Tırnaklı, Uğur
Loading...
Profile URL
Name Variants
Tirnakli, U
Tirnakli, U.
TIRNAKLI, Ugur
Tirnakli, Ugur
Tirnakli, U.
TIRNAKLI, Ugur
Tirnakli, Ugur
Job Title
Email Address
ugur.tirnakli@ieu.edu.tr
Main Affiliation
02.03. Physics
Status
Current Staff
Website
ORCID ID
Scopus Author ID
Turkish CoHE Profile ID
Google Scholar ID
WoS Researcher ID
Sustainable Development Goals
8
DECENT WORK AND ECONOMIC GROWTH
0
Research Products
9
INDUSTRY, INNOVATION AND INFRASTRUCTURE
0
Research Products
10
REDUCED INEQUALITIES
0
Research Products
17
PARTNERSHIPS FOR THE GOALS
0
Research Products
12
RESPONSIBLE CONSUMPTION AND PRODUCTION
0
Research Products
7
AFFORDABLE AND CLEAN ENERGY
0
Research Products
1
NO POVERTY
0
Research Products
5
GENDER EQUALITY
0
Research Products
13
CLIMATE ACTION
0
Research Products
4
QUALITY EDUCATION
0
Research Products
14
LIFE BELOW WATER
0
Research Products
2
ZERO HUNGER
0
Research Products
15
LIFE ON LAND
0
Research Products
16
PEACE, JUSTICE AND STRONG INSTITUTIONS
0
Research Products
6
CLEAN WATER AND SANITATION
0
Research Products
3
GOOD HEALTH AND WELL-BEING
1
Research Products
11
SUSTAINABLE CITIES AND COMMUNITIES
0
Research Products
Documents
83
Citations
1665
h-index
24
Documents
83
Citations
1508
Scholarly Output
11
Articles
10
Views / Downloads
18/30
Supervised MSc Theses
0
Supervised PhD Theses
0
WoS Citation Count
26
Scopus Citation Count
29
WoS h-index
4
Scopus h-index
4
Patents
0
Projects
3
WoS Citations per Publication
2.36
Scopus Citations per Publication
2.64
Open Access Source
8
Supervised Theses
0
| Journal | Count |
|---|---|
| Entropy | 3 |
| Physical Review E | 2 |
| Physica A-Statistical Mechanics and Its Applications | 1 |
| Physica d-nonlinear phenomena | 1 |
| Physica D-Nonlinear Phenomena | 1 |
Current Page: 1 / 2
Scopus Quartile Distribution
Competency Cloud
11 results
Scholarly Output Search Results
Now showing 1 - 10 of 11
Review Article Citation - WoS: 6Citation - Scopus: 8Nonextensive Footprints in Dissipative and Conservative Dynamical Systems(Mdpi, 2023) Rodriguez, Antonio; Pluchino, Alessandro; Tirnakli, Ugur; Rapisarda, Andrea; Tsallis, ConstantinoDespite its centennial successes in describing physical systems at thermal equilibrium, Boltzmann-Gibbs (BG) statistical mechanics have exhibited, in the last several decades, several flaws in addressing out-of-equilibrium dynamics of many nonlinear complex systems. In such circumstances, it has been shown that an appropriate generalization of the BG theory, known as nonextensive statistical mechanics and based on nonadditive entropies, is able to satisfactorily handle wide classes of anomalous emerging features and violations of standard equilibrium prescriptions, such as ergodicity, mixing, breakdown of the symmetry of homogeneous occupancy of phase space, and related features. In the present study, we review various important results of nonextensive statistical mechanics for dissipative and conservative dynamical systems. In particular, we discuss applications to both discrete-time systems with a few degrees of freedom and continuous-time ones with many degrees of freedom, as well as to asymptotically scale-free networks and systems with diverse dimensionalities and ranges of interactions, of either classical or quantum nature.Article Citation - WoS: 5Citation - Scopus: 5Multiple Waves of Covid-19: a Pathway Model Approach(Springer, 2023) Vasconcelos, Giovani L.; Pessoa, Nathan L.; Silva, Natan B.; Macedo, Antonio M. S.; Brum, Arthur A.; Ospina, Raydonal; Tirnakli, UgurA generalized pathway model, with time-dependent parameters, is applied to describe the mortality curves of the COVID-19 disease for several countries that exhibit multiple waves of infections. The pathway approach adopted here is formulated explicitly in time, in the sense that the model's growth rate for the number of deaths or infections is written as an explicit function of time, rather than in terms of the cumulative quantity itself. This allows for a direct fit of the model to daily data (new deaths or new cases) without the need of any integration. The model is applied to COVID-19 mortality curves for ten selected countries and found to be in very good agreement with the data for all cases considered. From the fitted theoretical curves for a given location, relevant epidemiological information can be extracted, such as the starting and peak dates for each successive wave. It is argued that obtaining reliable estimates for such characteristic points is important for studying the effectiveness of interventions and the possible negative impact of their relaxation, as it allows for a direct comparison of the time of adoption/relaxation of control measures with the peaks and troughs of the epidemic curve.Article Citation - WoS: 3Citation - Scopus: 3First-Principle Validation of Fourier's Law in D=1, 2, 3 Classical Systems(Elsevier, 2023) Tsallis, Constantino; Lima, Henrique Santos; Tırnaklı, Uğur; Eroğlu, DenizWe numerically study the thermal transport in the classical inertial nearest-neighbor XY ferromagnet in d = 1, 2, 3, the total number of sites being given by N = Ld, where L is the linear size of the system. For the thermal conductance sigma, we obtain sigma(T, L)L delta(d)= A(d) e-B(d) [L gamma (d)T ]eta(d) (with ez q(d) q equivalent to [1+(1-q)z]1/(1-q); ez1 = ez; A(d) > 0; B(d) > 0; q(d) > 1; eta(d) > 2; delta >= 0; gamma(d) > 0), for all values of L gamma(d)T for d = 1, 2, 3. In the L -> infinity limit, we have sigma proportional to 1/L rho sigma(d) with rho sigma(d) = delta(d)+gamma(d)eta(d)/[q(d)-1]. The material conductivity is given by kappa = sigma Ld proportional to 1/L rho kappa(d) (L -> infinity) with rho kappa(d) = rho sigma(d) - d. Our numerical results are consistent with 'conspiratory' d-dependences of (q, eta, delta, gamma), which comply with normal thermal conductivity (Fourier law) for all dimensions.(c) 2023 Published by Elsevier B.V.Article Citation - WoS: 2Citation - Scopus: 2Energy Distributions of Frenkel-Kontorova Atomic Chains: Transition From Conservative To Dissipative Dynamics(Elsevier, 2024) Afsar, Özgür; Tırnaklı, UğurWe investigate energy distributions of Frenkel-Kontorova-type atomic chains generated from large number of independent identically distributed (iid) random initial atomic positionings under two cases. In the first case, atoms at the free-end chains without dissipation (conservative case) are only coupled to one other atom, whereas each atom inside the bulk is coupled to its 2 nearest neighbours. Here, atoms located at the chain are all at the same type. Such kind of systems can be modelled by conservative standard map. We show that, when the coupling is non-linear (which leads chaotic arrangement of the atoms) for energy distribution, the Boltzmann-Gibbs statistical mechanics is constructed, namely, exponential form emerges as Boltzmann factor P(E)proportional to e(-beta E). However, when the coupling is linear (which leads linear arrangement of the atoms) the Boltzmann-Gibbs statistical mechanics fails and the exponential distribution is replaced by a q-exponential form, which generalizes the Boltzmann factor as P(E)proportional to eq(-beta)q(E)=[1-(1-q)beta E-q](1/(1-q)). We also show for each type of atom localization with N number of atoms, beta (or beta(q)) values can be given as a function of 1/N. In the second case, although the couplings among the atoms are exactly the same as the previous case, atoms located at the chain are now considered as being at different types. We show that, for energy distribution of such linear chains, each of the distributions corresponding to different dissipation parameters (gamma) are in the q-exponential form. Moreover, we numerically verify that beta(q )values can be given as a linear function of 1/& sum;(N)(n=1)(1-gamma)((n-2)). On the other hand, although energy distributions of the chaotic chains for different dissipation parameters are in exponential form, a linear scaling between beta and gamma values cannot be obtained. This scaling is possible if the energies of the chains are scaled with 1/(1-gamma)(-N). For both cases, clear data collapses among distributions are evident.Editorial Nonadditive Entropies and Nonextensive Statistical Mechanics(Mdpi, 2025) Tirnakli, Ugur[No abstract available]Article Citation - WoS: 4Citation - Scopus: 4Statistical Mechanical Characterization of Billiard Systems(Elsevier Ltd, 2024) Cetin, K.; Tırnaklı, Uğur; Oliveira, D.F.M.; Leonel, E.D.Area-preserving maps play an important role in diverse fields as they are widely used for modeling complex systems. In addition, these maps provide rich observations by presenting stable orbits and chaotic behavior separately or together in the phase space depending on the control parameter. In recent years, several studies on these maps, drawing inspiration from the phase space dynamics, have shown that nonextensive statistical mechanics provides appropriate instruments to characterize these systems. In this study, we perform a rigorous numerical analysis to delve into the statistical mechanical properties of a billiard system. Our primary goal is to confirm the presence of a q-Gaussian distribution, with an estimated q value of approximately 1.935. We accomplish this by examining the probability distribution of the cumulative sum of system iterates, focusing specifically on initial conditions within the stability islands. Our findings align seamlessly with the latest research in this field. Furthermore, we show that a multi-component probability distribution containing both Gaussian and q-Gaussians describes the entire system for some parameter regions where the phase space consists of stability islands together with the chaotic sea. © 2023 Elsevier LtdArticle Central Limit Behavior at the Edge of Chaos in the Z-Logistic Map(American Physical Society, 2025) Saberi, Abbas Ali; Tirnakli, Ugur; Tsallis, ConstantinoWe focus on the Feigenbaum-Coullet-Tresser point of the dissipative one-dimensional z-logistic map x(t+1) = 1-a|x(t )|(z) (z 1). We show that sums of iterates converge to q-Gaussian distributions P-q(y) = P-q(0) exp(q)(-beta(q)y(2)) = P-q(0 )[1 + (q-1)beta(q) y(2)](1/(1-q))(q >= 1; beta(q) > 0), which optimize the nonadditive entropic functional Sq under simple constraints. We propose and justify heuristically a closed-form prediction for the entropic index, q(z) = 1 + 2/(z + 1), and validate it numerically via data collapse for typical z values. The formula captures how the limiting law depends on the nonlinearity order and implies finite variance for z > 2 and divergent variance for 1 <= z <= 2. These results extend edge-of-chaos central limit behavior beyond the standard (z = 2) case and provide a simple predictive law for unimodal maps with varying maximum order.Article Fourier's Law Breakdown for the Planar-Rotor Chain With Long-Range Interactions(Elsevier, 2026) Lima, Henrique Santos; Tsallis, Constantino; Eroglu, Deniz; Tirnakli, UgurFourier's law, which linearly relates heat flux to the negative gradient of temperature, is a fundamental principle in thermal physics and widely applied across materials science and engineering. However, its validity in low-dimensional systems with long-range interactions remains only partially understood. We investigate here the thermal transport along a onedimensional chain of classical planar rotators with algebraically decaying interactions 1/ with distance ( >= 0), known as the inertial a-XY model. Using nonequilibrium simulations with thermal reservoirs at the boundaries, we numerically study the thermal conductance as a function of system sizea, temperature , and . We find that the results obey a universal scaling law characterized by a stretched-exponential function with -dependent parameters. Notably, a threshold at approximate to 2 separates two regimes: for >= , Fourier's law holds with size-independent conductivity = , while for < , anomalous transport is observed, corroborating (with higher precision) the results reported in Phys.Rev.E94,042117(2016). These findings provide a quantitative framework for understanding the breakdown of Fourier's law in systems with long-range interactions. The simulation is carried out by assuming the equations of motion, which include Langevin heat baths applied to the first and last particles, and are integrated using the Velocity Verlet algorithm. The conductance is calculated from the connection between Lagrangian heat flux and heat equation for typical values of (, , ). For large , the results can be collapsed into an universal -stretched exponential form, namely proportional to -() , where = [1 + (1-)]1/(1-). The parameters (, , ,) are -dependent, and is the index of the -stretched exponential. This form is achievable due to the ratio /( - 1) being almost constant with respect to the lattice size. These findings provide significant insights into heat conduction mechanisms in systems with long-range interactions.Article Citation - WoS: 1Citation - Scopus: 1Necessary Condition of Self-Organisation in Nonextensive Open Systems(Mdpi, 2023) Afşar, Ozgur; Tırnaklı, UğurIn this paper, we focus on evolution from an equilibrium state in a power law form by means of q-exponentials to an arbitrary one. Introducing new q-Gibbsian equalities as the necessary condition of self-organization in nonextensive open systems, we theoretically show how to derive the connections between q-renormalized entropies (Delta(S) over tilde (q)) and q-relative entropies (KLq) in both Bregman and Csiszar forms after we clearly explain the connection between renormalized entropy by Klimantovich and relative entropy by Kullback-Leibler without using any predefined effective Hamiltonian. This function, in our treatment, spontaneously comes directly from the calculations. We also explain the difference between using ordinary and normalized q-expectations in mean energy calculations of the states. To verify the results numerically, we use a toy model of complexity, namely the logistic map defined as Xt +1 = 1 - aX(t)(2), where a is an element of [0, 2] is the map parameter. We measure the level of self-organization using two distinct forms of the q-renormalized entropy through period doublings and chaotic band mergings of the map as the number of periods/chaotic-bands increase/decrease. We associate the behaviour of the q-renormalized entropies with the emergence/disappearance of complex structures in the phase space as the control parameter of the map changes. Similar to Shiner-Davison-Landsberg (SDL) complexity, we categorize the tendencies of the q-renormalized entropies for the evaluation of the map for the whole control parameter space. Moreover, we show that any evolution between two states possesses a unique q = q* value (not a range for q values) for which the q-Gibbsian equalities hold and the values are the same for the Bregmann and Csiszar forms. Interestingly, if the evolution is from a = 0 to a = a(c) similar or equal to 1.4011, this unique q* value is found to be q* similar or equal to 0.2445, which is the same value of qsensitivity given in the literature.Article Citation - WoS: 1Citation - Scopus: 2The Statistics of Q-Statistics(MDPI, 2024) Eroglu, Deniz; Boghosian, Bruce M.; Borges, Ernesto P.; Tirnakli, UgurAlmost two decades ago, Ernesto P. Borges and Bruce M. Boghosian embarked on the intricate task of composing a manuscript to honor the profound contributions of Constantino Tsallis to the realm of statistical physics, coupled with a concise exploration of q-Statistics. Fast-forward to Constantino Tsallis' illustrious 80th birthday celebration in 2023, where Deniz Eroglu and Ugur Tirnakli delved into Constantino's collaborative network, injecting renewed vitality into the project. With hearts brimming with appreciation for Tsallis' enduring inspiration, Eroglu, Boghosian, Borges, and Tirnakli proudly present this meticulously crafted manuscript as a token of their gratitude.
