907 research outputs found
Existence of the D0-D4 Bound State: a detailed Proof
We consider the supersymmetric quantum mechanical system which is obtained by
dimensionally reducing d=6, N=1 supersymmetric gauge theory with gauge group
U(1) and a single charged hypermultiplet. Using the deformation method and
ideas introduced by Porrati and Rozenberg, we present a detailed proof of the
existence of a normalizable ground state for this system
Computation of unsteady transonic flows through rotating and stationary cascades. 3: Acoustic far-field analysis
A small perturbation type analysis has been developed for the acoustic far field in an infinite duct extending upstream and downstream of an axial turbomachinery stage. The analysis is designed to interface with a numerical solution of the near field of the blade rows and, thereby, to provide the necessary closure condition to complete the statement of infinite duct boundary conditions for the subject problem. The present analysis differs from conventional inlet duct analyses in that a simple harmonic time dependence was not assumed, since a transient signal is generated by the numerical near-field solution and periodicity is attained only asymptotically. A description of the computer code developed to carry out the necessary convolutions numerically is included, as well as the results of a sample application using an impulsively initiated harmonic signal
Evolving Network With Different Edges
We proposed an evolving network model constituted by the same nodes but
different edges. The competition between nodes and different links were
introduced. Scale free properties have been found in this model by continuum
theory. Different network topologies can be generated by some tunable
parameters. Simulation results consolidate the prediction.Comment: 14 pages, 9 figures, some contents revised, fluctuation of x degree
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Zooming in on local level statistics by supersymmetric extension of free probability
We consider unitary ensembles of Hermitian NxN matrices H with a confining
potential NV where V is analytic and uniformly convex. From work by
Zinn-Justin, Collins, and Guionnet and Maida it is known that the large-N limit
of the characteristic function for a finite-rank Fourier variable K is
determined by the Voiculescu R-transform, a key object in free probability
theory. Going beyond these results, we argue that the same holds true when the
finite-rank operator K has the form that is required by the Wegner-Efetov
supersymmetry method of integration over commuting and anti-commuting
variables. This insight leads to a potent new technique for the study of local
statistics, e.g., level correlations. We illustrate the new technique by
demonstrating universality in a random matrix model of stochastic scattering.Comment: 38 pages, 3 figures, published version, minor changes in Section
Scaling Invariance in Spectra of Complex Networks: A Diffusion Factorial Moment Approach
A new method called diffusion factorial moment (DFM) is used to obtain
scaling features embedded in spectra of complex networks. For an Erdos-Renyi
network with connecting probability , the scaling
parameter is , while for the scaling
parameter deviates from it significantly. For WS small-world networks, in the
special region , typical scale invariance is found. For GRN
networks, in the range of , we have .
And the value of oscillates around abruptly. In the range
of , we have basically . Scale invariance is one
of the common features of the three kinds of networks, which can be employed as
a global measurement of complex networks in a unified way.Comment: 6 pages, 8 figures. to appear in Physical Review
Synchronization in Complex Systems Following the Decision Based Queuing Process: The Rhythmic Applause as a Test Case
Living communities can be considered as complex systems, thus a fertile
ground for studies related to their statistics and dynamics. In this study we
revisit the case of the rhythmic applause by utilizing the model proposed by
V\'azquez et al. [A. V\'azquez et al., Phys. Rev. E 73, 036127 (2006)]
augmented with two contradicted {\it driving forces}, namely: {\it
Individuality} and {\it Companionship}. To that extend, after performing
computer simulations with a large number of oscillators we propose an
explanation on the following open questions (a) why synchronization occurs
suddenly, and b) why synchronization is observed when the clapping period
() is ( is the mean self period
of the spectators) and is lost after a time. Moreover, based on the model, a
weak preferential attachment principle is proposed which can produce complex
networks obeying power law in the distribution of number edges per node with
exponent greater than 3.Comment: 16 pages, 5 figure
Temporal Series Analysis Approach to Spectra of Complex Networks
The spacing of nearest levels of the spectrum of a complex network can be
regarded as a time series. Joint use of Multi-fractal Detrended Fluctuation
Approach (MF-DFA) and Diffusion Entropy (DE) is employed to extract
characteristics from this time series. For the WS (Watts and Strogatz)
small-world model, there exist a critical point at rewiring probability . For a
network generated in the range, the correlation exponent is in the range of .
Above this critical point, all the networks behave similar with that at . For
the ER model, the time series behaves like FBM (fractional Brownian motion)
noise at . For the GRN (growing random network) model, the values of the
long-range correlation exponent are in the range of . For most of the GRN
networks the PDF of a constructed time series obeys a Gaussian form. In the
joint use of MF-DFA and DE, the shuffling procedure in DE is essential to
obtain a reliable result. PACS number(s): 89.75.-k, 05.45.-a, 02.60.-xComment: 10 pages, 9 figures, to appear in PR
A Hamiltonian approach for explosive percolation
We introduce a cluster growth process that provides a clear connection
between equilibrium statistical mechanics and an explosive percolation model
similar to the one recently proposed by Achlioptas et al. [Science 323, 1453
(2009)]. We show that the following two ingredients are essential for obtaining
an abrupt (first-order) transition in the fraction of the system occupied by
the largest cluster: (i) the size of all growing clusters should be kept
approximately the same, and (ii) the inclusion of merging bonds (i.e., bonds
connecting vertices in different clusters) should dominate with respect to the
redundant bonds (i.e., bonds connecting vertices in the same cluster).
Moreover, in the extreme limit where only merging bonds are present, a complete
enumeration scheme based on tree-like graphs can be used to obtain an exact
solution of our model that displays a first-order transition. Finally, the
proposed mechanism can be viewed as a generalization of standard percolation
that discloses an entirely new family of models with potential application in
growth and fragmentation processes of real network systems.Comment: 4 pages, 4 figure
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