Dynamic response of hysteretic systems with application to a system containing limited slip

A general class of single degree of freedom systems possessing rate-independent hysteresis is defined. The hysteretic behavior in a system belonging to this class is depicted as a sequence of single-valued functions; at any given time, the current function is determined by some set of mathematical rules concerning the entire previous response of the system. Existence and uniqueness of solutions are established and boundedness of solutions is examined.

An asymptotic solution procedure is used to derive an approximation to the response of viscously damped systems with a small hysteretic nonlinearity and trigonometric excitation. Two properties of the hysteresis loops associated with any given system completely determine this approximation to the response: the area enclosed by each loop, and the average of the ascending and descending branches of each loop.

The approximation, supplemented by numerical calculations, is applied to investigate the steady-state response of a system with limited slip. Such features as disconnected response curves and jumps in response exist for a certain range of system parameters for any finite amount of slip.

To further understand the response of this system, solutions of the initial-value problem are examined. The boundedness of solutions is investigated first. Then the relationship between initial conditions and resulting steady-state solution is examined when multiple steady-state solutions exist. Using the approximate analysis and numerical calculations, it is found that significant regions of initial conditions in the initial condition plane lead to the different asymptotically stable steady-state solutions.

Microorganisms of the East African Great Lakes and their response to environmental changes

We have reviewed the phytoplankton composition and succession in the East African Great Lakes, their response to environmental changes, and the communities of microorganisms of the microbial food web. Recent studies in some great lakes, as well as progress in understanding phytoplankton succession and response to environmental factors, enable us to update knowledge of the phytoplankton ecology of these lakes. In particular, we present information indicating that phytoplankton composition in lakes Tanganyika and Kivu may reflect recent changes as a result of global warming or species introduction. We also stress the importance of microbes (at the base of the food web) in these systems and suggest that the microbial food web, which has been mostly overlooked until recently, may play a very large role in determining productivity and nutrient cycling in these large lakes.

Time response of optical switching properties of Sb thin films under focused laser pulses

The time response of optical switching properties of Sb thin films under focused laser pulses is investigated. The results show that the response course can be divided into onset, opening, and closing stages. Formulas for their lengths are given. The onset and opening times decrease with increasing pumping light power density. The closing time is about 150 ns. For optical memory, if the power density of the readout and recording lasers changes from 5 x 10(9) to 15 x 10(9) W/m(2), the onset time changes from 2.5 to 0.30 mus, and the opening time is on the nanosecond scale. (C) 2003 Society of Photo-Optical Instrumentation Engineers.

Nonlinear response and optical limiting in SrBi2Ta2O9 thin films

SrBi2Ta2O9 (SBT) thin films on quartz substrates were prepared by use of the pulsed-laser deposition technique. The nonlinear refractive indices, n(2), Of the SBT films were measured by use of z-scan techniques with picosecond pulses. Large negative nonlinear refractive indices of 3.84 and 3.58 cm(2)/GW were obtained for the wavelengths 532 nm and 1.064 mum, respectively. The two-photon absorption coefficient was determined to be 7.3 cm/GW for 532 nm. The limiting behavior of SBT thin film on a quartz substrate was investigated in an f/5 defocusing geometry by use of 38-ps-duration, 532-nm, 1.064-mum. laser excitation. (C) 2001 Optical Society of America.