The method of invariant manifold is developed for a derivation of reduced description in kinetic equations of dilute polymeric solutions. It is demonstrated that this reduced description becomes universal in the limit of small Deborah and Weissenberg numbers, and it is represented by the...

Models of complex reactions in thermodynamically isolated systems often demonstrate evolution towards low-dimensional manifolds in the phase space. For this class of models, we suggest a direct method to construct such manifolds, and thereby to reduce the effective dimension of the problem. The...

The time-dependence of the occupation probabilities of neighboring wells due to diffusion in one dimension is formulated in terms of a set of generalized rate equations describing transitions between neighboring wells and escape across a final barrier. The equations contain rate coefficients,...

The quasi-equilibrium approximation is employed as a systematic tool for solving the problem of deriving constitutive equations from kinetic models of liquid-crystalline polymers. It is demonstrated how kinetic models of liquid-crystalline polymers can be approximated in a systematic way, how...

The quasi-equilibrium or maximum entropy approximation is applied in order to derive constitutive equations from kinetic models of polymer dynamics. It is shown in general and illustrated for an example how canonical distribution functions are obtained from the maximum entropy principle, how...

The role of damping on the phenomenon of Stochastic Resonance (SR) in a driven underdamped periodic potential system is studied. Using input energy per period of external drive as a quantifier, SR is observed in the model multistable system in the high frequency regime, due to the noise assisted...

The intracellular motion of the kinesin motor proteins, based on an asymmetric hand-over-hand mechanism, within a stochastically fluctuating medium is simulated via the Langevin dynamics in which the random intracellular fluctuations are represented by a white noise. The kinesin heads are...

The rotary motion of the F0 part of the F0F1-ATPase motor that synthesizes the ATP molecules used by the intracellular stepping motors, such as kinesins, is modeled within a stochastically fluctuating medium via the application of the Langevin dynamics wherein the random intramembrane...

In this paper, we report a novel effect of a particular kind of non-Gaussian noise (NGN), especially its deviation from Gaussian noise, on the spiking activity in a deterministic Hodgkin–Huxley (HH) neuron. It is found via numerical simulations that the coefficient of variation (CV),...

In this note I introduce some techniques to treat systems in contact with (stochastic) thermal baths. The methods and the level of rigour are those of theoretical physics.