Maximum Visibility Building Direction for Layered Manufacturing of Jewel Rings

Rapid prototyping is used in jewelry production since the introduction of Stereolithography Apparatus into the market. However, the building orientation is mainly decided by the experience of the operator rather than by any systematic analysis. A theory is therefore needed to analyze the best orientation of jewelry in rapid jewelry production. In this paper, a new orientation methodology is applied to jewel ring models to properly orient them for layer manufacturing. Jewel ring model built is then demonstrated to have better quality and less error. A case study is presented to illustrate the theory.The work described in this paper was supported by a grant from the Hong Kong Polytechnic University (Project No.: G-V617).Mechanical Engineerin

Optimal embedding parameters: A modelling paradigm

Reconstruction of a dynamical system from a time series requires the selection of two parameters, the embedding dimension $d_e$ and the embedding lag $\tau$. Many competing criteria to select these parameters exist, and all are heuristic. Within the context of modeling the evolution operator of the underlying dynamical system, we show that one only need be concerned with the product $d_e\tau$. We introduce an information theoretic criteria for the optimal selection of the embedding window $d_w=d_e\tau$. For infinitely long time series this method is equivalent to selecting the embedding lag that minimises the nonlinear model prediction error. For short and noisy time series we find that the results of this new algorithm are data dependent and superior to estimation of embedding parameters with the standard techniques

Ground state of a polydisperse electrorheological solid: Beyond the dipole approximation

The ground state of an electrorheological (ER) fluid has been studied based on our recently proposed dipole-induced dipole (DID) model. We obtained an analytic expression of the interaction between chains of particles which are of the same or different dielectric constants. The effects of dielectric constants on the structure formation in monodisperse and polydisperse electrorheological fluids are studied in a wide range of dielectric contrasts between the particles and the base fluid. Our results showed that the established body-centered tetragonal ground state in monodisperse ER fluids may become unstable due to a polydispersity in the particle dielectric constants. While our results agree with that of the fully multipole theory, the DID model is much simpler, which offers a basis for computer simulations in polydisperse ER fluids.Comment: Accepted for publications by Phys. Rev.

Measure representation and multifractal analysis of complete genomes

This paper introduces the notion of measure representation of DNA sequences. Spectral analysis and multifractal analysis are then performed on the measure representations of a large number of complete genomes. The main aim of this paper is to discuss the multifractal property of the measure representation and the classification of bacteria. From the measure representations and the values of the $D_{q}$ spectra and related $C_{q}$ curves, it is concluded that these complete genomes are not random sequences. In fact, spectral analyses performed indicate that these measure representations considered as time series, exhibit strong long-range correlation. For substrings with length K=8, the $D_{q}$ spectra of all organisms studied are multifractal-like and sufficiently smooth for the $C_{q}$ curves to be meaningful. The $C_{q}$ curves of all bacteria resemble a classical phase transition at a critical point. But the 'analogous' phase transitions of chromosomes of non-bacteria organisms are different. Apart from Chromosome 1 of {\it C. elegans}, they exhibit the shape of double-peaked specific heat function.Comment: 12 pages with 9 figures and 1 tabl

Elementary excitations in one-dimensional spin-orbital models: neutral and charged solitons and their bound states

We study, both numerically and variationally, the interplay between different types of elementary excitations in the model of a spin chain with anisotropic spin-orbit coupling, in the vicinity of the "dimer line" with an exactly known dimerized ground state. Our variational treatment is found to be in a qualitative agreement with the exact diagonalization results. Soliton pairs are shown to be the lowest excitations only in a very narrow region of the phase diagram near the dimer line, and the phase transitions are always governed by magnon-type excitations which can be viewed as soliton-antisoliton bound states. It is shown that when the anisotropy exceeds certain critical value, a new phase boundary appears. In the doped model on the dimer line, the exact elementary charge excitation is shown to be a hole bound to a soliton. Bound states of those "charged solitons" are studied; exact solutions for N-hole bound states are presented.Comment: 11 pages revtex, 6 figure

Feasibility of GNSS-R Altimetry Using CyGNSS 8-Satellite Constellation Mission Data

Ponencia expuesta en Scientific Assembly of the International Association of Geodesy (2021) celebrado en Beijing del 28 de junio al 2 de juli

CYGNSS Ocean Altimetry: A Status Report

Comunicación expuesta online en el CYGNSS Science Team Summer Meeting celebrado del 27 al 29 de julio de 202

Line shapes of dynamical correlation functions in Heisenberg chains

We calculate line shapes of correlation functions by use of complete diagonalization data of finite chains and analytical implications from conformal field theory, density of states, and Bethe ansatz. The numerical data have different finite size accuracy in case of the imaginary and real parts in the frequency and time representations of spin-correlation functions, respectively. The low temperature, conformally invariant regime crosses over at $T^*\approx 0.7J$ to a diffusive regime that in turn connects continuously to the high temperature, interacting fermion regime. The first moment sum rule is determined.Comment: 13 pages REVTEX, 18 figure