A NEW FINITE ELEMENT APPROXIMATION OF A STATE-CONSTRAINED OPTIMAL CONTROL PROBLEM

In this paper, we study numerical methods for an optimal control problem with pointwise state constraints. The traditional approaches often need to deal with the deltasingularity in the dual equation, which causes many difficulties in its theoretical analysis and numerical approximation. In our new approach we reformulate the state-constrained optimal control as a constrained minimization problems only involving the state, whose optimality condition is characterized by a fourth order elliptic variational inequality. Then direct numerical algorithms （nonconforming finite element approximation） are proposed for the inequality, and error estimates of the finite element approximation are derived. Numerical experiments illustrate the effectiveness of the new approach.     

Local observations of phase singularities in optical fields in waveguide structures

A linear copolymer made of two reciprocally attracting N-monomer blocks collapses to a compact phase through a novel transition, whose exponents are determined with extensive Monte Carlo simulations in two and three dimensions. In the former case, an identification with the statistical geometry of suitable percolation paths allows one to predict that the number of contacts between the blocks grows like N9/16. In the compact phase the blocks are mixed and, in two dimensions, also zipped, in such a way to form a spiral, double chain structure.     

Influencing the angular emission of a single molecule

We present the first experimental proof for the influence of a nearby nanosized metal object on the angular photon emission by a single molecule. Using a novel angular sensitive detection scheme, we directly quantify the redirection of angular emission for different molecular dipole orientations as an object is scanned laterally over the molecule at different heights. An excellent agreement between experiments and 2D-numerical simulations is found for molecules oriented perpendicular to the sample, whereas, for parallel orientations, the observed behavior contradicts the calculated behavior.     

Comparison of the ammonium oxalate extraction of fertilizer for K2O, method 983.02, with the ammonium citrate/EDTA extraction, method 993.31

The direct available method for phosphorus in fertilizers, Method 960.03, is an Official Method for extraction of both P2O5 and K2O. Because K2O is much more soluble and easier to extract than P2O5, the conditions of the extraction procedure are set for efficient extraction of P2O5, and the extraction of K2O is, in effect, a bonus. In 1993, a modified extraction procedure, using an extractant of ammonium citrate/ethylenediaminetetraacetic acid (EDTA) solution, was evaluated for P2O5 and then collaboratively studied. This now-modified extraction procedure for phosphorus is Official Method 993.31, which is used extensively as an alternative to Method 960.03 for phosphorus because it is less labor-intensive. Method 993.31 was also evaluated in our laboratory for K2O extraction, but it was never formally collaboratively studied for K2O. To demonstrate the suitability of Method 993.31 as an extraction procedure for K2O, as well as P2O5 in fertilizers, Method 993.31 extraction for K2O was compared with Method 983.02, the traditional ammonium oxalate extraction procedure for K2O. A wide range of fertilizer samples was extracted by using both procedures. The t-test for samples containing < 30% K2O had a t-value of 1.23 and a probability of 0.22, which indicates there was no significant difference in the results obtained by the 2 extraction methods. The t-test for samples containing > 30% K2O had a t-value of 0.30 and a probability of 0.77, also indicating no significant difference. It is recommended that Method 983.02 be modified to include the ammonium citrate/EDTA extraction procedure as an additional option for extraction of K2O from commercial fertilizers.