On the absorption of infrared radiation by electrons in semiconductor inversion layers

Resonances in the inversion layer for infrared fields normal to the interface do not occur at the electric subband splittings. They are shifted from the subband splittings by resonant screening of the infrared field. The corrections for (100) Si surfaces are shown to be comparable to the shifts ascribed to many-body effects.     

Strategic approaches to drug design. I. An integrated software framework for molecular modelling

Summary An integrated molecular graphics and computational chemistry framework is described which has been designed primarily to handle small molecules of up to 300 atoms. The system provides a means of integrating software from any source into a single framework. It is split into two functional subsystems. The first subsystem, called COSMIC. runs on low-cost, serial-linked colour graphics terminals and allows the user to prepare and examine structural data and to submit them for extensive computational chemistry. Links also allow access to databases, other modelling systems and user-written modules. Much of the output from COSMIC cannot be examined with low level graphics. A second subsystem, called ASTRAL, has been developed for the high-resolution Evans & Sutherland PS300 colour graphics terminal and is designed to manipulate complex display structures. The COSMIC minimisers, geometry investigators, molecular orbital displays, electrostatic isopotential generators and various interfaces and utilities are described.     

An evaluation of force-field treatments of aromatic interactions

Experimental measurements of edge-to-face aromatic interactions have been used to test a series of molecular mechanics force fields. The experimental data were determined for a range of differently substituted aromatic rings using chemical double mutant cycles on hydrogen-bonded zipper complexes. These complexes were truncated for the purposes of the molecular mechanics calculations so that problems of conformational searching and the optimisation of large structures could be avoided. Double-mutant cycles were then carried out in silico using these truncated systems. Comparison of the experimental aromatic interaction energies and the X-ray crystal structures of these truncated complexes with the calculated data show that conventional molecular mechanics force fields (MM2, MM3, AMBER and OPLS) do not perform well. However, the XED force field which explicitly represents electron anisotropy as an expansion of point charges around each atom reproduces the trends in interaction energy and the three-dimensional structures exceedingly well. Collapsing the XED charges onto atom centres or the use of semi-empirical atom-centred charges within the XED force field gives poor results. Thus the success of XED is not related to the methods used to assign the atomic charge distribution but can be directly attributed to the use of off-atom centre charges.     

FieldScreen: virtual screening using molecular fields. Application to the DUD data set

FieldScreen, a ligand-based Virtual Screening (VS) method, is described. Its use of 3D molecular fields makes it particularly suitable for scaffold hopping, and we have rigorously validated it for this purpose using a clustered version of the Directory of Useful Decoys (DUD). Using thirteen pharmaceutically relevant targets, we demonstrate that FieldScreen produces superior early chemotype enrichments, compared to DOCK. Additionally, hits retrieved by FieldScreen are consistently lower in molecular weight than those retrieved by docking. Where no X-ray protein structures are available, FieldScreen searches are more robust than docking into homology models or apo structures.     

$$L^{infty }$$ estimates on trajectories confined to a closed subset,for control systems with bounded time variation

Mathematical Programming - The term ‘distance estimate’ for state constrained control systems refers to an estimate on the distance of an arbitrary state trajectory from the subset of...     

Many-body effects in the first excited subband of the n-inversion layer of Si

We have calculated the self-energies of electrons in the lowest and first excited sub-bands of Si inversion layers. The self-consistent wavefunctions calculated in the Hartree approximation were used, and dynamic screening was approximated by the Lundqvist-Overhauser model. The correlation energy of an electron in the excited band is quite large: about ?10 meV at an inversion layer density of 10¹¹ cm^?2 to about ?16 meV at 3 × 10¹² cm^?2. The calculated separation between subbands is in very good agreement with available experimental measurements. An exciton is predicted with a binding energy of 0.9 meV at N_inv = 10¹² cm^?2 calculated in the static approximation.     

A maximum principle for optimal control problems with mixed constraints

Necessary conditions in the form of maximum principles are derivedfor optimal control problems with mixed control and state constraints.Traditionally, necessary condtions for problems with mixed constraintshave been proved under hypothesis which include the requirementthat the Jacobian of the mixed constraint functional, with respectto the control variable, have full rank. We show that it canbe replaced by a weaker ‘interiority’ hypothesis.This refinement broadens the scope of the optimality conditions,to cover some optimal control problems involving differentialalgebraic constraints, with index greater than unity.     

Second Order Sufficient Conditions for Optimal Control Problems with Non-unique Minimizers: An Abstract Framework

Standard second order sufficient conditions in optimal control theory provide not only the information that an extremum is a weak local minimizer, but also tell us that the extremum is locally unique. It follows that such conditions will never cover problems in which the extremum is continuously embedded in a family of constant cost extrema. Such problems arise in periodic control, when the cost is invariant under time translations, in shape optimization, where the cost is invariant under Euclidean transformations (translations and rotations of the extremal shape), and other areas where the domain of the optimization problem does not really comprise elements in a linear space, but rather an equivalence class of such elements. We supply a set of sufficient conditions for minimizers that are not locally unique, tailored to problems of this nature. The sufficient conditions are in the spirit of earlier conditions for ‘non-isolated’ minima, in the context of general infinite dimensional nonlinear programming problems provided by Bonnans, Ioffe and Shapiro, and require coercivity of the second variation in directions orthogonal to the constant cost set. The emphasis in this paper is on the derivation of directly verifiable sufficient conditions for a narrower class of infinite dimensional optimization problems of special interest. The role of the conditions in providing easy-to-use tests of local optimality of a non-isolated minimum, obtained by numerical methods, is illustrated by an example in optimal control.