Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations

We study difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order ordinary differential equations. We formulate conditions which guarantee a priori bounds on first differences of solutions to the discretized problem. We establish existence results for solutions to the discretized boundary value problems subject to nonlinear boundary conditions. We apply our results to show that solutions to the discrete problem converge to solutions of the continuous problem in an aggregate sense. (C) 2002 Elsevier Science Ltd. All rights reserved.

Existence of multiple solutions for second-order discrete boundary value problems

We give conditions on f involving pairs of discrete lower and discrete upper solutions which lead to the existence of at least three solutions of the discrete two-point boundary value problem yk+1 - 2yk + yk-1 + f (k, yk, vk) = 0, for k = 1,..., n - 1, y0 = 0 = yn,, where f is continuous and vk = yk - yk-1, for k = 1,..., n. In the special case f (k, t, p) = f (t) greater than or equal to 0, we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and Peterson and are in the spirit of our results for the continuous analogue. (C) 2002 Elsevier Science Ltd. All rights reserved.

Comparative evaluation of juvenoids for control of cat fleas (Siphonaptera : Pulicidae) in topsoil

The efficacy of a photostable formulation of methoprene and two photostable juvenoids, fenoxycarb and pyriproxyfen, and their residual activity in inhibiting the emergence of adult cat fleas, Ctenocephalides felis (Bouche), was studied in topsoil. Nursery pots composed of clay, peat, and plastic, and wooden flats were used to hold soil samples. Treated soil samples were exposed to sunlight during the 63-d study period. Methoprene was as effective as fenoxycarb and pyriproxyfen against cat fleas for up to 42 d in clay, peat, and plastic pots at a concentration of 64.56 mg (AI) /m(2) (6 mg [AI] /ft(2)), but its activity declined significantly thereafter. In contrast, fenoxycarb and pyriproxyfen showed strong residual activity for the entire 63 d. The activity of methoprene declined even more rapidly over time in wooden flats, while at the same concentrations the other two juvenoids showed significant residual activity for 63 d. Clay, peat, and plastic pots were therefore considered to be equally effective for evaluating the outdoor efficacy of juvenoids in comparison to the wooden flats. However, results obtained with wooden flats may be more realistic when testing residual activity of volatile chemicals such as methoprene. Fenoxycarb and pyriproxyfen showed strong efficacy and residual activity at concentrations of 8.07, 16.14, and 32.28 mg (AI) /m(2), whereas methoprene did not cause a significant reduction of adult emergence at levels below 64.56 mg (AI) /m(2). LC50 values for methoprene, fenoxycarb, and pyriproxyfen needed for preventing flea emergence when applied to topsoil were estimated to be 0.643, 0.031, and 0.028 ppm, respectively.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

Control of chaotic motion in a dual-spin spacecraft with nutational damping

Control of chaotic vibrations in a dual-spin spacecraft with an axial nutational damper is achieved using two techniques. The control methods are implemented on two realistic spacecraft parameter configurations that have been found to exhibit chaotic instability when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitudes and frequencies. Such a torque, in practice, may arise under malfunction of the control system or from an unbalanced rotor. Chaotic instabilities arising from these torques could introduce uncertainties and irregularities into a spacecraft's attitude motion and, consequently, could have disastrous effects on its operation. The two control methods, recursive proportional feedback and continuous delayed feedback, are recently developed techniques for control of chaotic motion in dynamic systems. Each technique is outlined and the effectiveness on this model compared and contrasted. Numerical simulations are performed, and the results are studied by means of time history, phase space, Poincare map, Lyapunov characteristic exponents, and bifurcation diagrams.

Control of chaotic instability in a dual-spin spacecraft with dissipation using energy methods

Control of chaotic instability in a rotating multibody system in the form of a dual-spin spacecraft with an axial nutational damper is achieved using an algorithm derived using energy methods. The control method is implemented on two realistic spacecraft parameter configurations which have been found to exhibit chaotic instability when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitudes and frequencies. Such a torque, in practice, may arise under malfunction of the control system or from an unbalanced rotor. Chaotic instabilities arising from these torques could introduce uncertainties and irregularities into a spacecraft's attitude and consequently impair pointing accuracy. The control method is formulated from nutational stability results derived using an energy sink approximation for a dual-spin spacecraft with an asymmetric platform and axisymmetric rotor. The effectiveness of the control method is shown numerically and the results are studied by means of time history, phase space, Poincare map, Lyapunov characteristic exponents and Bifurcation diagrams.

Control of chaotic instabilities in a spinning spacecraft with dissipation using Lyapunov's method

Control of chaotic instability in a simplified model of a spinning spacecraft with dissipation is achieved using an algorithm derived using Lyapunov's second method. The control method is implemented on a realistic spacecraft parameter configuration which has been found to exhibit chaotic instability for a range of forcing amplitudes and frequencies when a sinusoidally varying torque is applied to the spacecraft. Such a torque, may arise in practice from an unbalanced rotor or from vibrations in appendages. Numerical simulations are performed and the results are studied by means of time history, phase space, Poincare map, Lyapunov characteristic exponents and bifurcation diagrams. (C) 2002 Elsevier Science Ltd. All rights reserved.

A real symmetric Lanczos subspace implementation of quantum scattering using boundary inhomogeneities

We present an efficient and robust method for calculating state-to-state reaction probabilities utilising the Lanczos algorithm for a real symmetric Hamiltonian. The method recasts the time-independent Artificial Boundary Inhomogeneity technique recently introduced by Jang and Light (J. Chem. Phys. 102 (1995) 3262) into a tridiagonal (Lanczos) representation. The calculation proceeds at the cost of a single Lanczos propagation for each boundary inhomogeneity function and yields all state-to-state probabilities (elastic, inelastic and reactive) over an arbitrary energy range. The method is applied to the collinear H + H-2 reaction and the results demonstrate it is accurate and efficient in comparison with previous calculations. (C) 2002 Elsevier Science B.V. All rights reserved.

Boundary-layer transition measurements in hypervelocity flows in a shock tunnel

Experiments to investigate the transition process in hypervelocity boundary layers were performed in the T4 free-piston shock tunnel. An array of thin-film heat-transfer gauges was used to detect the location and extent of the transitional region on a 1500 mm long x 120 turn wide flat plate, which formed one of the walls of a duct. The experiments were performed in a Mach 6 flow of air with 6- and 12-MJ/kg nozzle-supply enthalpies at unit Reynolds numbers ranging from 1.6 x 10(6) to 4.9 x 10(6) m(-1). The results show that the characteristics typical of transition taking place through the initiation, growth, and merger of turbulent spots are evident in the heat-transfer signals. A 2-mm-high excrescence located 440 turn from the leading edge was found to be capable of generating a turbulent wedge within an otherwise laminar boundary layer at a unit Reynolds number of 2.6 x 10(6) m(-1) at the 6-MJ/kg condition. A tripping strip, located 100 mm from the leading edge and consisting of a line 37 teeth of 2 rum height equally spaced and spanning the test surface, was also found to be capable of advancing the transition location at the same condition and at the higher enthalpy condition.

Control of dimethylsulfoxide reductase expression in Rhodobacter capsulatus: the role of carbon metabolites and the response regulators DorR and RegA

Regulation of the expression of dimethylsulfoxide (DMSO) reductase was investigated in the purple phototrophic bacterium Rhodobacter capsulatus. Under phototrophic, anaerobic conditions with malate as carbon source, DMSO caused an approximately 150-fold induction of DMSO reductase activity. The response regulator DorR was required for DMSO-dependent induction and also appeared to slightly repress DMSO reductase expression in the absence of substrate. Likewise, when pyruvate replaced malate as carbon source there was an induction of DMSO reductase activity in cells grown at low light intensity (16 W m(-2)) and again this induction was dependent on DorR. The level of DMSO reductase activity in aerobically grown cells was elevated when pyruvate replaced malate as carbon source. One possible explanation for this is that acetyl phosphate, produced from pyruvate, may activate expression of DMSO reductase by direct phosphorylation of DorR, leading to low levels of induction of dor gene expression in the absence of DMSO. A mutant lacking the global response regulator of photosynthesis gene expression, RegA, exhibited high levels of DMSO reductase in the absence of DMSO, when grown phototrophically with malate as carbon source. This suggests that phosphorylated RegA acts as a repressor of dor operon expression under these conditions. It has been proposed elsewhere that RegA-dependent expression is negatively regulated by the cytochrome cbb(3) oxidase. A cco mutant lacking cytochrome cbb(3) exhibited significantly higher levels of Phi[dorA::lacZ] activity in the presence of DMSO compared to wild-type cells and this is consistent with the above model. Pyruvate restored DMSO reductase expression in the regA mutant to the same pattern as found in wild-type cells. These data suggest that R. capsulatus contains a regulator of DMSO respiration that is distinct from DorR and RegA, is activated in the presence of pyruvate, and acts as a negative regulator of DMSO reductase expression.

The development of a positive non-infectious control for the detection of Perkinsus using the Ray test

To establish a noncontagious control for the Ray thioglycollate test for the detection of Perkinsus in mollusks we evaluated nonviable stages of P. olseni for enlargement of hypnospores and blue/black iodine stain. Trophozoites made nonviable with formalin, irradiation or colchicine failed to swell in thioglycollate. They remained small and did not differentially stain in iodine. Trophozoites that had already developed into hypnospores in thioglycollate were rendered inactive by freezing, ethanol or formalin immersion. They retained their iodinophilic properties and thus could provide a partial control for the Ray Test.

Balancing acts: Respiratory sensations, motor control and human posture

1. The present brief review covers some novel aspects of integration between respiration and movement of the body. 2. There are potent viscerosomatic reflexes in animals involving small-diameter pulmonary afferents that, when excited, would limit exercise. However, recent studies using lobeline injections to excite pulmonary afferents in awake humans suggest that there is no evoked reflex motoneuronal inhibition. Instead, the noxious respiratory sensations generated by the vagal afferents may be crucial in the decision to stop exercise. 3. While respiratory movements may affect limb movements, the control of the trunk and limbs can involve interaction (and even interference) with key respiratory muscles, such as the diaphragm. Recent studies have revealed that not only does the diaphragm receive feed-forward drive prior to some limb movements, but that it also contracts both phasically and tonically during repetitive limb movements. 4. Thus, challenges to posture can indirectly challenge ventilation, while coordinated diaphragm contraction may contribute to control of the trunk.