Kinematic analysis of Bricard’s mechanism

We show how the tools of computational algebra can be used to analyze the configuration space of multibody systems. One advantage of this approach is that the mobility can be computed without using the Jacobian of the system. As an example, we treat thoroughly the well-known Bricard’s mechanism, but the same methods can be applied to a wide class of rigid multibody systems. It turns out that the configuration space of Bricard’s system is a smooth closed curve, which can be explicitly parametrized. Our computations also yield a new formulation of constraints which is better than the original one from the point of view of numerical simulations.     

On the numerical solution of involutive ordinary differential systems: enhanced linear algebra

^** Email: jukka.tuomela{at}joensuu.fi^*** Corresponding author. Email: arponen{at}maths.warwick.ac.uk^**** Email: villesamuli.normi{at}joensuu.fi We analyse some Runge–Kutta type methods for computing1D integral manifolds, i.e. solutions to ordin-ary differentialequations and differential-algebraic equations. We show thatwe can compute the solutions which respect all the constraintsof the problem reliably and reasonably quickly. Moreover, weshow that the so-called impasse points are regular points inour approach and hence require no special attention.     

Continuous-time monitoring of Landau-Zener interference in a cooper-pair box

Landau-Zener (LZ) tunneling can occur with a certain probability when crossing energy levels of a quantum two-level system are swept across the minimum energy separation. Here we present experimental evidence of quantum interference effects in solid-state LZ tunneling. We used a Cooper-pair box qubit where the LZ tunneling occurs at the charge degeneracy. By employing a weak nondemolition monitoring, we observe interference between consecutive LZ-tunneling events; we find that the average level occupancies depend on the dynamical phase. The system's unusually strong linear response is explained by interband relaxation. Our interferometer can be used as a high-resolution Mach-Zehnder-type detector for phase and charge.     

Rapid Screening of Indole-3-Acetic Acid and Other Indole Derivatives in Bacterial Culture Broths by Planar Chromatography

JPC – Journal of Planar Chromatography – Modern TLC - The aim of this study was to find suitable separation conditions for the rapid screening of indole derivatives in bacterial culture...     

Tensor invariants in numerical geometric integration of ODEs

We consider geometric numerical integration (GI) of ordinary differential equations (ODEs). We propose that in GI one needs concepts which are both geometric and algebraic. In this paper we start from an algebraic point of view: we introduce tensor invariants attached to an ODE as well as to an integrator. The notion of “sharing a tensor invariant” generalizes the well known notion of conserving a symplectic structure by an integrator. Several examples are given.     

Rotation Planar Extraction and Medium-Pressure Solid—Liquid Extraction of Onion (Allium cepa)

JPC – Journal of Planar Chromatography – Modern TLC - Extraction of onion (Allium cepa L.) with 80:20 (v/v) methanol—water in water by rotation planar extraction (RPE) and medium-...     

On the numerical solution of involutive ordinary differential systems

We consider a Galerkin finite element method that uses piecewisebilinears on a modified Shishkin mesh for a model singularlyperturbed convection–diffusion problem on the unit square.The method is shown to be convergent, uniformly in the perturbationparameter , of order N^–1in a global energy norm, providedonly that N^–1, where O(N²)mesh points are used. Thuson the new mesh the method yields more accurate results thanon Shishkin’s original piecewise uniform mesh, whereit is convergent of order N^–1lnN. Numerical experiments support our theoretical results. Received 14 September, 1998. Revised 24 September, 1999.