We discuss a piecewise-conserved constant of motion for a simple dissipative oscillatory mechanical system. The system is a harmonic oscillator with sliding (dry) friction. The piecewise-conserved constant of motion corresponds to the time average of the energy of the system during one halfperiod of the motion, and changes abruptly at the turning points of the motion. At late times the piecewis...

For a relativistic charged particle moving in a constant electromagnetic field, its velocity 4-vector has been well studied. However, despite the fact that both the electromagnetic field and the equations of motion are purely real, the resulting 4-velocity is seemingly due to a complex electromagnetic field. This work shows that this is not due to some complex formalism used (such as Clifford a...

Most metallic and ceramic materials are comprised of space-filling collections crystalline grains separated by grain boundaries. While this structure has been studied for more than a century, there few rigorous results regarding its global properties available in the literature. We present result three-dimensional structures that relates integral Gaussian curvature over boundaries to numbers qu...

This paper presents the analysis of vibration control of a laminated composite beam that including magnetostrictive layers. The formulation of problem is presented based on the shear deformation beam theory. For vibration suppression, the velocity feedback control with constant gain distributed is considered. Navier's method is applied to analyze the solution of vibration suppression of laminat...

Molecular dynamics simulations are used to study the mechanism and kinetics of hydrated electron diffusion. The electron center of mass is found to exhibit Brownian-type behavior with a diffusion coefficient considerably greater than that of the solvent. As previously postulated by both experimental and theoretical works, the instantaneous response of the electron to the librational motions of ...