1,971 research outputs found
Optical Theorem and the Inversion of Cross Section Data for Atom Scattering from Defects on Surfaces
The information content and properties of the cross section for atom
scattering from a defect on a flat surface are investigated. Using the Sudden
approximation, a simple expression is obtained that relates the cross section
to the underlying atom/defect interaction potential. An approximate inversion
formula is given, that determines the shape function of the defect from the
scattering data. Another inversion formula approximately determines the
potential due to a weak corrugation in the case of substitutional disorder. An
Optical Theorem, derived in the framework of the Sudden approximation, plays a
central role in deriving the equations that conveniently relate the interaction
potential to the cross section. Also essential for the result is the
equivalence of the operational definition for the cross section for scattering
by a defect, given by Poelsema and Comsa, and the formal definition from
quantum scattering theory. This equivalence is established here. The inversion
result is applied to determine the shape function of an Ag atom on Pt(111) from
scattering data.Comment: 29 pages, 9 Postscript figures, more info available at
http://www.fh.huji.ac.il/~dan
He Scattering from Random Adsorbates, Disordered Compact Islands and Fractal Submonolayers: Intensity Manifestations of Surface Disorder
A theoretical study is made on He scattering from three fundamental classes
of disordered ad-layers: (a) Translationally random adsorbates, (b) disordered
compact islands and (c) fractal submonolayers. The implications of the results
to experimental studies of He scattering from disordered surfaces are
discussed, and a combined experimental-theoretical study is made for Ag
submonolayers on Pt(111). Some of the main theoretical findings are: (1)
Structural aspects of the calculated intensities from translationally random
clusters were found to be strongly correlated with those of individual
clusters. (2) Low intensity Bragg interference peaks appear even for scattering
from very small ad-islands, and contain information on the ad-island local
electron structure. (3) For fractal islands, just as for islands with a
different structure, the off-specular intensity depends on the parameters of
the He/Ag interaction, and does not follow a universal power law as previously
proposed in the literature. In the experimental-theoretical study of Ag on
Pt(111), we use first experimental He scattering data from low-coverage (single
adsorbate) systems to determine an empirical He/Ag-Pt potential of good
quality. Then, we carry out He scattering calculations for high coverage and
compare with experiments. The conclusions are that the actual experimental
phase corresponds to small compact Ag clusters of narrow size distribution,
translationally disordered on the surface.Comment: 36 double-spaced pages, 10 figures; accepted by J. Chem. Phys.,
scheduled to appear March 8. More info available at
http://www.fh.huji.ac.il/~dani
Inversion of Randomly Corrugated Surfaces Structure from Atom Scattering Data
The Sudden Approximation is applied to invert structural data on randomly
corrugated surfaces from inert atom scattering intensities. Several expressions
relating experimental observables to surface statistical features are derived.
The results suggest that atom (and in particular He) scattering can be used
profitably to study hitherto unexplored forms of complex surface disorder.Comment: 10 pages, no figures. Related papers available at
http://neon.cchem.berkeley.edu/~dan
Reconstruction of thermally-symmetrized quantum autocorrelation functions from imaginary-time data
In this paper, I propose a technique for recovering quantum dynamical
information from imaginary-time data via the resolution of a one-dimensional
Hamburger moment problem. It is shown that the quantum autocorrelation
functions are uniquely determined by and can be reconstructed from their
sequence of derivatives at origin. A general class of reconstruction algorithms
is then identified, according to Theorem 3. The technique is advocated as
especially effective for a certain class of quantum problems in continuum
space, for which only a few moments are necessary. For such problems, it is
argued that the derivatives at origin can be evaluated by Monte Carlo
simulations via estimators of finite variances in the limit of an infinite
number of path variables. Finally, a maximum entropy inversion algorithm for
the Hamburger moment problem is utilized to compute the quantum rate of
reaction for a one-dimensional symmetric Eckart barrier.Comment: 15 pages, no figures, to appear in Phys. Rev.
Showcase Panel I: What Is Regulation For?
2018 National Lawyers Convention Transcripts
“The administrative state, with roots over a century old, was founded on the premise that Congress lacked the expertise to deal with the many complex issues facing government in a fast-changing country, and that it was unhelpfully mired in and influenced by politics, leading to bad outcomes when it did act. The alternative was to establish administrative agencies, each with assigned areas of responsibility, housing learned experts qualified to make policy decisions, deliberately insulated from political accountability. The Administrative Procedure Act (APA), passed in 1946, both governs the manner in which agencies may adopt and enforce regulations, and provides for judicial review of agency action. Supporters of the administrative state point to the successes of agency actions leading to a cleaner environment, more sensible use of finite resources, healthier foods, safety on the roads and rails, and many other areas of improved quality of life. But even looking past structural separation of powers issues written into the bones of the administrative state, critics assert that in the ensuing 70 years the APA has become an ineffective limitation on agency power, as agencies bypassed its requirements by issuing sub-regulatory guidance, letters, FAQs, and more. Compounding the problem, the critics continue, the courts have adopted a policy of deference to agency actions that grant agencies even more latitude. Is it time to revisit the APA? If so, how should it be updated?
Fractal Analysis of Protein Potential Energy Landscapes
The fractal properties of the total potential energy V as a function of time
t are studied for a number of systems, including realistic models of proteins
(PPT, BPTI and myoglobin). The fractal dimension of V(t), characterized by the
exponent \gamma, is almost independent of temperature and increases with time,
more slowly the larger the protein. Perhaps the most striking observation of
this study is the apparent universality of the fractal dimension, which depends
only weakly on the type of molecular system. We explain this behavior by
assuming that fractality is caused by a self-generated dynamical noise, a
consequence of intermode coupling due to anharmonicity. Global topological
features of the potential energy landscape are found to have little effect on
the observed fractal behavior.Comment: 17 pages, single spaced, including 12 figure
Counting flags in triangle-free digraphs
Motivated by the Caccetta-Haggkvist Conjecture, we prove that every digraph
on n vertices with minimum outdegree 0.3465n contains an oriented triangle.
This improves the bound of 0.3532n of Hamburger, Haxell and Kostochka. The main
new tool we use in our proof is the theory of flag algebras developed recently
by Razborov.Comment: 19 pages, 7 figures; this is the final version to appear in
Combinatoric
Elastic Scattering by Deterministic and Random Fractals: Self-Affinity of the Diffraction Spectrum
The diffraction spectrum of coherent waves scattered from fractal supports is
calculated exactly. The fractals considered are of the class generated
iteratively by successive dilations and translations, and include
generalizations of the Cantor set and Sierpinski carpet as special cases. Also
randomized versions of these fractals are treated. The general result is that
the diffraction intensities obey a strict recursion relation, and become
self-affine in the limit of large iteration number, with a self-affinity
exponent related directly to the fractal dimension of the scattering object.
Applications include neutron scattering, x-rays, optical diffraction, magnetic
resonance imaging, electron diffraction, and He scattering, which all display
the same universal scaling.Comment: 20 pages, 11 figures. Phys. Rev. E, in press. More info available at
http://www.fh.huji.ac.il/~dani
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