Generalized Burgers equations and Euler-Painlev transcendents. I

Initial-value problems for the generalized Burgers equation (GBE) ut+u betaux+lambdaualpha =(delta/2)uxx are discussed for the single hump type of initial data both continuous and discontinuous. The numerical solution is carried to the self-similar ``intermediate asymptotic'' regime when the solution is given analytically by the self-similar form. The nonlinear (transformed) ordinary differential equations (ODE's) describing the self-similar form are generalizations of a class discussed by Euler and Painlevé and quoted by Kamke. These ODE's are new, and it is postulated that they characterize GBE's in the same manner as the Painlev equations categorize the Kortweg-de Vries (KdV) type. A connection problem for some related ODE's satisfying proper asymptotic conditions at x=±[infinity], is solved. The range of amplitude parameter is found for which the solution of the connection problem exists. The other solutions of the above GBE, which display several interesting features such as peaking, breaking, and a long shelf on the left for negative values of the damping coefficient lambda, are also discussed. The results are compared with those holding for the modified KdV equation with damping. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Water bottles from China: Decoding visual grammar

On the ALEA Study Tour to China, Beryl Exley and her roomie Kathryn O’Sullivan pondered over their first night dilemma whilst staying at a hotel in Beijing. They read the room service guide (in English) which advised against drinking the tap water and confirming the supply of one bottle of complementary water per guest per day. The room service guide listed ‘special’ bottled water was the equivalent of $AUS7 per bottle. However the dilemma was this: sitting on the shelf above the fridge were three different kinds of water-like bottles. Each had a different label, written mainly in Chinese characters. Not wanting to mistake the bottles, Beryl and Kathryn set about decoding the text of the three bottles in question.

Some Exact-Solutions Describing Unsteady Plane Gas-Flows With Shocks

A new class of exact solutions of plane gasdynamic equations is found which describes piston-driven shocks into non-uniform media. The governing equations of these flows are taken in the coordinate system used earlier by Ustinov, and their similarity form is determined by the method of infinitesimal transformations. The solutions give shocks with velocities which either decay or grown in a finite or infinite time depending on the density distribution in the ambient medium, although their strength remains constant. The results of the present study are related to earlier investigations describing the propagation of shocks of constant strength into non-uniform media.

Effect of reduced rotation length on Araucaria wood quality.

The review of existing information has identified the following: - the juvenile core in Araucaria is probably contained within the first 15 growth rings in the pith, with spiral grain being a chief determinant of its extent within the stem; - a reduction in rotation length for a given site index will reduce ASV and mature wood volume, with an increase in the proportion of juvenile wood; - for a given rotation length, lower ASV stems were estimated to contain a lower proportion of juvenile wood (based on the assumptions made and crude simulations using WEEDS, PL YSIM and STEPS software); regardless of juvenile wood proportions, smaller stems will yield a higher proportion of pith-in material; - an increase in the proportion of juvenile wood, due to a reduction in rotation length, could affect wood quality due to an increase in the proportion of the recovery containing high spiral grain, shorter tracheids and higher micellar angle; - high spiral grain and high micellar angles adversely impact on wood quality through their influence on twist and longitudinal shrinkage, respectively; - positive outcomes from a reduction in rotation length might include an increase in the proportion of live knots in upper stem sections and a reduction in the extent of brown-stain heartwood; - the uniformity in basic density within Araucaria stems means reduced rotation lengths and lower stem ASVs are unlikely to have a major impact on this wood property, and - the effect of a reduction in rotation length on the incidence of compression wood and timber susceptible to kiln staining could not be established from the available information.

Multinomial solutions of the beach equation

Exact multinomial solutions of the beach equation for shallow water waves on a uniformly sloping beach are found and related to solution of the same equation found earlier by other investigators, using integral transform techniques. The use of these solutions for a general initialvalue problem for the equation under investigation is briefly discussed.

Some direct numerical approaches to the solution of the singular nonlinear transonic integral equation

The nonlinear singular integral equation of transonic flow is examined, noting that standard numerical techniques are not applicable in solving it. The difficulties in approximating the integral term in this expression were solved by special methods mitigating the inaccuracies caused by standard approximations. It was shown how the infinite domain of integration can be reduced to a finite one; numerical results were plotted demonstrating that the methods proposed here improve accuracy and computational economy.

Invariance group properties and exact solutions of equations describing time-dependent free surface flows under gravity

Using the method of infinitesimal transformations, a 6-parameter family of exact solutions describing nonlinear sheared flows with a free surface are found. These solutions are a hybrid between the earlier self-propagating simple wave solutions of Freeman, and decaying solutions of Sachdev. Simple wave solutions are also derived via the method of infinitesimal transformations. Incomplete beta functions seem to characterize these (nonlinear) sheared flows in the absence of critical levels.

Exact, self-similar, time-dependent free surface flows under gravity

A class of exact, self-similar, time-dependent solutions describing free surface flows under gravity is found which extends the self-propagating class of solutions discovered earlier by Freeman (1972) to those which decay with time.

Acute and chronic effects of dietary nitrate supplementation on blood pressure and the physiological responses to moderate-intensity and incremental exercise

Dietary nitrate (NO3−) supplementation with beetroot juice (BR) over 4–6 days has been shown to reduce the O2 cost of submaximal exercise and to improve exercise tolerance. However, it is not known whether shorter (or longer) periods of supplementation have similar (or greater) effects. We therefore investigated the effects of acute and chronic NO3− supplementation on resting blood pressure (BP) and the physiological responses to moderate-intensity exercise and ramp incremental cycle exercise in eight healthy subjects. Following baseline tests, the subjects were assigned in a balanced crossover design to receive BR (0.5 l/day; 5.2 mmol of NO3−/day) and placebo (PL; 0.5 l/day low-calorie juice cordial) treatments. The exercise protocol (two moderate-intensity step tests followed by a ramp test) was repeated 2.5 h following first ingestion (0.5 liter) and after 5 and 15 days of BR and PL. Plasma nitrite concentration (baseline: 454 ± 81 nM) was significantly elevated (+39% at 2.5 h postingestion; +25% at 5 days; +46% at 15 days; P < 0.05) and systolic and diastolic BP (baseline: 127 ± 6 and 72 ± 5 mmHg, respectively) were reduced by ∼4% throughout the BR supplementation period (P < 0.05). Compared with PL, the steady-state V̇o2 during moderate exercise was reduced by ∼4% after 2.5 h and remained similarly reduced after 5 and 15 days of BR (P < 0.05). The ramp test peak power and the work rate at the gas exchange threshold (baseline: 322 ± 67 W and 89 ± 15 W, respectively) were elevated after 15 days of BR (331 ± 68 W and 105 ± 28 W; P < 0.05) but not PL (323 ± 68 W and 84 ± 18 W). These results indicate that dietary NO3− supplementation acutely reduces BP and the O2 cost of submaximal exercise and that these effects are maintained for at least 15 days if supplementation is continued.

N-Carbamoyl-DL-aspartic acid

CsHaN205, PL a = 6.438 (2), b = 7.486 (3), c = 8.048 (4)A, a = 72.2(1), fl = 80.8(1), y = 76.4 (1) °, D m = 1.65 (1) (flotation), D c = 1.64 Mg m -3, Z = 2. Final R = 0.095 for 1205 observed reflections. The molecule assumes the sterically least favourable conformation with the side chain carboxyl group staggered between the a-carboxyl group and the N atom attached to C '~. The ureido group takes part in two specific interactions involving two nearly parallel hydrogen bonds in one and two convergent hydrogen bonds in the other.

Long waves in inviscid compressible atmosphere II

Solitary waves have been found in an adiabatic compressible atmosphere which, in ambient state, has winds and temperature gradient, generalizing our earlier results for the isothermal atmosphere. Explicit results are obtained for the special case of linear temperature and linear wind distributions in the undisturbed conditions. An important result of the study is that the number of possible critical speeds of the flow depends crucially on whether the maximum Richardson number (which is variable in the present example) is greater or less than 1/4.

Ethyl 2-acetyl-3-(4-chloroanilino)butanoate

The title compound, C14H18ClNO3, adopts an extended conformation, with all of the main chain torsion angles associated with the ester and amino groups trans. In the crystal, inversion dimers linked by pairs of N-H center dot center dot center dot O hydrogen bonds are observed.

Application of Artificial Viscosity in Establishing Supercritical Solutions to the Transonic Integra

The nonlinear singular integral equation of transonic flow is examined in the free-stream Mach number range where only solutions with shocks are known to exist. It is shown that, by the addition of an artificial viscosity term to the integral equation, even the direct iterative scheme, with the linear solution as the initial iterate, leads to convergence. Detailed tables indicating how the solution varies with changes in the parameters of the artificial viscosity term are also given. In the best cases (when the artificial viscosity is smallest), the solutions compare well with known results, their characteristic feature being the representation of the shock by steep gradients rather than by abrupt discontinuities. However, 'sharp-shock solutions' have also been obtained by the implementation of a quadratic iterative scheme with the 'artificial viscosity solution' as the initial iterate; the converged solution with a sharp shock is obtained with only a few more iterates. Finally, a review is given of various shock-capturing and shock-fitting schemes for the transonic flow equations in general, and for the transonic integral equation in particular, frequent comparisons being made with the approach of this paper.