A Unified Software Framework for Empirical Gramians

A common approach in model reduction is balanced truncation, which is based on Gramian matrices classifying certain attributes of states or parameters of a given dynamic system. Initially restricted to linear systems, the empirical Gramians not only extended this concept to nonlinear systems but also provided a uniform computational method. This work introduces a unified software framework supplying routines for six types of empirical Gramians. The Gramian types will be discussed and applied in a model reduction framework for multiple-input multiple-output systems

A note on the cross Gramian for non-symmetric systems

The cross Gramian matrix is a tool for model reduction and system identification, but it is only applicable to square control systems. For symmetric systems, the cross Gramian possesses a useful relation to the system's associated Hankel singular values. Yet, many real-life models are neither square nor symmetric. In this work, concepts from decentralized control are used to approximate a cross Gramian for non-symmetric and non-square systems. To illustrate this new non-symmetric cross Gramian, it is applied in the context of model order reduction

Precision measurement of the electric quadrupole moment of 31Al and determination of the effective proton charge in the sd-shell

he electric quadrupole coupling constant of the 31Al ground state is measured to be nu_Q = |eQV_{zz}/h| = 2196(21)kHz using two different beta-NMR (Nuclear Magnetic Resonance) techniques. For the first time, a direct comparison is made between the continuous rf technique and the adiabatic fast passage method. The obtained coupling constants of both methods are in excellent agreement with each other and a precise value for the quadrupole moment of 31Al has been deduced: |Q(31Al)| = 134.0(16) mb. Comparison of this value with large-scale shell-model calculations in the sd and sdpf valence spaces suggests that the 31Al ground state is dominated by normal sd-shell configurations with a possible small contribution of intruder states. The obtained value for |Q(31Al)| and a compilation of measured quadrupole moments of odd-Z even-N isotopes in comparison with shell-model calculations shows that the proton effective charge e_p=1.1 e provides a much better description of the nuclear properties in the sd-shell than the adopted value e_p=1.3 e

Study of 19^{19} Na at SPIRAL

NESTERInternational audienceThe excitation function for the elastic-scattering reaction p18Ne, p18Ne was measured with the first radioactive beam from the SPIRAL facility at the GANIL laboratory and with a solid cryogenic hydrogen target. Several broad resonances have been observed, corresponding to new excited states in the unbound nucleus 19Na. In addition, two-proton emission events have been identified and are discussed

A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)

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