A coupled forward–backward stochastic differential system (FBSDS) is formulated in spaces of fields for the incompressible Navier–Stokes equation in the whole space. It is shown to have a unique local solution, and further if either the Reynolds number is small or the dimension of the...

We present an overview of some results we have obtained recently (A. Sain, Manu and R. Pandit, Phys. Rev. Lett. 81 (1998) 4377) from a pseudospectral study of the randomly forced Navier–Stokes equation (RFNSE) stirred by a stochastic force with zero mean and a variance ∼k4−d−y, with k...

In this paper we prove the local existence and uniqueness of solutions for a class of stochastic fractional partial differential equations driven by multiplicative noise. We also establish that for this class of equations adding linear multiplicative noise provides a regularizing effect: the...

A mean-field approach (filtering out subgrid scales) is applied to the Boltzmann equation in order to derive a subgrid turbulence model based on kinetic theory. It is demonstrated that the only Smagorinsky type model which survives in the hydrodynamic limit on the viscosity time scale is the...

Two indicators are presented to compare the Second law performances of different design-variants of the same process unit. The first indicator relates the entropy production to quantities like the total transferred thermal energy and the total chemical conversion. This allows a useful...

A generalization of the Gibbs entropy postulate is proposed based on the BBGKY [Born–Bogoliubov–Green–Kirkwood–Yvon] hierarchy as the nonequilibrium entropy for a system of N interacting particles. By using this entropy and the methods of nonequilibrium thermodynamics, a master equation...

We analyze some models of nonequilibrium systems proposed in the past decade which derive the laws of irreversible thermodynamics from deterministic dynamics. We find that these models do not posses the crucial property of local thermodynamic equilibrium, since they represent noninteracting...

Markov chain models on a mesoscopic level are a widely used description for complex systems. They are based on the assumption that certain sets of microstates can be coarse grained as their internal dynamics is faster than the time scales considered in the modeling. Here we analyze...

Theoretical evidence derived from linear irreversible thermodynamics (LIT) jointly with Burnett’s solution of Boltzmann’s gas-kinetic equation is used to show that fluid mechanics and transport processes in both gaseous and liquid continua require the use of two independent velocities rather...

A non-equilibrium statistical theory for aging dissipative systems formed by atoms is developed and applied to electromigration damage in conductors. A modification of Black’s mean failure time is presented. We describe the experimental relationship between the initial rate of increase in the...