15,317 research outputs found
On the Schr\"odinger equations with isotropic and anisotropic fourth-order dispersion
This paper deals with the Cauchy problem associated to the nonlinear
fourth-order Schr\"odinger equation with isotropic and anisotropic mixed
dispersion. This model is given by the equation where represents either the operator (isotropic
dispersion) or (anisotropic
dispersion), and are given real parameters. We
obtain local and global well-posedness results in spaces of initial data with
low regularity, such as weak- spaces. Our analysis also includes the
biharmonic and anisotropic biharmonic equation for which, the
existence of self-similar solutions is obtained as consequence of his scaling
invariance. In a second part, we investigate the vanishing second order
dispersion limit in the framework of weak- spaces. We also analyze the
convergence of the solutions for the nonlinear fourth-order Schr\"odinger
equation , as goes to zero, in -norm, to the solutions of the
corresponding biharmonic equation
On the influence of tyre and structural properties on the stability of bicycles
In recent years the Whipple Carvallo Bicycle Model has been
extended to analyse high speed stability of bicycles. Various
researchers have developed models taking into account the effects
of front frame compliance and tyre properties, nonetheless, a systematic
analysis has not been yet carried out. This paper aims at analysing
parametrically the influence of front frame compliance and tyre properties
on the open loop stability of bicycles. Some indexes based
on the eigenvalues of the dynamic system are defined to evaluate
quantitatively bicycle stability. The parametric analysis is carried out
with a factorial design approach to determine the most influential
parameters. A commuting and a racing bicycle are considered and
numerical results show different effects of the various parameters
on each bicycle. In the commuting bicycle, the tyre properties have
greater influence than front frame compliance, and the weave mode
has the main effect on stability. Conversely, in the racing bicycle, the
front frame compliance parameters have greater influence than tyre
properties, and the wobble mode has the main effect on stability
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