This study reports on a novel two-step process for biodiesel production consisting of hydrolysis of oils in sub-critical water and subsequent supercritical dimethyl carbonate esterification. This process found to occur optimally at the subcritical water treatment (270°C/27MPa) for 25 min followed by a subsequent supercritical dimethyl carbonate treatment (300°C/9MPa) for 15 min to achieve a com...

It is not sufficiently appreciated that methly alcohol is very toxic. For econoi' reasons, methyl (wood) alcohol is employed as a substitute for tbyl (grain) alcohol, in what may be termed comparatively innocent products, such as perfumes, hair tonics, skin lotions, , '/ polishes, varnishes, etc. Government analysts, not infrequently, find it employed in the manufacture of various extracts for ...

Environmentally dependent subcritical crack growth, or stress-corrosion cracking, along ceramic-metal interfaces is studied for the silica glass-copper system. Tests were conducted in various gaseous and liquid environments in order to determine their relative effects on stress-corrosion cracking and to gain some insight into the mechanisms that control interfacial crack growth. In agreement wi...

Free-surface flow over a bottom topography with an asymptotic depth change (a `step') is considered for di erent ranges of Froude numbers varying from subcritical, transcritical, to supercritical. For the subcritical case, a linear model indicates that a train of transient waves propagates upstream and eventually alters the conditions there. This leading-order upstream influence is shown to hav...

A new modeling approach to subcritical crack propagation (i.e. static fatigue) in ceramics is introduced and applied to the case of ceramic fibers. This approach relies on classical fracture mechanics, in which the zone near the crack’s tip is modified by the environment (particularly through oxidation). Chemical reactions and diffusion are introduced naturally, which makes the model highly dep...

We analyze the rate of convergence towards self-similarity for the subcritical KellerSegel system in the radially symmetric two-dimensional case and in the corresponding one-dimensional case for logarithmic interaction. We measure convergence in Wasserstein distance. The rate of convergence towards self-similarity does not degenerate as we approach the critical case. As a byproduct, we obtain a...

We consider the equation ∆u − V (x)u + W (x)u = 0 and its parabolic counterpart in noncompact manifolds. Under some natural conditions on the positive functions V and W , which may only have ‘slow’ or no decay near infinity, we establish existence of positive solutions in both the critical and the subcritical case. This leads to the solutions, in the difficult positive curvature case, of many s...