Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

Electron exchange coupling for single-donor solid-state spin qubits

Intervalley interference between degenerate conduction band minima has been shown to lead to oscillations in the exchange energy between neighboring phosphorus donor electron states in silicon [B. Koiller, X. Hu, and S. Das Sarma, Phys. Rev. Lett. 88, 027903 (2002); Phys. Rev. B 66, 115201 (2002)]. These same effects lead to an extreme sensitivity of the exchange energy on the relative orientation of the donor atoms, an issue of crucial importance in the construction of silicon-based spin quantum computers. In this article we calculate the donor electron exchange coupling as a function of donor position incorporating the full Bloch structure of the Kohn-Luttinger electron wave functions. It is found that due to the rapidly oscillating nature of the terms they produce, the periodic part of the Bloch functions can be safely ignored in the Heitler-London integrals as was done by Koiller, Hu, and Das Sarma, significantly reducing the complexity of calculations. We address issues of fabrication and calculate the expected exchange coupling between neighboring donors that have been implanted into the silicon substrate using an 15 keV ion beam in the so-called top down fabrication scheme for a Kane solid-state quantum computer. In addition, we calculate the exchange coupling as a function of the voltage bias on control gates used to manipulate the electron wave functions and implement quantum logic operations in the Kane proposal, and find that these gate biases can be used to both increase and decrease the magnitude of the exchange coupling between neighboring donor electrons. The zero-bias results reconfirm those previously obtained by Koiller, Hu, and Das Sarma.

A high definition, finite difference time domain method

A high definition, finite difference time domain (HD-FDTD) method is presented in this paper. This new method allows the FDTD method to be efficiently applied over a very large frequency range including low frequencies, which are problematic for conventional FDTD methods. In the method, no alterations to the properties of either the source or the transmission media are required. The method is essentially frequency independent and has been verified against analytical solutions within the frequency range 50 Hz-1 GHz. As an example of the lower frequency range, the method has been applied to the problem of induced eddy currents in the human body resulting from the pulsed magnetic field gradients of an MRI system. The new method only requires approximately 0.3% of the source period to obtain an accurate solution. (C) 2003 Elsevier Science Inc. All rights reserved.

Skin-friction measurements in high-enthalpy hypersonic boundary layers

Skin-friction measurements are reported for high-enthalpy and high-Mach-number laminar, transitional and turbulent boundary layers. The measurements were performed in a free-piston shock tunnel with air-flow Mach number, stagnation enthalpy and Reynolds numbers in the ranges of 4.4-6.7, 3-13 MJ kg(-1) and 0.16 x 10(6)-21 x 10(6), respectively. Wall temperatures were near 300 K and this resulted in ratios of wall enthalpy to flow-stagnation enthalpy in the range of 0.1-0.02. The experiments were performed using rectangular ducts. The measurements were accomplished using a new skin-friction gauge that was developed for impulse facility testing. The gauge was an acceleration compensated piezoelectric transducer and had a lowest natural frequency near 40 kHz. Turbulent skin-friction levels were measured to within a typical uncertainty of +/-7%. The systematic uncertainty in measured skin-friction coefficient was high for the tested laminar conditions; however, to within experimental uncertainty, the skin-friction and heat-transfer measurements were in agreement with the laminar theory of van Driest (1952). For predicting turbulent skin-friction coefficient, it was established that, for the range of Mach numbers and Reynolds numbers of the experiments, with cold walls and boundary layers approaching the turbulent equilibrium state, the Spalding & Chi (1964) method was the most suitable of the theories tested. It was also established that if the heat transfer rate to the wall is to be predicted, then the Spalding & Chi (1964) method should be used in conjunction with a Reynolds analogy factor near unity. If more accurate results are required, then an experimentally observed relationship between the Reynolds analogy factor and the skin-friction coefficient may be applied.

An international perspective on sunken state vessels as underwater cultural heritage

On 2 November 2001, the General Assembly of the United Nations Scientific, Economic and Cultural Organisation (UNESCO) adopted the convention on the Protection of the Underwater Cultural Heritage. Among the many complex issues addressed in the convention is the legal status of sunken state-owned vessels, including warships. Prior to the adoption of this convention, no conventional or customary international law existed with regards to the question of abandonment of state-owned vessels or the application of the principle of sovereign immunity to sunken state vessels. While difficulties between coastal states and maritime and former colonial powers resulted in a regime that does not comprehensively address the issues, the convention does provide some guidance in this regard and may provide a basis for further development.

Composition and quality of harvest residues and soil organic matter under windrow residue management in young hoop pine plantations as revealed by solid-state C-13 NMR spectroscopy

Solid-state C-13 nuclear magnetic resonance (NMR) with cross-polarisation (CP) and magic-angle-spinning (MAS) was used to: (a) examine the changes in carbon (C) composition of windrowed harvest residues during the first 3 years of hoop pine plantations in subtropical Australia; (b) assess the impacts of windrowed harvest residues on soil organic matter (SOM) composition and quality in the 0-10 cm soil layer. Harvest residues were collected from 0-, 1-, 2- and 3-year-old windrows of ca. 2.5 m width (15 m apart for 0-, 1- and 2-year-old sites and 10 m apart for 3-year-old site). Soils from the 0 to 10 cm soil layer were collected from the 1-, 2- and 3-year-old sites. The 13C NMR spectra of the harvest residues indicated the presence of lignin in the hoop pine wood, foliage and newly incorporated organic matter (NIOM). Condensed tannin structures were found in the decay-resistant bark, small wood and foliage, but were absent in other residue components and SOM. The NMR spectra of small wood samples contained condensed tannin structures because the outer layer of bark was not removed. NIOM showed a shift from foliage-like structures (celluloses) to lignin-type structures, indicating an incorporation of woody residues from the decomposing harvest residues. Suberins were also present in the small wood, foliage and bark. The 13C CP NMR spectra of SOM indicated that in areas where windrows were present, SOM did not show compositional changes. However, an increase in SOM quality under the windrows in the second year after their formation as characterised by the alkyl C/O-alkyl C (A/O-A) ratio was mainly due to inputs from the decomposition of the labile, readily available components of the windrowed harvest residues. (C) 2002 Published by Elsevier Science B.V.

(-)-CGP 12177 increases contractile force and hastens relaxation of human myocardial preparations through a propranolol-resistant state of the beta1-adrenoceptor

Two forms of the activated beta(1)-adrenoceptor exist, one that is stabilized by (-)-noradrenaline and is sensitive to blockade by (-)-propranolol and another which is stabilized by partial agonists such as (-)-pindolol and (-)-CGP 12177 but is relatively insensitive to (-)-propranolol. We investigated the effects of stimulation of the propranolol-resistant PI-adrenoceptor in the human heart. Myocardium from non-failing and failing human hearts were set up to contract at 1 Hz. In right atrium from non-ailing hearts in the presence of 200 nM (-)-propranolol, (-)-CGP 12177 caused concentration-dependent increases in contractile force (-logEC(50)[M] 7.3+/-0.1, E-max 23+/-1% relative to maximal (-)-isoprenaline stimulation of beta(1)- and beta(2)-adrenoceptors, n=86 patients), shortening of the time to reach peak force (-logEC(50)[M] 7.4+/-0.1, E-max 37+/-5%, n=61 patients) and shortening of the time to reach 50% relaxation (t(50%), -logEC(50)[M] 7.3+/-0.1, E-max 33+/-2%, n=61 patients). The potency and maxima of the positive inotropic effects were independent of Ser49Gly- and Gly389Arg-beta(1)-adrenoceptor polymorphisms but were potentiated by the phosphodiesterase inhibitor 3-isobutyl-1-methylxanthine (-logEC(50)[M] 7.7+/-0.1, E-max 68+/-6%, n=6 patients, P

Constitutively active signal transducer and activator of transcription 5 can replace the requirement for growth hormone in adipogenesis of 3T3-F442A preadipocytes

Although it is the best characterized in vitro model of GH action, the mechanisms used by GH to induce differentiation of murine 3T3-F442A preadipocytes remain unclear. Here we have examined the role of three transcriptional regulators in adipogenesis. These regulators are either rapidly induced in response to GH [Stra13, signal transducer and activator of transcription (Stat) 3] or of central importance to GH signaling (Stat5). Retroviral transfection of 3T3-F442A preadipocytes was used to increase expression of Stra13, Stat3, and Stat5a. Only Stat5a transfection increased the expression of adipogenic markers peroxisome proliferator-activated receptor gamma, CCAAT enhancer binding protein (C/EBP)alpha, and adipose protein 2/fatty acid-binding protein in response to GH, as determined by quantitative RT-PCR. Transfection with constitutively active Stat3 and Stat5a revealed that constitutively active Stat5a but not Stat3 was able to replace the GH requirement for adipogenesis. Constitutively active Stat5a but not Stat3 was able to increase the formation of lipid droplets and expression of alpha-glycerol phosphate dehydrogenase toward levels seen in mature adipocytes. Constitutively active Stat5a was also able to increase the expression of transcripts for C/EBPalpha to similar levels as GH, and of C/EBPbeta, peroxisome proliferator-activated receptor gamma, and adipose protein 2/fatty acid-binding protein transcripts to a lesser extent. An in vivo role for GH in murine adipogenesis is supported by significantly decreased epididymal fat depot size in young GH receptor-deleted mice, before manifestation of the lipolytic actions of GH. We conclude that Stat5 is a critical factor in GH-induced, and potentially prolactin-induced, murine adipogenesis.