Design of a digital controller for spinning flexible spacecraft

An approach to digital control system design is applied to the analysis and design of a practical onboard digital attitude control system for a class of spinning vehicles characterized by a rigid body and two connected flexible appendages. The approach used is to design a continuous-data control system that will provide a satisfactory system response. Then, using the digital redesign method, a digital controller with onboard digital computer is designed to provide a digital control system whose states are similar to those of the continuous system at sampling instants. The simplicity of application of this approach is indicated by example. The example, using spinning Skylab parameters, is used to substantiate the conclusions

Low momentum nucleon-nucleon potential and shell model effective interactions

A low momentum nucleon-nucleon (NN) potential V-low-k is derived from meson exhange potentials by integrating out the model dependent high momentum modes of V_NN. The smooth and approximately unique V-low-k is used as input for shell model calculations instead of the usual Brueckner G matrix. Such an approach eliminates the nuclear mass dependence of the input interaction one finds in the G matrix approach, allowing the same input interaction to be used in different nuclear regions. Shell model calculations of 18O, 134Te and 135I using the same input V-low-k have been performed. For cut-off momentum Lambda in the vicinity of 2 fm-1, our calculated low-lying spectra for these nuclei are in good agreement with experiments, and are weakly dependent on Lambda.Comment: 5 pages, 5 figure

Family of Hermitian Low-Momentum Nucleon Interactions with Phase Shift Equivalence

Using a Schmidt orthogonalization transformation, a family of Hermitian low-momentum NN interactions is derived from the non-Hermitian Lee-Suzuki (LS) low-momentum NN interaction. As special cases, our transformation reproduces the Hermitian interactions for Okubo and Andreozzi. Aside from their common preservation of the deuteron binding energy, these Hermitian interactions are shown to be phase shift equivalent, all preserving the empirical phase shifts up to decimation scale Lambda. Employing a solvable matrix model, the Hermitian interactions given by different orthogonalization transformations are studied; the interactions can be very different from each other particularly when there is a strong intruder state influence. However, because the parent LS low-momentum NN interaction is only slightly non-Hermitian, the Hermitian low-momentum nucleon interactions given by our transformations, including the Okubo and Andreozzi ones, are all rather similar to each other. Shell model matrix elements given by the LS and several Hermitian low-momentum interactions are compared.Comment: 10 pages, 7 figure

Shell-model study of the N=82 isotonic chain with a realistic effective hamiltonian

We have performed shell-model calculations for the even- and odd-mass N=82 isotones, focusing attention on low-energy states. The single-particle energies and effective two-body interaction have been both determined within the framework of the time-dependent degenerate linked-diagram perturbation theory, starting from a low-momentum interaction derived from the CD-Bonn nucleon-nucleon potential. In this way, no phenomenological input enters our effective Hamiltonian, whose reliability is evidenced by the good agreement between theory and experiment.Comment: 7 pages, 11 figures, 3 tables, to be published in Physical Review

Low-momentum Hyperon-Nucleon Interactions

We present a first exploratory study for hyperon-nucleon interactions using renormalization group techniques. The effective two-body low-momentum potential V_low-k is obtained by integrating out the high-momentum components from realistic Nijmegen YN potentials. A T-matrix equivalence approach is employed, so that the low-energy phase shifts are reproduced by V_low-k up to a momentum scale Lambda ~ 500 MeV. Although the various bare Nijmegen models differ somewhat from each other, the corresponding V_low-k interactions show convergence in some channels, suggesting a possible unique YN interaction at low momenta.Comment: 4 pages, 6 figure

Three-body monopole corrections to the realistic interactions

It is shown that a very simple three-body monopole term can solve practically all the spectroscopic problems--in the $p$, $sd$ and $pf$ shells--that were hitherto assumed to need drastic revisions of the realistic potentials.Comment: 4 pages, 5figure

A simple electrostatic model applicable to biomolecular recognition

An exact, analytic solution for a simple electrostatic model applicable to biomolecular recognition is presented. In the model, a layer of high dielectric constant material (representative of the solvent, water) whose thickness may vary separates two regions of low dielectric constant material (representative of proteins, DNA, RNA, or similar materials), in each of which is embedded a point charge. For identical charges, the presence of the screening layer always lowers the energy compared to the case of point charges in an infinite medium of low dielectric constant. Somewhat surprisingly, the presence of a sufficiently thick screening layer also lowers the energy compared to the case of point charges in an infinite medium of high dielectric constant. For charges of opposite sign, the screening layer always lowers the energy compared to the case of point charges in an infinite medium of either high or low dielectric constant. The behavior of the energy leads to a substantially increased repulsive force between charges of the same sign. The repulsive force between charges of opposite signs is weaker than in an infinite medium of low dielectric constant material but stronger than in an infinite medium of high dielectric constant material. The presence of this behavior, which we name asymmetric screening, in the simple system presented here confirms the generality of the behavior that was established in a more complicated system of an arbitrary number of charged dielectric spheres in an infinite solvent.Comment: 15 pages, 6 figure