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Citation - WoS: 4
Citation - Scopus: 4
Convergence analysis and numerical solution of the benjamin-bona-mahony equation by lie-trotter splitting
(Tubitak Scientific & Technological Research Council Turkey, 2018) Zurnaci, Fatma; Gucuyenen Kaymak, Nurcan; Seydaoglu, Muaz; Tanoglu, Gamze
In this paper, an operator splitting method is used to analyze nonlinear Benjamin-Bona-Mahony-type equations. We split the equation into an unbounded linear part and a bounded nonlinear part and then Lie-Trotter splitting is applied to the equation. The local error bounds are obtained by using the approach based on the differential theory of operators in a Banach space and the quadrature error estimates via Lie commutator bounds. The global error estimate is obtained via Lady Windermere's fan argument. Finally, to confirm the expected convergence order, numerical examples are studied.
Citation - WoS: 73
Evidence for water-tuned structural differences in proteins: an approach emphasizing variations inlocal hydrophilicity
(Public Library Science, 2012) Akdogan, Yasar; Reichenwallner, Joerg; Hinderberger, Dariush
We present experimental evidence for the significant effect that water can have on the functional structure of proteins in solution. Human (HSA) and Bovine Serum Albumin (BSA) have an amino acid sequence identity of 75.52% and are chosen as model proteins. We employ EPR-based nanoscale distance measurements using double electron-electron resonance (DEER) spectroscopy and both albumins loaded with long chain fatty acids (FAs) in solution to globally (yet indirectly) characterize the tertiary protein structures from the bound ligands' points of view. The complete primary structures and crystal structures of HSA and as of recently also BSA are available. We complement the picture as we have recently determined the DEER-derived solution structure of HSA and here present the corresponding BSA solution structure. The characteristic asymmetric FA distribution in the crystal structure of HSA can surprisingly be observed by DEER in BSA in solution. This indicates that the BSA conformational ensemble in solution seems to be narrow and close to the crystal structure of HSA. In contrast, for HSA in solution a much more symmetric FA distribution was found. Thus, conformational adaptability and flexibility dominate in the HSA solution structure while BSA seems to lack these properties. We further show that differences in amino acid hydropathies of specific structural regions in both proteins can be used to correlate the observed difference in the global (tertiary) solution structures with the differences on the primary structure level.
Citation - WoS: 23
Exact solutions of forced burgers equations with time variable coefficients
(Elsevier, 2013) Buyukasik, Sirin A.; Pashaev, Oktay K.
In this paper, we consider a forced Burgers equation with time variable coefficients of the form U-t + (mu(t)/mu(t))U + UUx = (1/2 mu(t))U-xx - omega(2)(t)x, and obtain an explicit solution of the general initial value problem in terms of a corresponding second order linear ordinary differential equation. Special exact solutions such as generalized shock and multi-shock waves, triangular wave, N-wave and rational type solutions are found and discussed. Then, we introduce forced Burgers equations with constant damping and an exponentially decaying diffusion coefficient as exactly solvable models. Different type of exact solutions are obtained for the critical, over and under damping cases, and their behavior is illustrated explicitly. In particular, the existence of inelastic type of collisions is observed by constructing multi-shock wave solutions, and for the rational type solutions the motion of the pole singularities is described. (c) 2012 Elsevier B.V. All rights reserved.
Citation - WoS: 3
Exactly solvable madelung fluid and complex burgers equations: a quantum sturm-liouville connection
(Springer, 2012) Buyukasik, Sirin A.; Pashaev, Oktay K.
Quantum Sturm-Liouville problems introduced in our paper (BuyukaAYA +/- k et al. in J Math Phys 50:072102, 2009) provide a reach set of exactly solvable quantum damped parametric oscillator models. Based on these results, in the present paper we study a set of variable parametric nonlinear Madelung fluid models and corresponding complex Burgers equations, related to the classical orthogonal polynomials of Hermite, Laguerre and Jacobi types. We show that the nonlinear systems admit direct linearazation in the form of Schrodinger equation for a parametric harmonic oscillator, allowing us to solve exactly the initial value problems for these equations by the linear quantum Sturm-Liouville problem. For each type of equations, dynamics of the probability density and corresponding zeros, as well as the complex velocity field and related pole singularities are studied in details.
Citation - WoS: 5
Heme binding constricts the conformational dynamics of the cytochrome: Heme binding cavity
(Amer Chemical Soc, 2012) Akdogan, Yasar; Anbazhagan, Veerappan; Hinderberger, Dariush; Schneider, Dirk
Cytochrome b(559)' is a transmembrane protein formed by homodimerization of the 44-residue PsbF polypeptide and noncovalent binding of a heme cofactor. The PsbF polypeptide can dimerize in the absence and presence of heme. To monitor structural alterations associated with binding of heme to the apocytochrome, we analyzed the apo- and holo-cytochrome structure by electron paramagnetic resonance spectroscopy. Spin labeling of amino acids located close to the heme binding domain of the cytochrome revealed that the structure of the heme binding domain is unconstrained in the absence of heme. Heme binding restricts the conformational dynamics of the heme binding domain, resulting in the structurally more constricted holo-cytochrome structure.
Citation - WoS: 16
Citation - Scopus: 18
Solitary wave solution of nonlinear multi-dimensional wave equation by bilinear transformation method
(Elsevier Science Bv, 2007) Tanoglu, Gamze
The Hirota method is applied to construct exact analytical solitary wave solutions of the system of multi-dimensional nonlinear wave equation for n-component vector with modified background. The nonlinear part is the third-order polynomial, determined by three distinct constant vectors. These solutions have not previously been obtained by any analytic technique. The bilinear representation is derived by extracting one of the vector roots (unstable in general). This allows to reduce the cubic nonlinearity to a quadratic one. The transition between other two stable roots gives us a vector shock solitary wave solution. In our approach, the velocity of solitary wave is fixed by truncating the Hirota perturbation expansion and it is found in terms of all three roots. Simulations of solutions for the one component and one-dimensional case are also illustrated. (C) 2006 Published by Elsevier B.V.

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