318 research outputs found
Traffic on complex networks: Towards understanding global statistical properties from microscopic density fluctuations
We study the microscopic time fluctuations of traffic load and the global statistical properties of a dense traffic of particles on scale-free cyclic graphs. For a wide range of driving rates R the traffic is stationary and the load time series exhibits antipersistence due to the regulatory role of the superstructure associated with two hub nodes in the network. We discuss how the superstructure affects the functioning of the network at high traffic density and at the jamming threshold. The degree of correlations systematically decreases with increasing traffic density and eventually disappears when approaching a jamming density Rc. Already before jamming we observe qualitative changes in the global network-load distributions and the particle queuing times. These changes are related to the occurrence of temporary crises in which the network-load increases dramatically, and then slowly falls back to a value characterizing free flow
Disorder-induced critical behavior in driven diffusive systems
Using dynamic renormalization group we study the transport in driven
diffusive systems in the presence of quenched random drift velocity with
long-range correlations along the transport direction. In dimensions
we find fixed points representing novel universality classes of
disorder-dominated self-organized criticality, and a continuous phase
transition at a critical variance of disorder. Numerical values of the scaling
exponents characterizing the distributions of relaxation clusters are in good
agreement with the exponents measured in natural river networks
On unitarizability in the case of classical p-adic groups
In the introduction of this paper we discuss a possible approach to the
unitarizability problem for classical p-adic groups. In this paper we give some
very limited support that such approach is not without chance. In a forthcoming
paper we shall give additional evidence in generalized cuspidal rank (up to)
three.Comment: This paper is a merged and revised version of ealier preprints
arXiv:1701.07658 and arXiv:1701.07662. The paper is going to appear in the
Proceedings of the Simons Symposium on Geometric Aspects of the Trace Formul
Collective Charge Fluctuations in Single-Electron Processes on Nano-Networks
Using numerical modeling we study emergence of structure and
structure-related nonlinear conduction properties in the self-assembled
nanoparticle films. Particularly, we show how different nanoparticle networks
emerge within assembly processes with molecular bio-recognition binding. We
then simulate the charge transport under voltage bias via single-electron
tunnelings through the junctions between nanoparticles on such type of
networks. We show how the regular nanoparticle array and topologically
inhomogeneous nanonetworks affect the charge transport. We find long-range
correlations in the time series of charge fluctuation at individual
nanoparticles and of flow along the junctions within the network. These
correlations explain the occurrence of a large nonlinearity in the simulated
and experimentally measured current-voltage characteristics and non-Gaussian
fluctuations of the current at the electrode.Comment: 10 pages, 7 figure
Spectral and Dynamical Properties in Classes of Sparse Networks with Mesoscopic Inhomogeneities
We study structure, eigenvalue spectra and diffusion dynamics in a wide class
of networks with subgraphs (modules) at mesoscopic scale. The networks are
grown within the model with three parameters controlling the number of modules,
their internal structure as scale-free and correlated subgraphs, and the
topology of connecting network. Within the exhaustive spectral analysis for
both the adjacency matrix and the normalized Laplacian matrix we identify the
spectral properties which characterize the mesoscopic structure of sparse
cyclic graphs and trees. The minimally connected nodes, clustering, and the
average connectivity affect the central part of the spectrum. The number of
distinct modules leads to an extra peak at the lower part of the Laplacian
spectrum in cyclic graphs. Such a peak does not occur in the case of
topologically distinct tree-subgraphs connected on a tree. Whereas the
associated eigenvectors remain localized on the subgraphs both in trees and
cyclic graphs. We also find a characteristic pattern of periodic localization
along the chains on the tree for the eigenvector components associated with the
largest eigenvalue equal 2 of the Laplacian. We corroborate the results with
simulations of the random walk on several types of networks. Our results for
the distribution of return-time of the walk to the origin (autocorrelator)
agree well with recent analytical solution for trees, and it appear to be
independent on their mesoscopic and global structure. For the cyclic graphs we
find new results with twice larger stretching exponent of the tail of the
distribution, which is virtually independent on the size of cycles. The
modularity and clustering contribute to a power-law decay at short return
times
Scaling of avalanche queues in directed dissipative sandpiles
We simulate queues of activity in a directed sandpile automaton in 1+1
dimensions by adding grains at the top row with driving rate .
The duration of elementary avalanches is exactly described by the distribution
, limited either by the system size or by
dissipation at defects . Recognizing the probability
as a distribution of service time of jobs arriving at a server with frequency
, the model represents a new example of the server
queue in the queue theory. We study numerically and analytically the tail
behavior of the distributions of busy periods and energy dissipated in the
queue and the probability of an infinite queue as a function of driving rate.Comment: 11 pages, 9 figures; To appear in Phys. Rev.
Elliptic curves with torsion group
We exhibit several families of elliptic curves with torsion group isomorphic
to and generic rank at least . Families of this kind have been
constructed previously by several authors: Lecacheux, Kihara, Eroshkin and Woo.
We mention the details of some of them and we add other examples developed more
recently by Dujella and Peral, and MacLeod.
Then we apply an algorithm of Gusi\'c and Tadi\'c and we find the exact rank
over \Q(t) to be 3 and we also determine free generators of the Mordell-Weil
group for each family. By suitable specializations, we obtain the known and new
examples of curves over \Q with torsion and rank , which is the
current record
Unitary Dual of GL_n at archimedean places and global Jacquet-Langlands correspondence
In [7], results about the global Jacquet-Langlands correspondence, (weak and
strong) multiplicity-one theorems and the classification of automorphic
representations for inner forms of the general linear group over a number field
are established, under the condition that the local inner forms are split at
archimedean places. In this paper, we extend the main local results of [7] to
archimedean places so that this assumption can be removed. Along the way, we
collect several results about the unitary dual of general linear groups over
\bbR, \bbC or \bbH of independent interest
Global Jacquet-Langlands correspondence, multiplicity one and classification of automorphic representations
In this paper we show a local Jacquet-Langlands correspondence for all
unitary irreducible representations. We prove the global Jacquet-Langlands
correspondence in characteristic zero. As consequences we obtain the
multiplicity one and strong multiplicity one theorems for inner forms of GL(n)
as well as a classification of the residual spectrum and automorphic
representations in analogy with results proved by Moeglin-Waldspurger and
Jacquet-Shalika for GL(n).Comment: 49 pages; Appendix by N. Grba
Finite driving rates in interface models of Barkhausen noise
We consider a single-interface model for the description of Barkhausen noise
in soft ferromagnetic materials. Previously, the model had been used only in
the adiabatic regime of infinitely slow field ramping. We introduce finite
driving rates and analyze the scaling of event sizes and durations for
different regimes of the driving rate. Coexistence of intermittency, with
non-trivial scaling laws, and finite-velocity interface motion is observed for
high enough driving rates. Power spectra show a decay , with
for finite driving rates, revealing the influence of the internal
structure of avalanches.Comment: 7 pages, 6 figures, RevTeX, final version to be published in Phys.
Rev.
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