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

Higher dimensional Reidemeister torsion invariants for cusped hyperbolic 3-manifolds

For an oriented finite volume hyperbolic 3-manifold M with a fixed spin structure \eta, we consider a sequence of invariants {\tau_n(M; \eta)}. Roughly speaking, {\tau_n(M; \eta)} is the Reidemeister torsion of M with respect to the representation given by the composition of the lift of the holonomy representation defined by \eta, and the n-dimensional, irreducible, complex representation of SL(2,C). In the present work, we focus on two aspects of this invariant: its asymptotic behavior and its relationship with the complex-length spectrum of the manifold. Concerning the former, we prove that for suitable spin structures, log(\tau_n(M; \eta)) grows as -n^2 Vol(M)/4\pi, extending thus the result obtained by W. Mueller for the compact case. Concerning the latter, we prove that the sequence {\tau_n(M; \eta)} determines the complex-length spectrum of the manifold up to complex conjugation

Scanning probe microscopy imaging of metallic nanocontacts

We show scanning probe microscopy measurements of metallic nanocontacts between controlled electromigration cycles. The nanowires used for the thinning process are fabricated by shadow evaporation. The highest resolution obtained using scanning force microscopy is about 3 nm. During the first few electromigration cycles the overall slit structure of the nanocontact is formed. The slit first passes along grain boundaries and then at a later stage vertically splits grains in the course of consuming them. We find that first the whole wire is heated and later during the thinning process as the slit forms the current runs over several smaller contacts which needs less power.Comment: 4 pages, 4 figure

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

An Optimal Control Formulation for Inviscid Incompressible Ideal Fluid Flow

In this paper we consider the Hamiltonian formulation of the equations of incompressible ideal fluid flow from the point of view of optimal control theory. The equations are compared to the finite symmetric rigid body equations analyzed earlier by the authors. We discuss various aspects of the Hamiltonian structure of the Euler equations and show in particular that the optimal control approach leads to a standard formulation of the Euler equations -- the so-called impulse equations in their Lagrangian form. We discuss various other aspects of the Euler equations from a pedagogical point of view. We show that the Hamiltonian in the maximum principle is given by the pairing of the Eulerian impulse density with the velocity. We provide a comparative discussion of the flow equations in their Eulerian and Lagrangian form and describe how these forms occur naturally in the context of optimal control. We demonstrate that the extremal equations corresponding to the optimal control problem for the flow have a natural canonical symplectic structure.Comment: 6 pages, no figures. To appear in Proceedings of the 39th IEEEE Conference on Decision and Contro

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