207 research outputs found
Landau damping in the multiscale Vlasov theory
Vlasov kinetic theory is extended by adopting an extra one particle
distribution function as an additional state variable characterizing the
micro-turbulence internal structure. The extended Vlasov equation keeps the
reversibility, the Hamiltonian structure, and the entropy conservation of the
original Vlasov equation. In the setting of the extended Vlasov theory we then
argue that the Fokker-Planck type damping in the velocity dependence of the
extra distribution function induces the Landau damping. The same type of
extension is made also in the setting of fluid mechanics
Roles of Energy and Entropy in Multiscale Dynamics and Thermodynamics
Multiscale thermodynamics is a theory of relations among levels of
description. Energy and entropy are its two main ingredients. Their roles in
the time evolution describing approach of a level (starting level) to another
level involving less details (target level) is examined on several examples,
including the level on which macroscopic systems are seen as composed of
microscopic particles, mesoscopic levels as kinetic theory of ideal and van der
Waals gases, fluid mechanics, the level of chemical kinetics, and the level of
equilibrium thermodynamics. The entropy enters the emergence of the target
level in two roles. It expresses internal energy, that is the part of the
energy that cannot be expressed in terms of the state variables used on the
starting level, and it reveals emerging features characterizing the target
level by sweeping away unimportant details. In the case when the target level
is a mesoscopic level involving time evolution the roles of the energy and the
entropy is taken by two different potentials that are related to their rates.Comment: 36 pages, no figure
Multiscale Thermodynamics
Multiscale thermodynamics is a theory of relations among levels of
investigation of complex systems. It includes the classical equilibrium
thermodynamics as a special case but it is applicable to both static and time
evolving processes in externally and internally driven macroscopic systems that
are far from equilibrium and are investigated on microscopic, mesoscopic, and
macroscopic levels. In this paper we formulate the multiscale thermodynamics,
explain its origin, and illustrate it in mesoscopic dynamics that combines
levels.Comment: 53 pages no figure
Thermodynamics and Rate Thermodynamics
Approach of mesoscopic state variables to time independent equilibrium sates
(zero law of thermodynamics) gives birth to the classical equilibrium
thermodynamics. Approach of fluxes and forces to fixed points (equilibrium
fluxes and forces) that drive reduced mesoscopic dynamics gives birth to the
rate thermodynamics that is applicable to driven systems. We formulate the rate
thermodynamics and dynamics, investigate its relation to the classical
thermodynamics, to extensions involving more details, to the hierarchy
reformulations of dynamical theories, and to the Onsager variational principle.
We also compare thermodynamic and dynamic critical behavior observed in closed
and open systems. Dynamics and thermodynamics of the van der Waals gas provides
an illustration.Comment: 35 page
Multiscale Theory
Boltzmann kinetic equation is put into the form of an abstract time evolution
equation representing links connecting autonomous mesoscopic dynamical theories
involving varying amount of details. In the chronological order we present
results that led to the abstract time equation evolution in both state space
and the space of vector fields. In the final section we list some open
problems.Comment: Accepted in Journal of Nonequilibrium Thermodynamic
One and two-fiber orientation kinetic theories of fiber suspensions
http://dx.doi.org/10.1016/j.jnnfm.2012.10.009The morphology influencing rheological properties of suspensions of rigid spheres constitutes the flow induced collective ordering of the spheres characterized by two or more sphere distribution functions. When the rigid spheres are replaced by rigid fibers, the collective order in the position of the spheres is replaced by the flow induced orientation of the fibers that suffices to be characterized by one-fiber orientation distribution function. A flow induced collective ordering of fibers (both in position and orientation), that can only be characterized by two or more fiber distribution functions, can still however constitute an important part of the morphology. We show that two types of interaction among fibers, one being the Onsager-type topological interaction entering the free energy and the other the hydrodynamics interaction entering the dissipative part of the time evolution, give indeed rise to a collective order in the orientation influencing the rheology of fiber suspensions
Solid-fluid dynamics of yield-stress fluids
On the example of two-phase continua experiencing stress induced solid-fluid
phase transitions we explore the use of the Euler structure in the formulation
of the governing equations. The Euler structure guarantees that solutions of
the time evolution equations possessing it are compatible with mechanics and
with thermodynamics. The former compatibility means that the equations are
local conservation laws of the Godunov type and the latter compatibility means
that the entropy does not decrease during the time evolution. In numerical
illustrations, in which the one-dimensional Riemann problem is explored, we
require that the Euler structure is also preserved in the discretization.Comment: 51 pages, 7 figure
Role of thermodynamics in extensions of mesoscopic dynamical theories
Complex macroscopic systems (like for instance those encountered in nanotechnology
and biology) need to be investigated in a family of mesoscopic theories involving varying
amount of details. In this paper we formulate a general thermodynamics providing a uni-
versal framework for such multiscale viewpoint of mesoscopic dynamics. We then discuss
its role in making extensions (i.e. in lifting a mesoscopic theory to a more microscopic
level that involves more details)
Extra mass flux in fluid mechanics
The conditions of existence of extra mass flux in single component
dissipative non-relativistic fluids are clarified. By considering Galilean
invariance we show that if total mass flux is equal to total momentum density,
then mass, momentum, angular momentum and booster (center-of-mass) are
conserved. However, these conservation laws may be fulfilled also by other
means. We show an example of weakly non-local hydrodynamics where the
conservation laws are satisfied as well although the total mass flux is
different from momentum density
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