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5 papers · 1 filter
On Geometrical Couplings of Dissipation and Curl Forces
Oğul Esen, Partha Guha, Hasan Gümral
In this paper, we present several geometric ways to incorporate gyroscopic and dissipative forces to curl forces. We first present a proper metriplectic geometry. Then, using the H…
Reductions of Topologically Massive Gravity I: Hamiltonian Analysis of The Second Order Degenerate Lagrangians
Filiz Çağatay-Uçgun, Oğul Esen, Hasan Gümral
We study the Hamiltonian formalisms of the second order degenerate Clèment and Sarıoğlu-Tekin Lagrangians. The Dirac-Bergmann constraint algorithm is employed while arriving at the…
A regularized representation of the fractional Laplacian in n dimensions and its relation to Weierstrass-Mandelbrot type fractal functions
Thomas Michelitsch, Gérard Maugin, Shahram Derogar +1
We demonstrate that the fractional Laplacian (FL) is the principal characteristic operator of harmonic systems with {\it self-similar} interparticle interactions. We show that the…
Poisson Structures for Aristotelian Model of Three Body Motion
E. Abadoğlu, H. Gümral
We present explicitly Poisson structures, for both time-dependent and time-independent Hamiltonians, of a dynamical system with three degrees of freedom introduced and studied by C…
Trkalian fields and Radon transformation
K. Saygili
We write the spherical curl transformation for Trkalian fields using differential forms. Then we consider Radon transform of these fields. The Radon transform of a Trkalian field s…