On the interaction of point charges in an arbitrary domain

We develop a systematic approach to calculating the electrostatic force between point charges in an arbitrary domain with arbitrary boundary conditions. When the boundary is present, the simple expression for the force acting on a charge as “the charge times the field it is placed in” becomes ill-defined. However, this rule can be salvaged if the field in question is redefined to only include all terms that do not diverge at the charge position, in particular, those due to the charge itself. The proof requires handling the self-action energy divergence for point charges, which is accomplished by means of a geometrical regularization.     

Laser statistics and cavity length

The effect on the optical field of changing the cavity length of a laser, while keeping the resonance frequency constant, is examined. It is shown that the fully quantized laser theory gives explicit expressions for the length dependence of the light intensity distribution, that are not shared by the semiclassical theory, and are quite different above, at, and below threshold. Some possible experiments are suggested.     

Les corps viscoélastiques boltzmanniens

Sans résumé     

Electromagnetically Induced Transparency: Answering a Question of Romain

At the request of Romain, I derive analytical results describing the response of a three-level medium subjected to a strong pump beam and two weak probe beams. All three beams have a constant intensity. The results are the real and imaginary parts of the medium coherence, which is related to the nonlinear susceptibility. The main feature is that the three beams mix absorption and dispersion. There is a finite window of gain bounded by a point of electromagnetically induced transparency. This revised version was published online in July 2006 with corrections to the Cover Date.     

Bose–Einstein condensates in 1D- and 2D optical lattices

Bose–Einstein condensates of rubidium atoms are transferred into one- and two-dimensional optical lattice potentials. The phase coherence of the condensate wavefunction in the lattice potential is studied by suddenly releasing the atoms from the trapping potential and observing the multiple matter-wave interference pattern of several thousand expanding quantum gases. We show how arbitrary phase gradients can be mapped onto the periodic wavefunction through the application of a potential gradient. Furthermore, the experimentally measured strength of the momentum components is compared to a theoretical model of the condensate wavefunction in the lattice. Received: 3 July 2001 / Revised version: 26 September 2001 / Published online: 23 November 2001     

A New Acyclic α‐Hydrogen Bearing Nitroxide and its Corresponding Alkoxyamine for Stable Free Radical Polymerization

Summary: The synthesis of the new α‐hydrogen bearing nitroxide, 2,2,5‐trimethyl‐4‐(isopropyl)‐3‐azahexane‐3‐oxyl (BIPNO) ( 4 ), and its corresponding alkoxyamine, N‐tert‐butyl‐N‐(1‐isopropyl‐2‐methyl‐propyl)‐O‐(1‐phenyl‐ethyl)‐hydroxylamine (PhEt‐BIPNO) ( 7 ), are described in this paper. Reaction of styrene with the new nitroxide in the presence of a Jacobsen‐like manganese catalyst, Mn(salen)Cl, at ambient atmosphere afforded the alkoxyamine in 96% yield. Styrene and n‐butyl acrylate were polymerized in bulk in the presence of the new alkoxyamine. The alkoxyamine turned out to be a suitable “initiator” for controlled radical polymerization.

Structure of α‐hydrogen bearing nitroxide and its corresponding alkoxyamine.     

Optimization of a minimal sample preparation protocol for imaging mass spectrometry of unsectioned juvenile invertebrates

Tissue sections have long been the subject matter for the application of imaging mass spectrometry, but recently the technique has been adapted for many other purposes including bacterial colonies and 3D cell culture. Here, we present a simple preparation method for unsectioned invertebrate tissue without the need for fixing, embedding, or slicing. The protocol was used to successfully prepare a Hawaiian bobtail squid hatchling for analysis, and the resulting data detected ions that correspond to compounds present in the host only during its symbiotic colonization by Vibrio fischeri.     

Convergence of the cyclical relaxation method for linear inequalities

The relaxation method for linear inequalities is studied and new bounds on convergence obtained. An asymptotically tight estimate is given for the case when the inequalities are processed in a cyclical order. An improvement of the estimate by an order of magnitude takes place if strong underrelaxation is used. Bounds on convergence usually involve the so-called condition number of a system of linear inequalities, which we estimate in terms of their coefficient matrix. Paper presented at the XI. International Symposium on Mathematical Programming, Bonn, August 23–27, 1982.