Bihamiltonian geometry and separation of variables for Toda lattices

We discuss the bihamiltonian geometry of the Toda lattice (periodic and open). Using some recent results on the separation of variables for bihamiltonian manifolds, we show that these systems can be explicitly integrated via the classical Hamilton-Jacobi method in the so-called Darboux-Nijenhuis coordinates.Comment: 12 pages, Latex with amsmath and amssymb. Report of talks given at NEEDS9

Asset-based measurement of poverty

Poverty is generally defined as income or expenditure insufficiency, but the economic condition of a household also depends on its real and financial asset holdings. This paper investigates measures of poverty that rely on indicators of household net worth. We review and assess two main approaches followed in the literature: income-net worth measures and asset-poverty. We provide fresh cross-national evidence based on data from the Luxembourg Wealth Study.poverty indicators, income, wealth

Electron drift velocity measurements in liquid krypton–methane mixtures

Abstract Electron drift velocities have been measured in liquid krypton, pure and mixed with methane at different concentrations (1–10% in volume) versus electric field strength, and a possible effect of methane on electron lifetime has been investigated. While no effect on lifetime could be detected, since lifetimes were in all cases longer than what measurable, a very large increase in drift velocity (up to a factor 6) has been measured

Compositional inhomogeneities as a source of indirect combustion noise

The generation of indirect combustion noise by compositional inhomogeneities is examined theoretically. For this, the compact nozzle theory of~\cite{MARBLE_CANDEL_JSV1977} is extended to a multi-component gas mixture, and the chemical potential function is introduced as an additional acoustic source mechanism. Transfer functions for subcritical and supercritical nozzle flows are derived and the contribution of compositional noise is compared to entropy noise and direct noise by considering an idealized nozzle downstream of the combustor exit. It is shown that compositional noise is dependent on the local mixture composition and can exceed entropy noise for fuel-lean conditions and supercritical nozzle flows. This suggests that the compositional indirect noise requires potential consideration with the implementation of low-emission combustors.Financial support through NASA with award number NNX15AV04A and the Ford–Stanford Alliance project no. C2015-0590 is gratefully acknowledged.This is the author accepted manuscript. The final version is available from Cambridge University Press via http://dx.doi.org/10.1017/jfm.2016.39

A Novel Hierarchy of Integrable Lattices

In the framework of the reduction technique for Poisson-Nijenhuis structures, we derive a new hierarchy of integrable lattice, whose continuum limit is the AKNS hierarchy. In contrast with other differential-difference versions of the AKNS system, our hierarchy is endowed with a canonical Poisson structure and, moreover, it admits a vector generalisation. We also solve the associated spectral problem and explicity contruct action-angle variables through the r-matrix approach.Comment: Latex fil

Computational modeling of Li-ion batteries

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The quasi-bi-Hamiltonian formulation of the Lagrange top

Starting from the tri-Hamiltonian formulation of the Lagrange top in a six-dimensional phase space, we discuss the possible reductions of the Poisson tensors, the vector field and its Hamiltonian functions on a four-dimensional space. We show that the vector field of the Lagrange top possesses, on the reduced phase space, a quasi-bi-Hamiltonian formulation, which provides a set of separation variables for the corresponding Hamilton-Jacobi equation.Comment: 12 pages, no figures, LaTeX, to appear in J. Phys. A: Math. Gen. (March 2002

A Class of Coupled KdV systems and Their Bi-Hamiltonian Formulations

A Hamiltonian pair with arbitrary constants is proposed and thus a sort of hereditary operators is resulted. All the corresponding systems of evolution equations possess local bi-Hamiltonian formulation and a special choice of the systems leads to the KdV hierarchy. Illustrative examples are given.Comment: 8 pages, late