Bethe Ansatz and the Spectral Theory of affine Lie algebra--valued connections II. The non simply--laced case

We assess the ODE/IM correspondence for the quantum $\mathfrak{g}$-KdV model, for a non-simply laced Lie algebra $\mathfrak{g}$. This is done by studying a meromorphic connection with values in the Langlands dual algebra of the affine Lie algebra ${\mathfrak{g}}^{(1)}$, and constructing the relevant $\Psi$-system among subdominant solutions. We then use the $\Psi$-system to prove that the generalized spectral determinants satisfy the Bethe Ansatz equations of the quantum $\mathfrak{g}$-KdV model. We also consider generalized Airy functions for twisted Kac--Moody algebras and we construct new explicit solutions to the Bethe Ansatz equations. The paper is a continuation of our previous work on the ODE/IM correspondence for simply-laced Lie algebras.Comment: 37 pages, 1 figure. Continuation of arXiv:1501.07421. Minor change in the title. New subsection 5.1 on the action of the Weyl group on the Bethe Ansatz solution

Bethe Ansatz and the Spectral Theory of affine Lie algebra-valued connections I. The simply-laced case

We study the ODE/IM correspondence for ODE associated to $\hat{\mathfrak g}$-valued connections, for a simply-laced Lie algebra $\mathfrak g$. We prove that subdominant solutions to the ODE defined in different fundamental representations satisfy a set of quadratic equations called $\Psi$-system. This allows us to show that the generalized spectral determinants satisfy the Bethe Ansatz equations.Comment: 27 pages, final and published version. Minor change in the titl

Reductions of the dispersionless 2D Toda hierarchy and their Hamiltonian structures

We study finite-dimensional reductions of the dispersionless 2D Toda hierarchy showing that the consistency conditions for such reductions are given by a system of radial Loewner equations. We then construct their Hamiltonian structures, following an approach proposed by Ferapontov.Comment: 15 page

Global Sensitivity Methods for Design of Experiments in Lithium-ion Battery Context

Battery management systems may rely on mathematical models to provide higher performance than standard charging protocols. Electrochemical models allow us to capture the phenomena occurring inside a lithium-ion cell and therefore, could be the best model choice. However, to be of practical value, they require reliable model parameters. Uncertainty quantification and optimal experimental design concepts are essential tools for identifying systems and estimating parameters precisely. Approximation errors in uncertainty quantification result in sub-optimal experimental designs and consequently, less-informative data, and higher parameter unreliability. In this work, we propose a highly efficient design of experiment method based on global parameter sensitivities. This novel concept is applied to the single-particle model with electrolyte and thermal dynamics (SPMeT), a well-known electrochemical model for lithium-ion cells. The proposed method avoids the simplifying assumption of output-parameter linearization (i.e., local parameter sensitivities) used in conventional Fisher information matrix-based experimental design strategies. Thus, the optimized current input profile results in experimental data of higher information content and in turn, in more precise parameter estimates.Comment: Accepted for 21st IFAC World Congres