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

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 $p_{ER} < \frac{1}{N}$, the scaling parameter is $\delta = 0.51$, while for $p_{ER} \ge \frac{1}{N}$ the scaling parameter deviates from it significantly. For WS small-world networks, in the special region $p_r \in [0.05,0.2]$, typical scale invariance is found. For GRN networks, in the range of $\theta\in[0.33,049]$, we have $\delta=0.6\pm 0.1$. And the value of $\delta$ oscillates around $\delta=0.6$ abruptly. In the range of $\theta\in[0.54,1]$, we have basically $\delta>0.7$. 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

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 adde

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

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 ($T_c$) is $1.5 \cdot T_s < T_c < 2.0 \cdot T_s$ ($T_s$ 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

Opinion diversity and community formation in adaptive networks

It is interesting and of significant importance to investigate how network structures co-evolve with opinions. The existing models of such co-evolution typically lead to the final states where network nodes either reach a global consensus or break into separated communities, each of which holding its own community consensus. Such results, however, can hardly explain the richness of real-life observations that opinions are always diversified with no global or even community consensus, and people seldom, if not never, totally cut off themselves from dissenters. In this article, we show that, a simple model integrating consensus formation, link rewiring and opinion change allows complex system dynamics to emerge, driving the system into a dynamic equilibrium with co-existence of diversified opinions. Specifically, similar opinion holders may form into communities yet with no strict community consensus; and rather than being separated into disconnected communities, different communities remain to be interconnected by non-trivial proportion of inter-community links. More importantly, we show that the complex dynamics may lead to different numbers of communities at steady state with a given tolerance between different opinion holders. We construct a framework for theoretically analyzing the co-evolution process. Theoretical analysis and extensive simulation results reveal some useful insights into the complex co-evolution process, including the formation of dynamic equilibrium, the phase transition between different steady states with different numbers of communities, and the dynamics between opinion distribution and network modularity, etc.Comment: 12 pages, 8 figures, Journa

Random Topologies and the emergence of cooperation: the role of short-cuts

We study in detail the role of short-cuts in promoting the emergence of cooperation in a network of agents playing the Prisoner's Dilemma Game (PDG). We introduce a model whose topology interpolates between the one-dimensional euclidean lattice (a ring) and the complete graph by changing the value of one parameter (the probability p to add a link between two nodes not already connected in the euclidean configuration). We show that there is a region of values of p in which cooperation is largely enhanced, whilst for smaller values of p only a few cooperators are present in the final state, and for p \rightarrow 1- cooperation is totally suppressed. We present analytical arguments that provide a very plausible interpretation of the simulation results, thus unveiling the mechanism by which short-cuts contribute to promote (or suppress) cooperation

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