Regular Series

Vol. 43 (2012), No. 6, pp. 1257 – 1381

Fluctuation of Gold Price: A Multifractal Approach

Acta Phys. Pol. B 43, 1261 (2012)

page 1261 •


The time series for gold price has been investigated in past and it was observed that the time series has multifractal properties. The gold price data from 1973 to the present time has been divided into sets of five years each and the variation of degree of multifractality with time is investigated. An attempt has been made to physically interpret the results and to make future predictions of variation in price.

Coupled Nonlinear Oscillators: Metamorphoses of Amplitude Profiles for the Approximate Effective Equation — the Case of \(1:3\) Resonance

Acta Phys. Pol. B 43, 1275 (2012)

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We study dynamics of two coupled periodically driven oscillators. A classic example of such a system is a dynamic vibration absorber which consists of a small mass attached to the primary vibrating system of a large mass. Periodic solutions of the approximate effective equation (derived in our earlier papers) are determined within the Krylov–Bogoliubov–Mitropolsky approach to compute the amplitude profiles \(A\left ( {\mit \Omega } \right ) \). In the present paper, we investigate metamorphoses of the function \(A\left ( {\mit \Omega } \right ) \) induced by changes of the control parameters in the case of \(1:3\) resonances.

Eikonal Approach to \({\cal N}=4\) SYM Regge Amplitudes in the AdS/CFT Correspondence

Acta Phys. Pol. B 43, 1289 (2012)

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The high-energy behavior of \(\cal {N}= 4 \) SYM elastic amplitudes at strong coupling is studied by means of the AdS/CFT correspondence. We consider the eikonal method proposed by Janik and one of the authors, where the relevant minimal surface is a “generalized helicoid” in hyperbolic space (“Euclidean AdS\(_5\)”), from which the physical amplitude is obtained after an appropriate analytic continuation. We then compare our results with those obtained, using a minimal surface in AdS\(_5\) momentum space, by Alday and Maldacena for gluon–gluon scattering, and by Barnes and Vaman for quark–quark scattering (“Alday–Maldacena approach”). Exploiting a conformal transformation, we show that the eikonal amplitudes are dominated by the Euclidean version of the cusp contribution found in the Alday–Maldacena approach. The amplitudes in the two approaches are of Regge type at high-energy and with the same logarithmic Regge trajectory independently of the kind of colliding particles, in agreement with the expected universality of Regge trajectories.

Testing New Strongly Intensive Measures of Transverse Momentum Fluctuations

Acta Phys. Pol. B 43, 1333 (2012)

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Recently, the new strongly intensive measures of fluctuations \({\mit \Delta }\) and \({\mit \Sigma }\) have been proposed. In this publication their properties are tested using an example of event-by-event transverse momentum fluctuations. The obtained values are compared to the long used \({\mit \Phi }\) measure of \(p_{\rm T}\) fluctuations. Several tests are preformed within data produced by fast generators, as well as by the UrQMD model. The UrQMD calculations are presented for the systems and energies which are planned to be studied in the NA61/SHINE experiment at the CERN Super Proton Synchrotron.

Particle Clusters and Multiplicity Fluctuations in Narrow Rapidity Bins

Acta Phys. Pol. B 43, 1357 (2012)

page 1357 •


Effects of resonance, or cluster production on the random (Poissonian) fluctuations of multiplicity in rapidity bins has been analyzed. It is found that for narrow bins (up to some 0.25 in rapidity), and for realistic assumptions on the resonances or clusters, this effect is reasonably small.

Numerical Simulations of Magnetoacoustic Waves in the Gravitationally Stratified Solar Atmosphere

Acta Phys. Pol. B 43, 1365 (2012)

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We study impulsively-generated magnetoacoustic waves in the gravitationally stratified solar atmosphere which is permeated by a straight magnetic field. Our numerical model solves two-dimensional magnetohydrodynamic equations in the limit of an ideal plasma and for a temperature profile modelled by a smoothed step function. The results of our simulations agree with the theoretical application of Klein–Gordon equation to fast magnetoacoustic waves propagating in the solar atmosphere. The abovementioned equation introduces a cutoff frequency in the system. Therefore, as the first wave passes, the medium behind it starts to oscillate with a given frequency. Even a small amplitude perturbation in the photosphere generates shock waves in the corona. In addition to that, large impulses (larger than \(\sim 10~\)km\(\,\)s\(^{-1}\)) cause oscillations of the plasma in the transition region.


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