Explicit large nuclear charge limit of electronic ground states for Li, Be, B, C, N, O, F, Ne and basic aspects of the periodic table

This paper is concerned with the Schrödinger equation for atoms and ions with $N=1$ to 10 electrons. In the asymptotic limit of large nuclear charge $Z$, we determine explicitly the low-lying energy levels and eigenstates. The asymptotic energies and wavefunctions are in good quantitative agreement with experimental data for positive ions, and in excellent qualitative agreement even for neutral atoms ($Z=N$). In particular, the predicted ground state spin and angular momentum quantum numbers ($^1S$ for He, Be, Ne, $^2S$ for H and Li, $^4S$ for N, $^2P$ for B and F, and $^3P$ for C and O) agree with experiment in every case. The asymptotic Schrödinger ground states agree, up to small corrections, with the semiempirical hydrogen orbital configurations developed by Bohr, Hund, and Slater to explain the periodic table. In rare cases where our results deviate from this picture, such as the ordering of the lowest $^1D^o$ and $^3S^o$ states of the carbon isoelectronic sequence, experiment confirms our predictions and not Hund's

An assessment of warm fog: Nucleation, control, and recommended research

A state-of-the-art survey is given of warm fog research which has been performed up to, and including, 1974. Topics covered are nucleation, growth, coalescence, fog structures and visibility, effects of surface films, drop size spectrum, optical properties, instrumentation, liquid water content, condensation nuclei. Included is a summary of all reported fog modification experiments. Additional data is provided on air flow, turbulence, a summary of recommendations on instruments to be developed for determining turbulence, air flow, etc., as well as recommendations of various fog research tasks which should be performed for a better understanding of fog microphysics

On the Ehrenfest theorem of quantum mechanics

We give a mathematically rigorous derivation of Ehrenfest's equations for the evolution of position and momentum expectation values, under general and natural assumptions which include atomic and molecular Hamiltonians with Coulomb interactions.Comment: To appear in J. Math. Phy

Use of microwave radar data to interpret physical properties of ice and snow on the Greenland ice sheet

In situ observations of microwave radar backscatter were made at Dye-2 in south-central Greenland in 1993. Simultaneous observations of snow and ice physical properties were also acquired. Early in the season, it was found that 20° backscatter from the snow surface was determined mainly by the snow surface roughness. Later in the season the backscatter increases when temperatures are low. We attribute this fact to enhanced scattering from the ice within the radar resolution cell at the surface. This ice formed during the field season as a result of percolation and refreezing of surface meltwater. These observations have a direct implication for interpreting spaceborne SAR data acquired seasonally.No embarg

From Soft Walls to Infrared Branes

Five dimensional warped spaces with soft walls are generalizations of the standard Randall-Sundrum compactifications, where instead of an infrared brane one has a curvature singularity (with vanishing warp factor) at finite proper distance in the bulk. We project the physics near the singularity onto a hypersurface located a small distance away from it in the bulk. This results in a completely equivalent description of the soft wall in terms of an effective infrared brane, hiding any singular point. We perform explicitly this calculation for two classes of soft wall backgrounds used in the literature. The procedure has several advantages. It separates in a clean way the physics of the soft wall from the physics of the five dimensional bulk, facilitating a more direct comparison with standard two-brane warped compactifications. Moreover, consistent soft walls show a sort of universal behavior near the singularity which is reflected in the effective brane Lagrangian. Thirdly, for many purposes, a good approximation is obtained by assuming the bulk background away from the singularity to be the usual Randall-Sundrum metric, thus making the soft wall backgrounds better analytically tractable. We check the validity of this procedure by calculating the spectrum of bulk fields and comparing it to the exact result, finding very good agreement.Comment: 14 pages, 2 figures, v2: subsection on IR brane potentials and appendix on fermions added, version to appear in PR

Functional modelling in evolvable assembly systems

The design and reconfiguration of adaptive production systems is a key driver in modern advanced manufacturing. We summarise the use of an ap-proach from the field of functional modelling to capture the function, behaviour, and structure of a system. This model is an integral part of the Evolvable Assembly Systems architecture, allowing the system to adapt its behaviour in response to changing product requirements. The integrated approach is illustrated with an example taken from a real EAS instantiation

Supersymmetry and Electroweak Breaking in the Interval

Hypermultiplets are considered in the five-dimensional interval where all fields are continuous and the boundary conditions are dynamically obtained from the action principle. The orbifold boundary conditions are obtained as particular cases. We can interpret the Scherk-Schwarz supersymmetry breaking as a misalignment of boundary conditions while a new source of supersymmetry breaking corresponding to a mismatch of different boundary parameters is identified. The latter can be viewed as coming from boundary supersymmetry breaking masses for hyperscalars and the nature of the corresponding supersymmetry breaking parameter is analyzed. For some regions of the parameter space where supersymmetry is broken (either by Scherk-Schwarz boundary conditions or by boundary hyperscalar masses) electroweak symmetry breaking can be triggered at the tree level.Comment: 28 pages, 5 figure