Diophantine sets of polynomials over algebraic extensions of the rationals

Let L be a recursive algebraic extension of Q. Assume that, given alpha is an element of L, we can compute the roots in L of its minimal polynomial over Q and we can determine which roots are Aut(L)-conjugate to alpha. We prove that there exists a pair of polynomials that characterizes the Aut(L)-conjugates of alpha, and that these polynomials can be effectively computed. Assume furthermore that L can be embedded in R, or in a finite extension of Q(p) (with p an odd prime). Then we show that subsets of L[X](k) that are recursively enumerable for every recursive presentation of L[X], are diophantine over L[X]

Hilbert's Tenth Problem for rational function fields over p-adic fields

Let K be a p-adic field (a finite extension of some Q_p) and let K(t) be the field of rational functions over K. We define a kind of quadratic reciprocity symbol for polynomials over K and apply it to prove isotropy for a certain class of quadratic forms over K(t). Using this result, we give an existential definition for the predicate "v_t(x) >= 0" in K(t). This implies undecidability of diophantine equations over K(t)

Numerical simulation of long and slender cylinders vibrating in axial flow applied to the Myrrha reactor

Flow induced vibrations are an important concern in the design of nuclear reactors. One of the possible designs of the 4th generation nuclear reactors is a lead-cooled fast reactor of which MYYRHA is a prototype. The combination of high liquid density, flow velocity, low pitch-to-diameter ratio and the absence of grid spacers makes this design prone to flow induced vibrations. Although most vibrations are induced by cross flow, axial flow around this slender structure could also induce vibrations. In order to gain insight in the possible vibrations (either induced by cross flow, axial flow or an external excitation) this study examines the change of eigenmodes and frequencies of a bare rod due to the lead-bismuth flow. To do so partitioned simulations of the fluid structure interaction are performed in which the structure is initially perturbed according to an in-air eigenmode

Wind-structure interaction simulations for the prediction of ovalling vibrations in silo groups

Wind-induced ovalling vibrations were observed during a storm in October 2002 on several empty silos of a closely spaced group consisting of 8 by 5 thin-walled silos in the port of Antwerp (Belgium). The purpose of the present research is to investigate if such ovalling vibrations can be predicted by means of numerical simulations. More specifically, the necessity of performing computationally demanding wind-structure interaction (WSI) simulations is assessed. For this purpose, both one-way and two-way coupled simulations are performed. Before considering the entire silo group, a single silo in crosswind is simulated. The simulation results are in reasonably good agreement with observations and WSI simulations seem to be required for a correct prediction of the observed ovalling vibrations