Nonlinear vibration behavior of beam is an important issue of structural engineering. In this study, a mathematical modeling of a forced nonlinear vibration of Euler-Bernoulli beam resting on nonlinear elastic foundation is presented. The nonlinear vibration behavior of the beam is investigated by using a modified multi-level residue harmonic balance method. The main advantage of the method is ...

A 1x3 beam splitter using multi-mode interference based on self-imaging is demonstrated theoretically and experimentally in PhCWs. The total transmission of the 1x3 splitter is almost equal to the corresponding length of W1 PhCW. The input power is distributed equally between the output ports within 1dB from 1541nm to 1552nm. KeywordsSplitter; Self-imaging; multi-mode interference; Photonic Cry...

In particle-in-cell (PIC) simulation, errors in space charge forces are of random character. It results in an unphysical increase of effective beam emittance, even while symplectic integrator is used. To establish quantitative measure of this effect on beam dynamics, an analytical model of equilibrium beam affected by random errors in space charge field calculations is considered. An explicit e...

A diverse collection of correctness statements have been proposed and used in microprocessor verification efforts. Correctness statements have evolved from criteria that match a single step of the implementation against the specification to seemingly looser, multi-step, criteria. In this paper, we formally verify conditions under which two categories of multi-step correctness statements logical...