Dissipative Linear Stochastic Hamiltonian Systems

This paper is concerned with stochastic Hamiltonian systems which model a class of open dynamical systems subject to random external forces. Their dynamics are governed by Ito stochastic differential equations whose structure is specified by a Hamiltonian, viscous damping parameters and system-environment coupling functions. We consider energy balance relations for such systems with an emphasis on linear stochastic Hamiltonian (LSH) systems with quadratic Hamiltonians and linear coupling. For LSH systems, we also discuss stability conditions, the structure of the invariant measure and its relation with stochastic versions of the virial theorem. Using Lyapunov functions, organised as deformed Hamiltonians, dissipation relations are also considered for LSH systems driven by statistically uncertain external forces. An application of these results to feedback connections of LSH systems is outlined.Comment: 10 pages, 1 figure, submitted to ANZCC 201

Thermochemical generation of hydrogen

The direct fluid contact heat exchange with H2SO4 at about 330 C prior to high temperature decomposition at about 830 C in the oxygen release step of several thermochemical cycles for splitting water into hydrogen and oxygen provides higher heat transfer rates, savings in energy and permits use of cast vessels rather than expensive forged alloy indirect heat exchangers. Among several candidate perfluorocarbon liquids tested, only perfluoropropylene oxide polymers having a degree of polymerization from about 10 to 60 were chemically stable, had low miscibility and vapor pressure when tested with sulfuric acid at temperatures from 300 C to 400 C

Coherent Quantum Filtering for Physically Realizable Linear Quantum Plants

The paper is concerned with a problem of coherent (measurement-free) filtering for physically realizable (PR) linear quantum plants. The state variables of such systems satisfy canonical commutation relations and are governed by linear quantum stochastic differential equations, dynamically equivalent to those of an open quantum harmonic oscillator. The problem is to design another PR quantum system, connected unilaterally to the output of the plant and playing the role of a quantum filter, so as to minimize a mean square discrepancy between the dynamic variables of the plant and the output of the filter. This coherent quantum filtering (CQF) formulation is a simplified feedback-free version of the coherent quantum LQG control problem which remains open despite recent studies. The CQF problem is transformed into a constrained covariance control problem which is treated by using the Frechet differentiation of an appropriate Lagrange function with respect to the matrices of the filter.Comment: 14 pages, 1 figure, submitted to ECC 201

Directly Coupled Observers for Quantum Harmonic Oscillators with Discounted Mean Square Cost Functionals and Penalized Back-action

This paper is concerned with quantum harmonic oscillators consisting of a quantum plant and a directly coupled coherent quantum observer. We employ discounted quadratic performance criteria in the form of exponentially weighted time averages of second-order moments of the system variables. A coherent quantum filtering (CQF) problem is formulated as the minimization of the discounted mean square of an estimation error, with which the dynamic variables of the observer approximate those of the plant. The cost functional also involves a quadratic penalty on the plant-observer coupling matrix in order to mitigate the back-action of the observer on the covariance dynamics of the plant. For the discounted mean square optimal CQF problem with penalized back-action, we establish first-order necessary conditions of optimality in the form of algebraic matrix equations. By using the Hamiltonian structure of the Heisenberg dynamics and related Lie-algebraic techniques, we represent this set of equations in a more explicit form in the case of equally dimensioned plant and observer.Comment: 11 pages, a brief version to be submitted to the IEEE 2016 Conference on Norbert Wiener in the 21st Century, 13-15 July, Melbourne, Australi