845 research outputs found
On the accuracy of conservation of adiabatic invariants in slow-fast systems
Let the adiabatic invariant of action variable in slow-fast Hamiltonian
system with two degrees of freedom have two limiting values along the
trajectories as time tends to infinity. The difference of two limits is
exponentially small in analytic systems. An iso-energetic reduction and
canonical transformations are applied to transform the slow-fast systems to
form of systems depending on slowly varying parameters in a complexified phase
space. On the basis of this method an estimate for the accuracy of conservation
of adiabatic invariant is given for such systems.Comment: 27 pages, 14 figure
On the hadronic contribution to sterile neutrino production
Sterile neutrinos with masses in the keV range are considered to be a viable
candidate for warm dark matter. The rate of their production through
active-sterile neutrino transitions peaks, however, at temperatures of the
order of the QCD scale, which makes it difficult to estimate their relic
abundance quantitatively, even if the mass of the sterile neutrino and its
mixing angle were known. We derive here a relation, valid to all orders in the
strong coupling constant, which expresses the production rate in terms of the
spectral function associated with active neutrinos. The latter can in turn be
expressed as a certain convolution of the spectral functions related to various
mesonic current-current correlation functions, which are being actively studied
in other physics contexts. In the naive weak coupling limit, the appropriate
Boltzmann equations can be derived from our general formulae.Comment: 28 pages. v2: small clarifications added, published versio
Duality properties of indicatrices of knots
The bridge index and superbridge index of a knot are important invariants in
knot theory. We define the bridge map of a knot conformation, which is closely
related to these two invariants, and interpret it in terms of the tangent
indicatrix of the knot conformation. Using the concepts of dual and derivative
curves of spherical curves as introduced by Arnold, we show that the graph of
the bridge map is the union of the binormal indicatrix, its antipodal curve,
and some number of great circles. Similarly, we define the inflection map of a
knot conformation, interpret it in terms of the binormal indicatrix, and
express its graph in terms of the tangent indicatrix. This duality relationship
is also studied for another dual pair of curves, the normal and Darboux
indicatrices of a knot conformation. The analogous concepts are defined and
results are derived for stick knots.Comment: 22 pages, 9 figure
Fertilizing greenhouse vegetables
Caption title
Logics for Unranked Trees: An Overview
Labeled unranked trees are used as a model of XML documents, and logical
languages for them have been studied actively over the past several years. Such
logics have different purposes: some are better suited for extracting data,
some for expressing navigational properties, and some make it easy to relate
complex properties of trees to the existence of tree automata for those
properties. Furthermore, logics differ significantly in their model-checking
properties, their automata models, and their behavior on ordered and unordered
trees. In this paper we present a survey of logics for unranked trees
Estimating infarct severity from the ECG using a realistic heart model
The early phase of myocardial infarction is accompanied by changes in the ST segment of the ECG. This makes the ST segment the clinical marker for the detection of acute myocardial infarction. The determination of the infarct severity, location and size of the myocardial tissue at risk will support clinical decision making. In this study we used an inverse procedure to estimate the location and size of the infarcted heart region. The method estimates the local transmembrane amplitude based on the ECG amplitude near the J-point of the standard 12 leads signals using a patient specific volume conductor model. For the 5 available patient cases the positions as well as the size of the estimated infarct region were in accordance with results based on MRI
Validation of infarct size and location from the ECG by inverse body surface mapping
This paper describes the incorporation of body surface mapping algorithms to detect the position and size of acute myocardial infarctions using standard 12 lead ECG recording. The results are compared with the results from cardiac MRI scan analysis. In case patient specific volume conductor models are used, the position of the infarction could be accurately determined. When generalized patient volume conductor models were examined, the estimation of the infarct position became significantly less accurate. The calculations of the size of the infarctions need further improvement
Phase transitions in geometrothermodynamics
Using the formalism of geometrothermodynamics, we investigate the geometric
properties of the equilibrium manifold for diverse thermodynamic systems.
Starting from Legendre invariant metrics of the phase manifold, we derive
thermodynamic metrics for the equilibrium manifold whose curvature becomes
singular at those points where phase transitions of first and second order
occur. We conclude that the thermodynamic curvature of the equilibrium
manifold, as defined in geometrothermodynamics, can be used as a measure of
thermodynamic interaction in diverse systems with two and three thermodynamic
degrees of freedom
Systematic study of the effect of short range correlations on the form factors and densities of s-p and s-d shell nuclei
Analytical expressions of the one- and two-body terms in the cluster
expansion of the charge form factors and densities of the s-p and s-d shell
nuclei with N=Z are derived. They depend on the harmonic oscillator parameter b
and the parameter which originates from the Jastrow correlation
function. These expressions are used for the systematic study of the effect of
short range correlations on the form factors and densities and of the mass
dependence of the parameters b and . These parameters have been
determined by fit to the experimental charge form factors. The inclusion of the
correlations reproduces the experimental charge form factors at the high
momentum transfers (). It is found that while the parameter
is almost constant for the closed shell nuclei, He, O and
Ca, its values are larger (less correlated systems) for the open shell
nuclei, indicating a shell effect in the closed shell nuclei.Comment: Latex, 21 pages, 6 figures, 1 tabl
On recurrence and ergodicity for geodesic flows on noncompact periodic polygonal surfaces
We study the recurrence and ergodicity for the billiard on noncompact
polygonal surfaces with a free, cocompact action of or . In the
-periodic case, we establish criteria for recurrence. In the more difficult
-periodic case, we establish some general results. For a particular
family of -periodic polygonal surfaces, known in the physics literature
as the wind-tree model, assuming certain restrictions of geometric nature, we
obtain the ergodic decomposition of directional billiard dynamics for a dense,
countable set of directions. This is a consequence of our results on the
ergodicity of \ZZ-valued cocycles over irrational rotations.Comment: 48 pages, 12 figure
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