2,172 research outputs found
Optical design of two-reflector systems, the Monge-Kantorovich mass transfer problem and Fermat's principle
It is shown that the problem of designing a two-reflector system transforming
a plane wave front with given intensity into an output plane front with
prescribed output intensity can be formulated and solved as the
Monge-Kantorovich mass transfer problem.Comment: 25 pages, 2 figure
Modification of quantum measure in area tensor Regge calculus and positivity
A comparative analysis of the versions of quantum measure in the area tensor
Regge calculus is performed on the simplest configurations of the system. The
quantum measure is constructed in such the way that it reduces to the Feynman
path integral describing canonical quantisation if the continuous limit along
any of the coordinates is taken. As we have found earlier, it is possible to
implement also the correspondence principle (proportionality of the Lorentzian
(Euclidean) measure to (), being the action). For that a
certain kind of the connection representation of the Regge action should be
used, namely, as a sum of independent contributions of selfdual and
antiselfdual sectors (that is, effectively 3-dimensional ones). There are two
such representations, the (anti)selfdual connections being SU(2) or SO(3)
rotation matrices according to the two ways of decomposing full SO(4) group, as
SU(2) SU(2) or SO(3) SO(3). The measure from SU(2) rotations
although positive on physical surface violates positivity outside this surface
in the general configuration space of arbitrary independent area tensors. The
measure based on SO(3) rotations is expected to be positive in this general
configuration space on condition that the scale of area tensors considered as
parameters is bounded from above by the value of the order of Plank unit.Comment: 10 pages, plain LaTe
Kolmogorov-Type Theory of Compressible Turbulence and Inviscid Limit of the Navier-Stokes Equations in
We are concerned with the inviscid limit of the Navier-Stokes equations to
the Euler equations for compressible fluids in . Motivated by the
Kolmogorov hypothesis (1941) for incompressible flow, we introduce a
Kolmogorov-type hypothesis for barotropic flows, in which the density and the
sonic speed normally vary significantly. We then observe that the compressible
Kolmogorov-type hypothesis implies the uniform boundedness of some fractional
derivatives of the weighted velocity and sonic speed in the space variables in
, which is independent of the viscosity coefficient . It is shown
that this key observation yields the equicontinuity in both space and time of
the density in and the momentum in , as well as the uniform
bound of the density in and the velocity in independent of
, for some fixed and , where is the
adiabatic exponent. These results lead to the strong convergence of solutions
of the Navier-Stokes equations to a solution of the Euler equations for
barotropic fluids in . Not only do we offer a framework for
mathematical existence theories, but also we offer a framework for the
interpretation of numerical solutions through the identification of a function
space in which convergence should take place, with the bounds that are
independent of , that is in the high Reynolds number limit.Comment: 20 pages. arXiv admin note: text overlap with arXiv:1008.154
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