A new general three-dimensional hydrodynamic–magnetic boundary integral formulation for a magnetic free surfaces in viscous flows at low Reynolds numbers is developed. The formulation is based on an extension of the Lorentz reciprocal theorem for the incompressible flow of a magnetic fluid. Combining the reciprocal theorem and the fundamental solution of a creeping flow we obtain the integral r...

We present a finite element discretization of a non-linear diffusion equation used in the field of critical phenomena and, more recently, in the context of dynamic density functional theory. The discretized equation preserves the structure of the continuum equation. Specifically, it conserves the total number of particles and fulfills an H-theorem as the original partial differential equation. ...

In this paper an analytical model for cold rolling of strip has been described. This model is developed based on the slab method of analysis and the hydrodynamic lubrication. The characteristics of rolling are obtained from the equations of equilibrium and the plate was allowed to strain harden assuming that the lubricant behaves as a Newtonian fluid. The shear stress to the plate is obtained b...

In this paper an analytical model for cold rolling of strip has been described. This model is developed based on the slab method of analysis and the hydrodynamic lubrication. The characteristics of rolling are obtained from the equations of equilibrium and the plate was allowed to strain harden assuming that the lubricant behaves as a Newtonian fluid. The shear stress to the plate is obtained b...

Continuum equations are derived for the large-scale behavior of a class of cellular automaton models for fluids. The cellular automata are discrete analogues of molecular dynamics, in which particles with discrete velocities populate the links of a fixed array of sites. Kinetic equations for microscopic particle distributions are constructed. Hydrodynamic equations are then derived using the Ch...

We review the renormalization group method applied to non-equilibrium dynamics by tracing the way how the hydrodynamic equations can be derived as reduced dynamics of the Boltzmann equation as a typical example.

We present a family of equations of state within a quasiparticle model adjusted to lattice QCD and study the impact on azimuthal flow anisotropies and transverse momentum spectra within hydrodynamic simulations for heavyion collisions at energies relevant for LHC.

We investigate the effects of given pressure gradients on hydrodynamic flow equations. We obtain results in terms of implicit solutions and also in the framework of an extra-dimensional formalism involving the diffusion/Schrödinger equation.

We present a Lagrangian-Eulerian strategy for proving uniqueness and local existence of solutions of limited smoothness for a class of incompressible hydrodynamic models including Oldroyd-B type complex fluid models and zero magnetic resistivity magneto-hydrodynamics equations.

Symmetry constraints for dispersionless integrable equations are discussed. It is shown that under symmetry constraints the dispersionless Veselov-Novikov equation is reduced to the 1+ 1-dimensional hydrodynamic type systems. Mathematics Subject Classification. 35Q58, 37K15, 37K20.