2,905 research outputs found
Coherent states for the hydrogen atom
We construct wave packets for the hydrogen atom labelled by the classical
action-angle variables with the following properties. i) The time evolution is
exactly given by classical evolution of the angle variables. (The angle
variable corresponding to the position on the orbit is now non-compact and we
do not get exactly the same state after one period. However the gross features
do not change. In particular the wave packet remains peaked around the labels.)
ii) Resolution of identity using this overcomplete set involves exactly the
classical phase space measure. iii) Semi-classical limit is related to
Bohr-Sommerfield quantization. iv) They are almost minimum uncertainty wave
packets in position and momentum.Comment: 9 pages, 2 figures, minor change in language and journal reference
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Coarse grained description of the protein folding
We consider two- and three-dimensional lattice models of proteins which were
characterized previously. We coarse grain their folding dynamics by reducing it
to transitions between effective states. We consider two methods of selection
of the effective states. The first method is based on the steepest descent
mapping of states to underlying local energy minima and the other involves an
additional projection to maximally compact conformations. Both methods generate
connectivity patterns that allow to distinguish between the good and bad
folders. Connectivity graphs corresponding to the folding funnel have few loops
and are thus tree-like. The Arrhenius law for the median folding time of a
16-monomer sequence is established and the corresponding barrier is related to
easily identifiable kinetic trap states.Comment: REVTeX, 9 pages, 15 EPS figures, to appear in Phys. Rev.
Geometric and Statistical Properties of the Mean-Field HP Model, the LS Model and Real Protein Sequences
Lattice models, for their coarse-grained nature, are best suited for the
study of the ``designability problem'', the phenomenon in which most of the
about 16,000 proteins of known structure have their native conformations
concentrated in a relatively small number of about 500 topological classes of
conformations. Here it is shown that on a lattice the most highly designable
simulated protein structures are those that have the largest number of
surface-core switchbacks. A combination of physical, mathematical and
biological reasons that causes the phenomenon is given. By comparing the most
foldable model peptides with protein sequences in the Protein Data Bank, it is
shown that whereas different models may yield similar designabilities,
predicted foldable peptides will simulate natural proteins only when the model
incorporates the correct physics and biology, in this case if the main folding
force arises from the differing hydrophobicity of the residues, but does not
originate, say, from the steric hindrance effect caused by the differing sizes
of the residues.Comment: 12 pages, 10 figure
The effect of parallel static and microwave electric fields on excited hydrogen atoms
Motivated by recent experiments we analyse the classical dynamics of a
hydrogen atom in parallel static and microwave electric fields. Using an
appropriate representation and averaging approximations we show that resonant
ionisation is controlled by a separatrix, and provide necessary conditions for
a dynamical resonance to affect the ionisation probability.
The position of the dynamical resonance is computed using a high-order
perturbation series, and estimate its radius of convergence. We show that the
position of the dynamical resonance does not coincide precisely with the
ionisation maxima, and that the field switch-on time can dramatically affect
the ionisation signal which, for long switch times, reflects the shape of an
incipient homoclinic. Similarly, the resonance ionisation time can reflect the
time-scale of the separatrix motion, which is therefore longer than
conventional static field Stark ionisation. We explain why these effects should
be observed in the quantum dynamics.
PACs: 32.80.Rm, 33.40.+f, 34.10.+x, 05.45.Ac, 05.45.MtComment: 47 pages, 20 figure
Excitation of Small Quantum Systems by High-Frequency Fields
The excitation by a high frequency field of multi--level quantum systems with
a slowly varying density of states is investigated. A general approach to study
such systems is presented. The Floquet eigenstates are characterized on several
energy scales. On a small scale, sharp universal quasi--resonances are found,
whose shape is independent of the field parameters and the details of the
system. On a larger scale an effective tight--binding equation is constructed
for the amplitudes of these quasi--resonances. This equation is non--universal;
two classes of examples are discussed in detail.Comment: 4 pages, revtex, no figure
Multi-Timescale Perceptual History Resolves Visual Ambiguity
When visual input is inconclusive, does previous experience aid the visual system in attaining an accurate perceptual interpretation? Prolonged viewing of a visually ambiguous stimulus causes perception to alternate between conflicting interpretations. When viewed intermittently, however, ambiguous stimuli tend to evoke the same percept on many consecutive presentations. This perceptual stabilization has been suggested to reflect persistence of the most recent percept throughout the blank that separates two presentations. Here we show that the memory trace that causes stabilization reflects not just the latest percept, but perception during a much longer period. That is, the choice between competing percepts at stimulus reappearance is determined by an elaborate history of prior perception. Specifically, we demonstrate a seconds-long influence of the latest percept, as well as a more persistent influence based on the relative proportion of dominance during a preceding period of at least one minute. In case short-term perceptual history and long-term perceptual history are opposed (because perception has recently switched after prolonged stabilization), the long-term influence recovers after the effect of the latest percept has worn off, indicating independence between time scales. We accommodate these results by adding two positive adaptation terms, one with a short time constant and one with a long time constant, to a standard model of perceptual switching
Role of Secondary Motifs in Fast Folding Polymers: A Dynamical Variational Principle
A fascinating and open question challenging biochemistry, physics and even
geometry is the presence of highly regular motifs such as alpha-helices in the
folded state of biopolymers and proteins. Stimulating explanations ranging from
chemical propensity to simple geometrical reasoning have been invoked to
rationalize the existence of such secondary structures. We formulate a
dynamical variational principle for selection in conformation space based on
the requirement that the backbone of the native state of biologically viable
polymers be rapidly accessible from the denatured state. The variational
principle is shown to result in the emergence of helical order in compact
structures.Comment: 4 pages, RevTex, 4 eps figure
Basins of attraction on random topography
We investigate the consequences of fluid flowing on a continuous surface upon
the geometric and statistical distribution of the flow. We find that the
ability of a surface to collect water by its mere geometrical shape is
proportional to the curvature of the contour line divided by the local slope.
Consequently, rivers tend to lie in locations of high curvature and flat
slopes. Gaussian surfaces are introduced as a model of random topography. For
Gaussian surfaces the relation between convergence and slope is obtained
analytically. The convergence of flow lines correlates positively with drainage
area, so that lower slopes are associated with larger basins. As a consequence,
we explain the observed relation between the local slope of a landscape and the
area of the drainage basin geometrically. To some extent, the slope-area
relation comes about not because of fluvial erosion of the landscape, but
because of the way rivers choose their path. Our results are supported by
numerically generated surfaces as well as by real landscapes
Geometry of River Networks II: Distributions of Component Size and Number
The structure of a river network may be seen as a discrete set of nested
sub-networks built out of individual stream segments. These network components
are assigned an integral stream order via a hierarchical and discrete ordering
method. Exponential relationships, known as Horton's laws, between stream order
and ensemble-averaged quantities pertaining to network components are observed.
We extend these observations to incorporate fluctuations and all higher moments
by developing functional relationships between distributions. The relationships
determined are drawn from a combination of theoretical analysis, analysis of
real river networks including the Mississippi, Amazon and Nile, and numerical
simulations on a model of directed, random networks. Underlying distributions
of stream segment lengths are identified as exponential. Combinations of these
distributions form single-humped distributions with exponential tails, the sums
of which are in turn shown to give power law distributions of stream lengths.
Distributions of basin area and stream segment frequency are also addressed.
The calculations identify a single length-scale as a measure of size
fluctuations in network components. This article is the second in a series of
three addressing the geometry of river networks.Comment: 16 pages, 13 figures, 4 tables, Revtex4, submitted to PR
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Results of the ontology alignment evaluation initiative 2017
Ontology matching consists of finding correspondences between semantically related entities of different ontologies. The Ontology Alignment Evaluation Initiative (OAEI) aims at comparing ontology matching systems on precisely defined test cases. These test cases can be based on ontologies of different levels of complexity (from simple thesauri to expressive OWL ontologies) and use different evaluation modalities (e.g., blind evaluation, open evaluation, or consensus). The OAEI 2017 campaign offered 9 tracks with 23 test cases, and was attended by 21 participants. This paper is an overall presentation of that campaign
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