The fluctuation-dissipation theorem is the main tool for obtaining the response of a physical system. However, FDT fails in many situations (see [1] for review), such as phase transitions, spin glass, anomalous diffusion, and growth phenomena. We develop the hypothesis that the dynamics of a given system may lead to a fractal dimension $d_f$ different from the original spatial dimension $d$....
In my talk we consider the following topics:
1.Free and C-free probaility and completely positive maps.
2.Free independent projections as a model of Jozef Lukasiewicz
$n$-valued logic , $n>2$ and also model of continuous logic of Lukasiewicz-Tarski.
3.Main Theorem: : If $q$ is real number and $x,y$ are from interval $(0,1)$, then the Tsallis entropy is defined as
$$T_{q} (x,y) =...
In this talk, we present an integral equation formulation of run-and-tumble particles (RTPs) under two types of confinement: between parallel walls and within a harmonic potential. This reformulation allows us to obtain exact analytical results that are not accessible through the standard Fokker-Planck differential equation approach. A second objective is to draw analogies between the RTP...
Polymers are key materials in soft condensed matter with diverse applications. Recently, significant attention has been given to understanding the micromechanical behavior of single macromolecules under applied forces. Using molecular dynamics, we examined how constant and periodic forces affect polymer chain conformations in dilute solutions, modeled for good and poor solvents. We...
