Dynamic full-range Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry

We propose a technique for dynamic full-range Fourier-domain optical coherence tomography by using sinusoidal phase-modulating interferometry, where both the full-range structural information and depth-resolved dynamic information are obtained. A novel frequency-domain filtering algorithm is proposed to reconstruct a time-dependent complex spectral interferogram from the sinusoidally phase-modulated interferogram detected with a high-rate CCD camera. By taking the amplitude and phase of the inverse Fourier transform of the complex spectral interferogram, a time-dependent full-range cross-sectional image and depth-resolved displacement are obtained. Displacement of a sinusoidally vibrating glass cover slip behind a fixed glass cover slip is measured with subwavelength sensitivity to demonstrate the depth-resolved dynamic imaging capability of our system. (c) 2007 Society of Photo-Optical Instrumentation Engineers.

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.

Structural dynamic eutrophication models

This article discusses problems of modelling the seasonal succession of algal species in lakes and reservoirs, and the adaptive selection of certain groups of algae in response to changes in the inputs and relative concentrations of nutrients and other environmental variables. A new generation of quantitative models is being developed which attempts to translate some important biological properties of species (survival, variation, inheritance, reproductive rates and population growth) into predictions about the survival of the fittest, where ”fitness” is measured or estimated in thermodynamic terms. The concept of ”exergy” and its calculation is explored to examine maximal exergy as a measure of fitness in ecosystems, and its use for calculating changes in species composition by means of structural dynamic models. These models accomodate short-term changes in parameters that affect the adaptive responses (species selection) of algae.