WoS İndeksli Yayınlar Koleksiyonu

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

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A density functional study of bare and hydrogenated platinum clusters
(Elsevier, 2006) Sebetci, Ali; 20965
We perform density functional theory calculations using Gaussian atomic-orbital methods within the generalized gradient approximation for the exchange and correlation to study the interactions in the bare and hydrogenated platinum clusters. The minimum-energy structures, binding energies, relative stabilities. vibrational frequencies and the highest occupied and lowest unoccupied molecular-orbital gaps of PtnHm (n = 1-5, m = 0-2) clusters are calculated and compared with previously studied pure platinum and hydrogenated platinum clusters. We investigate any magic behavior in hydrogenated platinum clusters and find that Pt4H2 is snore stable than its neighboring sizes. The lowest energy structure of Pt-4 is found to be a distorted tetrahedron and that of Pt-5 found to be a bridge site capped tetrahedron which is a new global minimum for Pt-5 cluster. The successive addition of H atoms to Pt-n clusters leads to an oscillatory change in the magnetic moment of Pt-3-Pt-5 clusters. (c) 2006 Elsevier B.V. All rights reserved.
A Freely Damped Oscillating Fractional Dynamic System Modeled By Fractional Euler-Lagrange Equations
(Sage Publications Ltd, 2018) Agila, Adel; Baleanu, Dumitru; Baleanu, Dumitru; Eid, Rajeh; Irfanoglu, Bulent; 56389
The behaviors of some vibrating dynamic systems cannot be modeled precisely by means of integer representation models. Fractional representation looks like it is more accurate to model such systems. In this study, the fractional Euler-Lagrange equations model is introduced to model a fractional damped oscillating system. In this model, the fractional inertia force and the fractional damping force are proportional to the fractional derivative of the displacement. The fractional derivative orders in both forces are considered to be variable fractional orders. A numerical approximation technique is utilized to obtain the system responses. The discretization of the Coimbra fractional derivative and the finite difference technique are used to accomplish this approximation. The response of the system is verified by a comparison to a classical integer representation and is obtained based on different values of system parameters.
A Gronwall inequality via the generalized proportional fractional derivative with applications
(Springer, 2019) Alzabut, Jehad; Alzabut, Jehad; Abdeljawad, Thabet; Abdeljawad, Thabet; Jarad, Fahd; Jarad, Fahd; Sudsutad, Weerawat; 234808
In this paper, we provide a new version for the Gronwall inequality in the frame of the generalized proportional fractional derivative. Prior to the main results, we introduce the generalized proportional fractional derivative and expose some of its features. As an application, we accommodate the newly defined derivative to prove the uniqueness and obtain a bound in terms of Mittag-Leffler function for the solutions of a nonlinear delay proportional fractional system. An example is presented to demonstrate the applicability of the theory.
A Hamiltonian formulation and a direct numerical scheme for fractional optimal control problems
(Sage Publications Ltd, 2007) Agrawal, Om P.; Baleanu, Dumitru; Baleanu, Dumitru; 56389
This paper deals with a direct numerical technique for Fractional Optimal Control Problems (FOCPs). In this paper, we formulate the FOCPs in terms of Riemann-Liouville Fractional Derivatives (RLFDs). It is demonstrated that right RLFDs automatically arise in the formulation even when the dynamics of the system is described using left RLFDs only. For numerical computation, the FDs are approximated using the Grunwald-Letnikov definition. This leads to a set of algebraic equations that can be solved using numerical techniques. Two examples, one time-invariant and the other time-variant, are considered to demonstrate the effectiveness of the formulation. Results show that as the order of the derivative approaches an integer value, these formulations lead to solutions for integer order system. The approach requires dividing of the entire time domain into several sub-domains. Further, as the sizes of the sub-domains are reduced, the solutions converge to unique solutions. However, the convergence is slow. A scheme that improves the convergence rate will be considered in a future paper. Other issues to be considered in the future include formulations using other types of derivatives, nonlinear and stochastic fractional optimal controls, existence and uniqueness of the solutions, and the error analysis.
A Maid Came Free: From Sighting to Citing in Tracy Chevalier’s Girl with a Pearl Earring
(Routledge Journals, Taylor & Francis Ltd, 2018) Uzundemir, Ozlem; Uzundemir, Özlem; 49324
Tracy Chevalier's ekphrastic novel Girl with a Pearl Earring explores the relationship between literature and art, as it narrates Jan Vermeer's paintings from the perspective of the story's narrator, Griet, who works as a maid in the Vermeers's house. In her fictional account, Griet gradually becomes the painter's assistant as well as his model, and subverts the gender issues in ekphrasis; the silent and gazed-upon female image in the eponymous painting gains a voice to critique Vermeer's art. This article will deal with Griet's transformation from a young maid into an art critic with respect to the issues in painting, namely colour, light and realistic representation, as well as the paragone between the viewing subject and the viewed object in ekphrasis.
A Mechanical Model Based on Conformal Strain Energy and Its Application to Bending and Buckling of Nanobeam Structures
(Asme, 2019) Rahimi, Zaher; Baleanu, Dumitru; Sumelka, Wojciech; Baleanu, Dumitru; 56389
In the present work, a nonlocal model based on the conformal strain energy, utilizing the conformable derivative definition, has been obtained. The model has two additional free parameters compared to the classical (local) mechanical formulations. The first one specifies the amount of the integer and the noninteger gradient of strain in the strain energy relation, and the second one controls the order of the strain derivatives in the conformable energy relation. The obtained governing (nonlinear) equation has been solved by the Galerkin method and the effects of both free parameters have been shown. As a case study, the bending and buckling of nanobeam structures has been studied.
A New Analysis of the Fornberg-Whitham Equation Pertaining to A Fractional Derivative With Mittag-Leffler-Type Kernel
(Springer Heidelberg, 2018) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Baleanu, Dumitru; 56389
The mathematical model of breaking of non-linear dispersive water waves with memory effect is very important in mathematical physics. In the present article, we examine a novel fractional extension of the non-linear Fornberg-Whitham equation occurring in wave breaking. We consider the most recent theory of differentiation involving the non-singular kernel based on the extended Mittag-Leffler-type function to modify the Fornberg-Whitham equation. We examine the existence of the solution of the non-linear Fornberg-Whitham equation of fractional order. Further, we show the uniqueness of the solution. We obtain the numerical solution of the new arbitrary order model of the non-linear Fornberg-Whitham equation with the aid of the Laplace decomposition technique. The numerical outcomes are displayed in the form of graphs and tables. The results indicate that the Laplace decomposition algorithm is a very user-friendly and reliable scheme for handling such type of non-linear problems of fractional order.
A new and efficient numerical method for the fractional modeling and optimal control of diabetes and tuberculosis co-existence
(Amer inst Physics, 2019) Jajarmi, Amin; Baleanu, Dumitru; Ghanbari, Behzad; Baleanu, Dumitru; 56389
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.
A New Class of 2Q-Point Nonstationary Subdivision Schemes and Their Applications
(Mdpi, 2019) Ghaffar, Abdul; Baleanu, Dumitru; Bari, Mehwish; Ullah, Zafar; Iqbal, Mudassar; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; 56389
The main objective of this study is to introduce a new class of 2q-point approximating nonstationary subdivision schemes (ANSSs) by applying Lagrange-like interpolant. The theory of asymptotic equivalence is applied to find the continuity of the ANSSs. These schemes can be nicely generalized to contain local shape parameters that allow the user to locally adjust the shape of the limit curve/surface. Moreover, many existing approximating stationary subdivision schemes (ASSSs) can be obtained as nonstationary counterparts of the proposed ANSSs.
A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator
(Amer inst Physics, 2019) Baleanu, D.; Baleanu, Dumitru; Jajarmi, A.; Sajjadi, S. S.; Mozyrska, D.; 56389
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.
A novel numerical approach for a nonlinear fractional dynamical model of interpersonal and romantic relationships
(Mdpi, 2017) Singh, Jagdev; Baleanu, Dumitru; Kumar, Devendra; Al Qurashi, Maysaa; Baleanu, Dumitru
In this paper, we propose a new numerical algorithm, namely q-homotopy analysis Sumudu transform method (q-HASTM), to obtain the approximate solution for the nonlinear fractional dynamical model of interpersonal and romantic relationships. The suggested algorithm examines the dynamics of love affairs between couples. The q-HASTM is a creative combination of Sumudu transform technique, q-homotopy analysis method and homotopy polynomials that makes the calculation very easy. To compare the results obtained by using q-HASTM, we solve the same nonlinear problem by Adomian's decomposition method (ADM). The convergence of the q-HASTM series solution for the model is adapted and controlled by auxiliary parameter h and asymptotic parameter n. The numerical results are demonstrated graphically and in tabular form. The result obtained by employing the proposed scheme reveals that the approach is very accurate, effective, flexible, simple to apply and computationally very nice.
A zero-crossing technique for the multidetermination of thiamine HCl and pyridoxine HCl in their mixture by using one-dimensional wavelet transform
(Elsevier, 2003) Dinç, E; Baleanu, Dumitru; Baleanu, D; 56389
A new zero-crossing technique based on one-dimensional wavelet transform (WT) was developed and applied on a commercial vitamin product and binary mixtures containing thiamine HCl and pyridoxine HCl in the presence of the interference of the analysed signals. We selected from the data of the UV-Vis absorption spectra a signal consisting of 1150 points corresponding to the concentration range 8-32 mg/ml for both vitamins and we subjected it to one-dimensional continuous WT Mexican (MEXICAN) and Meyer (MEYER). Since the peaks of the transformed signals were bigger than original ones a zero crossing technique was applied to obtain the regression equations. The validity of Beer-Lambert law was assumed for the transformed signals. An appropriate scale setting was choosing to obtain an alternative calibration for each method. The basic concepts about wavelet method were briefly explained and MATLAB 6.5 software was used for one-dimensional wavelet analysis, The obtained results were successfully compared among each other and with those obtained by other literature methods. The developed method is rapid, easy to apply. not expensive and suitable for analysing of the overlapping signals of compounds in their mixtures without any chemical pre-treatment. (C) 2003 Elsevier Science B.V. All rights reserved.
Ammonia removal from anaerobically digested dairy manure by struvite precipitation
(Elsevier Sci Ltd, 2005) Uludag-Demirer, S; Demirer, GN; Chen, S
Ammonia is one of the most important contaminants impairing the quality of water resources. When this is considered along with the fact that the global demand for nitrogenous fertilizers is in constant rise, the need for recovery as well as removal of nitrogen is well justified. Crystallization of N and P in the form of struvite (MgNH4PO4 center dot 6H(2)O), which is a slow releasing and valuable fertilizer, is one possible technique for this purpose. This study investigated the removal of NR4+ through struvite precipitation from the effluents of one- (R1) and two-phase (R2) anaerobic reactors digesting dairy manure. To force the formation of struvite in the anaerobic reactor effluents, Ma(2+) ion was added by using both Mg(OH)(2) and MgCl2 center dot 6H(2)O. To prevent the effect of different total phosphorus (TP) concentration in the effluents of RI and R2, as well as to not limit the formation of struvite, an excess amount Of PO43- (0.14 M) was added in the form of NaHPO4. Different stoichiometric Mg2+:NH4+:PO43- ratios were tested to determine the required Mg2+ concentrations for maximum NH4+ removal by keeping NH4+:PO43- ratio constant for the effluents of reactors RI and R2. The results revealed that very high NH4+ removal efficiencies (above 95%) were possible by adding Mg 21 ions higher than 0.06 M concentration in the effluents from reactors RI and R2. It was also observed that the initial pH adjustment to 8.50 using NaOH did not result in any significant increase in the removal of NH4+ and the removal of NH4+ in the reactors treated with MgCl2 center dot 6H(2)O was higher than those treated with Mg(OH)(2) for the same Mg2+ concentration. (c) 2005 Published by Elsevier Ltd.
An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph Equations
(Mdpi, 2019) Khan, Hassan; Baleanu, Dumitru; Shah, Rasool; Kumam, Poom; Baleanu, Dumitru; Arif, Muhammad; 56389
In the present article, fractional-order telegraph equations are solved by using the Laplace-Adomian decomposition method. The Caputo operator is used to define the fractional derivative. Series form solutions are obtained for fractional-order telegraph equations by using the proposed method. Some numerical examples are presented to understand the procedure of the Laplace-Adomian decomposition method. As the Laplace-Adomian decomposition procedure has shown the least volume of calculations and high rate of convergence compared to other analytical techniques, the Laplace-Adomian decomposition method is considered to be one of the best analytical techniques for solving fractional-order, non-linear partial differential equationsparticularly the fractional-order telegraph equation.
An Efficient Computational Technique for Fractal Vehicular Traffic Flow
(Mdpi, 2018) Kumar, Devendra; Baleanu, Dumitru; Tchier, Fairouz; Singh, Jagdev; Baleanu, Dumitru; 56389
In this work, we examine a fractal vehicular traffic flow problem. The partial differential equations describing a fractal vehicular traffic flow are solved with the aid of the local fractional homotopy perturbation Sumudu transform scheme and the local fractional reduced differential transform method. Some illustrative examples are taken to describe the success of the suggested techniques. The results derived with the aid of the suggested schemes reveal that the present schemes are very efficient for obtaining the non-differentiable solution to fractal vehicular traffic flow problem.
An Efficient Nonstandard Finite Difference Scheme for a Class of Fractional Chaotic Systems
(Asme, 2018) Hajipour, Mojtaba; Baleanu, Dumitru; Jajarmi, Amin; Baleanu, Dumitru; 56389
In this paper, we formulate a new nonstandard finite difference (NSFD) scheme to study the dynamic treatments of a class of fractional chaotic systems. To design the new proposed scheme, an appropriate nonlocal framework is applied for the discretization of nonlinear terms. This method is easy to implement and preserves some important physical properties of the considered model, e.g., fixed points and their stability. Additionally, this scheme is explicit and inexpensive to solve fractional differential equations (FDEs). From a practical point of view, the stability analysis and chaotic behavior of three novel fractional systems are provided by the proposed approach. Numerical simulations and comparative results confirm that this scheme is also successful for the fractional chaotic systems with delay arguments.
An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov-Petrovskii-Piskunov Equation
(Mdpi, 2019) Veeresha, Pundikala; Baleanu, Dumitru; Prakasha, Doddabhadrappla Gowda; Baleanu, Dumitru; 56389
The q-homotopy analysis transform method (q-HATM) is employed to find the solution for the fractional Kolmogorov-Petrovskii-Piskunov (FKPP) equation in the present frame work. To ensure the applicability and efficiency of the proposed algorithm, we consider three distinct initial conditions with two of them having Jacobi elliptic functions. The numerical simulations have been conducted to verify that the proposed scheme is reliable and accurate. Moreover, the uniqueness and convergence analysis for the projected problem is also presented. The obtained results elucidate that the proposed technique is easy to implement and very effective to analyze the complex problems arising in science and technology.
Analysis and simplified modelling of simulation of tests for medium-duty truck collision with twin anti-ram bollards
(Taylor & Francis Ltd, 2020) Akyurek, Turgut; Akyürek, Turgut; 48511
An actual test of medium-duty truck collision with twin anti-ram bollards of steel tube is analysed and simulated with different mass-spring-damper models to study bollard design requirements. Test data is obtained from test report of a medium-duty truck crashed into two fixed twin bollards at speed 78.3 km/h. Maximum impact load and impact height at that time is important in the analysis. Bollard height should be close to or larger than the vehicle's centre of gravity height to avoid climbing of the truck on the bollard. However, increasing impact height yields also increase in failure risk of bollard. Foundation is also critical in success of the bollard in successfully stopping the vehicle. The bollard should be fixed to the frame embedded in the concrete foundation so that the deformation in concrete be minimised. The bollard should be so stiff to stop the vehicle while most of the impact energy is absorbed by the vehicle through deformation of its frontal sections. A single-degree freedom linear mass-spring-damper model is the simplest model, but its results are not in line with test data. Single-degree non-linear model simulates the peak load but not the load history. However, using engine mass instead of truck mass in the single-degree model provides acceptable impact force data for the bollard. Two-degree freedom mass-spring damper linear model seems to simulate both truck's and bollard's deformation in a good manner. Non-linear analysis simulates the collision in a more realistic way, but it requires more data to be determined with testing.
Analysis of logistic equation pertaining to a new fractional derivative with non-singular kernel
(Sage Publications Ltd, 2017) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Al Qurashi, Maysaa; Baleanu, Dumitru; 56389
In this work, we aim to analyze the logistic equation with a new derivative of fractional order termed in Caputo-Fabrizio sense. The logistic equation describes the population growth of species. The existence of the solution is shown with the help of the fixed-point theory. A deep analysis of the existence and uniqueness of the solution is discussed. The numerical simulation is conducted with the help of the iterative technique. Some numerical simulations are also given graphically to observe the effects of the fractional order derivative on the growth of population.
Analysis of mixed-order Caputo fractional system with nonlocal integral boundary condition
(Tubitak Scientific & Technological Research Council Turkey, 2018) Akman Yildiz, Tugba; Baleanu, Dumitru; Khodabakhshi, Neda; Baleanu, Dumitru; 56389
This paper deals with a mixed-order Caputo fractional system with nonlocal integral boundary conditions. This study can be considered as an extension of previous studies, since the orders of the equations lie on different intervals. We discuss the existence and uniqueness of the solution using fixed point methods. We enrich the study with an example.

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