697 research outputs found
Geothermal studies - Yellowstone National Park /test site 11/, Wyoming
Summary report of diamond drilling in thermal areas of Yellowstone National Park, and method for determining heat flow in thermal area
Prediction of strong shock structure using the bimodal distribution function
A modified Mott-Smith method for predicting the one-dimensional shock wave
solution at very high Mach numbers is constructed by developing a system of
fluid dynamic equations. The predicted shock solutions in a gas of Maxwell
molecules, a hard sphere gas and in argon using the newly proposed formalism
are compared with the experimental data, direct-simulation Monte Carlo (DSMC)
solution and other solutions computed from some existing theories for Mach
numbers M<50. In the limit of an infinitely large Mach number, the predicted
shock profiles are also compared with the DSMC solution. The density,
temperature and heat flux profiles calculated at different Mach numbers have
been shown to have good agreement with the experimental and DSMC solutionsComment: 22 pages, 9 figures, Accepted for publication in Physical Review
On the 3D steady flow of a second grade fluid past an obstacle
We study steady flow of a second grade fluid past an obstacle in three space
dimensions. We prove existence of solution in weighted Lebesgue spaces with
anisotropic weights and thus existence of the wake region behind the obstacle.
We use properties of the fundamental Oseen tensor together with results
achieved in \cite{Koch} and properties of solutions to steady transport
equation to get up to arbitrarily small \ep the same decay as the Oseen
fundamental solution
Stretching and folding versus cutting and shuffling: An illustrated perspective on mixing and deformations of continua
We compare and contrast two types of deformations inspired by mixing
applications -- one from the mixing of fluids (stretching and folding), the
other from the mixing of granular matter (cutting and shuffling). The
connection between mechanics and dynamical systems is discussed in the context
of the kinematics of deformation, emphasizing the equivalence between stretches
and Lyapunov exponents. The stretching and folding motion exemplified by the
baker's map is shown to give rise to a dynamical system with a positive
Lyapunov exponent, the hallmark of chaotic mixing. On the other hand, cutting
and shuffling does not stretch. When an interval exchange transformation is
used as the basis for cutting and shuffling, we establish that all of the map's
Lyapunov exponents are zero. Mixing, as quantified by the interfacial area per
unit volume, is shown to be exponentially fast when there is stretching and
folding, but linear when there is only cutting and shuffling. We also discuss
how a simple computational approach can discern stretching in discrete data.Comment: REVTeX 4.1, 9 pages, 3 figures; v2 corrects some misprints. The
following article appeared in the American Journal of Physics and may be
found at http://ajp.aapt.org/resource/1/ajpias/v79/i4/p359_s1 . Copyright
2011 American Association of Physics Teachers. This article may be downloaded
for personal use only. Any other use requires prior permission of the author
and the AAP
Third and fourth degree collisional moments for inelastic Maxwell models
The third and fourth degree collisional moments for -dimensional inelastic
Maxwell models are exactly evaluated in terms of the velocity moments, with
explicit expressions for the associated eigenvalues and cross coefficients as
functions of the coefficient of normal restitution. The results are applied to
the analysis of the time evolution of the moments (scaled with the thermal
speed) in the free cooling problem. It is observed that the characteristic
relaxation time toward the homogeneous cooling state decreases as the
anisotropy of the corresponding moment increases. In particular, in contrast to
what happens in the one-dimensional case, all the anisotropic moments of degree
equal to or less than four vanish in the homogeneous cooling state for .Comment: 15 pages, 3 figures; v2: addition of two new reference
Steady shear flow thermodynamics based on a canonical distribution approach
A non-equilibrium steady state thermodynamics to describe shear flows is
developed using a canonical distribution approach. We construct a canonical
distribution for shear flow based on the energy in the moving frame using the
Lagrangian formalism of the classical mechanics. From this distribution we
derive the Evans-Hanley shear flow thermodynamics, which is characterized by
the first law of thermodynamics relating infinitesimal
changes in energy , entropy and shear rate with kinetic
temperature . Our central result is that the coefficient is given by
Helfand's moment for viscosity. This approach leads to thermodynamic stability
conditions for shear flow, one of which is equivalent to the positivity of the
correlation function of . We emphasize the role of the external work
required to sustain the steady shear flow in this approach, and show
theoretically that the ensemble average of its power must be
non-negative. A non-equilibrium entropy, increasing in time, is introduced, so
that the amount of heat based on this entropy is equal to the average of
. Numerical results from non-equilibrium molecular dynamics simulation
of two-dimensional many-particle systems with soft-core interactions are
presented which support our interpretation.Comment: 23 pages, 7 figure
Convective Nonlinearity in Non-Newtonian Fluids
In the limit of infinite yield time for stresses, the hydrodynamic equations
for viscoelastic, Non-Newtonian liquids such as polymer melts must reduce to
that for solids. This piece of information suffices to uniquely determine the
nonlinear convective derivative, an ongoing point of contention in the rheology
literature.Comment: 4 page
Nonlinear viscosity and velocity distribution function in a simple longitudinal flow
A compressible flow characterized by a velocity field is
analyzed by means of the Boltzmann equation and the Bhatnagar-Gross-Krook
kinetic model. The sign of the control parameter (the longitudinal deformation
rate ) distinguishes between an expansion () and a condensation ()
phenomenon. The temperature is a decreasing function of time in the former
case, while it is an increasing function in the latter. The non-Newtonian
behavior of the gas is described by a dimensionless nonlinear viscosity
, that depends on the dimensionless longitudinal rate . The
Chapman-Enskog expansion of in powers of is seen to be only
asymptotic (except in the case of Maxwell molecules). The velocity distribution
function is also studied. At any value of , it exhibits an algebraic
high-velocity tail that is responsible for the divergence of velocity moments.
For sufficiently negative , moments of degree four and higher may diverge,
while for positive the divergence occurs in moments of degree equal to or
larger than eight.Comment: 18 pages (Revtex), including 5 figures (eps). Analysis of the heat
flux plus other minor changes added. Revised version accepted for publication
in PR
Unconstrained Hamiltonian formulation of General Relativity with thermo-elastic sources
A new formulation of the Hamiltonian dynamics of the gravitational field
interacting with(non-dissipative) thermo-elastic matter is discussed. It is
based on a gauge condition which allows us to encode the six degrees of freedom
of the ``gravity + matter''-system (two gravitational and four
thermo-mechanical ones), together with their conjugate momenta, in the
Riemannian metric q_{ij} and its conjugate ADM momentum P^{ij}. These variables
are not subject to constraints. We prove that the Hamiltonian of this system is
equal to the total matter entropy. It generates uniquely the dynamics once
expressed as a function of the canonical variables. Any function U obtained in
this way must fulfil a system of three, first order, partial differential
equations of the Hamilton-Jacobi type in the variables (q_{ij},P^{ij}). These
equations are universal and do not depend upon the properties of the material:
its equation of state enters only as a boundary condition. The well posedness
of this problem is proved. Finally, we prove that for vanishing matter density,
the value of U goes to infinity almost everywhere and remains bounded only on
the vacuum constraints. Therefore the constrained, vacuum Hamiltonian (zero on
constraints and infinity elsewhere) can be obtained as the limit of a ``deep
potential well'' corresponding to non-vanishing matter. This unconstrained
description of Hamiltonian General Relativity can be useful in numerical
calculations as well as in the canonical approach to Quantum Gravity.Comment: 29 pages, TeX forma
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