6 research outputs found
Hydrodynamics of thermal granular convection
A hydrodynamic theory is formulated for buoyancy-driven ("thermal") granular
convection, recently predicted in molecular dynamic simulations and observed in
experiment. The limit of a dilute flow is considered. The problem is fully
described by three scaled parameters. The convection occurs via a supercritical
bifurcation, the inelasticity of the collisions being the control parameter.
The theory is expected to be valid for small Knudsen numbers and nearly elastic
grain collisions.Comment: 4 pages, 4 EPS figures, some details adde
Onset of thermal convection in a horizontal layer of granular gas
The Navier-Stokes granular hydrodynamics is employed for determining the
threshold of thermal convection in an infinite horizontal layer of granular
gas. The dependence of the convection threshold, in terms of the inelasticity
of particle collisions, on the Froude and Knudsen numbers is found. A simple
necessary condition for convection is formulated in terms of the
Schwarzschild's criterion, well-known in thermal convection of (compressible)
classical fluids. The morphology of convection cells at the onset is
determined. At large Froude numbers, the Froude number drops out of the
problem. As the Froude number goes to zero, the convection instability turns
into a recently discovered phase separation instability.Comment: 6 pages, 6 figures. An extended version. A simple and universal
necessary criterion for convection presente
A geometric approach to time evolution operators of Lie quantum systems
Lie systems in Quantum Mechanics are studied from a geometric point of view.
In particular, we develop methods to obtain time evolution operators of
time-dependent Schrodinger equations of Lie type and we show how these methods
explain certain ad hoc methods used in previous papers in order to obtain exact
solutions. Finally, several instances of time-dependent quadratic Hamiltonian
are solved.Comment: Accepted for publication in the International Journal of Theoretical
Physic