Modulation theory is developed for a periodic peakon solution of the Camassa-Holm equation. An explicit simple wave solution of these modulation equations is then derived; this simple wave describing the evolution into an undular bore of an initial step. The characteristic on which the expansion fan occurs (propagating at a nonlinear group velocity) has a turning point, illustrating the fact th...

Formulations for a general theory of thermoelasticity to generate accurate thermal stresses for structural members of aeronautical vehicles were developed in 1954 by Boley. The formulation also provides three normal stresses and a shear stress along the entire length of the beam. The Poisson effect of the lateral and transverse normal stresses on a thermally loaded beam is taken into account in...

Light-sheet imaging is rapidly gaining importance for imaging intact biological specimens. Many of the latest innovations rely on the propagation-invariant Bessel or Airy beams to form an extended light sheet to provide high resolution across a large field of view. Shaping light to realize propagation-invariant beams often relies on complex programming of spatial light modulators or specialized...

Random Hermitian matrices are used to model complex systems without time-reversal invariance. Adding an external source to the model can have the effect of shifting some of the matrix eigenvalues, which corresponds to shifting some of the energy levels of the physical system. We consider the case when the n× n external source matrix has two distinct real eigenvalues: a with multiplicity r and z...

Diffraction places a fundamental limitation on the distance an optical beam propagates before its size increases and spatial details blur. We show here that imposing a judicious correlation between spatial and spectral degrees of freedom of a pulsed beam can render its transverse spatial profile independent of location along the propagation axis, thereby arresting the spread of the time-average...

We study the effect of technological knowledge on per-capita income and population in a Malthusian economy. Airy differential equations describe the evolution of knowledge. Consequently, the impact of technological knowledge on aggregate output is feeble before and strong after the Industrial Revolution. The economy exposed to Airy growth of knowledge evolves from a Malthusian regime into a Pos...