# G. Cigdem Yalcin

14.07

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Introduction

G. Cigdem Yalcin currently works at the Department of Physics, Istanbul University. G.Cigdem Yalcin does research in nonlinear dynamics, statistical physics and complex systems in multidiscipliner areas. Their most recent publication is 'Generalized statistical mechanics of cosmic rays: Application to positron-electron spectral indices.'

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Research Items (9)

- May 2017

We apply generalized statistical mechanics developed for complex systems to theoretically predict energy spectra of particle and anti-particle degrees of freedom in cosmic ray fluxes, based on a $q$-generalized Hagedorn theory for transverse momentum spectra and hard QCD scattering processes. QCD at largest center of mass energies predicts the entropic index to be $q=\frac{13}{11}$, whereas the escort duality of the nonextensive thermodynamic formalism predicts an energy split of effective temperature given by $\Delta kT =\pm \frac{1}{10} kT_H \approx \pm 18 $ MeV, where $T_H$ is the Hagedorn temperature. We carefully analyse the measured primary cosmic ray data of the AMS-02 collaboration and provide evidence that the predicted temperature split is indeed observed, leading to a different energy dependence of the $e^+$ and $e^-$ spectral indices. Moreover, we observe that at larger energies $E$ the measured $e^+e^-$ flux starts to deviate from our QCD-based statistical mechanics theory, with a crossover scale of $E^*=(50 \pm 10)$ GeV, which could be a hint for WIMP decay or other new physics setting in at this mass scale. Fits using linear combinations of the escort and non-escort $q$-generalized canonical distributions yield excellent agreement with the measured data in the entire energy range.

- Nov 2015

We demonstrate that dual entropy expressions of the Tsallis type apply
naturally to statistical-mechanical systems that experience an exceptional
contraction of their configuration space. The entropic index $\alpha>1$
describes the contraction process, while the dual index $\alpha ^{\prime
}=2-\alpha<1$ defines the contraction dimension at which extensivity is
restored. We study this circumstance along the three routes to chaos in
low-dimensional nonlinear maps where the attractors at the transitions, between
regular and chaotic behavior, drive phase-space contraction for ensembles of
trajectories. We illustrate this circumstance for properties of systems that
find descriptions in terms of nonlinear maps. These are size-rank functions,
urbanization and similar processes, and settings where frequency locking takes
place.

- Aug 2015

We analyse the probability densities of daily rainfall amounts at a variety
of locations on the Earth. The observed distributions of the amount of rainfall
fit well to a q-exponential distribution with exponent q close to q=1.3. We
discuss possible reasons for the emergence of this power law. On the contrary,
the waiting time distribution between rainy days is observed to follow a
near-exponential distribution. A careful investigation shows that a
q-exponential with q=1.05 yields actually the best fit of the data. A Poisson
process where the rate fluctuates slightly in a superstatistical way is
discussed as a possible model for this. We discuss the extreme value statistics
for extreme daily rainfall, which can potentially lead to flooding. This is
described by Frechet distributions as the corresponding distributions of the
amount of daily rainfall decay with a power law. On the other hand, looking at
extreme event statistics of waiting times between rainy days (leading to
droughts for very long dry periods) we obtain from the observed
near-exponential decay of waiting times an extreme event statistics close to
Gumbel distributions. We discuss superstatistical dynamical systems as simple
models in this context.

- Sep 2014

We show that size-rank distributions with power-law decay (often only over a limited extent) observed in a vast number of instances in a widespread family of systems obey Tsallis statistics. The theoretical framework for these distributions is analogous to that of a nonlinear iterated map near a tangent bifurcation for which the Lyapunov exponent is negligible or vanishes. The relevant statistical-mechanical expressions associated with these distributions are derived from a maximum entropy principle with the use of two different constraints, and the resulting duality of entropy indexes is seen to portray physically relevant information. Whereas the value of the index α fixes the distribution's power-law exponent, that for the dual index 2 - α ensures the extensivity of the deformed entropy.

- Dec 2013

The behavior of the electrical conductivity of polymethylmetacrylate (PMMA) thin films was examined with q-Gaussian analysis. To this effect, the time evolutions of Al–PMMA–Al thin films’ transient current data when subjected to an electric field at 295 K, 303 K and 313 K temperatures were considered; and the fitted long tailed q-Gaussian curves of the probability density functions were compared with normal Gaussian distributions. The q-exponential fits are definitely in better agreement with the experimental data than the normal Gaussian distributions. Additionally, it was shown that when the temperature parameter increases, the q value decreases. To the extent that q values can be considered to indicate the degree of correlation in a system, this result confirms that when the q value decreases, the correlation among PMMA atoms declines.

- Dec 2012

A thermodynamic device placed outdoors, or a local ecosystem, is subject to a
variety of different temperatures given by short-tem (daily) and long-term
(seasonal) variations. In the long term a superstatistical description makes
sense, with a suitable distribution function f(beta) of inverse temperature
beta over which ordinary statistical mechanics is averaged. We show that
f(beta) is very different at different geographic locations, and typically
exhibits a double-peak structure for long-term data. For some of our data sets
we also find a systematic drift due to global warming. For a simple
superstatistical model system we show that the response to global warming is
stronger if temperature fluctuations are taken into account.

- Jan 2012

We apply superstatistical techniques to an experimental time series of
measured transient current through a thin Aluminium-PMMA-Aluminium film. We
show that in good approximation the current can be approximated by local
Gaussian processes with fluctuating variance. The marginal density exhibits
`fat tails' and is well modelled by a superstatistical model. Our techniques
can be generally applied to other short time series as well.

- Nov 2011

Recently, we analyzed the temperature dependent q-Gaussian
characteristics of weak chaotic transient currents through thin
Aluminum-Polymethylmethacrylate-Aluminum films under voltages in the
range of ±10V at 22°C temperature.
In this work we investigate the role of q-Gaussian characteristics in
the conductivity mechanism of the Polymetylmethacrylate polymer in order
to understand the electron self-organization criticality in complex
polymers.

- Jul 2007

Nonlinear dynamical properties of sensitively recorded breathing signals (SRBS), which include cardiac induced air flow pulsations so-called pneumocardiogram (PNCG) signals, are investigated, in this methodological study. For this purpose, we assessed the SRBS of laboratory rat. The nonlinear behaviors of SRBS were investigated by the reconstructing phase space, using the autocorrelation function and the false nearest neighbor method. The chaotic SRBS attractors were discussed from the point of view of the cardiopulmonary system. This method can be used to assess the heart performance and respiratory mechanics, and might be useful to design for the physiological studies of cardiorespiratory system in small laboratory animals.