties of which change under the influence of internal or external influences. When these regions form a connected cluster, it will dominate and determine the properties of the entire system. And here there is a difference between theory and practice.

What is the problem in real percolation?

There are excellent classical percolation theories describing ideal infinite systems (link). However, such objects practically do not exist in nature, and most researchers actually study finite systems in which both the geometry of individual particles and the characteristics of the matrix, its surface, and particle placement conditions become essential. Therefore, the parameters of the percolation transition in real systems do not correspond to the predictions of theory and in many experimental studies are limited to general conclusions about the nonlinearity of the observed phenomena.

Therefore, we have developed a package for studying percolation structures, in which we statistically simulate the process of placing particles in a matrix and get an answer to most of the experimenters' questions.

We claim that our approach makes it possible to explain nonlinear phenomena in heterogeneous systems of various natures with high reliability and provides a tool for the conscious synthesis of new systems and processes.

• How are clusters of embedded particles formed and developed?
• Do particle sizes (size distribution), aspect number and geometry of the matrix affect the formation of the structure?
• How isotropic is the texture of heterogeneous material?
• How much does the existence of a surface affect the properties of a percolation cluster?
• What macroparameters of the system can be calculated using data on percolation stricture?
• How to describe the degradation of the structure of heterogeneous systems, etc.