2,694 research outputs found
How likely is an i.i.d. degree sequence to be graphical?
Given i.i.d. positive integer valued random variables D_1,...,D_n, one can
ask whether there is a simple graph on n vertices so that the degrees of the
vertices are D_1,...,D_n. We give sufficient conditions on the distribution of
D_i for the probability that this be the case to be asymptotically 0, {1/2} or
strictly between 0 and {1/2}. These conditions roughly correspond to whether
the limit of nP(D_i\geq n) is infinite, zero or strictly positive and finite.
This paper is motivated by the problem of modeling large communications
networks by random graphs.Comment: Published at http://dx.doi.org/10.1214/105051604000000693 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Induced representations of quantum kinematical algebras
We construct the induced representations of the null-plane quantum Poincar\'e
and quantum kappa Galilei algebras in (1+1) dimensions. The induction procedure
makes use of the concept of module and is based on the existence of a pair of
Hopf algebras with a nondegenerate pairing and dual bases.Comment: 8 pages,LaTeX2e, to be published in the Proceedings of XXIII
International Colloquium on Group-Theoretical Methods in Physics, Dubna
(Russia), 31.07--05.08, 200
Rheology of human blood plasma: Viscoelastic versus Newtonian behavior
We investigate the rheological characteristics of human blood plasma in shear
and elongational flows. While we can confirm a Newtonian behavior in shear flow
within experimental resolution, we find a viscoelastic behavior of blood plasma
in the pure extensional flow of a capillary break-up rheometer. The influence
of the viscoelasticity of blood plasma on capillary blood flow is tested in a
microfluidic device with a contraction-expansion geometry. Differential
pressure measurements revealed that the plasma has a pronounced flow resistance
compared to that of pure water. Supplementary measurements indicate that the
viscoelasticity of the plasma might even lead to viscoelastic instabilities
under certain conditions. Our findings show that the viscoelastic properties of
plasma should not be ignored in future studies on blood flow.Comment: 4 figures, 1 supplementary material Highlighted in
http://physics.aps.org/articles/v6/1
Induced Representations of Quantum Kinematical Algebras and Quantum Mechanics
Unitary representations of kinematical symmetry groups of quantum systems are
fundamental in quantum theory. We propose in this paper its generalization to
quantum kinematical groups. Using the method, proposed by us in a recent paper
(olmo01), to induce representations of quantum bicrossproduct algebras we
construct the representations of the family of standard quantum inhomogeneous
algebras . This family contains the quantum
Euclidean, Galilei and Poincar\'e algebras, all of them in (1+1) dimensions. As
byproducts we obtain the actions of these quantum algebras on regular co-spaces
that are an algebraic generalization of the homogeneous spaces and --Casimir
equations which play the role of --Schr\"odinger equations.Comment: LaTeX 2e, 20 page
Motility of small nematodes in disordered wet granular media
The motility of the worm nematode \textit{Caenorhabditis elegans} is
investigated in shallow, wet granular media as a function of particle size
dispersity and area density (). Surprisingly, we find that the nematode's
propulsion speed is enhanced by the presence of particles in a fluid and is
nearly independent of area density. The undulation speed, often used to
differentiate locomotion gaits, is significantly affected by the bulk material
properties of wet mono- and polydisperse granular media for .
This difference is characterized by a change in the nematode's waveform from
swimming to crawling in dense polydisperse media \textit{only}. This change
highlights the organism's adaptability to subtle differences in local structure
and response between monodisperse and polydisperse media
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