Simplification Methods for Sum-of-Squares Programs

A sum-of-squares is a polynomial that can be expressed as a sum of squares of other polynomials. Determining if a sum-of-squares decomposition exists for a given polynomial is equivalent to a linear matrix inequality feasibility problem. The computation required to solve the feasibility problem depends on the number of monomials used in the decomposition. The Newton polytope is a method to prune unnecessary monomials from the decomposition. This method requires the construction of a convex hull and this can be time consuming for polynomials with many terms. This paper presents a new algorithm for removing monomials based on a simple property of positive semidefinite matrices. It returns a set of monomials that is never larger than the set returned by the Newton polytope method and, for some polynomials, is a strictly smaller set. Moreover, the algorithm takes significantly less computation than the convex hull construction. This algorithm is then extended to a more general simplification method for sum-of-squares programming.Comment: 6 pages, 2 figure

Unparticle Physics Effects on D0-anti-D0 Mixing

The mixing of $K^0-\bar{K^0}$, $D^0-\bar{D^0}$ and $B_{(s)}^0-\bar{B^0_{(s)}}$ provides a sensitive probe to explore new physics beyond the Standard Model. The scale invariant unparticle physics recently proposed by Georgi can induce flavor-changing neutral current and contribute to the mixing at tree level. We investigate the unparticle effects on $B^0-\bar{B^0}$ and $D^0-\bar{D^0}$ mixing. Especially, the newly observed $D^0-\bar{D^0}$ mixing sets the most stringent constraints on the coupling of the unparticle to quarks.Comment: 9 pages, some errors corrected, published versio

Investigation of the fracture phenomena during the milling process of inorganic particulates and brittle fracture of polymer composites using fractal theory

This dissertation investigates the applicability and usefulness of applying Fractal mathematics and to the fracture of brittle particulates in Fluid Energy Mill devices, and in particular quantifying the resulting power law particle size distributions, examining the Surface Fractal Dimension of milled particulates, and relating the Izod Impact Strength values of composites of polypropylene and Calcium carbonate particulates which are large un-milled, small milled, as well as small and produced by the simultaneous milling and coating with nano-silica to the Surface Fractal Dimension of the impact fracture surfaces. First, the dissertation examines the behavior of un-coated and micron-sized wax pre-coated particulates in a specially designed Single-event Fluid Mill (SEFM), which is utilized to represent (for each pass) the Elementary Breakage Events in the Fluid Energy Milling process, and analyze the results in terms of the Fractal Theory. The results establish that brittle milled particulates have self-similar shape to the original particulates, which points to the self-similarity property of fractals. Particle size distribution (PSD) of milled particulates obeys Power Law expression. This allows the analysis of size reduction efficiency and specific kinetic energy of particulates during SEFM milling using fractal methods. For modeling the surface structure of particles by a fractal surface at various scales, Atomic Force Microscopy and the Gwyddion 2.25 software are used to measure the surface fractal dimension (Ds) of raw and ground particles. The results show that the surface fractal dimensions of CaCO3 and KCl particles are independent of scale or grinding. This is a strong indication that the fracture process is self-similar. The surfaces of CaCO3 and KCl particles are modeled very well by fractal surfaces. For the materials of CaCO3 and KCl, a relationship between the macro-mechanical property and the micro-structure is built. The fractal dimension of the fracture surface increases with energy per unit surface area for fracture. The dissertation also investigates the fractal behavior of the following Polypropylene (PP) based polymer composites performance during impact testing and establishes a quantitative relationship between the evolution of microstructure and fracture macro-mechanical properties by fractal theory. The results show that the Izod impact strength increases, as the fractal dimension of composite\u27s impact-fractured surface increases. PP is compounded with large un-milled , small milled, as well as small and produced by the simultaneous milling and coating with nano-silica Calcium carbonate at the 10 and 20 wt% levels. The Izod impact strengths of the composites are obtained and their values are related to their Surface Fractal Dimension. The results establish an excellent relationship, strongly indicating that increasing fracture surface roughness shows more inter-particle ligaments in the composites resulting tougher materials

Calorific values and ash contents of different organs of Masson pine (Pinus massoniana) in southern China

Calorific values of plants are important indices for evaluating and reflecting material cycle and energy conversion in forest ecosystems. Based on the data of Masson Pine (Pinus massoniana) in southern China, the calorific values (CVs) and ash contents (ACs) of different plant organs were analyzed systematically using hypothesis test and regression analysis in this paper. The results show: (i) the CVs and ACs of different plant organs are almost significantly different, and the order by AFCV (ash-free calorific value) from the largest to the smallest is foliage (23.55 kJ/g), branches (22.25 kJ/g), stem bark (21.71 kJ/g), root (21.52 kJ/g) and stem wood (21.35 kJ/g); and the order by AC is foliage (2.35%), stem bark (1.44%), root (1.42%), branches (1.08%) and stem wood (0.33%); (ii) the CVs and ACs of stem woods on top, middle and lower sections are significantly different, and the CVs are increasing from top to lower sections of trunk while the ACs are decreasing; (iii) the mean GCV (gross calorific value) and AFCV of aboveground part are larger than those of belowground part (roots), and the differences are also statistically significant; (iv) the CVs and ACs of different organs are related, to some extent, to diameter, height and origin of the tree, but the influence degrees of the factors on CVs and ACs are not the same

Is Zc(3900)Z_c(3900) a molecular state

Assuming the newly observed $Z_c(3900)$ to be a molecular state of $D\bar D^*(D^{*} \bar D)$, we calculate the partial widths of $Z_c(3900)\to J/\psi+\pi;\; \psi'+\pi;\; \eta_c+\rho$ and $D\bar D^*$ within the light front model (LFM). $Z_c(3900)\to J/\psi+\pi$ is the channel by which $Z_c(3900)$ was observed, our calculation indicates that it is indeed one of the dominant modes whose width can be in the range of a few MeV depending on the model parameters. Similar to $Z_b$ and $Z_b'$, Voloshin suggested that there should be a resonance $Z_c'$ at 4030 MeV which can be a molecular state of $D^*\bar D^*$. Then we go on calculating its decay rates to all the aforementioned final states and as well the $D^*\bar D^*$. It is found that if $Z_c(3900)$ is a molecular state of ${1\over\sqrt 2}(D\bar D^*+D^*\bar D)$, the partial width of $Z_c(3900)\to D\bar D^*$ is rather small, but the rate of $Z_c(3900)\to\psi(2s)\pi$ is even larger than $Z_c(3900)\to J/\psi\pi$. The implications are discussed and it is indicated that with the luminosity of BES and BELLE, the experiments may finally determine if $Z_c(3900)$ is a molecular state or a tetraquark.Comment: 17 pages, 6 figures, 3 table