16,819 research outputs found
Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries
The determination of the energy spectra of small spin systems as for instance
given by magnetic molecules is a demanding numerical problem. In this work we
review numerical approaches to diagonalize the Heisenberg Hamiltonian that
employ symmetries; in particular we focus on the spin-rotational symmetry SU(2)
in combination with point-group symmetries. With these methods one is able to
block-diagonalize the Hamiltonian and thus to treat spin systems of
unprecedented size. In addition it provides a spectroscopic labeling by
irreducible representations that is helpful when interpreting transitions
induced by Electron Paramagnetic Resonance (EPR), Nuclear Magnetic Resonance
(NMR) or Inelastic Neutron Scattering (INS). It is our aim to provide the
reader with detailed knowledge on how to set up such a diagonalization scheme.Comment: 29 pages, many figure
Infinitely many cyclic solutions to the Hamilton-Waterloo problem with odd length cycles
It is conjectured that for every pair of odd integers greater than
2 with , there exists a cyclic two-factorization of
having exactly factors of type and all the
others of type . The authors prove the conjecture in the affirmative
when and .Comment: 31 page
Dynamics simulation of human box delivering task
Thesis (M.S.) University of Alaska Fairbanks, 2018The dynamic optimization of a box delivery motion is a complex task. The key component is to achieve an optimized motion associated with the box weight, delivering speed, and location. This thesis addresses one solution for determining the optimal delivery of a box. The delivering task is divided into five subtasks: lifting, transition step, carrying, transition step, and unloading. Each task is simulated independently with appropriate boundary conditions so that they can be stitched together to render a complete delivering task. Each task is formulated as an optimization problem. The design variables are joint angle profiles. For lifting and carrying task, the objective function is the dynamic effort. The unloading task is a byproduct of the lifting task, but done in reverse, starting with holding the box and ending with it at its final position. In contrast, for transition task, the objective function is the combination of dynamic effort and joint discomfort. The various joint parameters are analyzed consisting of joint torque, joint angles, and ground reactive forces. A viable optimization motion is generated from the simulation results. It is also empirically validated. This research holds significance for professions containing heavy box lifting and delivering tasks and would like to reduce the chance of injury.Chapter 1 Introduction -- Chapter 2 Skeletal Human Modeling -- Chapter 3 Kinematics and Dynamics -- Chapter 4 Lifting Simulation -- Chapter 5 Carrying Simulation -- Chapter 6 Delivering Simulation -- Chapter 7 Conclusion and Future Research -- Reference
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