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Einstein's explanation of Brownian motion provided one of the cornerstones which underlie the modern approaches to stochastic processes. His approach is based on a random walk picture and is valid for Markovian processes lacking long-term…
Time evolution of the cities and of the languages is considered in terms of multiplicative noise and fragmentation processes; where power law (Pareto-Zipf law) and slightly asymmetric log-normal (Gauss) distribution result for the size…
Virtually every biological rate depends on temperature, yet the resulting rate-temperature relationships often deviate strongly from simple Arrhenius behavior. In this first part of a two-part review, we survey phenomenological models used…
In the present Short Note an idea is proposed to explain the emergence and the observation of processes in complex media that are driven by fractional non-Markovian master equations. Particle trajectories are assumed to be solely Markovian…
We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of…
A simplified version of a classical problem in thermodynamics -- the adiabatic piston -- is discussed in the framework of kinetic theory. We consider the limit of gases whose relaxation time is extremely fast so that the gases contained on…
We present certain mathematical aspects of an information method which was formulated in an attempt to investigate diffusion phenomena. We imagine a regular dynamical hamiltonian systems under the random perturbation of thermal (molecular)…
Combining intuitive probabilistic assumptions with the basic laws of classical thermodynamics, using the latter to express probabilistic parameters in terms of the thermodynamic quantities, we get a simple unified derivation of the…
Descriptions of molecular systems usually refer to two distinct theoretical frameworks. On the one hand the quantum pure state, i.e. the wavefunction, of an isolated system which is determined to calculate molecular properties and to…
The effects of chaotic advection and diffusion on fast chemical reactions in two-dimensional fluid flows are investigated using experimentally measured stretching fields and fluorescent monitoring of the local concentration. Flow symmetry,…
We investigate multivariate regular variation in the context of time-homogeneous Markov chains on general vector spaces and in random coefficient linear models. In the first part, we show that the regular variation of the stationary…
The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction…
The special relativity laws emerge as one-parameter (light speed) generalizations of the corresponding laws of classical physics. These generalizations, imposed by the Lorentz transformations, affect both the definition of the various…
In this paper, a new physical notion, intensity, is introduced. The notion of intensity occurs in a special statistics, known as Gentile statistics, which is asymptotically close to ordinary thermodynamics. The introduction of the new…
On the basis of the assumption that atoms play a role of effective Fermions at lattice distribution, the study of the long-range ordering is shown to be reduced to self-consistent consideration of single and collective excitations being…
That the laws of physics are the same at all times and places throughout the Universe is one of the basic assumptions of physics. Astronomical observations provide the only means to test this basic assumption on cosmological time and…
We consider diffusive lattice gases on a ring and analyze the stability of their density profiles conditionally to a current deviation. Depending on the current, one observes a phase transition between a regime where the density remains…
Chemical kinetics plays an important role in governing the thermal evolution in reactive flows problems. The possible interactions between chemical species increase drastically with the number of species considered in the system. Various…
Convergence of order $O(1/\sqrt{n})$ is obtained for the distance in total variation between the Poisson distribution and the distribution of the number of fixed size cycles in generalized random graphs with random vertex weights. The…
Using molecular dynamics simulation, we calculate the distribution of atomic jum ps in Cu$_{33}$Zr$_{67}$ in the liquid and glassy states. In both states the distribution of jump lengths can be described by a temperature independent…