Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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  • Article
    Citation - WoS: 23
    Citation - Scopus: 23
    Cold Sintering of Soda-Lime Glass
    (Elsevier Ltd., 2021) Karacasulu, Levent; Ögür, Ezgi; Pişkin, Cerem; Vakıfahmetoğlu, Çekdar
    Ordinary recycled soda lime glass powder was densified via cold sintering process with the aid of concentrated NaOH solution. Increase in processing time, temperature and concentration of the NaOH solution resulted in the formation of monolithic glass artifacts with higher relative densities. The sample densified the most (95.2%) was obtained when the sintering was performed at 250˚C with a 20 min dwell time using 15 M NaOH solution.
  • Article
    Citation - WoS: 12
    Citation - Scopus: 12
    Stability Analysis by a Nonlinear Upper Bound on the Derivative of Lyapunov Function
    (Elsevier Ltd., 2020) Şahan, Gökhan
    In this work, we give results for asymptotic stability of nonlinear time varying systems using Lyapunov-like Functions with indefinite derivative. We put a nonlinear upper bound for the derivation of the Lyapunov Function and relate the asymptotic stability conditions with the coefficients of the terms of this bound. We also present a useful expression for a commonly used integral and this connects the stability problem and Lyapunov Method with the convergency of a series generated by coefficients of upper bound. This generalizes many works in the literature. Numerical examples demonstrate the efficiency of the given approach. © 2020 European Control Association
  • Article
    Citation - WoS: 7
    Citation - Scopus: 8
    Diffraction of Flexural-Gravity Waves by a Vertical Cylinder of Non-Circular Cross Section
    (Elsevier Ltd., 2020) Dişibüyük, Nazile Buğurcan; Korobkin, A. A.; Yılmaz, Oğuz
    The linear three-dimensional problem of flexural-gravity wave (hydro-elastic wave) diffraction by a vertical cylinder of an arbitrary smooth cross section is studied using an asymptotic approach combined with the vertical mode method for water of finite depth. The surface of the water is covered by an infinite, continuous elastic ice plate. The rigid cylinder extends from the sea bottom to the ice surface. The ice plate is frozen to the cylinder. The ice deflection is described by the equation of a thin elastic plate of constant thickness with clamped edge conditions at the cylinder. The flow under the ice is described by the linear theory of potential flows. The coupled problem of wave diffraction is solved in two steps. First, the problem is solved without evanescent waves similar to the problem of water waves diffracted by a vertical cylinder. This solution does not satisfy the edge conditions. Second, a radiation problem with a prescribed motion of the ice plate edge is solved by the vertical mode method. The sum of these two solutions solve the original problem. Both solutions are obtained by an asymptotic method with a small parameter quantifying a small deviation of the cylinder cross section from a circular one. Third-order asymptotic solutions are obtained by solving a set of two-dimensional boundary problems for Helmholtz equations in the exterior of a circle. Strains along the edge, where the ice plate is frozen to the cylinder, are investigated for nearly square and elliptic cross sections of the vertical cylinders depending on the characteristics of ice and incident wave. The strains are shown to be highest in the places of high curvatures of the cross sections. The derived asymptotic formulae can be used in design of vertical columns in ice. They directly relate the strains in ice plate to the shape of the column. © 2020 Elsevier Ltd