285 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
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
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.
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
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
The effect of bandwidth in scale-free network traffic
We model information traffic on scale-free networks by introducing the
bandwidth as the delivering ability of links. We focus on the effects of
bandwidth on the packet delivering ability of the traffic system to better
understand traffic dynamic in real network systems. Such ability can be
measured by a phase transition from free flow to congestion. Two cases of node
capacity C are considered, i.e., C=constant and C is proportional to the node's
degree. We figured out the decrease of the handling ability of the system
together with the movement of the optimal local routing coefficient ,
induced by the restriction of bandwidth. Interestingly, for low bandwidth, the
same optimal value of emerges for both cases of node capacity. We
investigate the number of packets of each node in the free flow state and
provide analytical explanations for the optimal value of . Average
packets traveling time is also studied. Our study may be useful for evaluating
the overall efficiency of networked traffic systems, and for allevating traffic
jam in such systems.Comment: 6 pages, 4 figure
Orientation of the fifteenth and sixteenth century mosques in the former Yugoslavia
The paper presents the analysis of the orientation of 60 mosques built in the XV and XVI centuries in the Balkans' region of former Yugoslavia. The mosques have been selected according to their architectural value - mostly the dome mosques that were built by the most renowned builders. Based on the geographic coordinates, the qiblas of all mosques were calculated and the azimuths of their axes measured on orthophotographs. Statistical analysis has shown that the axes of these mosques vary in the horizon sector that is five times wider than the calculated sector of the correct qibla, with a systematic deviation of -10 degrees 15' in relation to the correct qibla. Connections between deviations of the architectural design (dome mosques and other mosques), location and elevation have not been identified. However, a connection between deviations and the time of construction has been identified: deviations from the qibla are smaller in mosques built at a later date. The paper has laid the groundwork for future analysis of the causes of the aforementioned deviations: in the XV and XVI centuries there were no accurate geographic coordinates of locations and the builders were not able to calculate (take over, measure) the exact qibla direction, regardless of the method they applied
Avalanches in complex spin networks
We investigate the magnetization reversal processes on classes of complex
spin networks with antiferromagnetic interaction along the network links. With
slow field ramping the hysteresis loop and avalanches of spin flips occur due
to topological inhomogeneity of the network, even without any disorder of the
magnetic interaction [B. Tadic, et al., Phys. Rev. Lett. 94 (2005) 137204].
Here we study in detail properties of the magnetization avalanches, hysteresis
curves and density of domain walls and show how they can be related to the
structural inhomogeneity of the network. The probability distribution of the
avalanche size, N_s(s), displays the power-law behaviour for small s, i.e.
N_s(s)\propto s^{-\alpha}. For the scale-free networks, grown with preferential
attachment, \alpha increases with the connectivity parameter M from 1.38 for
M=1 (trees) to 1.52 for M=25. For the exponential networks, \alpha is close to
1.0 in the whole range of M.Comment: 16 pages, 10 figures in 29 eps file
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