On sensitivity in optimal control problems

Two types of interpretations of multipliers in both static and dynamic optimization problems are described. It is snown that the Lagrange multipliers encountered in mathematical programming problems and the auxiliary functions arising in Pontryagintype optimal control problems sometimes have highly analogous interpretations as rates of change of the optimal attainable value of an objective function, or in some cases as bounds on average rates of change.     

The proton shell closure at 14C

Data for the ¹⁴C(³He, d)¹⁵N and ¹⁴C(t, ⁴He)¹³B reactions are compared to DWBA calculations to measure the spectroscopic factors for $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{and}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ proton transitions. Good fits are found for the stripping data, as well as to similar stripping data on ¹²C. These results lower the previous value for proton $\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ hole strength in ¹⁴C by a factor of two, indicating that the neutron closure of the p-shell has provided a very good proton closed shell at ¹⁴C. Stripping results to low-lying positive parity states in ¹⁵N are interpreted within a Nilsson scheme, which reproduces the experimental results, but which requires a large deformation for the s-d orbitals.     

Branching fractions for psi(2S)-to-J/psi transitions

We describe new measurements of the inclusive and exclusive branching fractions for psi(2S) transitions to J/psi using e(+)e(-) collision data collected with the CLEO detector operating at CESR. All branching fractions and ratios of branching fractions reported here represent either the most precise measurements to date or the first direct measurements. Indirectly and in combination with other CLEO measurements, we determine B(chi(cJ) --> gamma(J/psi)) and B[psi(2S) --> light hadrons].     

Reconstructing the electron in a fractionalized quantum fluid

The low-energy physics of the fractional Hall liquid is described in terms of quasiparticles that are qualitatively distinct from electrons. We show, however, that a long-lived electronlike quasiparticle also exists in the excitation spectrum: the state obtained by the application of an electron creation operator to a fractional quantum Hall ground state has a nonzero overlap with a complex, high energy bound state containing an odd number of composite-fermion quasiparticles. The electron annihilation operator similarly couples to a bound complex of composite-fermion holes. We predict that these bound states can be observed through a conductance resonance in experiments involving a tunneling of an external electron into the fractional quantum Hall liquid. A comment is made on the origin of the breakdown of the Fermi liquid paradigm in the fractional Hall liquid.     

Poloidal E x B drift used as an effective rotational transform to achieve long confinement times in a toroidal electron plasma

Electron plasmas with mean densities of 5.0 x 10(6) cm(-3) have been confined for as long as 18 ms in a partially toroidal trap with a purely toroidal magnetic field (B(0)=196 G, R(o)=43 cm, a=5 cm). Confinement is limited to 2.0 ms unless feedback is employed to suppress the growth of a toroidal version of the m=1 diocotron mode. The confinement time is much longer than all characteristic single-particle drift time scales and therefore confirms the existence of an equilibrium in which the space-charge-generated E x B drift acts as an effective rotational transform.     

Low temperature solid-state NMR experiments of half-integer quadrupolar nuclides: caveats and data analysis

Solid-state NMR spectroscopy of half-integer quadrupolar nuclides has received a lot of interest recently with the advent of new methodologies and higher magnetic fields. We present here the extension of our previous low temperature method to an 18.8T system. This new probe entailed a total redesign including a cross coil and variable capacitors that are operational at cryogenic temperatures. The limitations to sensitivity are also discussed; including a new diode network, the utilization of a cryogenic band pass filter, and the consequences of the RF profiles of the coil. Further, details of the spectroscopy of quadrupolar nuclei in a protein are discussed, such as the observation of the outer transitions and how to distinguish them from the desired +/-1/2 transition.     

Forced folding and structural analysis of metastable proteins

A significant fraction of the proteins encoded by the human and other genomes appears to be significantly unfolded in vitro. This will undoubtedly hamper attempts to characterize their structure by classical crystallographic or solution NMR methods. Here we show that encapsulation of a metastable protein within the restricted volume a reverse micelle can be used to force fold the protein and allow its characterization by modern methods of NMR spectroscopy. This may have significant utility in the context of structural proteomics. In addition, variation of the inner volume of the reverse micelle can be used to probe the character of the manifold of unfolded states.