A method for the reconstruction of unknown non-monotonic growth functions in the chemostat

We propose an adaptive control law that allows one to identify unstable steady states of the open-loop system in the single-species chemostat model without the knowledge of the growth function. We then show how one can use this control law to trace out (reconstruct) the whole graph of the growth function. The process of tracing out the graph can be performed either continuously or step-wise. We present and compare both approaches. Even in the case of two species in competition, which is not directly accessible with our approach due to lack of controllability, feedback control improves identifiability of the non-dominant growth rate.Comment: expansion of ideas from proceedings paper (17 pages, 8 figures), proceedings paper is version v

Progress at the WITCH experiment

The WITCH-experiment will measure the energy spectrum of the recoiling daughter ions in $\beta$-decay to search for non-standard scalar and tensor type interaction. To facilitate this a Penning trap is used to store the radioactive ions. Thus the recoil ions can leave the source without any energy loss and their energy can be probed by the subsequent retardation spectrometer. The experiment is being set up at present at ISOLDE/CERN. The principle and the status of the WITCH-experiment will be presented. (12 refs)

WITCH: a recoil spectrometer for weak interaction and nuclear physics studies

An experimental set-up is described for the precise measurement of the recoil energy spectrum of the daughter ions from nuclear beta decay. The experiment is called WITCH, short for Weak Interaction Trap for CHarged particles, and is set up at the ISOLDE facility at CERN. The principle of the experiment and its realization are explained as well as the main physics goal. A cloud of radioactive ions stored in a Penning trap serves as the source for the WITCH experiment, leading to the minimization of scattering and energy loss of the decay products. The energy spectrum of the recoiling daughter ions from the $\beta$--decays in this ion cloud will be measured with a retardation spectrometer. The principal aim of the WITCH experiment is to study the electroweak interaction by determining the beta--neutrino angular correlation in nuclear $\beta$--decay from the shape of this recoil energy spectrum. This will be the first time that the recoil energy spectrum of the daughter ions from $\beta$--decay can be measured for a wide variety of isotopes, independent of their specific properties

Isospin mixing in the ground state of sup 5 sup 2 Mn

The presence of isospin mixing into the ground state of sup 5 sup 2 Mn was studied via anisotropic positron emission from nuclei. With this method the isospin forbidden Fermi-component in the Gamow-Teller dominated beta decay was determined. It is shown that sample purity and the control of positron scattering is of vital importance. Comparison between theory and experiment shows that shell model calculations of the isospin mixing probability deviate by a factor three to seven from experiment. For more recent Hartree-Fock-RPA based calculations the difference is over two orders of magnitude

HPGe detectors for low-temperature nuclear orientation

Using the low-temperature nuclear orientation (LTNO) technique one can study various interesting properties of atomic nuclei and nuclear decay which can be deduced from the measurements of the angular distributions of charged particles emitted during the decay. However, the use of particle detectors working in conditions of LTNO devices (which are generally not available commercially) is a necessary precondition for the realization of these experiments. Planar HPGe detectors for detection of charged particles at "liquid helium" temperatures were developed and produced at NPI Rez. Relatively simple technology using vacuum evaporation and diffusion was employed. The performance of detectors at low temperatures was tested and their characteristics measured in a testing cryostat before using them in real experiments. The HPGe detectors were extensively used in a whole range of LTNO experiments with various physical objectives - in offline (IKS Leuven) as well as online (CERN-ISOLDE, Louvain-la- Neuve - LISOL) experiments. In the framework of the project "Meson-Exchange Enhancement of First-Forbidden $\beta$-Transitions in the Lead Region", the measurements of angular distribution of emitted $\beta$-particles allowed to determine experimentally the "meson-exchange currents" contribution to the $\beta$-decay. In the project "Isospin Mixing in N~Z nuclei", the isospin-forbidden $\beta$-transitions of the nuclei in region (A = 50-100) were studied in order to obtain information on the isospin structure of the nuclear states. A new project looking for the possible presence of the tensor currents contribution to the $\beta$-decay is being prepared for the CERN-ISOLDE facility

Fundamental weak interaction studies using polarised nuclei and ion traps

Two experiments to search for new physics beyond the standard model for electroweak interactions by measuring correlations between different spin and momentum vectors in nuclear beta -decay are discussed. In the first experiment the correlation between the emission asymmetry and the longitudinal polarisation of positrons emitted by polarised nuclei is determined. This type of measurement is sensitive to the presence of right-handed currents but also to possible scalar and tensor-type currents in the weak interaction. The aim of the second experiment is to determine the beta nu -correlation in beta -decay by measuring the energy spectrum of the recoil ions, using a Penning trap and a retardation spectrometer. In this case the focus is on the search for scalar currents in the weak interaction. The results of the experiments presented here are complementary to results from experiments in muon decay and at high-energy colliders

Search for right-handed currents in the β±\beta^{\pm} decay of 118/Sb^{118}/Sb

We report on a recent experiment searching for right-handed currents in the /sup 118/Sb nuclear beta -decay. The correlation between the spin polarization and the beta -emission asymmetry of the positrons from the /sup 118/Sb decay is sensitive to the helicity structure of the weak interaction. A precision measurement of this correlation improves the limit on right-handed currents in beta -decay. (7 refs)