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

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

The Low Column Density Lyman-alpha Forest

We develop an analytical method based on the lognormal approximation to compute the column density distribution of the Lyman-alpha forest in the low column density limit. We compute the column density distributions for six different cosmological models and found that the standard, COBE-normalized CDM model cannot fit the observations of the Lyman-alpha forest at z=3. The amplitude of the fluctuations in that model has to be lowered by a factor of almost 3 to match observations. However, the currently viable cosmological models like the lightly tilted COBE-normalized CDM+Lambda model, the CHDM model with 20% neutrinos, and the low-amplitude Standard CDM model are all in agreement with observations, to within the accuracy of our approximation, for the value of the cosmological baryon density at or higher than the old Standard Bing Bang Nucleosynthesis value of 0.0125 for the currently favored value of the ionizing radiation intensity. With the low value for the baryon density inferred by Hogan & Rugers (1996), the models can only marginally match observations.Comment: three postscript figures included, submitted to ApJ

String Organization of Field Theories: Duality and Gauge Invariance

String theories should reduce to ordinary four-dimensional field theories at low energies. Yet the formulation of the two are so different that such a connection, if it exists, is not immediately obvious. With the Schwinger proper-time representation, and the spinor helicity technique, it has been shown that field theories can indeed be written in a string-like manner, thus resulting in simplifications in practical calculations, and providing novel insights into gauge and gravitational theories. This paper continues the study of string organization of field theories by focusing on the question of local duality. It is shown that a single expression for the sum of many diagrams can indeed be written for QED, thereby simulating the duality property in strings. The relation between a single diagram and the dual sum is somewhat analogous to the relation between a old- fashioned perturbation diagram and a Feynman diagram. Dual expressions are particularly significant for gauge theories because they are gauge invariant while expressions for single diagrams are not.Comment: 20 pages in Latex, including seven figures in postscrip

Experimental demonstration of continuous variable polarization entanglement

We report the experimental transformation of quadrature entanglement between two optical beams into continuous variable polarization entanglement. We extend the inseparability criterion proposed by Duan, et al. [Duan00] to polarization states and use it to quantify the entanglement between the three Stokes operators of the beams. We propose an extension to this scheme utilizing two quadrature entangled pairs for which all three Stokes operators between a pair of beams are entangled.Comment: 4 pages, 4 figure

Speciation without chromatography: Part I. Determination of tributyltin in aqueous samples by chloride generation, headspace solid-phase microextraction and inductively coupled plasma time of flight mass spectrometry

An analytical procedure was developed for the determination of tributyltin in aqueous samples. The relatively high volatility of the organometal halide species confers suitability for their headspace sampling from the vapour phase above natural waters or leached solid samples. Tributyltin was collected from the sample headspace above various chloride-containing matrices, including HCl, sodium chloride solution and sea-water, by passive sampling using a polydimethylsiloxane/divinylbenzene (PDMS/DVB)-coated solid-phase microextraction (SPME) fiber. Inductively coupled plasma time-of-flight mass spectrometry (ICP-TOFMS) was used for detection following thermal desorption of analytes from the fiber. A detection limit of 5.8 pg ml–1(as tin) was realized in aqueous samples. Method validation was achieved using NRCC PACS-2 (Sediment) certified reference material, for which reasonable agreement between certified and measured values for tributyltin content was obtained

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