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Logarithmic and hyperbolic spirals associated with Schrodinger's equation
Journal of Differential Equations, 2022Geometric properties of the solutions of the equation \[ Q''+\frac{2}{\zeta}Q'-Q+ia(\zeta Q)'=0, \quad 00\), and become singular as \(\zeta \to 0^+\) They rotate around \((0, 0)\) with \({\theta}'_j(\zeta)
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Logarithmic spiral — A splendid curve
Resonance, 2004Due to its various peculiarities, logarithmic spiral drew the attention of mathematicians and was called ‘spiral mirabilis’ by Jacob Bernoulli I. In this article some properties of logarithmic spiral have been described along with the appearance as well as applications of the curve in art and nature.
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On a Property of Logarithmic Spirals
Mathematics Magazine, 1968Logarithmic spirals, analyzing curve on surface of cylinder, existence and conditions of ellipticity conditions, determining curve transformation into ellipse based on logarithmic spiral ...
N. X. Vinh, A. Zirakzadeh
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Beautiful Math--Aesthetic Patterns Based on Logarithmic Spirals
IEEE Computer Graphics and Applications, 2013A simple, fast method generates various visually appealing spiral patterns. The method is based on the concept that spiral patterns comprise a symmetry group of tilings. It employs invariant mappings and a dynamical system to create seamless colored patterns.
, Xinchang Wang, , Peichang Ouyang
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Logarithmic Spiral Bevel Gear Tooth Contact Inspection
Applied Mechanics and Materials, 2010Introduction of spiral bevel gear tooth contact detection method, detection method based on the principle of EPG in the Y9550-type bevel gear roll tester on a pair of spiral bevel gear tooth contact area of sample detection experiment, obtained by experiment logarithmic spiral bevel gear contact area of the location, shape and size of the result.
Qiang Li +3 more
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A certain feature of logarithmic spirals
Journal of Mathematical Sciences, 2011A curve formed by inversion of a logarithmic spiral is called a double logarithmic spiral. The curves in this family possess the following property: there always exists such a spiral with continuous and monotone curvature satisfying any possible boundary conditions (endpoints, tangents, and curvatures).
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Original Research on Logarithmic Spiral Bevel Gear
Applied Mechanics and Materials, 2011In this article, logarithmic spiral curve is successfully applied to bevel gear transmission and used as dentiform line of helicoid bevel gear. Put forward a novel logarithmic spiral bevel gear drive. Because spiral angle on each point of logarithmic spiral curve is constant, the problem of variational spiral angle is solved faultlessly.
Hong Bo Yan +3 more
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Fractals, logarithmic spiral and coherent states
AIP Conference Proceedings, 2012Self-similarity properties of fractal structures and logarithmic spiral are related to quantum dissipative dynamics, squeezed coherent states and noncommutative geometry in the plane.
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Turbulent Wall Jets on Logarithmic Spiral Surfaces
Aeronautical Quarterly, 1966SummaryBy considering the equations of motion it has been shown that the flow in the outer part of a two-dimensional, curved, turbulent wall jet is approximately self-preserving if the ratio of jet thickness to wall radius of curvature is constant along the jet. This condition is satisfied for a jet blowing over a surface of logarithmic spiral profile,
J. A. Giles, A. P. Hays, R. A. Sawyer
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Logarithmic Spirals and Computer Art
1989Interesting geometric patterns are obtained by mapping a rectangular region in one coordinate system onto an annular region in another coordinate system. The mapping involves logarithmic spirals and several examples are presented which involve interlocking spirals, cubes and dragon patterns.
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