7,120 research outputs found
Use of LARS system for the quantitative determination of smoke plume lateral diffusion coefficients from ERTS images of Virginia
A technique for measuring smoke plume of large industrial sources observed by satellite using LARSYS is proposed. A Gaussian plume model is described, integrated in the vertical, and inverted to yield a form for the lateral diffusion coefficient, Ky. Given u, wind speed; y sub l, the horizontal distance of a line of constant brightness from the plume symmetry axis a distance x sub l, downstream from reference point at x=x sub 2, y=0, then K sub y = u ((y sub 1) to the 2nd power)/2 x sub 1 1n (x sub 2/x sub 1). The technique is applied to a plume from a power plant at Chester, Virginia, imaged August 31, 1973 by LANDSAT I. The plume bends slightly to the left 4.3 km from the source and estimates yield Ky of 28 sq m/sec near the source, and 19 sq m/sec beyond the bend. Maximum ground concentrations are estimated between 32 and 64 ug/cu m. Existing meteorological data would not explain such concentrations
Do Athermal Amorphous Solids Exist?
We study the elastic theory of amorphous solids made of particles with finite
range interactions in the thermodynamic limit. For the elastic theory to exist
one requires all the elastic coefficients, linear and nonlinear, to attain a
finite thermodynamic limit. We show that for such systems the existence of
non-affine mechanical responses results in anomalous fluctuations of all the
nonlinear coefficients of the elastic theory. While the shear modulus exists,
the first nonlinear coefficient B_2 has anomalous fluctuations and the second
nonlinear coefficient B_3 and all the higher order coefficients (which are
non-zero by symmetry) diverge in the thermodynamic limit. These results put a
question mark on the existence of elasticity (or solidity) of amorphous solids
at finite strains, even at zero temperature. We discuss the physical meaning of
these results and propose that in these systems elasticity can never be
decoupled from plasticity: the nonlinear response must be very substantially
plastic.Comment: 11 pages, 11 figure
Cosine and Sine Operators Related with Orthogonal Polynomial Sets on the Intervall [-1,1]
The quantization of phase is still an open problem. In the approach of
Susskind and Glogower so called cosine and sine operators play a fundamental
role. Their eigenstates in the Fock representation are related with the
Chebyshev polynomials of the second kind. Here we introduce more general cosine
and sine operators whose eigenfunctions in the Fock basis are related in a
similar way with arbitrary orthogonal polynomial sets on the intervall [-1,1].
To each polynomial set defined in terms of a weight function there corresponds
a pair of cosine and sine operators. Depending on the symmetry of the weight
function we distinguish generalized or extended operators. Their eigenstates
are used to define cosine and sine representations and probability
distributions. We consider also the inverse arccosine and arcsine operators and
use their eigenstates to define cosine-phase and sine-phase distributions,
respectively. Specific, numerical and graphical results are given for the
classical orthogonal polynomials and for particular Fock and coherent states.Comment: 1 tex-file (24 pages), 11 figure
Boundedness of Pseudodifferential Operators on Banach Function Spaces
We show that if the Hardy-Littlewood maximal operator is bounded on a
separable Banach function space and on its associate space
, then a pseudodifferential operator
is bounded on whenever the symbol belongs to the
H\"ormander class with ,
or to the the Miyachi class
with ,
. This result is applied to the case of
variable Lebesgue spaces .Comment: To appear in a special volume of Operator Theory: Advances and
Applications dedicated to Ant\'onio Ferreira dos Santo
Robustness of Density of Low Frequency States in Amorphous Solids
Low frequency quasi-localized modes of amorphous glasses appear to exhibit
universal density of states, depending on the frequencies as . To date various models of glass formers with short range binary
interaction, and network glasses with both binary and ternary interactions,
were shown to conform with this law. In this paper we examine granular
amorphous solids with long-range electrostatic interactions, and find that they
exhibit the same law. To rationalize this wide universality class we return to
a model proposed by Gurevich, Parshin and Schober (GPS) and analyze its
predictions for interaction laws with varying spatial decay, exploring this
wider than expected universality class. Numerical and analytic results are
provided for both the actual system with long range interaction and for the GPS
model.Comment: 10 Pages, 7 Figures, Physical Review
Asymptotically exact probability distribution for the Sinai model with finite drift
We obtain the exact asymptotic result for the disorder-averaged probability
distribution function for a random walk in a biased Sinai model and show that
it is characterized by a creeping behavior of the displacement moments with
time, ~ t^{\mu n} where \mu is dimensionless mean drift. We employ a
method originated in quantum diffusion which is based on the exact mapping of
the problem to an imaginary-time Schr\"{odinger} equation. For nonzero drift
such an equation has an isolated lowest eigenvalue separated by a gap from
quasi-continuous excited states, and the eigenstate corresponding to the former
governs the long-time asymptotic behavior.Comment: 4 pages, 2 figure
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