Statefinder diagnostic for the modified polytropic Cardassian universe

We apply the Statefinder diagnostic to the Modified Polytropic Cardassian Universe in this work. We find that the Statefinder diagnostic is quite effective to distinguish Cardassian models from a series of other cosmological models. The $s-r$ plane is used to classify the Modified Polytropic Cardassian models into six cases. The evolutionary trajectories in the $s-r$ plane for the cases with different $n$ and $\beta$ reveal different evolutionary properties of the universe. In addition, we combine the observational $H(z)$ data, the Cosmic Microwave Background (CMB) data and the Baryonic Acoustic Oscillation (BAO) data to make a joint analysis. We find that \textbf{Case 2} can be excluded at the 68.3% confidence level and any case is consistent with the observations at the 95.4% confidence level.Comment: Comments: Final version for publication in Physical Review D [minor revision to match the appear version] Journal-ref: Physical Review D 75, 083515 (2007

H Space: Interactive Augmented Reality Art

open accessThis artwork exploits recent research into augmented reality systems, such as the HoloLens, for building creative interaction in augmented reality. The work is being conducted in the context of interactive art experiences. The first version of the audience experience of the artwork, “H Space”, was informally tested in the SIGGRAPH 2018 Art Gallery context. Experiences with a later, improved, version was evaluated at Tsinghua University. The latest distributed version will be shown in Sydney. The paper describes the concept, the background in both the art and the technological domain and points to some of the key computer human interaction art research issues that the work highlights

The Limit of the Boltzmann Equation to the Euler Equations for Riemann Problems

The convergence of the Boltzmann equaiton to the compressible Euler equations when the Knudsen number tends to zero has been a long standing open problem in the kinetic theory. In the setting of Riemann solution that contains the generic superposition of shock, rarefaction wave and contact discontinuity to the Euler equations, we succeed in justifying this limit by introducing hyperbolic waves with different solution backgrounds to capture the extra masses carried by the hyperbolic approximation of the rarefaction wave and the diffusion approximation of contact discontinuity.Comment: 59 page

Broadcast in sparse conversion optical networks using fewest converters

Wavelengths and converters are shared by communication requests in optical networks. When a message goes through a node without a converter, the outgoing wavelength must be the same as the incoming one. This constraint can be removed if the node uses a converter. Hence, the usage of converters increases the utilization of wavelengths and allows more communication requests to succeed. Since converters are expensive, we consider sparse conversion networks, where only some specified nodes have converters. Moreover, since the usage of converters induces delays, we should minimize the use of available converters. The Converters Usage Problem (CUP) is to use a minimum number of converter so that each node can send messages to all the others (broadcasting). In this dissertation, we study the CUP in sparse conversion networks. We design a linear algorithm to find a wavelength assignment in tree networks such that, with the usage of a minimum number of available converters, every node can send messages to all the others. This is a generalization of [35], where each node has a converter. Our algorithm can assign wavelengths efficiently and effectively for one-to-one, multicast, and broadcast communication requests. A converter wavelength-dominates a node if there is a uniform wavelength path between them. The Minimal Wavelength Dominating Set Problem (MWDSP) is to locate a minimum number of converters so that all the other nodes in the network are wavelength-dominated. We use a linear complexity dynamic programming algorithm to solve the MWDSP for networks with bounded treewidth. One such solution provides a low bound for the optimal solution to the CUP

Cosmological constraints from Radial Baryon Acoustic Oscillation measurements and Observational Hubble data

We use the Radial Baryon Acoustic Oscillation (RBAO) measurements, distant type Ia supernovae (SNe Ia), the observational $H(z)$ data (OHD) and the Cosmic Microwave Background (CMB) shift parameter data to constrain cosmological parameters of $\Lambda$CDM and XCDM cosmologies and further examine the role of OHD and SNe Ia data in cosmological constraints. We marginalize the likelihood function over $h$ by integrating the probability density $P\propto e^{-\chi^{2}/2}$ to obtain the best fitting results and the confidence regions in the $\Omega_{m}-\Omega_{\Lambda}$ plane.With the combination analysis for both of the {\rm $\Lambda$}CDM and XCDM models, we find that the confidence regions of 68.3%, 95.4% and 99.7% levels using OHD+RBAO+CMB data are in good agreement with that of SNe Ia+RBAO+CMB data which is consistent with the result of Lin et al's work. With more data of OHD, we can probably constrain the cosmological parameters using OHD data instead of SNe Ia data in the future.Comment: 8 pages, 6 figures, 2 tables, accepted for publication in Physics Letters