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Celikoglu A.,Ege University | Tirnakli U.,Ege University | Tirnakli U.,Institute of Theoretical and Applied Physics ITAP
Physica A: Statistical Mechanics and its Applications | Year: 2013

The waiting time distribution between successive events and the unified scaling law is studied using the coherent noise model. It is shown that, although this model generates uncorrelated event sizes and does not exhibit criticality, it still provides the unified scaling law. We argue the role of characteristic kink observed in the unified scaling law and the meaning of the parameter C used to fix the peak of the kink to unity. Our results indicate that the parameter C is indeed a physical quantity localizing the end of the linear tendency in the scaling law, which corresponds to the completion of the dominance of correlated events in time. © 2013 Elsevier B.V. All rights reserved.

Afsar O.,Ege University | Tirnakli U.,Ege University | Tirnakli U.,Institute of Theoretical and Applied Physics ITAP
EPL | Year: 2013

We generalize Huberman-Rudnick universal scaling law for all periodic windows of the logistic map and show the robustness of q-Gaussian probability distributions in the vicinity of chaos threshold. Our scaling relation is universal for the self-similar windows of the map which exhibit period-doubling subharmonic bifurcations. Using this generalized scaling argument, for all periodic windows, as chaos threshold is approached, a developing convergence to q-Gaussian is numerically obtained both in the central regions and tails of the probability distributions of sums of iterates. © Copyright EPLA, 2013.

Afsar O.,Ege University | Tirnakli U.,Ege University | Tirnakli U.,Institute of Theoretical and Applied Physics ITAP
Physica D: Nonlinear Phenomena | Year: 2014

We numerically introduce the relationships among correlation, fractality, Lyapunov divergence and q-Gaussian distributions. The scaling arguments between the range of the q-Gaussian and correlation, fractality, Lyapunov divergence are obtained for periodic windows (i.e., periods 2, 3 and 5) of the logistic map as chaos threshold is approached. Firstly, we show that the range of the q-Gaussian (g) tends to infinity as the measure of the deviation from the correlation dimension (Dcorr=0.5) at the chaos threshold, (this deviation will be denoted by l), approaches to zero. Moreover, we verify that a scaling law of type 1/g∞lτ is evident with the critical exponent τ=0.23±0.01. Similarly, as chaos threshold is approached, the quantity l scales as ∞(a-ac)γ, where the exponent is γ=0.84±0.01. Secondly, we also show that the range of the q-Gaussian exhibits a scaling law with the correlation length (1/g∞ξ-μ), Lyapunov divergence (1/g∞λμ) and the distance to the critical box counting fractal dimension (1/g∞(D-Dc)μ) with the same exponent μ≅0.43. Finally, we numerically verify that these three quantities (ξ, λ, D-Dc) scale with the distance to the critical control parameter of the map (i.e., a-ac) in accordance with the universal Huberman-Rudnick scaling law with the same exponent ν=0.448±0.003. All these findings can be considered as a new evidence supporting that the central limit behaviour at the chaos threshold is given by a q-Gaussian. © 2014 Elsevier B.V. All rights reserved.

Pribulla T.,Slovak Academy of Sciences | Vanko M.,Slovak Academy of Sciences | Ammler-von Eiff M.,Thuringer Landessternwarte Tautenburg | Andreev M.,Ukrainian Academy of Sciences | And 59 more authors.
Astronomische Nachrichten | Year: 2012

We present a new observational campaign, Dwarf, aimed at detection of circumbinary extrasolar planets using the timing of the minima of low-mass eclipsing binaries. The observations will be performed within an extensive network of relatively small to medium-size telescopes with apertures of ∼20-200 cm. The starting sample of the objects to be monitored contains (i) low-mass eclipsing binaries with M and K components, (ii) short-period binaries with a sdB or sdO component, and (iii) post-common-envelope systems containing a WD, which enable to determine minima with high precision. Since the amplitude of the timing signal increases with the orbital period of an invisible third component, the timescale of the project is long, at least 5-10 years. The paper gives simple formulas to estimate the suitability of individual eclipsing binaries for the circumbinary planet detection. Intrinsic variability of the binaries (photospheric spots, flares, pulsation etc.) limiting the accuracy of the minima timing is also discussed. The manuscript also describes the best observing strategy and methods to detect cyclic timing variability in the minima times indicating the presence of circumbinary planets. First test observations of the selected targets are presented. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Hakioglu T.,Technical University of Istanbul | Hakioglu T.,Institute of Theoretical and Applied Physics ITAP | Gunay M.,Bilkent University | Gunay M.,Institute of Theoretical and Applied Physics ITAP
Physica C: Superconductivity and its Applications | Year: 2016

Noncentrosymmetric superconductors (NCSs) with broken inversion symmetry can have spin-dependent order parameters (OPs) with mixed parity which can also have nodes in the pair potential as well as the energy spectra. These nodes are distinct features that are not present in conventional superconductors. They appear as points or lines in the momentum space where the latter can have angular or radial geometries dictated by the dimensionality, the lattice structure and the pairing interaction. In this work we study the nodes in time reversal symmetry (TRS) preserving NCSs at the OP, the pair potential, and the energy spectrum levels. Nodes are examined by using spin independent pairing interactions respecting the rotational C∞v symmetry in the presence of spin-orbit coupling (SOC). The pairing symmetries and the nodal topology are affected by the relative strength of the pairing channels which is studied for the mixed singlet-triplet, pure singlet, and pure triplet. Complementary to the angular line nodes widely present in the literature, the C∞v symmetry here allows radial line nodes (RLNs) due to the nonlinear momentum dependence in the OPs. The topology of the RLNs in the mixed case shows a distinctly different characterization than the half-spin quantum vortex at the Dirac point. We apply this NCS physics to the inversion symmetry broken exciton condensates (ECs) in double quantum wells where the point and the RLNs can be found. On the other hand, for a pure triplet condensate, two fully gapped and topologically distinct regimes exist, separated by a QSHI-like zero energy superconducting state with even number of Majorana modes. We also remark on how the point and the RLNs can be manipulated, enabling an external control on the topology. © 2016 Elsevier B.V.

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