Narrow Results

Most signatures of new physics have been studied on the transverse plane with respect to the beam direction at the LHC where background is much reduced. In this paper we propose the analysis of inclusive longitudinal (pseudo)rapidity correlations among final-state (charged) particles in order to search for (un)particles belonging to a hidden sector beyond the Standard Model, using a selected sample of p–p minimum bias events (applying appropriate off-line cuts on events based on, e.g. minijets, high-multiplicity, event shape variables, high-p_⊥ leptons and photons, etc.) collected at the early running of the LHC. To this aim, we examine inclusive and semi-inclusive two-particle correlation functions, forward–backward correlations, and factorial moments of the multiplicity distribution, without resorting to any particular model but under very general (though simplifying) assumptions. Finally, motivated by some analysis techniques employed in the search for quark–gluon plasma in heavy-ion collisions, we investigate the impact of such intermediate (un)particle stuff on the (multi)fractality of parton cascades in p–p collisions, by means of a Lévy stable law description and a Ginzburg–Landau model of phase transitions. Results from our preliminary study seem encouraging for possible dedicated analyses at LHC and Tevatron experiments.

Experimental data on transverse momentum spectra of strange particles $(K_S^0,K^{-},K^{\ast 0},\varphi ,\mathrm{\Lambda },{\mathrm{\Lambda }}^{\ast },{\mathrm{\Sigma }}^{\ast },{\mathrm{\Xi }}^{-},\mathrm{\Omega })$ produced in $pp$ collisions at $\sqrt{s}=200\mathrm{\text{GeV}}$ obtained by the STAR and PHENIX collaborations at RHIC are analyzed in the framework of $z$-scaling approach. The concept of the $z$-scaling is based on fundamental principles of self-similarity, locality, and fractality of hadron interactions at high energies. General properties of the data $z$-presentation are studied. Self-similarity of fractal structure of protons and fragmentation processes with strange particles is discussed. A microscopic scenario of constituent interactions developed within the $z$-scaling scheme is used to study the dependence of momentum fractions and recoil mass on the collision energy, transverse momentum and mass of produced inclusive particle, and to estimate the constituent energy loss. We consider that obtained results can be useful in study of strangeness origin, in searching for new physics with strange probes, and can serve for better understanding of fractality of hadron interactions at small scales.

Fractal self-similarity of hadron interactions demonstrated by the $z$-scaling of inclusive spectra is studied. The scaling regularity reflects fractal structure of the colliding hadrons (or nuclei) and takes into account general features of fragmentation processes expressed by fractal dimensions. The self-similarity variable $z$ is a function of the momentum fractions $x_1$ and $x_2$ of the colliding objects carried by the interacting hadron constituents and depends on the momentum fractions $y_a$ and $y_b$ of the scattered and recoil constituents carried by the inclusive particle and its recoil counterpart, respectively. Based on entropy principle, new properties of the $z$-scaling concept are found. They are conservation of fractal cumulativity in hadron interactions and quantization of fractal dimensions characterizing hadron structure and fragmentation processes at a constituent level.

We examine the convergence properties of the generalized Hénon–Heiles system, by using the multivariate version of the Newton–Raphson iterative scheme. In particular, we numerically investigate how the perturbation parameter $\delta$ influences several aspects of the method, such as its speed and efficiency. Color-coded diagrams are used for revealing the basins of convergence on the configuration plane. Additionally, we compute the degree of fractality of the convergence basins on the configuration space, as a function of the perturbation parameter, by using different tools, such the uncertainty dimension and the (boundary) basin entropy. Our analysis suggests that the perturbation parameter strongly influences the number of the equilibrium points, as well as the geometry and the structure of the associated basins of convergence. Furthermore, the highest degree of fractality, along with the appearance of nonconverging points, occur near the critical values of the perturbation parameter.

The two-dimensional intermittency and its self-affine nature are investigated for p–p collisions at $\sqrt{s}=13$TeV in the two-dimensional anisotropic $(\eta -\varphi )$ space. The UrQMD model has been employed to generate and accumulate the p–p collisions data. Our investigation is made in the framework of scaled factorial moment (SFM) method. The concept of Hurst exponent $H$ is incorporated to bring a qualitative comparison between the UrQMD generated minimum bias (MB) events and the events at a particular impact parameter $b=0.4$ fm. The variation of the fractal strength with the variation of $H$ as well as with the variation of the order of the moment $q$ has been analyzed. Also, the nonlinearity in the variation of SFM with that of $H$ has been accompanied in this paper. It is observed that the fractal strength and the intermittent type of fluctuations are found to be much stronger in the region with $H<1$ compared to the region with $H>1$ and the self-affine nature in the fluctuations increases as $H$ deviates from unity.

We study the fractal dimension of the contour of the liquid-gas interface in a spray. Our images include both the linking region and the break-up region, and are obtained with a high-resolution shadowgraph technique. This means that the images can then be subjected to an intensity filtering, equivalent to a threshold analysis, that enables the establishment of the fractal range.

The complexity of the Nautilus pompilius shell is analyzed in terms of its fractal dimension and its equiangular spiral form. Our findings assert that the shell is fractal from its birth and that its growth is dictated by a self-similar criterion (we obtain the fractal dimension of the shell as a function of time). The variables that have been used for the analysis show an exponential dependence on the number of chambers/age of the cephalopod, a property inherited from its form.

This paper deals with the target excitation dependence of the multifractal specific heat of pions produced in nucleus-nucleus collisions at 60 and 200 AGeV. Fluctuation pattern of pions is studied in two dimensions considering anisotropy of phase space. The parameter characterizing the anisotropy of phase space, Hurst exponent, is extracted by fitting one-dimensional factorial moment saturation curves. Values of intermittency exponent α_q and generalized dimension D_q are determined. The fluctuation pattern reveals multifractal behavior at all target excitations at both energies. The multifractal specific heat c is found to depend on target excitation and the dependence is found to be more pronounced at lower energy. The results are discussed in detail.

In the context of current Narratology, a novel can be regarded as an information generator system. This information can be symbolically and numerically codified and, subsequently, studied by nonlinear characteristic geometrical methods. Using this approach, geometric structures underlying the narrative discourse become evident. In this work, using a particular novel as our experimental data source, a formal expression for a discrete dynamical system is deduced, which generates a representative orbit of the narrative discourse evolution. The fractal dimension of this orbit is calculated from the correlation dimension and its deterministic character is unambiguously proved by solving the associated embedding problem. Finally, we describe the general features that a novel must satisfy in order to apply the proposed procedure.

Since the existence of market memory could implicate the rejection of the efficient market hypothesis, the aim of this paper is to find any evidence that selected emergent capital markets (eight European and BRIC markets, namely Hungary, Romania, Estonia, Czech Republic, Brazil, Russia, India and China) evince long-range dependence or the random walk hypothesis. In this paper, the Hurst exponent as calculated by R/S fractal analysis and Detrended Fluctuation Analysis is our measure of long-range dependence in the series. The results reinforce our previous findings and suggest that if stock returns present long-range dependence, the random walk hypothesis is not valid anymore and neither is the market efficiency hypothesis.

Using the covering theory in fractal geometry, we obtain the fractality of self-similar substitution networks introduced by Li et al. [Scale-free effect of substitution networks, Physica A 492 (2018) 1449–1455].

In this work, we analyze the high-frequency time series of the deposits collected from the systemic biggest Greek banks during the recent economic crisis in Greece. Our focus has been to reveal hidden fractal and periodic patterns using a hybrid approach, which combines correlation and frequency analysis of the original and difference series in a synergistic manner. We find that during the first period of the recorded series featured by the dramatic decrease of deposits, the short time behavior exhibits Brownian motion characteristics with fractal dimension close to 1.5, while a cyclical pattern of monthly repetition (21 days) is detected in the difference series to bound fractal behavior. The Brownian property is also observed in the second uprising segment of deposit series, but it lasts more (50 days) and no well-defined cyclical pattern is detected. Our work reveals that the economic crisis in Greece has gradually eroded the cyclical behavior of daily differences in bank deposits, while maintaining a short-term Brownian motion pattern, albeit with an increased duration.

We investigate whether the fractal markets hypothesis and its focus on liquidity and investment horizons give reasonable predictions about the dynamics of the financial markets during turbulences such as the Global Financial Crisis of late 2000s. Compared to the mainstream efficient markets hypothesis, the fractal markets hypothesis considers the financial markets as complex systems consisting of many heterogenous agents, which are distinguishable mainly with respect to their investment horizon. In the paper, several novel measures of trading activity at different investment horizons are introduced through the scaling of variance of the underlying processes. On the three most liquid US indices — DJI, NASDAQ and S&P500 — we show that the predictions of the fractal markets hypothesis actually fit the observed behavior adequately.

This paper aims to provide a consistent, finite-valued, and mathematically well-defined reformulation of Feynman’s path-integral measure for quantum fields obtained by studying the Wiener stochastic process in the infinite-dimensional Hilbert space of quantum states. This reformulation will undoubtedly have a crucial role in formulating quantum gravity within a mathematically well-defined framework. In fact, this study is fundamentally different from any previous research on the relationship between Feynman’s path-integral and the Wiener stochastic process. In this research, we focus on the fact that the classic Wiener measure is no longer applicable in infinite-dimensional Hilbert spaces due to fundamental differences between displacements in low and extremely high dimensions. Thus, an analytic norm motivated by the role of the fractal functions in the Wilsonian renormalization approach is worked out to properly characterize Brownian motion in the Hilbert space of quantum states on a compact flat manifold. This norm, the so-called fractal norm, pushes the rougher functions (physically the quantum states with higher energies) to the farther points of the Hilbert space until the fractal functions as the roughest ones are moved to infinity. Implementing the Wiener stochastic process with the fractal norm, results in a modified form of the Wiener measure called the Wiener fractal measure, which is a well-defined measure for Feynman’s path-integral formulation of quantum fields. Wiener fractal measure has a complicated formula of non-local terms but produces the Klein–Gordon action at the first order of approximation. Using complex integrals to compensate for the removal of non-local terms appearing in higher orders of approximation, the Wiener fractal measure turns into a complex measure and generates Feynman’s path-integral formulation of scalar quantum fields. This brings us to the main objective of this study. Finally, some various significant aspects of quantum field theory (such as renormalizability, RG flow, Wick rotation, regularization, etc.) are revisited by means of the analytical aspects of the Wiener fractal measure.