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1
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Nodal Domains in Chaotic Microwave Rough Billiards with and without Ray-Splitting Properties

100%
Hul O., Savytskyy N., Tymoshchuk O., Bauch S., Sirko L.
Acta Physica Polonica A
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2006
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vol. 109
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issue 1
73-87
EN
We study experimentally nodal domains of wave functions (electric field distributions) lying in the regime of Breit-Wigner ergodicity in the chaotic microwave half-circular ray-splitting rough billiard. Using the rough billiard without ray-splitting properties we also study the wave functions lying in the regime of Shnirelman ergodicity. The wave functionsΨ_N of the ray-splitting billiard were measured up to the level number N=204. In the case of the rough billiard without ray-splitting properties, the wave functions were measured up to N=435. We show that in the regime of Breit-Wigner ergodicity most of wave functions are delocalized in the n, l basis. In the regime of Shnirelman ergodicity wave functions are homogeneously distributed over the whole energy surface. For such wave functions, lying both in the regimes of Breit-Wigner and Shnirelman ergodicity, the dependence of the number of nodal domainsƝ_N on the level number N was found. We show that in the regimes of Breit-Wigner and Shnirelman ergodicity least squares fits of the experimental data reveal the numbers of nodal domains that in the asymptotic limit N→∞ coincide within the error limits with the theoretical predictionƝ_N/N≃ 0.062. Finally, we demonstrate that the signed area distributionΣ_A can be used as a useful criterion of quantum chaos.
2
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Roughness Method to Estimate Fractal Dimension

100%
Błachowski A., Ruebenbauer K.
Acta Physica Polonica A
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2009
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vol. 115
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issue 3
636-640
EN
A method based on the pattern roughness was introduced for determination of the fractal dimension and tested for fractals like the Sierpiński carpet, the Sierpiński triangle, standard Cantor set, the Menger sponge and the Sierpiński tetrahedron. It was tested for non-fractal pattern like two- and four-dimensional gray scale random dust as well. It was found that for all these patterns the Hausdorff dimension is reproduced with relatively high accuracy. Roughness method is based on simple, fast and easy to implement algorithm applicable in any topological dimension. It is particularly suited for patterns being composed of the hierarchy of structures having the same topological dimension as the space embedding them. It is applicable to "fuzzy" patterns with overlapping structures, where other methods are useless. It is designed for pixelized structures, the latter structures resulting as typical experimental data sets.
3
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Discrete Space-Time by Means of the Weyl-Dirac Theory

100%
Agop M., Chicos L., Gîrţu M.
Acta Physica Polonica A
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2007
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vol. 112
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issue 1
3-12
EN
A connection between the Weyl-Dirac theory and scale relativity theory through the hydrodynamic models (relativistic and non-relativistic approaches) is established. In such conjecture, considering that the motions of the microparticles take place on continuous but non-differentiable curves i.e. on fractals, a Weyl-Dirac type equation was found. Some correspondences with known hydrodynamic models, particularly Białynicki-Birula's approach, are analyzed. All these results reflect the fractal structure of the space-time (a concept in agreement with the new ideas on the space-time)
4
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System Dynamics Control through the Fractal Potential

80%
Timofte A., Casian Botez I., Scurtu D., Agop M.
Acta Physica Polonica A
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2011
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vol. 119
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issue 3
304-311
EN
Implications of the fractal potential in the system dynamics using an extended scale relativity model assuming the fractal character of the particle movements, are established. So, in the dissipative approximation of the model it is shown that the fractal potential comes from the non-differentiability of the space-time, i.e. by means of imaginary part of a complex speed field. In the dispersive approximation of the same model, the fractalization of the differential part of the complex speed field induces a normalized fractal potential which controls through coherence the system dynamics. In such context the type I superconductivity results: the temperature dependences of the superconducting parameter, the accumulator effect etc.
5
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Fractal Transport Phenomena through the Scale Relativity Model

80%
Colotin M., Pompilian G., Nica P., Gurlui S., Paun V., Agop M.
Acta Physica Polonica A
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2009
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vol. 116
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issue 2
157-164
EN
A correspondence between Nottale's scale relativity model and Cresson's mathematical procedures is analyzed. It results that the "synchronization" of the movements at different scales (fractal scale, differential scale etc.) gives conductive type properties to the fractal fluid, while the absence of "synchronization" is inducing properties of convective type. The behavior of a conductive fractal fluid is illustrated through the numerical simulation of plasma diffusion that is generated by laser ablation. Rotational and irrotational convective behaviors of a fractal fluid are established. Particularly, at Compton spatial and temporal scales, the irrotational behavior implies the standard Schrödinger equation.
6
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World Financial 2014-2016 Market Bubbles: Oil Negative - US Dollar Positive

80%
Wątorek M., Drożdż S., Oświęcimka P.
Acta Physica Polonica A
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2016
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vol. 129
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issue 5
932-936
EN
Based on the log-periodic power law methodology, with the universal preferred scaling factor λ ≈2, the negative bubble on the oil market in 2014-2016 has been detected. Over the same period a positive bubble on the so-called commodity currencies expressed in terms of the US dollar appears to take place with the oscillation pattern which largely is mirror reflected relative to oil price oscillation pattern. It documents recent strong anticorrelation between the dynamics of the oil price and of the USD. A related forecast made at the time of FENS 2015 conference (beginning of November) turned out to be quite satisfactory. These findings provide also further indication that such a log-periodically accelerating down-trend signals termination of the corresponding decreases.
7
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Asymmetry in the Subsequent Movements' Proportions of Share Prices Included in the WIG

80%
Szmagliński A.
Acta Physica Polonica A
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2015
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vol. 127
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issue 3A
A-136-A-138
EN
The intraday data of stock prices allow us to collect in the form of histogram the subsequent movements' proportions in price and time. Here we continue the previous work [Acta Phys. Pol. A 123, 621 (2013)], concerning the properties of subsequent price movements' proportions in the opposite directions and proportions of subsequent price movements in the same direction. Here we distinguish between the proportions with growing and decreasing second price movement in the proportion. We investigate quantitatively the effect of breaking the turning point of resistance and support levels depending on the percentage size of price movements. In the same way we treat the main peak in the histogram for the equal subsequent price movements.
8
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Effect of Detrending on Multifractal Characteristics

80%
Oświęcimka P., Drożdż S., Kwapień J., Górski A.
Acta Physica Polonica A
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2013
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vol. 123
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issue 3
597-603
EN
Different variants of multifractal detrended fluctuation analysis technique are applied in order to investigate various (artificial and real-world) time series. Our analysis shows that the calculated singularity spectra are very sensitive to the order of the detrending polynomial used within the multifractal detrended fluctuation analysis method. The relation between the width of the multifractal spectrum (as well as the Hurst exponent) and the order of the polynomial used in calculation is evident. Furthermore, type of this relation itself depends on the kind of analyzed signal. Therefore, such an analysis can give us some extra information about the correlative structure of the time series being studied.
9
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Wave-Particle Duality through a Hydrodynamic Model of the Fractal Space-Time Theory

80%
Agop M., Nica P., Harabagiu A.
Acta Physica Polonica A
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2008
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vol. 113
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issue 6
1571-1588
EN
Considering that the microparticle movements take place on fractal curves, the wave-particle duality is studied in the fractal space-time theory (scale relativity theory). The Nottale model was extended by assuming arbitrary fractal dimension, D_F, of the fractal curves and third-order terms in the equation of motion of a complex speed field. It results that, in a fractal fluid, the convection, dissipation, and dispersion are reciprocally compensating at any scale (differentiable or non-differentiable), whereas a generalized Schrödinger equation is obtained for an irrotational movement of the fractal fluid. The absence of the dispersion implies a generalized Navier-Stokes type equation and the usual Schrödinger equation results for the irrotational movement in D_F=2 of the fractal fluid. The absence of dissipation implies a generalized Korteweg-de Vries type equation. In such conjecture, the duality is analyzed through a hydrodynamic formulation. At the differentiable scale, the duality is achieved by the flowing regimes of the fractal fluid, while at the non-differentiable scale, a fractal potential controls, through the coherence, the duality.
10
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Subsequent Movements' Proportions of Share Prices Included in the WIG over Recent Years

80%
Szmagliński A.
Acta Physica Polonica A
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2013
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vol. 123
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issue 3
621-623
EN
A large amount of stock prices intraday data allow us to create a summary of subsequent movements' proportions of the collected share prices in the form of histogram. We have created two kinds of histograms: one for proportions of subsequent increasing and decreasing price movements and the second for proportions of subsequent price movements in the same direction. We have also created the same kinds of histograms for duration of price movements. All the histograms quite well fit the gamma probability distribution. The distribution coefficients' values ν and λ for price are above 1, for time are below 1. Some proportions of price movements occur more frequently than others, creating peaks on the graph. Similar regularity occurs for the time factor. This property is often used in trading.
11
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Fractals, Log-Periodicity and Financial Crashes

80%
Oświęcimka P., Drożdż S., Kwapień J., Górski A.
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EN
Presence of self-similar patterns in the financial dynamics is by now well established and even convincingly quantified within the multifractal formalism. Here we focus attention on one particular aspect of this self-similarity which potentially is related to the discrete-scale invariance underlying the system composition and manifests itself by the log-periodic oscillations cascading self-similarly through various time scales. Such oscillations accumulate at the turning (critical) points that in the financial dynamics are often identified as crashes. This property thus allows us to develop a methodology that may be useful also for prediction. A model Weierstrass-type function is used to illustrate the relevant effects and several examples demonstrating that such effects in the real financial markets take place indeed, are reviewed.
12
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Anderson Localization in Quantum Chaos: Scaling and Universality

80%
García-García A., Wang J.
Acta Physica Polonica A
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2007
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vol. 112
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issue 4
635-653
EN
The one-parameter scaling theory is a powerful tool to investigate Anderson localization effects in disordered systems. In this paper we show that this theory can be adapted to the context of quantum chaos provided that the classical phase space is homogeneous, not mixed. The localization problem in this case is defined in momentum, not in real space. We then employ the one-parameter scaling theory to: (a) propose a precise characterization of the type of classical dynamics related to the Wigner-Dyson and Poisson statistics which also predicts in which situations Anderson localization corrections invalidate the relation between classical chaos and random matrix theory encoded in the Bohigas-Giannoni-Schmit conjecture, (b) to identify the universality class associated with the metal-insulator transition in quantum chaos. In low dimensions it is characterized by classical superdiffusion, in higher dimensions it has in general a quantum origin as in the case of disordered systems. We illustrate these two cases by studying 1d kicked rotors with non-analytical potentials and a 3d kicked rotor with a smooth potential.
13
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Some Aspects Concerning the "Memorization Effect" in Complex Fluid

80%
Agop M., Ochiuz L., Timofte D., Barlescu V., Danila M., Gheorghita L., Paun V., Solovastru L., Popa C.
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vol. 126
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issue 3
663-670
EN
In the frame of a non-standard scale relativity model, the specific momentum, states density and internal energy conservations laws are obtained. The chaoticity, either through turbulence in the fractal hydrodynamics approach, or through stochasticization in the Schrödinger type approach, is generated only by the non-differentiability of the movement trajectories of the complex fluid entities. Using the conservation laws mentioned above, by numerical simulations, hysteretic type effects (dynamics of hysteretic cycles) occur.
14
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Accuracy Analysis of the Box-Counting Algorithm

80%
Górski A., Drożdż S., Mokrzycka A., Pawlik J.
Acta Physica Polonica A
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2012
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vol. 121
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issue 2B
B-28-B-30
EN
Accuracy of the box-counting algorithm for numerical computation of the fractal exponents is investigated. To this end several sample mathematical fractal sets are analyzed. It is shown that the standard deviation obtained for the fit of the fractal scaling in the log-log plot strongly underestimates the actual error. The real computational error was found to have power scaling with respect to the number of data points in the sample (n_{tot}). For fractals embedded in two-dimensional space the error is larger than for those embedded in one-dimensional space. For fractal functions the error is even larger. Obtained formula can give more realistic estimates for the computed generalized fractal exponents' accuracy.
15
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Multifractality of Nonlinear Transformations with Application in Finances

61%
Grech D., Pamuła G.
Acta Physica Polonica A
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2013
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vol. 123
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issue 3
529-537
EN
We study the multifractal effects of nonlinear transformations of monofractal, stationary time series and apply the found results to measure the "true" unbiased multifractality generated only by multiscaling properties of initial (primary) data before transformations. A difference is stressed between "naive" observed multifractal effects calculated directly within detrended multifractal analysis as the spread Δh of the generalized Hurst exponents h(q) and the more reliable unbiased multifractality received after subtraction of residual bias effects generated by nonlinear transformations of initial data and coupled with finite size effects in time series. This property is investigated for volatile series of the real main world financial indices. A difference between multifractal properties of intraday and interday quotes is also pointed out in this context for the Warsaw Stock Exchange WIG index. Finally, based on the observed feature of real nonstationary data, a new measure of unbiased multifractality in signals is introduced. This measure comes from an analysis of the whole generalized Hurst exponent profile instead of looking just at its edge behavior h^{±} ≡ h(q→ ±∞). Such an approach seems to be particularly useful when h(q) is not a monotonic function of the moment order q. Interesting examples with extreme events from finance are presented. They convince that an analysis directed only on investigation of the edges h^{±} in multifractal spectrum may be misleading.
16
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On quantum iterated function systems

51%
Jadczyk A.
Open Physics
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2004
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vol. 2
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issue 3
492-503
EN
A Quantum Iterated Function System on a complex projective space is defined through a family of linear operators on a complex Hilbert space. The operators define both the maps and their probabilities by one algebraic formula. Examples with conformal maps (relativistic boosts) on the Bloch sphere are discussed.
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