225 research outputs found
Nonextensive statistics in viscous fingering
Measurements in turbulent flows have revealed that the velocity field in
nonequilibrium systems exhibits -exponential or power law distributions in
agreement with theoretical arguments based on nonextensive statistical
mechanics. Here we consider Hele-Shaw flow as simulated by the Lattice
Boltzmann method and find similar behavior from the analysis of velocity field
measurements. For the transverse velocity, we obtain a spatial -Gaussian
profile and a power law velocity distribution over all measured decades. To
explain these results, we suggest theoretical arguments based on Darcy's law
combined with the non-linear advection-diffusion equation for the concentration
field. Power law and -exponential distributions are the signature of
nonequilibrium systems with long-range interactions and/or long-time
correlations, and therefore provide insight to the mechanism of the onset of
fingering processes.Comment: 8 pages including 3 figures; to appear in PHYSICA
Propagation-Dispersion Equation
A {\em propagation-dispersion equation} is derived for the first passage
distribution function of a particle moving on a substrate with time delays. The
equation is obtained as the continuous limit of the {\em first visit equation},
an exact microscopic finite difference equation describing the motion of a
particle on a lattice whose sites operate as {\em time-delayers}. The
propagation-dispersion equation should be contrasted with the
advection-diffusion equation (or the classical Fokker-Planck equation) as it
describes a dispersion process in {\em time} (instead of diffusion in space)
with a drift expressed by a propagation speed with non-zero bounded values. The
{\em temporal dispersion} coefficient is shown to exhibit a form analogous to
Taylor's dispersivity. Physical systems where the propagation-dispersion
equation applies are discussed.Comment: 12 pages+ 5 figures, revised and extended versio
Determining stress states using dike swarms: The Lauma Dorsa example
Initial examination of the Magellan coverage of Venus has revealed between 150 and 300 large, radially lineated landforms distributed across the planet's surface. Where the lineaments have been examined in detail, the majority fail to exhibit signatures indicative of relief at or above the resolution of the radar; however, when the sense of topographic relief may be ascertained, the lineaments commonly appear as fissures or flat-floored trenches interpreted as graben. Individual lineaments can display graben, fissure, and zero relief behavior along their length, suggesting either that these differences are a function of the resolution of the radar, or that the morphological distinctions are real but somehow genetically linked. In many instances, radial lineaments exhibiting these characteristics are directly associated with surface volcanism, including flanking and terminal flows, superimposed shield domes and pit chains, and central, calderalike topographic lows. These observable characteristics, as well as theoretical studies and comparison with similar terrestrial features, have led to the working hypothesis that many of the radial fracture systems on Venus are the surface manifestation of subsurface dikes propagating laterally from a central magma source. If this interpretation is correct, studies of terrestrial dikes suggest that the lineament directions, with localized exceptions and barring subsequent deformation, should be perpendicular to the orientation of the least compressive stress at the time of their formation. To test this hypothesis, we briefly examine a radial fracture system (63.7 degrees N, 195 degrees E) located between two deformation belts in Vinmara Planitia, and verify that the lineaments to the east behave in the expected manner. We have also chosen this feature, however, because of its proximity to Lauma Dorsa to the west. On the basis of Venera 15/16 data, both compressional and extensional origins for this deformation belt have been proposed. By examining the stratigraphy and applying our interpretation that the fracture system is linked to the presence of subsurface dikes, we present an independent evaluation of the stress state associated with Lauma Dorsa, and thus contribute to the assessment of its origin
Viscous fingering in miscible, immiscible and reactive fluids
With the Lattice Boltzmann method (using the BGK approximation) we
investigate the dynamics of Hele-Shaw flow under conditions corresponding to
various experimental systems. We discuss the onset of the instability
(dispersion relation), the static properties (characterization of the
interface) and the dynamic properties (growth of the mixing zone) of simulated
Hele-Shaw systems. We examine the role of reactive processes (between the two
fluids) and we show that they have a sharpening effect on the interface similar
to the effect of surface tension.Comment: 6 pages with 2 figure, to be published in J.Mod.Phys
Spin scattering of a particle for periodic boundary conditions
We have studied anomalous diffusion of a particle in a random medium in which
the passage of the particle may modify the state of the visited sites. The
simplicity of the dynamics allows analytic solution. Interesting propagation
and organization behaviors will be reported.Comment: pdf fil
Propagation and organization in lattice random media
We show that a signal can propagate in a particular direction through a model
random medium regardless of the precise state of the medium. As a prototype, we
consider a point particle moving on a one-dimensional lattice whose sites are
occupied by scatterers with the following properties: (i) the state of each
site is defined by its spin (up or down); (ii) the particle arriving at a site
is scattered forward (backward) if the spin is up (down); (iii) the state of
the site is modified by the passage of the particle, i.e. the spin of the site
where a scattering has taken place, flips (). We consider one dimensional and triangular lattices, for which we give a
microscopic description of the dynamics, prove the propagation of a particle
through the scatterers, and compute analytically its statistical properties. In
particular we prove that, in one dimension, the average propagation velocity is
, with the probability that a site has a spin
, and, in the triangular lattice, the average propagation velocity is
independent of the scatterers distribution: . In both cases, the
origin of the propagation is a blocking mechanism, restricting the motion of
the particle in the direction opposite to the ultimate propagation direction,
and there is a specific re-organization of the spins after the passage of the
particle. A detailed mathematical analysis of this phenomenon is, to the best
of our knowledge, presented here for the first time.Comment: 30 pages, 15 separate figures (in PostScript); submitted to J. Stat.
Phy
Statistics of precursors to fingering processes
We present an analysis of the statistical properties of hydrodynamic field
fluctuations which reveal the existence of precursors to fingering processes.
These precursors are found to exhibit power law distributions, and these power
laws are shown to follow from spatial -Gaussian structures which are
solutions to the generalized non-linear diffusion equation.Comment: 7 pages incl. 5 figs; tp appear in Europhysics Letter
Coupling of thermal and mass diffusion in regular binary thermal lattice-gases
We have constructed a regular binary thermal lattice-gas in which the thermal
diffusion and mass diffusion are coupled and form two nonpropagating diffusive
modes. The power spectrum is shown to be similar in structure as for the one in
real fluids, in which the central peak becomes a combination of coupled entropy
and concentration contributions. Our theoretical findings for the power spectra
are confirmed by computer simulations performed on this model.Comment: 5 pages including 3 figures in RevTex
Is the Tsallis entropy stable?
The question of whether the Tsallis entropy is Lesche-stable is revisited. It
is argued that when physical averages are computed with the escort
probabilities, the correct application of the concept of Lesche-stability
requires use of the escort probabilities. As a consequence, as shown here, the
Tsallis entropy is unstable but the thermodynamic averages are stable. We
further show that Lesche stability as well as thermodynamic stability can be
obtained if the homogeneous entropy is used as the basis of the formulation of
non-extensive thermodynamics. In this approach, the escort distribution arises
naturally as a secondary structure.Comment: 6 page
Spatially extensive uniform stress fields on Venus inferred from radial dike swarm geometries: The Aphrodite Terra example
The high resolution and near global coverage of Magellan radar images is facilitating attempts to systematically investigate the stresses that have deformed the venusian crust. Here we continue earlier efforts to utilize approximately 170 large, radially lineated structures interpreted as dike swarms to assess the orientation of the regional maximum horizontal compressive stress (MHCS) which existed in their vicinities during emplacement. Examination of swarms near the equator reveals a link to broad scale regional structures, such as Aphrodite Terra, across distances in excess of 1000 km, suggesting the existence of first order stress fields which affect areas of more than 10(exp 6) sq km in a uniform fashion. Focusing further upon the Aphrodite Terra region, the MHCS field in the surrounding lowlands inferred from radial swarms is oriented approximately normal to the slope of the highland topography. This stress configuration appears, at a simple level, to be incompatible with that expected during either upwelling or downwelling construction of the highlands. In addition, the relatively undeformed geometry of the radial structures within the highlands implies that these dike swarm features formed more recently than their highly deformed surroundings. We conclude that the differential stresses which existed during emplacement of the dike swarms within and adjacent to the Aphrodite Terra highlands are related to the gravitational relaxation of pre-existing topography
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