Study of \gamma-charge correlation in heavy ion collisions, various approaches

Event-by-event \gamma-charge correlation is used in studying systems going through QCD chiral phase transition. In this paper various methods for measuring \gamma-charge correlation in heavy ion collisions have been discussed. Dynamical fluctuation due to formation of domains of DCC that can affect \gamma-charge correlation has been discussed. We study known detector and statistical effects involved in these measurements and suggest suitable robust observables \Delta\nu_{dyn} and r_{m,1} sensitive to small \gamma-charge correlation signal. These variables are constructed based on moments of multiplicity distributions of photon and charged particles. Estimations of expected measurable signals of \gamma-charge correlation from various available models such as for ideal Boltzmann gas of pions, monte-carlo models based on transport and mini-jets have been discussed. Collision centrality dependence of the observables have been estimated from Central Limit Theorem and found to be consistent with the model predictions. We find that observables show high sensitivity to fraction of DCC events and have nonlinear dependence on fraction of pions carrying DCC signals. Variation of r_{m,1} with orders of its higher moments m is an observable to extract the nature and strength of \gamma-charge correlation.Comment: 12 pages, 11 figure

Fourier Coefficients of Asynchronous Collective Motions in Heavy-ion Collisions

We present a novel scenario in heavy-ion collisions where different modes of collective motions evolve asynchronously in the created nuclear medium. Such physics mechanisms could each dominate at a distinct evolution stage, or coexist simultaneously without coordinating with each other. If we employ a separate single-harmonic Fourier expansion to describe how each asynchronous collective motion affects particle emission, the particle azimuthal distribution should be the product of all these expansions. Consequently, cross terms between collectivity modes appear, and their contributions to experimental observables could be significant. In particular, we argue that the chiral magnetic effect (CME) and elliptic flow can develop asynchronously, with their convolution affecting the observable that is sensitive to the shear-induced CME. We will use the event-by-event anomalous-viscous fluid dynamics model to illustrate the effects of this scenario. Besides giving new insights into searches for the CME, we also propose a feasible experimental test based on conventional flow harmonics

The Study of Noncollectivity by the Forward-Backward Multiplicity Correlation Function

We propose a forward-backward multiplicity correlation function $C^N_{FB}$, which is experimentally accessible, to measure the noncollectivity contribution. We find that $C^N_{FB}$ is sensitive to the jet contribution for the particle-rich case. Surprisingly, it will automatically decrease for the particle-rare case. Our study indicates that similar decreasing trend observed previously is mainly driven by particle scarcity instead of jets. The function is studied in Au+Au collision at $\sqrt{s_{NN}}=200$ GeV with a multiphase transport model (AMPT). We find that the jet fraction is about 10% at transverse momentum ($p_T$) around 2.5 GeV/$c$ and reaches up to 30% at 3.5 GeV/$c$. The implication of this study in the investigation of the noncollectivity contribution in elliptic anisotropy parameter $v_2$ is also discussed.Comment: 5 pages, 4 figure

Reflected Backward Stochastic Differential Equations Driven by L\'{e}vy Process

In this paper, we deal with a class of reflected backward stochastic differential equations associated to the subdifferential operator of a lower semi-continuous convex function driven by Teugels martingales associated with L\'{e}vy process. We obtain the existence and uniqueness of solutions to these equations by means of the penalization method. As its application, we give a probabilistic interpretation for the solutions of a class of partial differential-integral inclusions.Comment: 14 page

Elliptic flow in the Gaussian model of eccentricity fluctuations

We discuss a specific model of elliptic flow fluctuations due to Gaussian fluctuations in the initial spatial $x$ and $y$ eccentricity components \left\{\mean{(\sigma_y^2-\sigma_x^2)/(\sigma_x^2+\sigma_y^2)}, \mean{2\sigma_{xy}/(\sigma_x^2+\sigma_y^2)} \right\}. We find that in this model \vfour, elliptic flow determined from 4-particle cumulants, exactly equals the average flow value in the reaction plane coordinate system, \mean{v_{RP}}, the relation which, in an approximate form, was found earlier by Bhalerao and Ollitrault in a more general analysis, but under the same assumption that $v_2$ is proportional to the initial system eccentricity. We further show that in the Gaussian model all higher order cumulants are equal to \vfour. Analysis of the distribution in the magnitude of the flow vector, the $Q-$distribution, reveals that it is totally defined by two parameters, \vtwo, the flow from 2-particle cumulants, and \vfour, thus providing equivalent information compared to the method of cumulants. The flow obtained from the $Q-$distribution is again \vfour=\mean{v_{RP}}.Comment: Very minor changes, as submitted to Phys. Lett.

Footprints of the (Nearly) Perfect Liquid

In relativistic heavy-ion collisions, the system has gone through a series of evolution, almost at every stage of its evolution it leaves behind footprints in flow observable. Those footprints contain valuable information of the bulk property of the (nearly) perfect liquid. By examing footprints of the nearly perfect liquid, we address a few important issues, including the ideal hydrodynamic limit, estimation of $\eta/s$, testing the Number of Constituent Quark scaling at low energy, in small system, at large transverse momentum, and in forward region. Future prospect of flow study is discussed.Comment: 8 pages, 9 figures - To appear in the conference proceedings for Quark Matter 2009, March 30 - April 4, Knoxville, Tennessee. Minor correction

Electric power network fractal and its relationship with power system fault

Mreža elektro-energetskog sustava ima karakteristike fraktala. Ima osnovnu značajku složene mreže: sličnost samoj sebi. Autori su najprije izračunali vrijednosti fraktalne dimenzije za nekoliko elektro-energetskih rešetki, uključujući sustav 9 sabirnica WSCC (Western Systems Coordinating Council), sustav 14 sabirnica IEEE, sustav 30 sabirnica IEEE, sustav 39 sabirnica IEEE, sustav 118 sabirnica IEEE i sustav 300 sabirnica IEEE, kao i nekoliko stvarnih energetskih rešetki kao što su 500 kV glavne China Southern Power Grid (CSPG), 500 kV glavne energetske rešetke provincije Guangdong te 500 kV i 220 kV miješane energetske rešetke provincije Guangdong, itd. Na temelju fraktalne vrijednosti energetske rešetke analizirana je usporedba i odnos između fraktalne vrijednosti i intenziteta kvarenja energetskog sustava. Osnovni je zaključak da će za isti nivo napona, što je veća skala, energetska rešetka vjerojatno imati veću fraktalnu vrijednost i veći intenzitet kvarenja. Kod iste skale, što je gušća energetska rešetka to će vjerojatno biti veća fraktalna vrijednost i veći intenzitet kvarenja rešetke. Zaključci pružaju novi uvid u prosudbu statusa osjetljivosti energetskog sustava s interdisciplinarnog gledišta te voditi do novih smjerova u istraživanju.Electric power system network is with fractal characteristic. It has the basic feature of a complex network: self-similarity. The authors first calculated the fractal dimension values for several electric power grids, including WSCC (Western Systems Coordinating Council) 9 bus system, IEEE14 bus system, IEEE 30 bus system, IEEE 39 bus system, IEEE 118 bus system and IEEE 300 bus system; as well as some real power grids such as China Southern Power Grid (CSPG) 500 kV main power grid, Guangdong province 500 kV main power grid, and Guangdong province 500 kV and 220 kV mixed power grid, etc. Based on the power grid fractal value, a comparison and relationship between the fractal value and power system failure rate is analysed. The basic conclusion is that for the same voltage level, the larger the scale is, the larger fractal value and higher failure rate the power grid will possibly have. For the same scale, the denser the power grid, the larger fractal value and higher failure rate the power grid will probably have. The conclusions provide a new vision on the power system vulnerability status judgment from an interdisciplinary view and lead to a new research direction