WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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An Overview of Mean Field Theory in Combinatorial Optimization Problems
(Amer inst Physics, 2004) Kasap, S; Trafalis, TB
In the last three decades, there has been significant interest in using mean field theory of statistical physics for combinatorial optimization. This has led to the development of powerful optimization techniques such as neural networks (NNs), simulated annealing (SA), and mean field annealing (MFA). MFA replaces the stochastic nature of SA with a set of deterministic equations named as mean field equations. The mean field equations depend on the energy function of the NNs and are solved at each temperature during the annealing process of SA. MFA advances to the optimal solution in a fundamentally different way than stochastic methods. The use of mean field techniques for the combinatorial optimization problems are reviewed in this study.
Citation - WoS: 1
Citation - Scopus: 1
Fmml: a Feature Model Markup Language
(Amer inst Physics, 2011) Nabdel, Leili; Karatas, Ahmet Serkan; Oguztuzun, Halit; Dogru, Ali
Feature modeling is a common way of representing commonality and variability in Software Product Line Engineering. Alternative notations are available to represent feature models. Compared with graphical notations, text-based notations can be more amenable to automated processing and tool interoperability. In this paper, we propose an XML-based feature modeling language to represent extended feature models with complex relationships.
Citation - WoS: 9
Optical Analysis of Tlins2xse2(1-X) Mixed Crystals
(Amer inst Physics, 2014) Guler, I.
The ellipsometry measurements were carried out on TlInS2xSe2(1-x) mixed crystals in the spectral range of 1.5-6.0 eV at room temperature. The refractive index, extinction coefficient, real and imaginary parts of dielectric function were found as a result of ellipsometric measurements. The energies of interband transitions (critical point energies) of the TlInS2xSe2(1-x) mixed crystals were obtained by means of the second derivative of the real and imaginary parts of dielectric function. The variation of the critical point energies with the isomorphic anion substitution that is sulfur for selenium atoms was established. (C) 2014 AIP Publishing LLC.
Citation - WoS: 13
Citation - Scopus: 12
Magnetohydrodynamic Mixed Convection Flow of Jeffery Fluid With Thermophoresis, Soret and Dufour Effects and Convective Condition
(Amer inst Physics, 2019) Baleanu, Dumitru; Husnine, S. M.; Shabbir, Khurram; Iftikhar, Nazish
The aim of this paper is to investigate heat and mass transfer of Jeffery fluid on a stretching sheet. Moreover, the influence of magnetic field with mixed convection, convective boundary condition and Soret and Dufour effects is also brought into the consideration along with chemical reaction and thermophoresis condition. The problem is modeled by system of partial differential equations and solutions are obtained by optimal homotopy analysis method. In addition, for comprehensive interpretation of the influence of the system parameters results are shown by graphs and tables. (C) 2019 Author(s).
Citation - WoS: 133
Citation - Scopus: 131
New Fractional Derivatives With Non-Singular Kernel Applied To the Burgers Equation
(Amer inst Physics, 2018) Atangana, Abdon; Baleanu, Dumitru; Saad, Khaled M.
In this paper, we extend the model of the Burgers (B) to the new model of time fractional Burgers (TFB) based on Liouville-Caputo (LC), Caputo-Fabrizio (CF), and Mittag-Leffler (ML) fractional time derivatives, respectively. We utilize the Homotopy Analysis Transform Method (HATM) to compute the approximate solutions of TFB using LC, CF, and ML in the Liouville-Caputo sense. We study the convergence analysis of HATM by computing the interval of the convergence, the residual error function (REF), and the average residual error (ARE), respectively. The results are very effective and accurate. Published by AIP Publishing.
Citation - WoS: 114
Citation - Scopus: 108
Numerical Solutions of the Fractional Fisher's Type Equations With Atangana-Baleanu Fractional Derivative by Using Spectral Collocation Methods
(Amer inst Physics, 2019) Khader, M. M.; Gomez-Aguilar, J. F.; Baleanu, Dumitru; Saad, K. M.
The main objective of this paper is to investigate an accurate numerical method for solving a biological fractional model via Atangana-Baleanu fractional derivative. We focused our attention on linear and nonlinear Fisher's equations. We use the spectral collocation method based on the Chebyshev approximations. This method reduced the nonlinear equations to a system of ordinary differential equations by using the properties of Chebyshev polynomials and then solved them by using the finite difference method. This is the first time that this method is used to solve nonlinear equations in Atangana-Baleanu sense. We present the effectiveness and accuracy of the proposed method by computing the absolute error and the residual error functions. The results show that the given procedure is an easy and efficient tool to investigate the solution of nonlinear equations with local and non-local singular kernels.
Fractals Arising From Newton's Method
(Amer inst Physics, 2012) Cilingir, Figen
We consider the dynamics as a special class of rational functions that are obtained from Newton's method when applied to a polynomial equation. Finding solutions of these equations leads to some beautiful images in complex functions. These images represent the basins of attraction of roots of complex functions. We seek the answer "What is the dynamics near the chosen parabolic fixed points?". In addition, we will provide a detailed history of Fractal and Dynamical System Theory.
Citation - WoS: 29
Citation - Scopus: 28
The General Bilinear Techniques for Studying the Propagation of Mixed-Type Periodic and Lump-Type Solutions in a Homogenous-Dispersive Medium
(Amer inst Physics, 2020) Osman, Mohamed S.; Zhu, Wen-Hui; Zhou, Li; Baleanu, Dumitru; Liu, Jian-Guo
This paper aims to construct new mixed-type periodic and lump-type solutions via dependent variable transformation and Hirota's bilinear form (general bilinear techniques). This study considers the (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili equation, which describes the weakly dispersive waves in a homogeneous medium in fluid dynamics. The obtained solutions contain abundant physical structures. Consequently, the dynamical behaviors of these solutions are graphically discussed for different choices of the free parameters through 3D plots.
Citation - WoS: 41
Citation - Scopus: 42
Eley-Rideal and Hot Atom Reactions Between Hydrogen Atoms on Ni(100): Electronic Structure and Quasiclassical Studies
(Amer inst Physics, 2001) Guvenc, ZB; Sha, XW; Jackson, B
The reactions of gas-phase H (or D) atoms with D (or H) atoms adsorbed onto a Ni(100) surface are studied. Electronic structure calculations based on density functional theory are used to examine the interaction of H atoms with the Ni(100) surface, as well as the interactions between two H atoms near the metal surface. A model potential-energy surface based on ideas from effective medium theory is fit to the results of these electronic structure calculations. Quasiclassical trajectory methods are used to simulate the interaction of low energy H and D atom beams with H and D-covered Ni(100) surfaces. It is found that hot-atom processes dominate the formation of molecular hydrogen. The distribution of energy in the product molecules is examined with regard to the various pathways available for reaction. The initial adsorbate coverage is varied and is shown to control the relative amounts of reflection, reaction, sticking, and subsurface penetration. Our results are compared with those from similar studies on Cu(111) and available experimental data for Ni(100). (C) 2001 American Institute of Physics.
Citation - WoS: 26
Citation - Scopus: 31
Asymptotic Solutions of Fractional Interval Differential Equations With Nonsingular Kernel Derivative
(Amer inst Physics, 2019) Ahmadian, A.; Salimi, M.; Ferrara, M.; Baleanu, D.; Salahshour, S.
Realizing the behavior of the solution in the asymptotic situations is essential for repetitive applications in the control theory and modeling of the real-world systems. This study discusses a robust and definitive attitude to find the interval approximate asymptotic solutions of fractional differential equations (FDEs) with the Atangana-Baleanu (A-B) derivative. In fact, such critical tasks require to observe precisely the behavior of the noninterval case at first. In this regard, we initially shed light on the noninterval cases and analyze the behavior of the approximate asymptotic solutions, and then, we introduce the A-B derivative for FDEs under interval arithmetic and develop a new and reliable approximation approach for fractional interval differential equations with the interval A-B derivative to get the interval approximate asymptotic solutions. We exploit Laplace transforms to get the asymptotic approximate solution based on the interval asymptotic A-B fractional derivatives under interval arithmetic. The techniques developed here provide essential tools for finding interval approximation asymptotic solutions under interval fractional derivatives with nonsingular Mittag-Leffler kernels. Two cases arising in the real-world systems are modeled under interval notion and given to interpret the behavior of the interval approximate asymptotic solutions under different conditions as well as to validate this new approach. This study highlights the importance of the asymptotic solutions for FDEs regardless of interval or noninterval parameters. Published under license by AIP Publishing.
Citation - WoS: 15
Citation - Scopus: 18
Fractional Curve Flows and Solitonic Hierarchies in Gravity and Geometric Mechanics
(Amer inst Physics, 2011) Vacaru, Sergiu I.; Baleanu, Dumitru
Methods from the geometry of nonholonomic manifolds and Lagrange-Finsler spaces are applied in fractional calculus with Caputo derivatives and for elaborating models of fractional gravity and fractional Lagrange mechanics. The geometric data for such models are encoded into (fractional) bi-Hamiltonian structures and associated solitonic hierarchies. The constructions yield horizontal/vertical pairs of fractional vector sine-Gordon equations and fractional vector mKdV equations when the hierarchies for corresponding curve fractional flows are described in explicit forms by fractional wave maps and analogs of Schrodinger maps. (C) 2011 American Institute of Physics. [doi:10.1063/1.3589964]
Citation - WoS: 4
Citation - Scopus: 4
Preface: Recent Advances in Fractional Dynamics
(Amer inst Physics, 2016) Baleanu, Dumitru; Li, Changpin; Srivastava, H. M.
This Special Focus Issue contains several recent developments and advances on the subject of Fractional Dynamics and its widespread applications in various areas of the mathematical, physical, and engineering sciences. Published by AIP Publishing.
Citation - WoS: 237
Citation - Scopus: 248
New Variable-Order Fractional Chaotic Systems for Fast Image Encryption
(Amer inst Physics, 2019) Deng, Zhen-Guo; Baleanu, Dumitru; Zeng, De-Qiang; Wu, Guo-Cheng
New variable-order fractional chaotic systems are proposed in this paper. A concept of short memory is introduced where the initial point in the Caputo derivative is varied. The fractional order is defined by the use of a piecewise constant function which leads to rich chaotic dynamics. The predictor-corrector method is adopted, and numerical solutions of fractional delay equations are obtained. Then, this concept is extended to fractional difference equations, and generalized chaotic behaviors are discussed numerically. Finally, the new fractional chaotic models are applied to block image encryption and each block has a different fractional order. The new chaotic system improves security of the image encryption and saves the encryption time greatly. Published under license by AIP Publishing.
Citation - WoS: 172
Citation - Scopus: 183
A New and Efficient Numerical Method for the Fractional Modeling and Optimal Control of Diabetes and Tuberculosis Co-Existence
(Amer inst Physics, 2019) Ghanbari, Behzad; Baleanu, Dumitru; Jajarmi, Amin
The main objective of this research is to investigate a new fractional mathematical model involving a nonsingular derivative operator to discuss the clinical implications of diabetes and tuberculosis coexistence. The new model involves two distinct populations, diabetics and nondiabetics, while each of them consists of seven tuberculosis states: susceptible, fast and slow latent, actively tuberculosis infection, recovered, fast latent after reinfection, and drug-resistant. The fractional operator is also considered a recently introduced one with Mittag-Leffler nonsingular kernel. The basic properties of the new model including non-negative and bounded solution, invariant region, and equilibrium points are discussed thoroughly. To solve and simulate the proposed model, a new and efficient numerical method is established based on the product-integration rule. Numerical simulations are presented, and some discussions are given from the mathematical and biological viewpoints. Next, an optimal control problem is defined for the new model by introducing four control variables reducing the number of infected individuals. For the control problem, the necessary and sufficient conditions are derived and numerical simulations are given to verify the theoretical analysis.
Citation - WoS: 304
Citation - Scopus: 329
A New Fractional Model and Optimal Control of a Tumor-Immune Surveillance With Non-Singular Derivative Operator
(Amer inst Physics, 2019) Jajarmi, A.; Sajjadi, S. S.; Mozyrska, D.; Baleanu, D.
In this paper, we present a new fractional-order mathematical model for a tumor-immune surveillance mechanism. We analyze the interactions between various tumor cell populations and immune system via a system of fractional differential equations (FDEs). An efficient numerical procedure is suggested to solve these FDEs by considering singular and nonsingular derivative operators. An optimal control strategy for investigating the effect of chemotherapy treatment on the proposed fractional model is also provided. Simulation results show that the new presented model based on the fractional operator with Mittag-Leffler kernel represents various asymptomatic behaviors that tracks the real data more accurately than the other fractional- and integer-order models. Numerical simulations also verify the efficiency of the proposed optimal control strategy and show that the growth of the naive tumor cell population is successfully declined. Published under license by AIP Publishing.
Oscillation Criteria for Second Order Impulsive Delay Differential Equation
(Amer inst Physics, 2004) Taş, Kenan; Alzabut, J; Zafert, A; Baleanu, Dumitru; Matematik
A necessary and sufficient condition is obtained for oscillation of bounded solutions of second order impulsive delay differential equations of the form (r(t)x(t))'+p(t)f(x(i(t)))=0, t not equal theta Delta(r(theta(i))x'(theta(i)))+b(i)g(x(sigma(theta(i)))) = 0, i is an element of Z, Deltax(theta(i)) = 0. An example is also inserted to illustrate the effect of impulses on the oscillatory behavior of the solutions.
Compatibility of Non-Generic Supersymmetries and Geometric Duality for a Subclass of Generalized Pp-Wave Metrics
(Amer inst Physics, 2004) Baleanu, D; Baleanu, Dumitru; Baskal, S; Matematik
Spinning point particle theories accommodate non-generic supercharges in connection with the existence of Killing-Yano tensors. Killing-Yano tensors of order two and three and their corresponding Killing tensors are found for a subclass of generalized pp-wave metrics. These metrics include the pp-wave itself, its possible generalizations and the Siklos metric which is conformal to that. The compatibility between geometric duality and non-generic symmetries is discussed within the context of the metric solutions. It is found that some of the metric solutions admit anti-de Sitter spacetimes while some are found to be purely radiative.
Citation - WoS: 2
Citation - Scopus: 2
Comment on "maxwell's Equations and Electromagnetic Lagrangian Density in Fractional Form" [J. Math. Phys. 53, 033505 ( 2012)]
(Amer inst Physics, 2014) Al-Jamel, A.; Widyan, H.; Baleanu, D.; Rabei, Eqab M.
In a recent paper, Jaradat et al. [J. Math. Phys. 53, 033505 (2012)] have presented the fractional form of the electromagnetic Lagrangian density within the Riemann-Liouville fractional derivative. They claimed that the Agrawal procedure [O. P. Agrawal, J. Math. Anal. Appl. 272, 368 (2002)] is used to obtain Maxwell's equations in the fractional form, and the Hamilton's equations of motion together with the conserved quantities obtained from fractional Noether's theorem are reported. In this comment, we draw the attention that there are some serious steps of the procedure used in their work are not applicable even though their final results are correct. Their work should have been done based on a formulation as reported by Baleanu and Muslih [Phys. Scr. 72, 119 (2005)]. (C) 2014 AIP Publishing LLC.
Reproducing Kernel Method for Strongly Non-Linear Equation
(Amer inst Physics, 2018) Akgul, Esra Karatas; Baleanu, Dumitru; Akgul, Ali
In this paper, we search the efficiency of the reproducing kernel method (RKM) in solving the strongly nonlinear equation. An example is presented to prove the power of the technique. The results attained from the technique are compared with the other techniques. Results prove that the presented technique is very effective.
Citation - WoS: 46
Kinetic Model for Eley-Rideal and Hot Atom Reactions Between H Atoms on Metal Surfaces
(Amer inst Physics, 2002) Jackson, B; Sha, XW; Guvenc, ZB
A simple kinetic model is used to describe the interaction of H and D atomic beams with H- and D-covered metal surfaces. The atoms incident from the gas phase can have a direct Eley-Rideal reaction with an adsorbate, reflect, penetrate into the bulk, knock an adsorbate out of its binding site, or trap to form a hot atom. These hot mobile atoms can go on to react with other adsorbates, or eventually relax and stick. A coarse-graining approach, which takes advantage of the large difference between the time scales for the kinetics experiments and the reaction dynamics, allows us to derive relatively simple kinetic equations for reaction rates and coverages. The approach is similar to a kinetic random walk model developed by Kuppers and co-workers [J. Phys. Chem. 109, 4071 (1998)] except that our equations can be used to derive analytical expressions for saturation coverages, rates, and yields. The model is applied to the case of H atom reactions on a Ni(100) surface, and a detailed comparison is made with both experimental and quasiclassical studies. (C) 2002 American Institute of Physics.

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