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Using a complex deformation q=exp(is) of su(2) we obtain extensions of the finite-dimensional representations towards the infinite-dimensional ones. A generalised q-deformation of su(2), as a Hopf algebra is introduced. We present the corresponding Schrodinger picture, by using a differential realisation, and a large class of potentials is obtained.A connection between the unirreps with q a root of unity and the comensurability of the potentials is investigated. The smooth transition between... Source: http://arxiv.org/abs/q-alg/9612007v1

We develop a formalism that describes the bending and twisting of axoneme-like filament bundles. We obtain general formulas to determine the relative sliding between any arbitrary filaments in a bundle subjected to unconstrained deformations. Particular examples for bending, twisting, helical and toroidal shapes, and combinations of these are discussed. Resulting equations for sliding and transversal shifting, expressed in terms of the curvature and torsion of the bundle, are applied to... Source: http://arxiv.org/abs/q-bio/0411026v2

We provide a simple analytic formula in terms of elementary functions for the Laplace transform j_{l}(p) of the spherical Bessel function than that appearing in the literature, and we show that any such integral transform is a polynomial of order l in the variable p with constant coefficients for the first l-1 powers, and with an inverse tangent function of argument 1/p as the coefficient of the power l. We apply this formula for the Laplace transform of the memory function related to the... Source: http://arxiv.org/abs/math-ph/0102020v2

We generalize the nonlinear one-dimensional equation for a fluid layer surface to any geometry and we introduce a new infinite order differential equation for its traveling solitary waves solutions. This equation can be written as a finite-difference expression, with a general solution that is a power series expansion with coefficients satisfying a nonlinear recursion relation. In the limit of long and shallow water, we recover the Korteweg-de Vries equation together with its single-soliton... Source: http://arxiv.org/abs/math-ph/0201056v1

We introduce a generalized similarity analysis which grants a qualitative description of the localised solutions of any nonlinear differential equation. This procedure provides relations between amplitude, width, and velocity of the solutions, and it is shown to be useful in analysing nonlinear structures like solitons, dublets, triplets, compact supported solitons and other patterns. We also introduce kink-antikink compact solutions for a nonlinear-nonlinear dispersion equation, and we... Source: http://arxiv.org/abs/math-ph/0003030v2

Although the auger-like 'swimming' motility of the African trypanosome was described upon its discovery over one hundred years ago, the precise biomechanical and biophysical properties of trypanosome flagellar motion has not been elucidated. In this study, we describe five different modes of flagellar beat/wave patterns in African trypanosomes by microscopically examining the flagellar movements of chemically tethered cells. The dynamic nature of the different beat/wave patterns suggests that... Source: http://arxiv.org/abs/physics/0309026v2

We generalize the non-linear one-dimensional equation of a fluid layer for any depth and length as an infinite order differential equation for the steady waves. This equation can be written as a q-differential one, with its general solution written as a power series expansion with coefficients satisfying a nonlinear recurrence relation. In the limit of long and shallow water (shallow channels) we reobtain the well known Korteweg-de-Vries equation together with its single-soliton solution. Source: http://arxiv.org/abs/q-alg/9612006v1

A potential representation for the subset of traveling solutions of nonlinear dispersive evolution equations is introduced. The procedure involves a reduction of a third order partial differential equation to a first order ordinary differential equation. In this representation it can be shown that solitons and solutions with compact support only exist in systems with linear or quadratic dispersion, respectively. In particular, this article deals with so the called K(n,m) equations. It is shown... Source: http://arxiv.org/abs/math-ph/0201054v1

We use a one-scale similarity analysis which gives specific relations between the velocity, amplitude and width of localized solutions of nonlinear differential equations, whose exact solutions are generally difficult to obtain. We also introduce kink-antikink compact solutions for the nonlinear-nonlinear dispersion K(2,2) equation, and we construct a basis of scaling functions similar with those used in the multiresolution analysis. These approaches are useful in describing nonlinear... Source: http://arxiv.org/abs/nlin/0008026v1

The fractal properties of the transverse Talbot images are analysed with two well-known scaling methods, the wavelet transform modulus maxima (WTMM) and the wavelet transform multifractal detrended fluctuation analysis (WT-MFDFA). We use the widths of the singularity spectra, Delta alpha=alpha_H-alpha_min, as a characteristic feature of these Talbot images. The tau scaling exponents of the q moments are linear in q within the two methods, which proves the monofractality of the transverse... Source: http://arxiv.org/abs/1301.4150v2

This work reports on calculations of the deformation energy of a nucleus plus an emitted cluster as a soliton moving on its surface. The potential barrier against the emission of a soliton is calculated within the macroscopic-microscopic method. The outer turning point of the barrier determines limitations on the geometrical and kinematical parameters for the formation of a surface soliton. For large asymmetry, the two-center shell model is used to assign a structure to the soliton.... Source: http://arxiv.org/abs/nucl-th/0003056v1

We use a multi-scale similarity analysis which gives specific relations between the velocity, amplitude and width of localized solutions of nonlinear differential equations, whose exact solutions are generally difficult to obtain. Source: http://arxiv.org/abs/math-ph/0201043v1

byT. Lyons; M. Ginther; P. Mascarenas; E. Rickard; J. Robinson; J. Braeger; H. Liu; A. Ludu

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We study the dynamics and the optimization of the shock deceleration supported by a payload when its airborne carrier impacts the ground. We build a nonlinear elastic model for a container prototype and an elastic suspension system for the payload. We model the dynamics of this system and extract information on maximum deceleration, energy transfer between the container and payload, and energy resonant damping. We designed the system and perform lab experiments for various terminal velocities... Topics: Soft Condensed Matter, Condensed Matter Source: http://arxiv.org/abs/1408.4190