A numerical study of a two-layer model for the growth of granular matter in a silo

The problem of filling a silo of given bounded cross-section with granular matter can be described by the two-layer model of Hadeler and Kuttler [8]. In this paper we discuss how similarity quasi-static solutions for this model can be numerically characterized by the direct finite element solution of a semidefinite elliptic Neumann problem. We also discuss a finite difference scheme for the dynamical model through which we can show that the growing profiles of the heaps in the silo evolve in finite time towards such similarity solutions.Comment: Submitted to Proceedings of the MASCOT2015 - IMACS/ISGG Workshop, Rome, Ital

AGRESTE Program. Part 2: French test-sites

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Direct lunar descent optimisation by finite elements in time approach

In this paper a direct approach to trajectory optimisation, based on Finite Elements in Time (FET) discretisation is presented. Trajectory optimisation is performed combining the effectiveness and flexibility of Finite Elements in Time in solving complex boundary values problems with a common nonlinear programming algorithm. In order to avoid low accuracy proper to direct approaches, a mesh adaptivity strategy is implemented which exploits the ability of finite elements to represent both continuous and discontinuous functions. The effectiveness and accuracy of direct transcription by FET are proved by a selected number of sample problems. Finally an optimal landing manoeuvre is presented to show the power of the proposed approach in solving even complex and realistic problems

Numerical solutions for lunar orbits

Starting from a variational formulation based on Hamilton’s Principle, the paper exploits the finite element technique in the time domain in order to solve orbital dynamic problems characterised by constrained boundary value rather than initial value problems. The solution is obtained assembling a suitable number of finite elements inside the time interval of interest, imposing the desired constraints, and solving the resultant set of non-linear algebraic equations by means of Newton-Raphson method. In particular, in this work this general solution strategy is applied to periodic orbits determination. The effectiveness of the approach in finding periodic orbits in the unhomogeneous gravity field of the Moon is assessed by means of relevant examples, and the results are compared with those obtained by standard time marching techniques as well as with analytical results

Plant regulation of microbial enzyme production in situ

Soil extracellular enzymes regulate the rate at which complex organic forms of nitrogen (N) become bio-available. Much research has focused on the limitations to heterotrophic enzyme production via lab incubations, but little has been done to understand the limitations to enzyme production in situ. We created root and symbiotic mycelia exclusion treatments using mesh in-growth bags in the field to isolate the effect of roots and other portions of the microbial community on enzyme production. When fertilized with complex protein N we found increases in N-degrading enzyme concentrations only when root in-growth was allowed. No response was observed when complex N was added to root-free treatments. Expanding on economic rules of microbial element limitation theory developed from lab incubation data, we suggest this is due to active transport of labile carbon (C) from roots to associated microbial communities in root bags. Roots alleviate C-limitation of microbial enzyme synthesis, representing a trade off between plants and microbes- plant C for microbial derived N