13,023 research outputs found
Verification of a localization criterion for several disordered media
We analytically compute a localization criterion in double scattering
approximation for a set of dielectric spheres or perfectly conducting disks
uniformly distributed in a spatial volume which can be either spherical or
layered. For every disordered medium, we numerically investigate a localization
criterion, and examine the influence of the system parameters on the wavelength
localization domains.Comment: 30 pages, LateX, amstex, revtex styles, 20 figure
Stiff polymer in monomer ensemble
We make use of the previously developed formalism for a monomer ensemble and
include angular dependence of the segments of the polymer chains thus
described. In particular we show how to deal with stiffness when the polymer
chain is confined to certain regions. We investigate the stiffness from the
perspectives of a differential equation, integral equations, or recursive
relations for both continuum and lattice models. Exact analytical solutions are
presented for two cases, whereas numerical results are shown for a third case.Comment: 10 pages, including 6 figure
Enstrophy dissipation in two-dimensional turbulence
Insight into the problem of two-dimensional turbulence can be obtained by an
analogy with a heat conduction network. It allows the identification of an
entropy function associated to the enstrophy dissipation and that fluctuates
around a positive (mean) value. While the corresponding enstrophy network is
highly nonlocal, the direction of the enstrophy current follows from the Second
Law of Thermodynamics. An essential parameter is the ratio of the intensity of driving as a function of
wavenumber , to the dissipation strength , where is the
viscosity. The enstrophy current flows from higher to lower values of ,
similar to a heat current from higher to lower temperature. Our probabilistic
analysis of the enstrophy dissipation and the analogy with heat conduction thus
complements and visualizes the more traditional spectral arguments for the
direct enstrophy cascade. We also show a fluctuation symmetry in the
distribution of the total entropy production which relates the probabilities of
direct and inverse enstrophy cascades.Comment: 8 pages, revtex
A Computational Interpretation of Context-Free Expressions
We phrase parsing with context-free expressions as a type inhabitation
problem where values are parse trees and types are context-free expressions. We
first show how containment among context-free and regular expressions can be
reduced to a reachability problem by using a canonical representation of
states. The proofs-as-programs principle yields a computational interpretation
of the reachability problem in terms of a coercion that transforms the parse
tree for a context-free expression into a parse tree for a regular expression.
It also yields a partial coercion from regular parse trees to context-free
ones. The partial coercion from the trivial language of all words to a
context-free expression corresponds to a predictive parser for the expression
Entire solutions of hydrodynamical equations with exponential dissipation
We consider a modification of the three-dimensional Navier--Stokes equations
and other hydrodynamical evolution equations with space-periodic initial
conditions in which the usual Laplacian of the dissipation operator is replaced
by an operator whose Fourier symbol grows exponentially as \ue ^{|k|/\kd} at
high wavenumbers . Using estimates in suitable classes of analytic
functions, we show that the solutions with initially finite energy become
immediately entire in the space variables and that the Fourier coefficients
decay faster than \ue ^{-C(k/\kd) \ln (|k|/\kd)} for any . The
same result holds for the one-dimensional Burgers equation with exponential
dissipation but can be improved: heuristic arguments and very precise
simulations, analyzed by the method of asymptotic extrapolation of van der
Hoeven, indicate that the leading-order asymptotics is precisely of the above
form with . The same behavior with a universal constant
is conjectured for the Navier--Stokes equations with exponential
dissipation in any space dimension. This universality prevents the strong
growth of intermittency in the far dissipation range which is obtained for
ordinary Navier--Stokes turbulence. Possible applications to improved spectral
simulations are briefly discussed.Comment: 29 pages, 3 figures, Comm. Math. Phys., in pres
Testing for Markovian Character and Modeling of Intermittency in Solar Wind Turbulence
We present results of statistical analysis of solar wind turbulence using an
approach based on the theory of Markov processes. It is shown that the
Chapman-Kolmogorov equation is approximately satisfied for the turbulent
cascade. We evaluate the first two Kramers-Moyal coefficients from experimental
data and show that the solution of the resulting Fokker-Planck equation agrees
well with experimental probability distributions. Our results suggest the
presence of a local transfer mechanism for magnetic field fluctuations in solar
wind turbulence
Signatures of two-dimensionalisation of 3D turbulence in presence of rotation
A reason has been given for the inverse energy cascade in the
two-dimensionalised rapidly rotating 3D incompressible turbulence. For such
system, literature shows a possibility of the exponent of wavenumber in the
energy spectrum's relation to lie between -2 and -3. We argue the existence of
a more strict range of -2 to -7/3 for the exponent in the case of rapidly
rotating turbulence which is in accordance with the recent experiments. Also, a
rigorous derivation for the two point third order structure function has been
provided helping one to argue that even with slow rotation one gets, though
dominated, a spectrum with the exponent -2.87, thereby hinting at the
initiation of the two-dimensionalisation effect with rotation.Comment: An extended and typos-corrected version of the earlier submissio
Material studies related to lunar surface exploration, volume 3 Final report, 6 Mar. 1967 - 30 Jun. 1968
Mechanical properties of lunar soils related to lunar exploratio
Coherent laminar and turbulent motion of toroidal vortex bundles
Motivated by experiments performed in superfluid helium, we study numerically
the motion of toroidal bundles of vortex filaments in an inviscid fluid. We
find that the evolution of these large-scale vortex structures involves the
generalised leapfrogging of the constituent vortex rings. Despite three
dimensional perturbations in the form of Kelvin waves and vortex reconnections,
toroidal vortex bundles retain their coherence over a relatively large distance
(compared to their size), in agreement with experimental observations.Comment: 22 pages, 12 figure
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