The low energy X-ray spectrometry technique as applied to semiconductors.

We describe the recent introduction of low energy X-ray emission spectrometry as a metrology technique to control the fabrication process in the integrated circuit industry. The benefits of this particular analytical method and the wide field of potential applications are addressed.     

Uniform electron gases

We show that the traditional concept of the uniform electron gas (UEG)—a homogeneous system of finite density, consisting of an infinite number of electrons in an infinite volume—is inadequate to model the UEGs that arise in finite systems. We argue that, in general, a UEG is characterized by at least two parameters, viz. the usual one-electron density parameter ρ and a new two-electron parameter η. We outline a systematic strategy to determine a new density functional E (ρ, η) across the spectrum of possible ρ and η values.     

Limit theory for random walks in degenerate time-dependent random environments

We study continuous-time (variable speed) random walks in random environments on ${\mathbb{Z}}^d$, $d\ge 2$, where, at time t, the walk at x jumps across edge $(x,y)$ at time-dependent rate $a_t(x,y)$. The rates, which we assume stationary and ergodic with respect to space–time shifts, are symmetric and bounded but possibly degenerate in the sense that the total jump rate from a vertex may vanish over finite intervals of time. We formulate conditions on the environment under which the law of diffusively-scaled random walk path tends to Brownian motion for almost every sample of the rates. The proofs invoke Moser iteration to prove sublinearity of the corrector in pointwise sense; a key additional input is a conversion of certain weighted energy norms to ordinary ones. Our conclusions apply to random walks on dynamical bond percolation and interacting particle systems as well as to random walks arising from the Helffer–Sjöstrand representation of gradient models with certain non-strictly convex potentials.     

A 3000 K laboratory emission spectrum of water

An emission spectrum of hot water with a temperature of about 3000 K is obtained using an oxy-acetylene torch. This spectrum contains a very large number of transitions. The spectrum, along with previous cooler laboratory emission spectra and an absorption spectrum recorded from a sunspot, is analyzed in the 500-2000 cm(-1) region. Use of a calculated variational linelist for water allows significant progress to be made on assigning transitions involving highly excited vibrational and rotational states. In particular emission from rotationally excited states up to J=42 and vibrational levels with up to eight quanta of bending motion are assigned.     

Intramolecular interactions and <Emphasis Type="Italic">cis</Emphasis> peptidic bonds

The cis Gly–Gly peptidic bond observed in dihydrofolate reductase, which takes place between a beta sheet and an alpha helix is chosen as an example to study the various factors which influence this conformation. The peptidic chain of 16 amino acids is studied by a QM/MM scheme (6-31+G* B3LYP—Amber 99). Both electronic and classical contributions to the total energy take part to the stabilization of the cis conformation. A special role is played by the alpha helix when it is bonded to the carbonyl group of the bond of interest. Contribution to the Fernando Bernardi Memorial Issue.     

Thinking outside the box: the uniform electron gas on a hypersphere

We discuss alternative homogeneous electron gas systems in which a finite number n of electrons are confined to a D-dimensional sphere. We derive the first few terms of the high-density (r(s) → 0, where r(s) is the Seitz radius) energy expansions for these systems and show that, in the thermodynamic limit (n → ∞), these terms become identical to those of D-dimensional jellium.     

On Cluster Properties of Classical Ferromagnets in an External Magnetic Field

Correlation functions of ferromagnetic spin systems satisfying a Lee-Yang property are studied. It is shown that, for classical systems in a non-vanishing uniform external magnetic field h, the connected correlation functions decay exponentially in the distances between the spins, i.e., the inverse correlation length (“mass gap”), m(h), is strictly positive. Our proof is very short and transparent and is valid for complex values of the external magnetic field h, provided that \(\mathrm {Re}\, h \not = 0\). It implies a mean-field lower bound on m(h), as \(h \searrow 0\), first established by Lebowitz and Penrose for the Ising model. Our arguments also apply to some quantum spin systems.     

Quantitative immunofluorescent assay of full-length,recombinant CD4 in solution and mapping of its epitopes

A specific, rapid, and sensitive method for the detection of CD4 in solution was developed using pairs of fluorescently stained monoclonal antibodies which do not cross-compete. The assay is quantitated by flow cytometry using Simply Cellular microbeads (SC beads) as the primary support for the first anti-CD4 mAb. This method uses the standard conditions for anti-CD4 monoclonal antibody binding, washing, detection, and quantitation by flow cytometry of the CD4 antigen either bound to the SC beads or expressed on the cell surface. The monoclonal antibody used (Leu 3a PE) is the standard reference used to evaluate the CD4 concentration. This method differs from ELISA techniques, which need an antigen standard curve and thus can be influenced by the quality and source of the antigen. This type of assay is also a procedure which enables determination of the level of oligomerization of the bound antigen. It can be used for any antigen to which monoclonal antibodies recognizing at least two distinct epitopes are available. The use of soluble or full-length CD4 derivatives as potential therapeutic agents against AIDS, would benefit from a precise quantitation of the CD4 molecules which still have their proper tertiary structure.     

Exact wave functions of two-electron quantum rings

We demonstrate that the Schr?dinger equation for two electrons on a ring, which is the usual paradigm to model quantum rings, is solvable in closed form for particular values of the radius. We show that both polynomial and irrational solutions can be found for any value of the angular momentum and that the singlet and triplet manifolds, which are degenerate, have distinct geometric phases. We also study the nodal structure associated with these two-electron states.