3,240 research outputs found
A geometric characterization of Schauder basis
Concerning basis in a Banach space, a characterization for a weak basis to be a Schauder basis is given in terms of the geometrical behavior of the set of linear, closed hulls wich are generated by subsequences of the expansion sequences of the basis
Thermal properties of an impurity immersed in a granular gas of rough hard spheres
We study in this work the dynamics of a granular impurity immersed in a
low-density granular gas of identical particles. For description of the
kinetics of the granular gas and the impurity particles we use the rough hard
sphere collisional model. We take into account the effects of non-conservation
of energy upon particle collision. We find an (approximate) analytical solution
of the pertinent kinetic equations for the single-particle velocity
distribution functions that reproduces reasonably well the properties of
translational/rotational energy non-equipartition. We assess the accuracy of
the theoretical solution by comparing with computer simulations. For this, we
use two independent computer data sets, from molecular dynamics (MD) and from
Direct Simulation Monte Carlo method (DSMC). Both approach well, with different
degrees, the kinetic theory within a reasonable range of parameter values.Comment: 4 pages, 2 figures. Written for Powders and Grains 2017 conference
proceedin
On the emergence of large and complex memory effects in nonequilibrium fluids
Control of cooling and heating processes is essential in many industrial and
biological processes. In fact, the time evolution of an observable quantity may
differ according to the previous history of the system. For example, a system
that is being subject to cooling and then, at a given time for which
the instantaneous temperature is , is suddenly put in
contact with a temperature source at may continue cooling
down temporarily or, on the contrary, undergo a temperature rebound. According
to current knowledge, there can be only one "spurious" and small peak/low.
However, our results prove that, under certain conditions, more than one
extremum may appear. Specifically, we have observed regions with two extrema
and a critical point with three extrema. We have also detected cases where
extraordinarily large extrema are observed, as large as the order of magnitude
of the stationary value of the variable of interest. We show this by studying
the thermal evolution of a low density set of macroscopic particles that do not
preserve kinetic energy upon collision, i.e., a granular gas. We describe the
mechanism that signals in this system the emergence of these complex and large
memory effects, and explain why similar observations can be expected in a
variety of systems.Comment: 15 pages, 5 figure
Steady base states for non-Newtonian granular hydrodynamics
We study in this work steady laminar flows in a low density granular gas
modelled as a system of identical smooth hard spheres that collide
inelastically. The system is excited by shear and temperature sources at the
boundaries, which consist of two infinite parallel walls. Thus, the geometry of
the system is the same that yields the planar Fourier and Couette flows in
standard gases. We show that it is possible to describe the steady granular
flows in this system, even at large inelasticities, by means of a
(non-Newtonian) hydrodynamic approach. All five types of Couette-Fourier
granular flows are systematically described, identifying the different types of
hydrodynamic profiles. Excellent agreement is found between our classification
of flows and simulation results. Also, we obtain the corresponding non-linear
transport coefficients by following three independent and complementary
methods: (1) an analytical solution obtained from Grad's 13-moment method
applied to the inelastic Boltzmann equation, (2) a numerical solution of the
inelastic Boltzmann equation obtained by means of the direct simulation Monte
Carlo method and (3) event-driven molecular dynamics simulations. We find that,
while Grad's theory does not describe quantitatively well all transport
coefficients, the three procedures yield the same general classification of
planar Couette-Fourier flows for the granular gasComment: 33 pages, 11 figures; v2: improved version accepted for publication
in J. Fluid Mec
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