Supersymmetric Quantum Mechanics and SUSY Dependent SU(2) Symmetry for a Spin-1/2 Charged Particle in a Magnetic Field

We find that in a supersymmetric quantum mechanics (SUSY QM) system, in addition to supersymmetric algebra, an associated SU(2) algebra can be obtained by using semiunitary (SUT) operator and projection operator, and the relevant constants of motion can be constructed. Two typical quantum systems are investigated as examples to demonstrate the above finding. The first example is the quantum system of a nonrelativistic charged particle moving in x-y plane and coupled to a magnetic field along z axis. The second example is provided with the Dirac particle in a magnetic field. Similarly there exists an SU_τ(2) \otimes SU_σ(2) symmetry in the context of the relativistic Pauli Hamiltonian squared. We show that there exists also an SU(2) symmetry associated with the supersymmetry of the Dirac particle.     

Micromechanical investigation of granular ratcheting using a discrete model of polygonal particles

We use a two-dimensional model of polygonal particles to investigate granular ratcheting. Ratcheting is a long-term response of granular materials under cyclic loading, where the same amount of permanent deformation is accumulated after each cycle. We report on ratcheting for low frequencies and extremely small loading amplitudes. The evolution of the sub-network of sliding contacts allows us to understand the micromechanics of ratcheting. We show that the contact network evolves almost periodically under cyclic loading as the sub-network of the sliding contacts reaches different stages of anisotropy in each cycle. Sliding contacts lead to a monotonic accumulation of permanent deformation per cycle in each particle. The distribution of these deformations appears to be correlated in form of vortices inside the granular assembly.     

Micromechanical investigation of granular ratcheting using a discrete model of polygonal particles

We use a two-dimensional model of polygonal particles to investigate granular ratcheting. Ratcheting is a long-term response of granular materials under cyclic loading, where the same amount of permanent deformation is accumulated after each cycle. We report on ratcheting for low frequencies and extremely small loading amplitudes. The evolution of the sub-network of sliding contacts allows us to understand the micromechanics of ratcheting. We show that the contact network evolves almost periodically under cyclic loading as the sub-network of the sliding contacts reaches different stages of anisotropy in each cycle. Sliding contacts lead to a monotonic accumulation of permanent deformation per cycle in each particle. The distribution of these deformations appears to be correlated in form of vortices inside the granular assembly.     

Solving Two Kinds of JC Models Relating to Two-Photon Process by Supersymmetric Transformation

We propose two kinds of new Jaynes Cummings models relating to two-photon process by using the supersymmetric unitary transformation. The corresponding energy eigenvalues and eigenvectors are obtained.     

Exact Solutions of Supersymmetric KdV-a System via Bosonization Approach

Bosonization approach is applied in solving the most general N=1 supersymmetric Korteweg de-Vries equation with an arbitrary parameter a (sKdV-a) equation. By introducing some fermionic parameters in the expansion of the superfield, the sKdV-a equation is transformed to a new coupled bosonic system. The Lie point symmetries of this model are considered and similarity reductions of it are conducted. Several types of similarity reduction solutions of the coupled bosonic equations are simply obtained for all values of a. Some kinds of exact solutions of the sKdV-a equation are discussed which was not considered integrable previously.     

Optimal synthesis of three-revolute manipulators

An optimization method is proposed and discussed in order to synthesize a three-revolute open chain manipulator whose structure can have minimum size encumbrance and a workspace with prescribed constraints. The sequential quadratic programming optimization technique used has been successfully applied to the formulated problem as illustrated in some examples.A first version of this paper was presented at AIMETA 92, 11th Italian Congress of Theoretical and Applied Mechanics, Trento, 28 September–2 October 1992.     

Second-Order Shell Kinematics Implied by Rotation Constraint-Equation

The paper presents a general methodology of introducing the shell-type variables which is based on the rotation constraint-equation (RC-equation). The RC-equation is proven to be equivalent to the polar decomposition of the deformation gradient formula, and the rotations which it yields are interpreted in terms of rotations of vectors of an ortho-normal basis. The deformation function and rotations are assumed as polynomials of the thickness coordinate ζ, and in this form used in the RC-equation. Solving this equation, we can express the coefficients of the quadratic deformation function in terms of the following shell-type variables: (a) the mid-surface position x ₀, (b) the constant rotation Q ₀, (c) the rotation vector ψ ^* for the ζ-dependent rotations, and (d) the normal components U ₃₃ ⁰ and U ₃₃ ¹ of the right stretching tensor. This new methodology (i) ensures that all shell kinematical variables are consistent with the RC-equation, which is justified on 3D grounds, (ii) provides a general framework from which various Reissner-type hypotheses can be obtained by suitable assumptions. As an example, two generalized Reissner hypotheses are derived: one with two normal stretches, and the other with the in-plane twist and the bubble-like warping parameters. This revised version was published online in June 2006 with corrections to the Cover Date.     

Effects of relativistic kinematics in heavy ion elastic scattering

Relativistic corrections to the reaction kinematic parameters were made for elastic scattering of ⁶Li, ¹²C and ⁴⁰Ar from ⁴⁰Ca, ⁹⁰Zr and ²⁰⁸Pb targets at incident energies between 20 and 100 MeV/nucleon. The results of optical model calculations show that the effects of such corrections are important when describing the angular distributions of elastic scattering cross sections for heavy ion scattering at incident energies as low as around 40 MeV/nucleon. The effects on the total reaction cross sections on the other hand, were found to be small within the energy range studied when the optical model potential is fixed.     

Protein backbone structure determination using RDC: An inverse kinematics approach with fast and exact solutions

Residual dipolar couplings (RDC) of proteins dissolved in anisotropic media promise to speed up the determination of protein structures. We consider the backbone as a robotic mechanism and formulate inverse kinematics problems using RDC restraints from two media. The φ, ψ of each secondary structure element (SSE) are computed from oriented vectors in consecutive peptide planes. We search for the optimum conformation joining the solutions of two independent backbone halves. The matrix transforming the vector Z of a global frame from one SSE into the other determines their orientation. Three distance constraints between two oriented SSE determine their relative position by solving nine polynomial equations. The benefit of this method is that complete and accurate solutions are obtained overcoming the local minima problems of heuristic procedures. The algorithm is implemented on MAPLE using the least number of experimental data; the runtimes take an order of seconds on a common PC. © 2013 Wiley Periodicals, Inc.     

Gravity compensation of parallel kinematics mechanism with revolute joints using torsional springs

Abstract

Passive gravity compensation technologies based on counterweight and torsional springs is rarely discussed due to the unavailability of an exact mathematical manipulation to determine the required spring constants to achieve the static balance. This article proposes using these springs for a parallel kinematics mechanism with revolute joints. Either the spring constants or initial spring displacements are determined by a constrained optimization approach aiming at minimizing the total potential energy of the mechanism or the static reaction in the actuation direction at the actuators, along a prescribed trajectory. This results in reduced actuation forces/ torques and hence reduced power consumption.