This paper provides some necessary and sufficient conditions for a
generalMarkovian Gaussian master equation to have a unique pure steady state.
The conditions are described by simple matrix equations; thus the so-called
environment engineering problem for pure-Gaussian-state preparation can be
straightforwardly dealt with in the linear algebraic framework. In fact, based
on one of those conditions, for an arbitrary given pure Gaussian state,we
obtain a complete parametrization of the Gaussian master equation having that
state as a unique steady state; this leads to a systematic procedure for
engineering a desired dissipative system.We demonstrate some examples including
Gaussian cluster states.Comment: 8 page
SUMMARYA tuned liquid damper (TLD), which consists of rigid tanks partially filled by liquid, is a type of passive control device relying upon liquid sloshing forces or moments to change the dynamical properties and to dissipate vibrational energy of a structure. An analytical non-linear model is proposed for a TLD using rectangular tanks filled with shallow liquid under pitching vibration, utilizing a shallow water wave theory. The model includes the linear damping of the sloshing liquid, which is an important parameter in the study of a TLD as it affects the efficiency of the TLD. Shaking table experiments were conducted for verification; good agreement between the analytical simulations and the experimental results was observed in a small excitation amplitude range. The simulations of TLD-structure interaction by using the proposed model show that the TLD can efficiently suppress resonant pitching vibration of a structure. It is also found that the effectiveness of a TLD for suppressing the pitching vibration depends not only on the mass of liquid in the TLD but also on the configuration of the liquid as well as upon the position where the TLD is located. If the configuration of the liquid, i.e. the liquid depth and the TLD tank size, is designed suitably, the TLD can have a large suppressing moment and can be very effective even with a small mass of liquid.
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