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.     

Photofragmentation of closo-carboranes part 1: Energetics of decomposition

The ionic fragmentation following B 1s and C 1s excitation of three isomeric carborane cage compounds [closo-dicarbadodecaboranes: orthocarborane (1,2-C2B10H12), metacarborane (1,7-C2B10H12), and paracarborane (1,12-C2B10H12)] is compared with the energetics of decomposition. The fragmentation yields for all three molecules are quite similar. Thermodynamic cycles are constructed for neutral and ionic species in an attempt to systemically characterize single-ion closo-carborane creation and fragmentation processes. Lower energy decomposition processes are favored. Among the ionic species, the photon-induced decomposition is dominated by BH+ and BH2(+) fragment loss. Changes in ion yield associated with core to bound excitations are observed.     

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.     

A method for integrated process simulation in the mining industry

This paper proposes a method of Integrated Process Simulation (MIPS), which considers the dynamic, stochastic and systemic characteristics of mining operations to support investment decisions in this industry. This MIPS supports development of a Decision Support System (DSS) that considers product quality, process productivity and production costs. A case study is described that used the MIPS to make better investment decisions. The MIPS has proven, in practice, to be effective in several applications; for example, in defining the maintenance policy for critical equipment in an iron ore concentration plant; the process for removing impurities and simulating the company's budget to evaluate the viability of different business plans.     

Reaction Chemistry at Discrete Organometallic Fragments on Black Phosphorus

Black phosphorus (bP) is a two-dimensional van der Waals material unique in its potential to serve as a support for single-site catalysts due to its similarity to molecular phosphines, ligands quintessential in homogeneous catalysis. However, there is a scarcity of synthetic methods to install single metal centers on the bP lattice. Here, we demonstrate the functionalization of bP nanosheets with molecular Re and Mo complexes. A suite of characterization techniques, including infrared, X-ray photoelectron and X-ray absorption spectroscopy as well as scanning transmission electron microscopy corroborate that the functionalized nanosheets contain a high density of discrete metal centers directly bound to the bP surface. Moreover, the supported metal centers are chemically accessible and can undergo ligand exchange transformations without detaching from the surface. The steric and electronic properties of bP as a ligand are estimated with respect to molecular phosphines. Sterically, bP resembles tri(tolyl)phosphine when monodentate to a metal center, and bis(diphenylphosphino)propane when bidentate, whereas electronically bP is a σ-donor as strong as a trialkyl phosphine. This work is foundational in elucidating the nature of black phosphorus as a ligand and underscores the viability of using bP as a basis for single-site catalysts.