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Yayın Tulczyjew's triplet with an Ehresmann connection I: Trivialization and reduction(World Scientific, 2023-03-30) Esen, Oğul; Kudeyt, Mahmut; Sütlü, SerkanWe study the trivialization and the reduction of Tulczyjew's triplet, in the presence of a symmetry and an Ehresmann connection associated to it. We thus establish a geometric pathway for the Legendre transformations on singular dynamical systems.Yayın On extensions, Lie-Poisson systems, and dissipation(Heldermann Verlag, 2022-07-06) Esen, Oğul; Özcan, Gökhan; Sütlü, SerkanLie-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.Yayın Matched pair analysis of the Vlasov plasma(American Institute of Mathematical Sciences-AIMS, 2021-06) Esen, Oğul; Sütlü, SerkanWe present the Hamiltonian (Lie-Poisson) analysis of the Vlasov plasma, and the dynamics of its kinetic moments, from the matched pair decomposition point of view. We express these (Lie-Poisson) systems as couplings of mutually interacting (Lie-Poisson) subdynamics. The mutual interaction is beyond the well-known semi-direct product theory. Accordingly, as the geometric framework of the present discussion, we address the matched pair Lie-Poisson formulation allowing mutual interactions. Moreover, both for the kinetic moments and the Vlasov plasma cases, we observe that one of the constitutive subdynamics is the compressible isentropic fluid flow, and the other is the dynamics of the kinetic moments of order >= 2. In this regard, the algebraic/geometric (matched pair) decomposition that we offer, is in perfect harmony with the physical intuition. To complete the discussion, we present a momentum formulation of the Vlasov plasma, along with its matched pair decomposition.Yayın Transient multi-domain thermal modeling of interrupted cutting with coated tools(Springer Science and Business Media Deutschland GmbH, 2021-09) Karagüzel, UmutInterrupted cutting operations, such as milling, produce fluctuating tool temperatures which directly affect the process outputs. Thus, prediction of cutting tool temperatures enables process planning, selection of materials for tool substrate and coating layers, and tool geometric design for improved productivity in machining operations. Theoretical analysis of temperature is a cost effective way to predict the tool temperatures. Considering the industrial needs, a theoretical model should be fast, easy to implement, and reliable. To that end, a novel hybrid model, which assembles analytical and numerical methods, is proposed in this study. This novel transient thermal model simulates the interrupted cutting with coated cutting tools. The proposed model includes an analytical heat flux calculation at the tool-chip interface considering the sticking-sliding contact behavior. The determined heat flux is, then, used to perform a numerical solution of the transient heat conduction problem in the cutting tool geometry with temperature-dependent thermal properties. The developed model is validated with experimental results found in literature under different cutting conditions. The results show that the model can predict the maximum temperatures generated in a thermal cycle with an accuracy of 2–10%. Thus, the proposed model can be further used to determine the process parameters, properties of coating layers, and tool geometric design.
