62,207 research outputs found
A simple approach to the correlation of rotovibrational states in four-atomic molecules
The problem of correlation between quantum states of four-atomic molecules in
different geometrical configurations is reviewed in detail. A general, still
simple rule is obtained which allows one to correlate states of a linear
four-atomic molecule with those of any kind of non-linear four-atomic molecule.Comment: 16 pages (+8 figures), Postscript (ready to print!
CAR: A MATLAB Package to Compute Correspondence Analysis with Rotations
Correspondence analysis (CA) is a popular method that can be used to analyse relationships between categorical variables. Like principal component analysis, CA solutions can be rotated both orthogonally and obliquely to simple structure without affecting the total amount of explained inertia. We describe a MATLAB package for computing CA. The package includes orthogonal and oblique rotation of axes. It is designed not only for advanced users of MATLAB but also for beginners. Analysis can be done using a user-friendly interface, or by using command lines. We illustrate the use of CAR with one example.
Quantization of the conformal arclength functional on space curves
By a conformal string in Euclidean space is meant a closed critical curve
with non-constant conformal curvatures of the conformal arclength functional.
We prove that (1) the set of conformal classes of conformal strings is in 1-1
correspondence with the rational points of the complex domain and (2) any conformal class has a model conformal
string, called symmetrical configuration, which is determined by three
phenomenological invariants: the order of its symmetry group and its linking
numbers with the two conformal circles representing the rotational axes of the
symmetry group. This amounts to the quantization of closed trajectories of the
contact dynamical system associated to the conformal arclength functional via
Griffiths' formalism of the calculus of variations.Comment: 24 pages, 6 figures. v2: final version; minor changes in the
exposition; references update
Fusion process of Lennard-Jones clusters: global minima and magic numbers formation
We present a new theoretical framework for modelling the fusion process of
Lennard-Jones (LJ) clusters. Starting from the initial tetrahedral cluster
configuration, adding new atoms to the system and absorbing its energy at each
step, we find cluster growing paths up to the cluster sizes of up to 150 atoms.
We demonstrate that in this way all known global minima structures of the
LJ-clusters can be found. Our method provides an efficient tool for the
calculation and analysis of atomic cluster structure. With its use we justify
the magic number sequence for the clusters of noble gas atoms and compare it
with experimental observations. We report the striking correspondence of the
peaks in the dependence on cluster size of the second derivative of the binding
energy per atom calculated for the chain of LJ-clusters based on the
icosahedral symmetry with the peaks in the abundance mass spectra
experimentally measured for the clusters of noble gas atoms. Our method serves
an efficient alternative to the global optimization techniques based on the
Monte-Carlo simulations and it can be applied for the solution of a broad
variety of problems in which atomic cluster structure is important.Comment: 47 pages, MikTeX, 17 figure
On subgroups of minimal topological groups
A topological group is minimal if it does not admit a strictly coarser
Hausdorff group topology. The Roelcke uniformity (or lower uniformity) on a
topological group is the greatest lower bound of the left and right
uniformities. A group is Roelcke-precompact if it is precompact with respect to
the Roelcke uniformity. Many naturally arising non-Abelian topological groups
are Roelcke-precompact and hence have a natural compactification. We use such
compactifications to prove that some groups of isometries are minimal. In
particular, if U_1 is the Urysohn universal metric space of diameter 1, the
group Iso(U_1) of all self-isometries of U_1 is Roelcke-precompact,
topologically simple and minimal. We also show that every topological group is
a subgroup of a minimal topologically simple Roelcke-precompact group of the
form Iso(M), where M is an appropriate non-separable version of the Urysohn
space.Comment: To appear in Topology and its Applications. 39 page
Factors affecting the operation of laser-triggered gas switch (LTGS) with multi-electrode spark gap
Multi-electrode spark switches can be used for switching applications at elevated voltages or for command triggering. Symmetrical field graded electrodes allow the electrical stress across individual gaps to be controlled, thus maximising the hold off voltage and reducing switch pre-fire. The paper considers some aspects of multielectrode switch design and their influence on switching behavior. Non-symmetrical, uni-directional electrode topologies can be employed with advantages over traditional symmetrical design. The choice of working gas and gas pressure can influence switching performance in terms of delay-time and jitter. Transient analysis of switch characteristics has been undertaken in order to understand multi-electrode switching
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