Continuous dependence on the geometry and on the initial time for a class of parabolic problems I

In this paper, we investigate the continuous dependence on the geometry and the initial time for solutions u( x , t) of a class of nonlinear parabolic initial‐boundary value problems. Copyright © 2007 John Wiley & Sons, Ltd.     

Improved bounds for some nonstandard problems in generalized heat conduction

We consider the Maxwell-Cattaneo system of equations for generalized heat conduction where the temperature and heat flux satisfy a nonstandard auxiliary condition which prescribes a combination of their values initially and at a later time. We obtain L₂ bounds for the temperature and heat flux by means of Lagrange identities. These bounds extend the range of validity for the parameter in the nonstandard condition under a constraint on the coefficients in the differential equations.     

Pointwise and L2 bounds in some nonstandard problems for the heat equation

We consider some initial-boundary value problems for the linear and nonlinear heat equation where the gradient of the solution is prescribed on the boundary. Assuming that a solution exists, we obtain bounds for the solution and its gradient by maximum principle arguments or by means of differential and integral inequalities.     

Some remarks on Saint-Venant's principle

We consider a three-dimensional hyperelastic cylinder in Ω = D × [0, ∞]. We study the asymptotic behaviour of the deformations of the cross-sections in an equilibrium state. In this case we show that the solutions either have exponential decay or exponential growth. We give some initial conditions such that the latter case occurs.     

Design and synthesis of aromatic inhibitors of anthranilate synthase

Aromatic analogues of chorismate were synthesised as potential inhibitors of anthranilate synthase. Molecular modelling using GOLD2.1 showed that these analogues docked into the active site of Serratia marcescens anthranilate synthase in the same conformation as chorismate. Most compounds were found to be micromolar inhibitors of S. marcescens anthranilate synthase. The most potent analogue, 3-(1-carboxy-ethoxy)-4-hydroxybenzoate (K(I) 3 microM), included a lactyl ether side chain. This appears to be a good replacement for the enol-pyruvyl side chain of chorismate.     

The water rise in front of a model planing hull

It is known that the water “splashes-up” or rises above the undisturbed surface immediately in front of a planing surface. This rise is greatest in front of a flat planing plate and a number of attempts have been made to reduce the experimental measurements of this phenomenon to some kind of order. Since it was first independently proposed by both Schnitzer and Smiley in 1952, all attempts to correlate the flat plate splash-up have started with the assumption that splash is only a function of the immersed length of the plate and is independent of trim angle at least below about 20°. In part, this was because the three early studies which compared this hypothesis with experimental data omitted those portions of the data which did not support the hypothesis. The present paper concludes that this forty year old hypothesis is fallacious and that the water rise in front of any prismatic planing surface is best approximated by $$\frac{d}{{\sqrt {bl} }} = k\sin ^2 {\mathbf{\tau }}$$ whered is the vertical water rise at the water/keel intersection;b is the beam;l is the submerged length of the keel;τ is the trim angle;k: is a constant determined from experiment, approximated by,k = 2e ^?2.5β , whereβ is the deadrise angle in radians. It might be thought that this is a slight contribution, of little practical import, but for one thing. Starting in the 1950's most towing tank experimenters in the United States abandoned the difficult measurement of model draft and obtained only the “actually wetted length” from underwater photographs. But theoretical planing force calculations require a knowledge of the relationship between a hull and the undisturbed water plane. Thus if modern experimental data is to be compared with theory, it is necessary to estimate what the undefined splash-up or water rise was during each experiment, in order to estimate the model's true position in space. The paper concludes by criticizing the format of some modern reports of experiments with model planing hulls and suggests that, in addition to the usual graphical presentations, measured data should always be reported numerically. Also, that when relevant data is omitted from a plot, the facts of such omission should be clearly stated.