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Boundary Shape and Casimir Energy
(IOP Publishing Ltd., 2009) Ahmedov, Hacı; Duru, İsmail Hakkı
Casimir energy changes are investigated for geometries obtained by small but arbitrary deformations of a given geometry for which the vacuum energy is already known for the massless scalar field. As a specific case, deformation of a spherical shell is studied. From the deformation of the sphere we show that the Casimir energy is a decreasing function of the surface-to-volume ratio. The decreasing rate is higher for less smooth deformations.
Citation - WoS: 15
Citation - Scopus: 16
Vortex Images and Q-Elementary Functions
(IOP Publishing Ltd., 2008) Pashaev, Oktay; Yılmaz, Oğuz
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.
Citation - WoS: 6
Citation - Scopus: 6
Integrable Hierarchies and Information Measures
(IOP Publishing Ltd., 2008) Parwani, Rajesh R.; Pashaev, Oktay
In this paper we investigate integrable models from the perspective of information theory, exhibiting various connections. We begin by showing that compressible hydrodynamics for a one-dimensional isentropic fluid, with an appropriately motivated information theoretic extension, is described by a general nonlinear Schrödinger (NLS) equation. Depending on the choice of the enthalpy function, one obtains the cubic NLS or other modified NLS equations that have applications in various fields. Next, by considering the integrable hierarchy associated with the NLS model, we propose higher order information measures which include the Fisher measure as their first member. The lowest members of the hierarchy are shown to be included in the expansion of a regularized Kullback-Leibler measure while, on the other hand, a suitable combination of the NLS hierarchy leads to a Wootters type measure related to a NLS equation with a relativistic dispersion relation. Finally, through our approach, we are led to construct integrable relativistic NLS equations.
Citation - WoS: 29
Citation - Scopus: 41
Soliton resonances in a generalized nonlinear Schrödinger equation
(IOP Publishing Ltd., 2008) Pashaev, Oktay; Lee, Jyh Hao; Rogers, Colin
It is shown that a generalized nonlinear Schrödinger equation proposed by Malomed and Stenflo admits, for a specific range of parameters, resonant soliton interaction. The equation is transformed to the 'resonant' nonlinear Schrödinger equation, as originally introduced to describe black holes in a Madelung fluid and recently derived in the context of uniaxial wave propagation in a cold collisionless plasma. A Hirota bilinear representation is obtained and soliton solutions are thereby derived. The one-soliton solution interpretation in terms of a black hole in two-dimensional spacetime is given. For the two-soliton solution, resonant interactions of several kinds are found. The addition of a quantum potential term is considered and the reduction is obtained to the resonant NLS equation. © 2008 IOP Publishing Ltd.
Citation - WoS: 4
Citation - Scopus: 4
The Cauchy Problem for the Planar Spin-Liquid Model
(IOP Publishing Ltd., 2005) Pashaev, Oktay; Chang, Nai-Heng
In this paper, we study the Cauchy problem of a two-dimensional model for a moving ferromagnetic continuum and prove global existence and uniqueness of solutions. In addition, equivalence to the coupled system of nonlinear Schrödinger equations interacting with a Chern-Simons gauge field is established.

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