Positivity-preserving H∞ model reduction for positive systems

This is the post-print version of the Article - Copyright @ 2011 ElevierThis paper is concerned with the model reduction of positive systems. For a given stable positive system, our attention is focused on the construction of a reduced-order model in such a way that the positivity of the original system is preserved and the error system is stable with a prescribed H∞ performance. Based upon a system augmentation approach, a novel characterization on the stability with H∞ performance of the error system is first obtained in terms of linear matrix inequality (LMI). Then, a necessary and sufficient condition for the existence of a desired reduced-order model is derived accordingly. Furthermore, iterative LMI approaches with primal and dual forms are developed to solve the positivity-preserving H∞ model reduction problem. Finally, a compartmental network is provided to show the effectiveness of the proposed techniques.The work was partially supported by GRF HKU 7137/09E

The Effect of Rapid Thermal Annealing on InAs/GaAs Quantum Dot Solar Cells

The effect of post-growth annealing on InAs/GaAs quantum dot solar cells (QDSCs) has been studied. A significant improvement in photoemission, photocurrent density, and spectral response has been observed with post-growth annealing. The optimal anneal temperature was found to be 700°C, which lead to an 18% improvement in current density from 4.9 mA cm-2 for as-grown sample to 5.8 mA cm-2. We assign this enhanced performance to the reduced density of inherent point defects that was formed at the quantum dot (QD) and GaAs barrier. Post-growth thermal anneal treatment of QDSCs is demonstrated as a simple route for achieving improved device performance

Real time demonstration of high bitrate quantum random number generation with coherent laser light

We present a random number generation scheme that uses broadband measurements of the vacuum field contained in the radio-frequency sidebands of a single-mode laser. Even though the measurements may contain technical noise, we show that suitable algorithms can transform the digitized photocurrents into a string of random numbers that can be made arbitrarily correlated with a subset of the quantum fluctuations (high quantum correlation regime) or arbitrarily immune to environmental fluctuations (high environmental immunity). We demonstrate up to 2 Gbps of real time random number generation that were verified using standard randomness tests

Magnification Bias Corrections to Galaxy-Lensing Cross-Correlations

Galaxy-galaxy or galaxy-quasar lensing can provide important information on the mass distribution in the Universe. It consists of correlating the lensing signal (either shear or magnification) of a background galaxy/quasar sample with the number density of a foreground galaxy sample. However, the foreground galaxy density is inevitably altered by the magnification bias due to the mass between the foreground and the observer, leading to a correction to the observed galaxy-lensing signal. The aim of this paper is to quantify this correction. The single most important determining factor is the foreground redshift z: the correction is small if the foreground galaxies are at low redshifts but can become non-negligible for sufficiently high redshifts. For instance, we find that for the multipole l=1000, the correction is above 1%*(5s-2)/b for z<0.37, and above 5%*(5s-2)/b for z<0.67, where s is the number count slope of the foreground sample, and b its galaxy bias. These considerations are particularly important for geometrical measures, such as the Jain and Taylor ratio or its generalization by Zhang et al. Assuming (5s-2)/b=1, we find that the foreground redshift should be limited to z<0.45 in order to avoid biasing the inferred dark energy equation of state w by more than 5%, and that even for a low foreground redshift (< 0.45), the background samples must be well separated from the foreground to avoid incurring a bias of similar magnitude. Lastly, we briefly comment on the possibility of obtaining these geometrical measures without using galaxy shapes, using instead magnification bias itself.Comment: 10 pages, 7 figures; v2: minor revisions, as accepted for publication in Physical Review

Surface diffusion coefficients for room acoustics : free-field measures

A surface diffusion coefficient is needed in room acoustics to enable the quality of diffusing surfaces to be evaluated. It may also facilitate more accurate geometric room acoustic models. This paper concentrates on diffusion coefficients derived from free-field polar responses. An extensive set of two- and three-dimensional measurements and predictions was used to test the worth of different diffusion coefficient definitions. The merits and problems associated with these types of coefficients are discussed, and past parameters reviewed. Two new coefficients are described. The new measure based on the autocorrelation function is forwarded as the best free-field coefficient. The strengths and weaknesses of the coefficient are defined. © 2000 Acoustical Society of America

Recovery of continuous wave squeezing at low frequencies

We propose and demonstrate a system that produces squeezed vacuum using a pair of optical parametric amplifiers. This scheme allows the production of phase sidebands on the squeezed vacuum which facilitate phase locking in downstream applications. We observe strong, stably locked, continuous wave vacuum squeezing at frequencies as low as 220 kHz. We propose an alternative resonator configuration to overcome low frequency squeezing degradation caused by the optical parametric amplifiers.Comment: 9 pages, 4 figure

An experimental investigation of criteria for continuous variable entanglement

We generate a pair of entangled beams from the interference of two amplitude squeezed beams. The entanglement is quantified in terms of EPR-paradox [Reid88] and inseparability [Duan00] criteria, with observed results of $\Delta^{2} X_{x|y}^{+} \Delta^{2} X_{x|y}^{-} = 0.58 \pm 0.02$ and $\sqrt{\Delta^{2} X_{x \pm y}^{+} \Delta^{2} X_{x \pm y}^{-}} = 0.44 \pm 0.01$, respectively. Both results clearly beat the standard quantum limit of unity. We experimentally analyze the effect of decoherence on each criterion and demonstrate qualitative differences. We also characterize the number of required and excess photons present in the entangled beams and provide contour plots of the efficacy of quantum information protocols in terms of these variables.Comment: 4 pages, 5 figure

The Evolution of Bias - Generalized

Fry (1996) showed that galaxy bias has the tendency to evolve towards unity, i.e. in the long run, the galaxy distribution tends to trace that of matter. Generalizing slightly Fry's reasoning, we show that his conclusion remains valid in theories of modified gravity (or equivalently, complex clustered dark energy). This is not surprising: as long as both galaxies and matter are subject to the same force, dynamics would drive them towards tracing each other. This holds, for instance, in theories where both galaxies and matter move on geodesics. This relaxation of bias towards unity is tempered by cosmic acceleration, however: the bias tends towards unity but does not quite make it, unless the formation bias were close to unity. Our argument is extended in a straightforward manner to the case of a stochastic or nonlinear bias. An important corollary is that dynamical evolution could imprint a scale dependence on the large scale galaxy bias. This is especially pronounced if non-standard gravity introduces new scales to the problem: the bias at different scales relaxes at different rates, the larger scales generally more slowly and retaining a longer memory of the initial bias. A consistency test of the current (general relativity + uniform dark energy) paradigm is therefore to look for departure from a scale independent bias on large scales. A simple way is to measure the relative bias of different populations of galaxies which are at different stages of bias relaxation. Lastly, we comment on the possibility of directly testing the Poisson equation on cosmological scales, as opposed to indirectly through the growth factor.Comment: 8 pages, 2 figures. References added. Accepted for publication in Physical Review

Harmonic entanglement with second-order non-linearity

We investigate the second-order non-linear interaction as a means to generate entanglement between fields of differing wavelengths. And show that perfect entanglement can, in principle, be produced between the fundamental and second harmonic fields in these processes. Neither pure second harmonic generation, nor parametric oscillation optimally produce entanglement, such optimal entanglement is rather produced by an intermediate process. An experimental demonstration of these predictions should be imminently feasible.Comment: 4 pages, 4 figure