Fox, Henrici, and Moler made famous a “Method of Particular Solutions” for computing eigenvalues and eigenmodes of the Laplacian in planar regions such as polygons. We explain why their formulation of this method breaks down when applied to regions that are insufficiently simple and propose a modification that avoids these difficulties. The crucial changes are to introduce points in the interio...

In this work, we look at the symmetry of normal modes in symmetric structures, particularly structures with cyclic symmetry. We show that normal modes of symmetric structures have different levels of symmetry, or symmetricity. One novel theoretical result of this work is that, for a ring structure with m subunits, the symmetricity of the normal modes falls into m groups of equal size, with norm...

In our previous study, we found that a normal DC motor can be used for vibro-tactile and pseudo-force presentation. In the present study, we developed a new vibration actuator using a DC motor that can generate much stronger vibrations than a normal DC motor and produce very low frequency of vibrations. We proposed that the stator of the motor could be used as both the vibration mass and fixed ...

A double-Gaussian model and the Schmidt modes are found for the biphoton wave function characterizing spontaneous parametric down-conversion with the degenerate collinear phase-matching of the type I and with a pulsed pump. The obtained results are valid for all durations of the pump pulses, short, long and intermediately long.

We discuss the classical motion of a spring of arbitrary mass coupled to two arbitrary massive blocks attached at its ends. A general approach to the problem is presented and some general results are obtained. Examples for which a simple elastic function can be inferred are discussed and the normal modes and normal frequencies obtained. An approximation procedure to the evaluation of the normel...