Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/11147/7148

Browse

Filters

2008 - 200912010 - 20111

Settings

Author: search.filters.author.Yılmaz, OğuzPublisher: search.filters.publisher.IOP Publishing Ltd.

Search Results

Now showing 1 - 2 of 2
  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    Hamiltonian Dynamics of N Vortices in Concentric Annular Region
    (IOP Publishing Ltd., 2011) Pashaev, Oktay; Yılmaz, Oğuz; Pashaev, Oktay; Yılmaz, Oğuz; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    The problem of N vortex dynamics in annular domain is considered. The region is canonical one and allows by conformal mapping apply results to an arbitrary position of two cylinders in the plane. Using previous solution, obtained by the authors in terms of the q-elementary functions [1] we now concentrate on the Hamiltonian formulation of the problem. The integrability of the problem of two vortices in the annular domain according to Liouville has been proved by using canonical transformations. Different motion characteristics depending on initial conditions are studied.
  • Article
    Citation - WoS: 15
    Citation - Scopus: 16
    Vortex Images and Q-Elementary Functions
    (IOP Publishing Ltd., 2008) Pashaev, Oktay; Yılmaz, Oğuz; Pashaev, Oktay; Yılmaz, Oğuz; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of Technology
    In the present paper, the problem of vortex images in the annular domain between two coaxial cylinders is solved by the q-elementary functions. We show that all images are determined completely as poles of the q-logarithmic function, and are located at sites of the q-lattice, where a dimensionless parameter q = r 2 2/r 2 1 is given by the square ratio of the cylinder radii. The resulting solution for the complex potential is represented in terms of the Jackson q-exponential function. Our approach in this paper provides an efficient path to rediscover known solutions for the vortex-cylinder pair problem and yields new solutions as well. By composing pairs of q-exponents to the first Jacobi theta function and conformal mapping to a rectangular domain we show that our solution coincides with the known one, obtained before by elliptic functions. The Schottky-Klein prime function for the annular domain is factorized explicitly in terms of q-exponents. The Hamiltonian, the Kirchhoff-Routh and the Green functions are constructed. As a new application of our approach, the uniformly rotating exact N-vortex polygon solutions with the rotation frequency expressed in terms of q-logarithms at Nth roots of unity are found. In particular, we show that a single vortex orbits the cylinders with constant angular velocity, given as the q-harmonic series. Vortex images in two particular geometries with only one cylinder as the q → ∞ limit are studied in detail.