Q-Dependent Susceptibilities in Ferromagnetic Quasiperiodic Z-Invariant Ising Models

We study the q-dependent susceptibility chi(q) of a series of quasiperiodic Ising models on the square lattice. Several different kinds of aperiodic sequences of couplings are studied, including the Fibonacci and silver-mean sequences. Some identities and theorems are generalized and simpler derivations are presented. We find that the q-dependent susceptibilities are periodic, with the commensurate peaks of chi(q) located at the same positions as for the regular Ising models. Hence, incommensurate everywhere-dense peaks can only occur in cases with mixed ferromagnetic-antiferromagnetic interactions or if the underlying lattice is aperiodic. For mixed-interaction models the positions of the peaks depend strongly on the aperiodic sequence chosen.Comment: LaTeX2e, 26 pages, 9 figures (27 eps files). v2: Misprints correcte

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

Study of design parameters for squeeze film air journal bearing – excitation frequency and amplitude

The paper presents a design of squeeze film air journal bearing based on the design rules derived from CFX and FEA simulation study of an air film in between two flat plates, one of which was driven in a sinusoidal manner. The rules are that the oscillation frequency should be at least 15 kHz and that the oscillation amplitude be as large as possible to ensure a greater film thickness and to allow the bearing to reach its stable equilibrium quickly. The proposed journal bearing is made from AL2024-T3, of 20.02 mm outer diameter, 600 mm length and 2 mm thickness. Three 20-mm long fins are on the outer surface of the bearing tube and are spaced 120° apart; three longitudinal flats are milled equi-spaced between the fins and two piezoelectric actuators are mounted lengthwise on each flat. Such a design produces a modal shape on the bearing tube which resembles a triangle. When excited in this mode at the frequency of 16.37 kHz, and a voltage of 75 V AC with 75 V DC offset acting on the piezoelectric actuators, the air gap underneath of the bearing tube behaves as a squeeze air film with a response amplitude of 3.22 μm. The three design rules were validated by experiments

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

Radiative transfer theory for polarimetric remote sensing of pine forest

The radiative transfer theory is applied to interpret polarimetric radar backscatter from pine forest with clustered vegetation structures. To take into account the clustered structures with the radiative transfer theory, the scattering function of each cluster is calculated by incorporating the phase interference of scattered fields from each component. Subsequently, the resulting phase matrix is used in the radiative transfer equations to evaluate the polarimetric backscattering coefficients from random medium layers embedded with vegetation clusters. Upon including the multi-scale structures, namely, trunks, primary and secondary branches, as well as needles, we interpret and simulate the polarimetric radar responses from pine forest for different frequencies and looking angles. The preliminary results are shown to be in good agreement with the measured backscattering coefficients at the Landes maritime pine forest during the MAESTRO-1 experiment

Application of theoretical models to active and passive remote sensing of saline ice

The random medium model is used to interpret the polarimetric active and passive measurements of saline ice. The ice layer is described as a host ice medium embedded with randomly distributed inhomogeneities, and the underlying sea water is considered as a homogeneous half-space. The scatterers in the ice layer are modeled with an ellipsoidal correlation function. The orientation of the scatterers is vertically aligned and azimuthally random. The strong permittivity fluctuation theory is employed to calculate the effective permittivity and the distorted Born approximation is used to obtain the polarimetric scattering coefficients. We also calculate the thermal emissions based on the reciprocity and energy conservation principles. The effects of the random roughness at the air-ice, and ice-water interfaces are accounted for by adding the surface scattering to the volume scattering return incoherently. The above theoretical model, which has been successfully applied to analyze the radar backscatter data of the first-year sea ice near Point Barrow, AK, is used to interpret the measurements performed in the CRRELEX program

Design and analytically full-wave validation of the invisibility cloaks, concentrators, and field rotators created with a general class of transformations

We investigate a general class of electromagnetic devices created with any continuous transformation functions by rigorously calculating the analytical expressions of the electromagnetic field in the whole space. Some interesting phenomena associated with these transformation devices, including the invisibility cloaks, concentrators, and field rotators, are discussed. By carefully choosing the transformation function, we can realize cloaks which are insensitive to perturbations at both the inner and outer boundaries. Furthermore, we find that when the coating layer of the concentrator is realized with left-handed materials, energy will circulate between the coating and the core, and the energy transmits through the core of the concentrator can be much bigger than that transmits through the concentrator. Therefore, such concentrator is also a power flux amplifier. Finally, we propose a spherical field rotator, which functions as not only a wave vector rotator, but also a polarization rotator, depending on the orientations of the spherical rotator with respect to the incident wave direction. The functionality of these novel transformation devices are all successfully confirmed by our analytical full wave method, which also provides an alternate computational efficient validation method in contrast to numerical validation methods.Comment: 22 pages, 3 figure

Duality and Symmetry in Chiral Potts Model

We discover an Ising-type duality in the general $N$-state chiral Potts model, which is the Kramers-Wannier duality of planar Ising model when N=2. This duality relates the spectrum and eigenvectors of one chiral Potts model at a low temperature (of small $k'$) to those of another chiral Potts model at a high temperature (of $k'^{-1}$). The $\tau^{(2)}$-model and chiral Potts model on the dual lattice are established alongside the dual chiral Potts models. With the aid of this duality relation, we exact a precise relationship between the Onsager-algebra symmetry of a homogeneous superintegrable chiral Potts model and the $sl_2$-loop-algebra symmetry of its associated spin-$\frac{N-1}{2}$ XXZ chain through the identification of their eigenstates.Comment: Latex 34 pages, 2 figures; Typos and misprints in Journal version are corrected with minor changes in expression of some formula

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