227 research outputs found
Elementary preamble to a theory of granular gases
Granular materials partake almost dramatically at times of the properties of
solids and, under different circumstances, of some properties of gases. Here,
within the mechanics of mass points, an elementary analysis, involving
predominantly velocities rather than places, is shown to lead to a global
equation concerning the shuffling motions (in addition to continuity and
Cauchy's equations); it involves a stirring tensor and rules the evolution of a
Reynolds' tensor.Comment: 17 page
Mechanics of Systems of Affine Bodies. Geometric Foundations and Applications in Dynamics of Structured Media
In the present paper we investigate the mechanics of systems of
affinely-rigid bodies, i.e., bodies rigid in the sense of affine geometry.
Certain physical applications are possible in modelling of molecular crystals,
granular media, and other physical objects. Particularly interesting are
dynamical models invariant under the group underlying geometry of degrees of
freedom. In contrary to the single body case there exist nontrivial potentials
invariant under this group (left and right acting). The concept of relative
(mutual) deformation tensors of pairs of affine bodies is discussed. Scalar
invariants built of such tensors are constructed. There is an essential novelty
in comparison to deformation scalars of single affine bodies, i.e., there exist
affinely-invariant scalars of mutual deformations. Hence, the hierarchy of
interaction models according to their invariance group, from Euclidean to
affine ones, can be considered.Comment: 50 pages, 4 figure
A quest for on 'extended' continuum mechanics
EnEarlier re ections on balance equations possibly appropriate for hyper uids or pseudo uids (re ections broached originally so as to dispose of lack of strict objectivity in standard thermal quantities) are instanced again with a different slant. It is alleged that partially chaotic motions can be efficiently branded by assigning pertinent averages, moments and variances and these gauges can be all (not only the first two) considered mechanical; hence the qualifier ‘extended’. A few immediate consequences of the approach are derived, open problems are listed, connections or dissensions with widely acknowledged notions are discussed
Spin fluids and hyperfluids
The general theory of continua with microstructure reviewed in [2] (and, in particular, the theory of gyrocontinua studied in [1]) is adapted to apply to perfect spin fluids and hyperuids [10]. Obvious changes are needed due to the prevailing interest for solids in [1] and to some extent in [2]; here, in addition, the conservative character of the continuum is exploited. Finally, the roles of metric, coframe, connection, torsion and curvature in fluids are explored.
Covariant Balance Laws in Continua with Microstructure
The purpose of this paper is to extend the Green-Naghdi-Rivlin balance of
energy method to continua with microstructure. The key idea is to replace the
group of Galilean transformations with the group of diffeomorphisms of the
ambient space. A key advantage is that one obtains in a natural way all the
needed balance laws on both the macro and micro levels along with two
Doyle-Erickson formulas
Affine symmetry in mechanics of collective and internal modes. Part I. Classical models
Discussed is a model of collective and internal degrees of freedom with
kinematics based on affine group and its subgroups. The main novelty in
comparison with the previous attempts of this kind is that it is not only
kinematics but also dynamics that is affinely-invariant. The relationship with
the dynamics of integrable one-dimensional lattices is discussed. It is shown
that affinely-invariant geodetic models may encode the dynamics of something
like elastic vibrations
Cancellation of vorticity in steady-state non-isentropic flows of complex fluids
In steady-state non-isentropic flows of perfect fluids there is always
thermodynamic generation of vorticity when the difference between the product
of the temperature with the gradient of the entropy and the gradient of total
enthalpy is different from zero. We note that this property does not hold in
general for complex fluids for which the prominent influence of the material
substructure on the gross motion may cancel the thermodynamic vorticity. We
indicate the explicit condition for this cancellation (topological transition
from vortex sheet to shear flow) for general complex fluids described by
coarse-grained order parameters and extended forms of Ginzburg-Landau energies.
As a prominent sample case we treat first Korteweg's fluid, used commonly as a
model of capillary motion or phase transitions characterized by diffused
interfaces. Then we discuss general complex fluids. We show also that, when the
entropy and the total enthalpy are constant throughout the flow, vorticity may
be generated by the inhomogeneous character of the distribution of material
substructures, and indicate the explicit condition for such a generation. We
discuss also some aspects of unsteady motion and show that in two-dimensional
flows of incompressible perfect complex fluids the vorticity is in general not
conserved, due to a mechanism of transfer of energy between different levels.Comment: 12 page
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