Two-component {CH} system: Inverse Scattering, Peakons and Geometry

An inverse scattering transform method corresponding to a Riemann-Hilbert problem is formulated for CH2, the two-component generalization of the Camassa-Holm (CH) equation. As an illustration of the method, the multi - soliton solutions corresponding to the reflectionless potentials are constructed in terms of the scattering data for CH2.Comment: 22 pages, 3 figures, draft, please send comment

A study of human performance in a rotating environment

Consideration is given to the lack of sufficient data relative to the response of man to the attendant oculovestibular stimulations induced by multi-directional movement of an individual within the rotating environment to provide the required design criteria. This was done to determine the overall impact of artificial gravity simulations on potential design configurations and crew operational procedures. Gross locomotion and fine motor performance were evaluated. Results indicate that crew orientation, rotational rates, vehicle design configurations, and operational procedures may be used to reduce the severity of the adverse effects of the Coriolis and cross-coupled angular accelerations acting on masses moving within a rotating environment. Results further indicate that crew selection, motivation, and short-term exposures to the rotating environment may be important considerations for future crew indoctrination and training programs

Generalized poisson brackets and nonlinear Liapunov stability application to reduces mhd

A method is presented for obtaining Liapunov functionals (LF) and proving nonlinear stability. The method uses the generalized Poisson bracket (GPB) formulation of Hamiltonian dynamics. As an illustration, certain stationary solutions of ideal reduced MHD (RMHD) are shown to be nonlinearly stable. This includes Grad-Shafranov and Alfven solutions

Lagrange-Poincare field equations

The Lagrange-Poincare equations of classical mechanics are cast into a field theoretic context together with their associated constrained variational principle. An integrability/reconstruction condition is established that relates solutions of the original problem with those of the reduced problem. The Kelvin-Noether theorem is formulated in this context. Applications to the isoperimetric problem, the Skyrme model for meson interaction, metamorphosis image dynamics, and molecular strands illustrate various aspects of the theory.Comment: Submitted to Journal of Geometry and Physics, 45 pages, 1 figur

Microfluidics-based approaches to the isolation of African trypanosomes

African trypanosomes are responsible for significant levels of disease in both humans and animals. The protozoan parasites are free-living flagellates, usually transmitted by arthropod vectors, including the tsetse fly. In the mammalian host they live in the bloodstream and, in the case of human-infectious species, later invade the central nervous system. Diagnosis of the disease requires the positive identification of parasites in the bloodstream. This can be particularly challenging where parasite numbers are low, as is often the case in peripheral blood. Enriching parasites from body fluids is an important part of the diagnostic pathway. As more is learned about the physicochemical properties of trypanosomes, this information can be exploited through use of different microfluidic-based approaches to isolate the parasites from blood or other fluids. Here, we discuss recent advances in the use of microfluidics to separate trypanosomes from blood and to isolate single trypanosomes for analyses including drug screening

An integrable shallow water equation with peaked solitons

We derive a new completely integrable dispersive shallow water equation that is biHamiltonian and thus possesses an infinite number of conservation laws in involution. The equation is obtained by using an asymptotic expansion directly in the Hamiltonian for Euler's equations in the shallow water regime. The soliton solution for this equation has a limiting form that has a discontinuity in the first derivative at its peak.Comment: LaTeX file. Figure available from authors upon reques

Functional integration for Regge gravity

A summary is given of recent exact results concerning the functional integration measure in Regge gravity.Comment: 9 pages, AMSLaTex file; talk given at the Second Meeting on Constrained Dynamics and Quantum Gravity, Santa Margherita Ligure, Italy, 17-21 September 199

Kinetic and ion pairing contributions in the dielectric spectra of electrolyte aqueous solutions

Understanding dielectric spectra can reveal important information about the dynamics of solvents and solutes from the dipolar relaxation times down to electronic ones. In the late 1970s, Hubbard and Onsager predicted that adding salt ions to a polar solution would result in a reduced dielectric permittivity that arises from the unexpected tendency of solvent dipoles to align opposite to the applied field. So far, this effect has escaped an experimental verification, mainly because of the concomitant appearance of dielectric saturation from which the Hubbard-Onsager decrement cannot be easily separated. Here we develop a novel non-equilibrium molecular dynamics simulation approach to determine this decrement accurately for the first time. Using a thermodynamic consistent all-atom force field we show that for an aqueous solution containing sodium chloride around 4.8 Mol/l, this effect accounts for 12\% of the total dielectric permittivity. The dielectric decrement can be strikingly different if a less accurate force field for the ions is used. Using the widespread GROMOS parameters, we observe in fact an {\it increment} of the dielectric permittivity rather than a decrement. We can show that this increment is caused by ion pairing, introduced by a too low dispersion force, and clarify the microscopic connection between long-living ion pairs and the appearance of specific features in the dielectric spectrum of the solution