Asymptotic solutions to a class of nonlinear oscillation systems

In this paper, we present an asymptotic method for the analysis of a class of strongly nonlinear oscillators, derive second-order approximate solutions to them expressed in terms of their amplitudes and phases, and obtain the equations governing the amplitudes and phases, by which the amplitudes of the corresponding limit cycles and their behaviour can be determined. As an example, we investigate the modified van der Pol oscillator and give the second-order approximate analytical solution of its limit cycle. The comparison with the numerical solutions shows that the two results agree well with each other.

Weak Zone Related Seismic Cycles in Progressive Failure Leading to Collapse in Brittle Crust

Until quite recently our understanding of the basic mechanical process responsible for earthquakes and faulting was not well known. It can be argued that this was partly a consequence of the complex nature of fracture in crust and in part because evidence of brittle phenomena in the natural laboratory of the earth is often obliterated or obscured by other geological processes. While it is well understood that the spatial and temporal complexity of earthquakes and the fault structures emerge from geometrical and material built-in heterogeneities, one important open question is how the shearing becomes localized into a band of intense fractures. Here the authors address these questions through a numerical approach of a tectonic plate by considering rockmass heterogeneity both in microscopic scale and in mesoscopic scale. Numerical simulations of the progressive failure leading to collapse under long-range slow driving forces in the far-field show earthquake-like rupture behavior. $En Echelon$ crack-arrays are reproduced in the numerical simulation. It is demonstrated that the underlying fracturing induced acoustic emissions (or seismic events) display self-organized criticality------from disorder to order. The seismic cycles and the geometric structures of the fracture faces, which are found greatly depending on the material heterogeneity (especially on the macroscopic scale), agree with that observed experimentally in real brittle materials. It is concluded that in order to predict a main shock, one must have extremely detailed knowledge on very minor features of the earth's crust far from the place where the earthquake originated. If correct, the model proposed here seemingly provides an explanation as to why earthquakes to date are not predicted so successfully. The reason is not that the authors do not understand earthquake mechanisms very well but that they still know little about our earth's crust.

Heteroclinic cycles in lattice dynamical systems

A criterion of spatial chaos occurring in lattice dynamical systems-heteroclinic cycle-is discussed. It is proved that if the system has asymptotically stable heteroclinic cycle, then it has asymptotically stable homoclinic point which implies spatial chaos.

Internal resonance of an L-shaped beam with a limit stop .1. Free vibration

Real-life structures often possess piecewise stiffness because of clearances or interference between subassemblies. Such an aspect can alter a system's fundamental free vibration response and leads to complex mode interaction. The free vibration behaviour of an L-shaped beam with a limit stop is analyzed by using the frequency response function and the incremental harmonic balance method. The presence of multiple internal resonances, which involve interactions among the first five modes and are extremely complex, have been discovered by including higher harmonics in the analysis. The results show that mode interaction may occur if the higher harmonics of a vibration mode are close to the natural frequency of a higher mode. The conditions for the existence of internal resonance are explored, and it is shown that a prerequisite is the presence of bifurcation points in the form of intersecting backbone curves. A method to compute such intersections by using only one harmonic in the free vibration solution is proposed. (C) 1996 Academic Press Limited

Internal resonance of an L-shaped beam with a limit stop .2. Forced vibration

A limit stop is placed at the elbow of an L-shaped beam whose linear natural frequencies are nearly commensurable. As a result of this hardening device the non-linear system exhibits multiple internal resonances, which involve various degree of coupling between the first five modes of the beam in free vibration. A point load is so placed as to excite several modes and the resulting forced vibration is examined. In the undamped case, three in-phase and two out-of-phase solution branches have been found. The resonance curve is extremely complicated, with multiple branches and interactions between the first four modes. The amplitudes of the higher harmonics are highly influenced by damping, the presence of which can effectively attenuate internal resonances. Consequently parts of the resonance curve may be eliminated, with the resulting response comprising different distinctive branches. (C) 1996 Academic Press Limited

Laminar Burning Velocities and Markstein Lengths of Premixed Methane/Air Flames near the Lean Flammability Limit in Microgravity

Effects of flame stretch on the laminar burning velocities of near-limit fuel-lean methane/air flames have been studied experimentally using a microgravity environment to minimize the complications of buoyancy. Outwardly propagating spherical flames were employed to assess the sensitivities of the laminar burning velocity to flame stretch, represented by Markstein lengths, and the fundamental laminar burning velocities of unstretched flames. Resulting data were reported for methane/air mixtures at ambient temperature and pressure, over the specific range of equivalence ratio that extended from 0.512 (the microgravity flammability limit found in the combustion chamber) to 0.601. Present measurements of unstretched laminar burning velocities were in good agreement with the unique existing microgravity data set at all measured equivalence ratios. Most of previous 1-g experiments using a variety of experimental techniques, however, appeared to give significantly higher burning velocities than the microgravity results. Furthermore, the burning velocities predicted by three chemical reaction mechanisms, which have been tuned primarily under off-limit conditions, were also considerably higher than the present experimental data. Additional results of the present investigation were derived for the overall activation energy and corresponding Zeldovich numbers, and the variation of the global flame Lewis numbers with equivalence ratio. The implications of these results were discussed. 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Measurement of the diffraction-limit wavefront with double-shearing interferometers

In order to measure the diffraction-limit wavefront, we present three types of common-path double-shearing interferometers based on the theory of double shearing. Two pairs of half-aperture or whole-aperture wedge plates are used to introduce opposite tilt to realize the double-shearing function. By comparing the fringe widths in two fields, the marginal wavefront aberration can be obtained. In the paper, we give three different configurations: half-aperture configuration, whole-field configuration and double-interferometer configuration. The half-aperture configuration has the features of high sensitivity, stabilization and easy alignment. For the whole-field configuration, the interference fringes are displayed in two whole fields. Consequently, the divergent or convergent characteristic and aberration types of a wavefront can be identified visually. The whole-field configuration can be changed to the double-interferometer configuration for continuous test. Both small and large wavefront aberrations can be measured by the double-interferometer configuration. The minimum detectable wavefront aberration (W-0)(min) comes to 0.03 lambda. Lastly, we present the experimental results for the three types of double-shearing interferometers.

On the dynamic readout of sub-diffraction-limit pit arrays with a silver thin film

Fast moving arrays of periodic sub-diffraction-limit pits were dynamically read out via a silver thin film. The mechanism of the dynamic readout is analysed and discussed in detail, both experimentally and theoretically. The analysis and experiment show that, in the course of readout, surface plasmons can be excited at the silver/air interface by the focused laser beam and amplified by the silver thin film. The surface plasmons are transmitted into the substrate/silver interface with a large enhancement. The surface waves at the substrate/silver interface are scattered by the sinusoidal pits of sub-diffraction-limit size. The scattered waves are collected by a converging lens and guided into the detector for the readout.

20-W average power, high repetition rate, nanosecond pulse with diffraction limit from an all-fiber MOPA system

In this article, we report an all-fiber master oscillator power amplifier (MOPA) system, which can provide high repetition rate and nanosecond pulse with diffraction-limit. The system was constructed using a (2 + 1) X 1 multimode combiner. The Q-Switched, LD pumped Nd:YVO4 solid-state laser wets used (is master oscillator. The 976-nm fiber-coupled module is used as pump source. A 10-m long China-made Yb3+-doped D-shape double-clad large-mode-area fiber was used as amplifier fiber. The MOPA produced as much as 20-W average power with nanosecond pulse and near diffraction limited. The pulse duration is maintained at about 15 its during 50-175 kHz. The system employs a simple and compact architecture and is therefore suitable for the use in practical applications such as scientific and military airborne LIDAR and imaging. Based oil this system. the amplification performances of. the all fiber amplifier is investigated. (C) 2008 Wiley Periodicals, Inc.

Effects of rhFSH regimen and time interval on ovarian responses to repeated stimulation cycles in rhesus monkeys during a physiologic breeding season

We studied the effects of repeated stimulation by recombinant human FSH (rhFSH) at various time intervals during a physiologic breeding season in rhesus monkeys. Ovarian recovery and responses were assessed by ultrasonography, serum steroid concentrations

Compensatory growth and food consumption in gibel carp, Carassius auratus gibelio, and Chinese longsnout catfish, Leiocassis longirostris, experiencing cycles of feed deprivation and re-feeding

The compensatory responses of juvenile gibel carp and Chinese longsnout catfish to four cycles of 1 part of a study designed to determine feeding regimes that would maximise growth rates. Both species showed compensatory growth in the re-feeding periods. The compensation was not sufficient for the deprived fish to match the growth trajectories of controls fed to satiation daily. The compensatory growth response was more clearly defined in the later cycles. The deprived fish showed hyperphagia during the 2-week periods of re-feeding and the hyperphagic response was clearer in the later cycles. The hyperphagia tended to persist for both weeks of the re-feeding period. The gibel carp showed no difference in gross growth efficiency between deprived and control fish. In the catfish, the gross growth efficiency of the deprived fish was marginally higher than that of control fish, but the efficiency varied erratically from week to week. Over the experiment, the deprived fish achieved growth rates 75-80% of those shown by control fish, although fed at a frequency of 66%. There was no evidence of growth over-compensation with the deprivation-re-feeding protocol used in this study. (C) 2004 Elsevier B.V. All rights reserved.

Comparative mechanisms of photosynthetic carbon acquisition in Hizikia fusiforme under submersed and emersed conditions

The economic seaweed Hizikia fusiforme (Harv.) Okamura (Sargassaceae, Phaeophyta) usually experiences periodical exposures to air at low tide. Photosynthetic carbon acquisition mechanisms were comparatively studied under submersed and emersed conditions in order to establish a general understanding of its photosynthetic characteristics associated with tidal cycles. When submersed in seawater, H fusiforme was capable of acquiring HCO3- as a source of inorganic carbon (Ci) to drive photosynthesis, while emersed and exposed to air, it used atmospheric CO2 for photosynthesis. The pH changes surrounding the H fusiforme fronds had less influence on the photosynthetic rates under emersed condition than under submersed condition. When the pH was as high as 10.0, emersed H fusiforme could photosynthesize efficiently, but the submersed alga exhibited very poor photosynthesis. Extracellular carbonic anhydrase (CA) played an important role in the photosynthetic acquisitions of exogenous Ci in water as well as in air. Both the concentrations of dissolved inorganic carbon in general seawater and CO2 in air were demonstrated to limit the photosynthesis of H fusiforme, which was sensitive to O-2. It appeared that the exogenous carbon acquisition system, being dependent of external CA activity, operates in a way not enough to raise intracellular CO2 level to prevent photorespiration. The inability of H fusiforme to achieve its maximum photosynthetic rate at the current ambient Ci levels under both submersed and emersed conditions suggested that the yield of aquaculture for this economic species would respond profitably to future increases in CO2 concentration in the sea and air.

Effect of cycles of feed deprivation on growth and food consumption of immature three-spined sticklebacks and European minnows

Individual juvenile three-spined sticklebacks Gasterosteus aculeatus and European minnow Phoxinus phoxinus, from sympatric populations, were subjected to four cycles of I week of food deprivation and 2 weeks of ad libitum feeding. Mean specific growth rate during the weeks of deprivation was negative and did not differ between species. The three-spined stickleback showed sufficient growth compensation to recover to the growth trajectory shown by control fish daily fed ad libitum. The compensation was generated by hyperphagia during the re-feeding periods, and in the last two periods of re-feeding, the gross growth efficiencies of deprived three-spined sticklebacks were greater than in control fish. The expression of the compensatory changes in growth and food consumption became clearer over the successive periods of re-feeding. The European minnow developed only a weak compensatory growth response and the mass trajectory of the deprived fish deviated more and more from the control trajectory During re-feeding periods, there were no significant differences in food consumption or gross growth efficiency between control and deprived European minnows. The differences between the two species are discussed in terms of the possible costs of compensatory growth, the control of growth and differences in feeding biology (C) 2003 The Fisheries Society of the British Isles.