Related papers: Generalized Fractal Kinetics in Complex Systems (A…
Field equations with time and coordinates derivatives of noninteger order are derived from stationary action principle for the cases of power-law memory function and long-range interaction in systems. The method is applied to obtain a…
An exact description of the statistical motion of active particles in three dimension is presented in the framework of a generalized diffusion equation. Such a generalization contemplates a non-local, in time and space, connecting (memory)…
The self consistent version of the density functional theory (DFT) is presented, which allows to calculate the ground state and dynamic properties of finite multi-electron systems such as atoms, molecules and clusters. The exact functional…
We derive the kinetic theory of fluctuations in physically and numerically stable particle-in-cell (PIC) simulations of electrostatic plasmas. The starting point is the single-time correlations at the simulation start between the…
Modern density functional approximations achieve moderate accuracy at low computational cost for many electronic structure calculations. Some background is given relating the gradient expansion of density functional theory to the WKB…
The right tail asymptotic series consisting of attenuating exponential terms are derived for the densities of Galton-Watson processes with fractional probability generating functions. The frequencies in the exponential factors form fractal…
We describe an efficient and parsimonious matrix-based theory for studying the ensemble behavior of self-propellers and active swimmers, such as nanomotors or motile bacteria, that are typically studied by differential-equation-based…
In this study we obtained analytically relaxation function in terms of rotational correlation functions based on Brownian motion for complex disordered systems in a stochastic framework. We found out that rotational relaxation function has…
We present a kinetic-energy density-functional theory and the corresponding kinetic-energy Kohn-Sham (keKS) scheme on a lattice and show that by including more observables explicitly in a density-functional approach already simple…
Complex systems such as protein conformational fluctuations and supercooled liquids exhibit a long relaxation time and are considered to posses multiple relaxation times. We analytically obtain the exact correlation function for stochastic…
Having established the fact that interacting classical kicked rotor systems exhibit long-lived prethermal phase with quasi-conserved average Hamiltonian before entering into chaotic heating regime, we use spatio-temporal fluctuation…
We derive a closed equation for the empirical concentration of colloidal particles in the presence of both hydrodynamic and direct interactions. The ensemble average of our functional Langevin equation reproduces known deterministic Dynamic…
In this work we present the explicit calculation of Probability Distribution Function for a model system of granular gas within the framework of Tsallis Non-Extensive Statistical Mechanics, using the stochastic approach by Beck [C. Beck,…
Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the…
The long-time behavior of certain fast-decaying infinite temperature correlation functions on one-, two- and three-dimensional lattices of classical spins with various kinds of nearest-neighbor interactions is studied numerically, and…
We consider the evolution of correlation functions in a non-Markov version of the contact model in the continuum. The memory effects are introduced by assuming the fractional evolution equation for the statistical dynamics. This leads to a…
The universal symmetry, or conservation, of complexity underlies any law or principle of system dynamics and describes the unceasing transformation of dynamic information into dynamic entropy as the unique way to conserve their sum, the…
We study effects of fluctuations on the mesoscopic length-scale on systems with mesoscopic inhomogeneities. Equations for the correlation function and for the average volume fraction are derived in the self-consistent Gaussian…
We connect two different generalizations of Boltzmann's kinetic theory by requiring the same stationary solution. Non-extensive statistics can be produced by either using corresponding collision rates nonlinear in the one-particle densities…
Relations similar to work and exchange fluctuations have been recently derived for open systems dynamically evolving in the presence of an ancilla. Extending these relations and constructing a non-equilibrium Helmholtz equation we derive a…