Generation of the global workspace roadmap of the 3-RPR using rotary disk search

Path planning for parallel manipulators in the configuration space can be a challenging task due to the existence of multiple direct kinematic solutions. Hence the aim of this paper is to define a generalised hierarchical path planning scheme for trajectory generation between two configurations in the configuration space for manipulators that exhibit more than one solution in their direct kinematics. This process is applied to the 3-RPR mechanism, constrained to a 2-DOF system by setting active joint parameter ρ1 to a constant. The overall reachable workspace is discretised and deconstructed into smaller patches, which are then stitched together creating a global workspace roadmap. Using the roadmap, path feasibility is obtained and local path planning is used to generate a complete trajectory. This method can determine a singularity-free path between any two connectible points in the configuration space, including assembly mode changes. © 2014 Elsevier Ltd

Path planning and assembly mode-changes of 6-DOF Stewart-Gough-type parallel manipulators

© 2016 International Federation for the Promotion of Mechanism and Machine Science The Stewart-Gough platform (SGP) is a six degree-of-freedom (DOF) parallel manipulator whose reachable workspace is complex due to its closed-loop configuration and six DOF outputs. As such, methods of path planning that involve storing the entire reachable workspace in memory at high resolutions are not feasible due to this six-dimensional workspace. In addition, complete path planning algorithms struggle in higher dimensional applications without significant customisations. As a result, many workspace analysis algorithms and path planning schemes use iterative techniques, particularly when tracking the manipulator's many direct kinematic solutions. The aim of this paper is to present the viability of singularity-free path planning in the Stewart-Gough platform's 6-dimensional workspace on modern-day computing systems by demonstrating its assembly mode-changing capability. The entire workspace volume is found using flood-fill algorithms with smooth and singularity-free trajectories generated within this known workspace. Workspace volume analysis was also performed with results comparable to other works

Overlapping Unit Cells in 3d Quasicrystal Structure

A 3-dimensional quasiperiodic lattice, with overlapping unit cells and periodic in one direction, is constructed using grid and projection methods pioneered by de Bruijn. Each unit cell consists of 26 points, of which 22 are the vertices of a convex polytope P, and 4 are interior points also shared with other neighboring unit cells. Using Kronecker's theorem the frequencies of all possible types of overlapping are found.Comment: LaTeX2e, 11 pages, 5 figures (8 eps files), uses iopart.class. Final versio

Generalized Supersymmetric Perturbation Theory

Using the basic ingredient of supersymmetry, we develop a simple alternative approach to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wave functions do not involve tedious calculations which appear in the available perturbation theories. The model applicable in the same form to both the ground state and excited bound states, unlike the recently introduced supersymmetric perturbation technique which, together with other approaches based on logarithmic perturbation theory, are involved within the more general framework of the present formalism.Comment: 13 pages article in LaTEX (uses standard article.sty). No Figures. Sent to Ann. Physics (2004

Entangling two superconducting LC coherent modes via a superconducting flux qubit

Based on a pure solid-state device consisting of two superconducting LC circuits coupled to a superconducting flux qubit, we propose in this paper that the maximally entangled coherent states of the two LC modes can be generated for arbitrary coherent states through flux qubit controls.Comment: 5 pages, 2 figure

Are Preoperative Kattan and Stephenson Nomograms Predicting Biochemical Recurrence after Radical Prostatectomy Applicable in the Chinese Population?

Purpose. Kattan and Stephenson nomograms are based on the outcomes of patients with prostate cancer recruited in the USA, but their applicability to Chinese patients is yet to be validated. We aim at studying the predictive accuracy of these nomograms in the Chinese population. Patients and Methods. A total of 408 patients who underwent laparoscopic or open radical resection of prostate from 1995 to 2009 were recruited. The preoperative clinical parameters of these patients were collected, and they were followed up regularly with PSA monitored. Biochemical recurrence was defined as two or more consecutive PSA levels >0.4 ng/mL after radical resection of prostate or secondary cancer treatment. Results. The overall observed 5-year and 10-year biochemical recurrence-free survival rates were 68.3% and 59.8%, which was similar to the predicted values by the Kattan and Stephenson nomograms, respectively. The results of our study achieved a good concordance with both nomograms (Kattan: 5-years, 0.64; Stephenson: 5-years, 0.62, 10-years, 0.71). Conclusions. The incidence of prostate cancer in Hong Kong is increasing together with the patients’ awareness of this disease. Despite the fact that Kattan nomograms were derived from the western population, it has been validated in our study to be useful in Chinese patients as well

Determination of the parameters of a Skyrme type effective interaction using the simulated annealing approach

We implement for the first time the simulated annealing method (SAM) to the problem of searching for the global minimum in the hyper-surface of the chi-square function which depends on the values of the parameters of a Skyrme type effective nucleon-nucleon interaction. We undertake a realistic case of fitting the values of the Skyrme parameters to an extensive set of experimental data on the ground state properties of many nuclei ranging from normal to exotic ones. The set of experimental data used in our fitting procedure includes the radii for the valence $1d_{5/2}$ and $1f_{7/2}$ neutron orbits in the $^{17}$O and $^{41}$Ca nuclei, respectively, and the breathing mode energies for several nuclei, in addition to the typically used data on binding energy, charge radii and spin-orbit splitting. We also include in the fit the critical density $\rho_{cr}$ and further constrain the values of the Skyrme parameters by requiring that (i) the quantity $P = 3\rho \frac{dS}{d\rho}$, directly related to the slope of the symmetry energy $S$, must be positive for densities up to $3\rho_0$ (ii) the enhancement factor $\kappa$, associated with the isovector giant dipole resonance, should lie in the range of $0.1 - 0.5$ and (iii) the Landau parameter $G_0^\prime$ is positive at $\rho = \rho_0$. We provide simple but consistent schemes to account for the center of mass corrections to the binding energy and charge radii.Comment: 33 pages, 4 figures, Phys. Rev. C (in press

New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain

In this paper we show how an infinite system of coupled Toda-type nonlinear differential equations derived by one of us can be used efficiently to calculate the time-dependent pair-correlations in the Ising chain in a transverse field. The results are seen to match extremely well long large-time asymptotic expansions newly derived here. For our initial conditions we use new long asymptotic expansions for the equal-time pair correlation functions of the transverse Ising chain, extending an old result of T.T. Wu for the 2d Ising model. Using this one can also study the equal-time wavevector-dependent correlation function of the quantum chain, a.k.a. the q-dependent diagonal susceptibility in the 2d Ising model, in great detail with very little computational effort.Comment: LaTeX 2e, 31 pages, 8 figures (16 eps files). vs2: Two references added and minor changes of style. vs3: Corrections made and reference adde

On the duality relation for correlation functions of the Potts model

We prove a recent conjecture on the duality relation for correlation functions of the Potts model for boundary spins of a planar lattice. Specifically, we deduce the explicit expression for the duality of the n-site correlation functions, and establish sum rule identities in the form of the M\"obius inversion of a partially ordered set. The strategy of the proof is by first formulating the problem for the more general chiral Potts model. The extension of our consideration to the many-component Potts models is also given.Comment: 17 pages in RevTex, 5 figures, submitted to J. Phys.

Roots of Unity: Representations of Quantum Groups

Representations of Quantum Groups U_q (g_n), g_n any semi simple Lie algebra of rank n, are constructed from arbitrary representations of rank n-1 quantum groups for q a root of unity. Representations which have the maximal dimension and number of free parameters for irreducible representations arise as special cases.Comment: 23 page