Plant delta(15)N associated with arbuscular mycorrhization, drought and nitrogen deficiency

It has long been evident that plant (15)N chiefly reflects the processes which fractionate (15)N/(14)N rather than the (15)N of plant N source(s). It has emerged recently that one of the most important fractionating processes contributing to the whole plant (15)N is the presence/absence, type or species of mycorrhiza, especially when interacting with nutrient deficiency. Ecto- and ericoid mycorrhizas are frequently associated with (15)N-depleted foliar (15)N, commonly as low as -12 per thousand. As shown by the present study, plants having no mycorrhiza, or those infected with various species of arbuscular mycorrhiza (AM)-forming fungi, interact with varying concentrations of soil nitrogen [N] and moisture to enrich plant (15)N by as much as 3.5 per thousand. Hence the lack of a mycorrhiza, or variation in the species of AM-forming fungal associations, can account for about 25% of the usually reported variations of foliar (15)N found in field situations and do so by (15)N enrichment rather than depletion. Copyright 1999 John Wiley & Sons, Ltd.     

On the Dirichlet Problem of Mixed Type for Lower Hybrid Waves in Axisymmetric Cold Plasmas

For a class of linear second order partial differential equations of mixed elliptic-hyperbolic type, which includes a well known model for analyzing possible heating in axisymmetric cold plasmas, we give results on the weak well-posedness of the Dirichlet problem and show that such solutions are characterized by a variational principle. The weak solutions are shown to be saddle points of natural functionals suggested by the divergence form of the PDEs. Moreover, the natural domains of the functionals are the weighted Sobolev spaces to which the solutions belong. In addition, all critical levels will be characterized in terms of global extrema of the functionals restricted to suitable infinite dimensional linear subspaces. These subspaces are defined in terms of a robust spectral theory with weights which is associated to the linear operator and is developed herein. Similar characterizations for the weighted eigenvalue problem and nonlinear variants will also be given. Finally, topological methods are employed to obtain existence results for nonlinear problems including perturbations in the gradient which are then applied to the well-posedness of the linear problem with lower order terms.     

On the global “two-sided” characteristic Cauchy problem for linear wave equations on manifolds

The global characteristic Cauchy problem for linear wave equations on globally hyperbolic Lorentzian manifolds is examined, for a class of smooth initial value hypersurfaces satisfying favourable global properties. First it is shown that, if geometrically well-motivated restrictions are placed on the supports of the (smooth) initial datum and of the (smooth) inhomogeneous term, then there exists a continuous global solution which is smooth “on each side” of the initial value hypersurface. A uniqueness result in Sobolev regularity \(H^{1/2+\varepsilon }_{\mathrm {loc}}\) is proved among solutions supported in the union of the causal past and future of the initial value hypersurface, and whose product with the indicator function of the causal future (resp. past) of the hypersurface is past compact (resp. future compact). An explicit representation formula for solutions is obtained, which prominently features an invariantly defined, densitised version of the null expansion of the hypersurface. Finally, applications to quantum field theory on curved spacetimes are briefly discussed.     

Elastic rods in life- and material-sciences: A general integrable model

The study of elastic deformations in thin rods has recently seen renewed interest due to the close connection between these systems and coarse-grained models of widespread application in life- and material-sciences. Until now, the analysis has been restricted to the solution of equilibrium equations for continuous models characterized by constant bending and twisting elastic moduli and/or by isotropic rod section. However, more realistic models often require more general conditions: indeed this is the case whenever microscopic information issuing from atomistic simulations is to be transferred to analytic or semi-analytic coarse-grained or macroscopic models. In this paper we will show that integrable, indeed solvable, equations are obtained under quite general conditions and that regular (e.g. circular helical) solutions emerge from reasonable choices of elastic stiffnesses.     

A miniature pulser-preamplifier for ultrasonic transducers

In order to avoid difficulties experienced with conventional ultrasonic systems using several feet of shielded cable to connect transducer and electronics, a miniature pulser-preamplifier was developed to fit the transducer holder. Its characteristics proved superior to most devices in common use.     

Error growth in the numerical integration of periodic orbits by multistep methods, with application to reversible systems

We study the growth with time of (the coefficients of the asymptoticexpansion of) the error in the numerical integration with linearmultistep methods of periodic solutions of systems of ordinarydifferential equations. Particular attention is devoted to reversiblesystems. It turns out that symmetric linear multistep methodscannot be recommended in spite of the fact that they mimic thereversibility of the true flow. For reversible second-ordersystems, linear multistep methods without parasitic double rootsare useful.