Search results for " balance equations"
showing 2 items of 2 documents
Balance equations-based properties of the Rabi Hamiltonian
2014
A stationary physical system satisfies peculiar balance conditions involving mean values of appropriate observables. In this paper we show how to deduce such quantitative links, named balance equations, demonstrating as well their usefulness in bringing to light physical properties of the system without solving the Schrodinger equation. The knowledge of such properties in the case of Rabi Hamiltonian is exploit to provide arguments to make easier the variational engineering of the ground state of this model.
Estimation of the mean crystal size and the moments of the crystal size distribution in batch crystallization processes
2016
International audience; A cascade high gain observer is designed to estimate the first four leading moments of the crystal size distribution (CSD) and the mean crystal size in batch crystallization processes. The proposed observer is based on a well-known transformation of the partial differential equation describing the CSD to a set of ordinary differential equations (the method of moments). Due to numerical difficulties resulting from the important differences in the magnitudes of the moments, a set of new variables is computed to allow a good estimation of the moments and thus the mean crystal size. In this work, only solute concentration and crystallizer temperature are used to estimate…