Waltzing peakons and compacton pairs in a cross-coupled Camassa-Holm equation

We consider singular solutions of a system of two cross-coupled Camassa-Holm (CCCH) equations. This CCCH system admits peakon solutions, but it is not in the two-component CH integrable hierarchy. The system is a pair of coupled Hamiltonian partial differential equations for two types of solutions on the real line, each of which separately possesses exp(-|x|) peakon solutions with a discontinuity in the first derivative at the peak. However, there are no self-interactions, so each of the two types of peakon solutions moves only under the induced velocity of the other type. We analyse the `waltzing' solution behaviour of the cases with a single bound peakon pair (a peakon couple), as well as the over-taking collisions of peakon couples and the antisymmetric case of the head-on collision of a peakon couple and a peakon anti-couple. We then present numerical solutions of these collisions, which are inelastic because the waltzing peakon couples each possess an internal degree of freedom corresponding to their `tempo' -- that is, the period at which the two peakons of opposite type in the couple cycle around each other in phase space. Finally, we discuss compacton couple solutions of the cross-coupled Euler-Poincar\'e (CCEP) equations and illustrate the same types of collisions as for peakon couples, with triangular and parabolic compacton couples. We finish with a number of outstanding questions and challenges remaining for understanding couple dynamics of the CCCH and CCEP equations

The Genetic-Induced Hearing Loss Can Block the Effect of Noise Trauma in Waltzing Guinea pig

AbstractThe waltzing guinea pig may be a good model to investigate if genetic factor can change the sensitivity in noise-induced hearing loss. A total of 34 waltzig guinea pigs were studied and we found that there is no any significant increased sensitivity to noise trauma if the age-induced hearing loss was considered in waltzing guinea pig

Applications of Scanning Electron Microscopy and X-Ray Microanalysis in Inner Ear Pathology

Surface pathology of inner ear structures so far described in detail concern cochlear and vestibular hair cells and the stria vascularis. In man, surgical intervention into the inner ear is very uncommon and when performed is in general with the primary objective of destroying the diseased peripheral end organs. The vast majority of inner ear tissue available for use with scanning electron microscopy (SEM) is therefore obtained from animals. The present paper reviews the progression of surface pathology caused by aminoglycoside antibiotics, acoustic overstimulation and in a guinea pig strain with genetic inner ear disease. The primary site of onset of surface pathology differs, depending on the underlying cause. Advanced surface pathology shows a similar type of morphological degeneration independent of cause. The combination of SEM and energy dispersive X-ray microanalysis (XRMA) of inner ear pathology has as yet been reported in only three studies, all concerning inner ear fluids or otoconia

Pursuit-evasion predator-prey waves in two spatial dimensions

We consider a spatially distributed population dynamics model with excitable predator-prey dynamics, where species propagate in space due to their taxis with respect to each other's gradient in addition to, or instead of, their diffusive spread. Earlier, we have described new phenomena in this model in one spatial dimension, not found in analogous systems without taxis: reflecting and self-splitting waves. Here we identify new phenomena in two spatial dimensions: unusual patterns of meander of spirals, partial reflection of waves, swelling wavetips, attachment of free wave ends to wave backs, and as a result, a novel mechanism of self-supporting complicated spatio-temporal activity, unknown in reaction-diffusion population models.Comment: 15 pages, 15 figures, submitted to Chao

Pairing, waltzing and scattering of chemotactic active colloids

An interacting pair of chemotactic (anti-chemotactic) active colloids, that can rotate their axes of self-propulsion to align {parallel (anti-parallel)} to a chemical gradient, shows dynamical behaviour that varies from bound states to scattering. The underlying two-body interactions are purely dynamical, non-central, non-reciprocal, and controlled by changing the catalytic activity and phoretic mobility. Mutually chemotactic colloids trap each other in a final state of fixed separation; the resulting `active dimer' translates. A second type of bound state is observed where the polar axes undergo periodic cycles leading to phase-synchronised circular motion around a common point. These bound states are formed depending on initial conditions and can unbind on increasing the speed of self propulsion. Mutually anti-chemotactic swimmers always scatter apart. We also classify the fixed points underlying the bound states, and the bifurcations leading to transitions from one type of bound state to another, for the case of a single swimmer in the presence of a localised source of solute