Stability of parametrically excited differential equations

Sufficient stability criteria for classes of parametrically excited differential equations are developed and applied to example problems of a dynamical nature.

Stability requirements are presented in terms of 1) the modulus of the amplitude of the parametric terms, 2) the modulus of the integral of the parametric terms and 3) the modulus of the derivative of the parametric terms.

The methods employed to show stability are Liapunov’s Direct Method and the Gronwall Lemma. The type of stability is generally referred to as asymptotic stability in the sense of Liapunov.

The results indicate that if the equation of the system with the parametric terms set equal to zero exhibits stability and possesses bounded operators, then the system will be stable under sufficiently small modulus of the parametric terms or sufficiently small modulus of the integral of the parametric terms (high frequency). On the other hand, if the equation of the system exhibits individual stability for all values that the parameter assumes in the time interval, then the actual system will be stable under sufficiently small modulus of the derivative of the parametric terms (slowly varying).

Design of a highly stable, high-conversion-efficiency pumping source for optical parametric amplifier by extending efficient crystal length

The objective of this study is to improve the stability of pumping source of optical parametric amplifier. Analysis by simulation leads to the conclusion that the stability of the second harmonic can be improved by using properly the intensity of fundamental light and corresponding length of the crystal. By the method of the noncollinear two-pass second harmonic or the tandem second harmonic, the efficient crystal length is extended to a proper value, and the stability of the second harmonic output has been improved two times more than that for the fundamental light, and the conversion-efficiency is about 70% in experiment. When the variation of the fundamental light is about 10%, the variation of the second harmonic intensity has been controlled within 5%. (c) 2006 Elsevier Ltd. All rights reserved.

Reconciling yield stability with international fisheries agencies precautionary preferences: the role of non constant discount factors in age structured models

International fisheries agencies recommend exploitation paths that satisfy two features. First, for precautionary reasons exploitation paths should avoid high fishing mortality in those fisheries where the biomass is depleted to a degree that jeopardise the stock's capacity to produce the Maximum Sustainable Yield (MSY). Second, for economic and social reasons, captures should be as stable (smooth) as possible over time. In this article we show that a conflict between these two interests may occur when seeking for optimal exploitation paths using age structured bioeconomic approach. Our results show that this conflict be overtaken by using non constant discount factors that value future stocks considering their relative intertemporal scarcity.

Rare earth doped beta-diketone complexes as promising high-density optical recording materials for blue optoelectronics

Some kinds of rare earth beta-diketone complexes with blue-violet light absorption edge were synthesized using the ligands of thenoyltrifluoroacctone (HTTA), 2, 2'-dipyridyl (BIPY) and different metal ions (Gd3+, Sm3+ and La3+). Their contents, structures and optoelectronic parameters were monitored by elemental analysis, MS, IR and UV spectra. The solubility of rare earth beta-diketone complexes in 2, 2, 3, 3-tetrafluoro-1-propanol (TFP) and absorption properties of their films in the region 300-800 nm were measured. The influence on the difference of absorption maximum from rare earth beta-diketone complexes to beta-diketone ligand by different metal ions was studied. In addition, the thermal stability of rare earth beta-diketone complexes was also reported. (C) 2005 Elsevier B.V. All rights reserved.

Rare earth dibenzoylmethane complexes for potential application as high-density recordable optical recording materials

Three kinds of rare earth complexes derived from dibenzoylmethane (DBM) ligand were synthesized by reacting free ligand and different rare earth ions(La (3+), Sm3+ and Gd3+). Their contents and structures were postulated based on elemental analysis, LDI-TOF-MS, FT-IR spectra and UV-Vis spectra. Smooth films on K9 glass substrates were prepared using the spin-coating method. Their solubility in organic solvents, absorption and reflection properties of thin film and thermal stability of these complexes were evaluated. These complexes would be a promising recording material for high-density digital versatile disc-recordable (HD-DVD-R) system. (c) 2007 Elsevier B.V. All rights reserved.

The intensity distribution and thermal stability of InnoSlab laser

Partially end-pumped slab laser is an innovative solid state laser, namely InnoSlab. Combining the hybrid resonator with partially end-pumping, the output power can be scaled with high beam quality. In this paper, the output intensity distributions are simulated by coordinate transformation fast Fourier transform (FFT) algorithm, comparing the thermal lens influence. As the simulated curves showed, the output mode is still good when the thermal lens effect is strong, indicating the good thermal stability of InnoSlab laser. Such a new kind of laser can be designed and optimized on the base of this simulation.

A Q-swicthed all-solid-state single-longitudinal-mode laser with adjustable pulse-width and high repetition rate

A single-longitudinal-mode (SLM) laser-diode pumped Nd: YAG laser with adjustable pulse width is developed by using the techniques of pre-lasing and changing polarization of birefingent crystal. The Q-switching voltage is triggered by the peak of the pre-lasing pulse to achieve the higher stability of output pulse energy. The output energy of more than 1 mJ is obtained with output energy stability of 3% (rms) at 100 Hz. The pulse-width can be adjusted from 30 ns to 300 ns by changing the Q-switching voltage. The probability of putting out single-longitudinal-mode pulses is almost 100%. The laser can be run over four hours continually without mode hopping.

Structure and thermal stability of novel fluorophosphate glasses

A systematic investigation on glass formation in the PbF2-InF3-BaHPO4 ternary system has been carried out. These glasses have characterized by IR spectra, Raman spectra and differential thermal analysis. The results show that the structure of these glasses is mainly affected by BaHPO4 and InF3 contents. With decreasing BaHPO4 content, the glass structure gradually transforms from metaphosphate to polyphosphate. When InF3 content is low, it mainly acts as network modifier, when its content is high; it enters glass matrix and forms In(O,F)(6) groups connecting the polymerized phosphorus oxygen species. PbF2 mainly acts as network modifier in this system. Systematic variations of the glass transition temperature and the thermal stability index agree well with these results. The most stable glass with Delta T = 230 degrees C and S = 21.79 K is obtained. (c) 2004 Elsevier B.V. All rights reserved.

Spectroscopic properties and thermal stability of Er3+-doped tungsten-tellurite glass for waveguide amplifier application

Tungsten-tellurite glass with molar composition of 60TeO(2)-30WO(3)-10Na(2)O has been investigated for developing planar broadband waveguide amplifier application. Spectroscopic properties and thermal stability of Er3+-doped tungsten-tellurite glass have been discussed. The results show that the introduction Of WO3 increases significantly the glass transition temperature and the maximum phonon energy. Er3+-doped tungsten-tellurite glass exhibits high glass transition temperature (377 degrees C), large emission cross-section (0.91 x 10(-20) cm(2)) at 1532 nm and broad full width at half maximum (FWHM), which make it preferable for broadband Er3+-doped waveguide amplifier application. (c) 2005 Elsevier B.V. All rights reserved.

Thermal stability and crystallochemical analysis for CoII based coordination polymers with TPP and TPPS porphyrins

Artículo CrystEngComm 2013

Study on the hydrolytic property and thermal stability of LiAlO2 substrate

The hydrolytic property and thermal stability of LiAlO2 (LAO), important factors for its application, were examined by AFM and X-ray rocking curve. We found that H2O may be deleterious for LAO surface polishing when the root mean square (RMS) value is less than 1 nm. However, when the RMS value is more than 1 nm it may be useful for LAO polishing. (100)-plane LAO substrates are annealed in the range of 850-900 degrees C in flux N-2, Slick AlN layer probably is produced on the substrate surface. M-plane GaN layer has grown on the substrate by metal-organic chemical vapor deposition (MOCVD) method. Theses results show that LiAlO2 crystal is a promising substrate of fabricating high-efficiency LEDs by MOCVD. (c) 2006 Elsevier B.V. All rights reserved.

Analysis of four decades of high elevation climate data

Four decades of instrumented climate records at D1 on Niwot Ridge suggest that high elevation data are an important - and even unique - part of the full climate picture. High elevation data provide information on changing lapse rates as well as model verification for global warming, which is predicted to occur earliest in high latitudes and at high elevations. The D1 records show climatic trends that arguably support global warming, assuming that greater planetary wave amplitude is verification of warming. Lapse rates reflect conditions of air mass stability, atmospheric moisture, and could [sic] cover, which contribute to feedback processes involving temperature, precipitation, and snowpack. The D1 record show a period, 1981-1985, when the lapse rate increased significantly, and this change was not detected by other data.

The effects of a trip wire and unsteadiness on a high speed highly loaded low-pressure turbine blade

This paper presents the effect of a single spanwise 2D wire upon the downstream position of boundary layer transition under steady and unsteady inflow conditions. The study is carried out on a high turning, high-speed, low pressure turbine (LPT) profile designed to take account of the unsteady flow conditions. The experiments were carried out in a transonic cascade wind tunnel to which a rotating bar system had been added. The range of Reynolds and Mach numbers studied includes realistic LPT engine conditions and extends up to the transonic regime. Losses are measured to quantify the influence of the roughness with and without wake passing. Time resolved measurements such as hot wire boundary layer surveys and surface unsteady pressure are used to explain the state of the boundary layer. The results suggest that the effect of roughness on boundary layer transition is a stability governed phenomena, even at high Mach numbers. The combination of the effect of the roughness elements with the inviscid Kelvin-Helmholtz instability responsible for the rolling up of the separated shear layer (Stieger [1]) is also examined. Wake traverses using pneumatic probes downstream of the cascade reveal that the use of roughness elements reduces the profile losses up to exit Mach numbers of 0.8. This occurs with both steady and unsteady inflow conditions.

SOI diode temperature sensor operated at ultra high temperatures-a critical analysis

This paper investigates the performance of diode temperature sensors when operated at ultra high temperatures (above 250°C). A low leakage Silicon On Insulator (SOI) diode was designed and fabricated in a 1 μm CMOS process and suspended within a dielectric membrane for efficient thermal insulation. The diode can be used for accurate temperature monitoring in a variety of sensors such as microcalorimeters, IR detectors, or thermal flow sensors. A CMOS compatible micro-heater was integrated with the diode for local heating. It was found that the diode forward voltage exhibited a linear dependence on temperature as long as the reverse saturation current remained below the forward driving current. We have proven experimentally that the maximum temperature can be as high as 550°C. Long term continuous operation at high temperatures (400°C) showed good stability of the voltage drop. Furthermore, we carried out a detailed theoretical analysis to determine the maximum operating temperature and exlain the presence of nonlinearity factors at ultra high temperatures. © 2008 IEEE.

Adaptive control of combustion instabilities for unknown sign of the high frequency gain

A type of adaptive, closed-loop controllers known as self-tuning regulators present a robust method of eliminating thermoacoustic oscillations in modern gas turbines. These controllers are able to adapt to changes in operating conditions, and require very little pre-characterisation of the system. One piece of information that is required, however, is the sign of the system's high frequency gain (or its 'instantaneous gain'). This poses a problem: combustion systems are infinite-dimensional, and so this information is never known a priori. A possible solution is to use a Nussbaum gain, which guarantees closed-loop stability without knowledge of the sign of the high frequency gain. Despite the theory for such a controller having been developed in the 1980s, it has never, to the authors' knowledge, been demonstrated experimentally. In this paper, a Nussbaum gain is used to stabilise thermoacoustic instability in a Rijke tube. The sign of the high frequency gain of the system is not required, and the controller is robust to large changes in operating conditions - demonstrated by varying the length of the Rijke tube with time. Copyright © 2008 by Simon J. Illingworth & Aimee S. Morgans.