FEF - Makale Koleksiyonu | Matematik Bölümü / Department of MathematicsMatematik Bölümüne ait makale koleksiyonu içerir.https://hdl.handle.net/11729/562024-03-29T01:47:36Z2024-03-29T01:47:36ZTulczyjew's triplet for Lie groups III: higher order dynamics and reductions for iterated bundlesEsen, OğulGümral, HasanSütlü, Serkanhttps://hdl.handle.net/11729/53642023-02-10T11:27:37Z2021-01-01T00:00:00ZTulczyjew's triplet for Lie groups III: higher order dynamics and reductions for iterated bundles
Esen, Oğul; Gümral, Hasan; Sütlü, Serkan
Given a Lie group G, we elaborate the dynamics on T*T*G and T*TG, which is given by a Hamiltonian, as well as the dynamics on the Tul-czyjew symplectic space TT * G, which may be defined by a Lagrangian or a Hamiltonian function. As the trivializations we adapted respect the group structures of the iterated bundles, we exploit all possible subgroup reductions (Poisson, symplectic or both) of higher order dynamics.
2021-01-01T00:00:00ZOn extensions, Lie-Poisson systems, and dissipationEsen, OğulÖzcan, GökhanSütlü, Serkanhttps://hdl.handle.net/11729/48122024-03-26T16:50:27Z2022-07-06T00:00:00ZOn extensions, Lie-Poisson systems, and dissipation
Esen, Oğul; Özcan, Gökhan; Sütlü, Serkan
Lie-Poisson systems on the dual spaces of unified products are studied. Having been equipped with a twisted 2-cocycle term, the extending structure framework allows not only to study the dynamics on 2-cocycle extensions, but also to (de)couple mutually interacting Lie-Poisson systems. On the other hand, symmetric brackets; such as the double bracket, the Cartan-Killing bracket, the Casimir dissipation bracket, and the Hamilton dissipation bracket are worked out in detail. Accordingly, the collective motion of two mutually interacting irreversible dynamics, as well as the mutually interacting metriplectic flows, are obtained. The theoretical results are illustrated in three examples. As an infinite-dimensional physical model, decompositions of the BBGKY hierarchy are presented. As for the finite-dimensional examples, the coupling of two Heisenberg algebras, and the coupling of two copies of 3D dynamics are studied.
Acknowledgments. This paper is a part of the project “Matched pairs of Lagrangian and Hamiltonian Systems” supported by TÜBİTAK (the Scientific and Technological Research Council of Turkey) with the project number 117F426, the support of which is acknowledged by the authors.
2022-07-06T00:00:00ZInverse solution of thermoacoustic wave equation for cylindrical layered mediaElmas, DemetÜnalmış Uzun, Banuhttps://hdl.handle.net/11729/43602024-03-26T16:21:39Z2022-03-30T00:00:00ZInverse solution of thermoacoustic wave equation for cylindrical layered media
Elmas, Demet; Ünalmış Uzun, Banu
Thermoacoustic imaging is a crossbred approach taking advantages of electromagnetic and ultrasound disciplines, together. A significant number of current medical imaging strategies are based on reconstruction of source distribution from information collected by sensors over a surface covering the region to be imaged. Reconstruction in thermoacoustic imaging depends on the inverse solution of thermoacoustic wave equation. Homogeneous assumption of tissue to be imaged results in degradation of image quality. In our paper, inverse solution of the thermoacoustic wave equation using layered tissue model consisting of concentric annular layers on a cylindrical cross-section is investigated for cross-sectional thermoacustic imaging of breast and brain. By using Green’s functions and surface integral methods we derive an exact analytic inverse solution of thermoacoustic wave equation in frequency domain. Our inverse solution is an extension of conventional solution to layered cylindrical structures. By carrying out simulations, using numerical test phantoms consisting of thermoacoustic sources distributed in the layered model, our layered medium assumption solution was tested and benchmarked with conventional solutions based on homogeneous medium assumption in frequency domain. In thermoacoustic image reconstruction, where the medium is assumed as homogeneous medium, the solution of nonhomogeneous thermoacoustic wave equation results in geometrical distortions, artifacts and reduced image resolution due to inconvenient medium assumptions.
2022-03-30T00:00:00ZSlant curves in the Lorentzian warped product manifold - I× fE²Dursun, Uğurhttps://hdl.handle.net/11729/43372024-03-26T16:13:22Z2022-03-15T00:00:00ZSlant curves in the Lorentzian warped product manifold - I× fE²
Dursun, Uğur
In this work, we study slant curves in the 3-dimensional Lorentzian warped product - I× fE², where E² is a 2-dimensional Euclidean plane, I⊆ R is an open interval equipped with the metric dt², and f is a positive smooth function on I. First we give a characterization of slant curves, and then we obtain a classification of all slant curves in - I× fE². We also compute their curvature and torsion, and we obtaine some results on slant curves and helices in the de Sitter space S13(1) and in the Minkowski space E13. Moreover we determined some biharmonic slant curves in S13(1).
2022-03-15T00:00:00Z