166 research outputs found
Effective action in spherical domains
The effective action on an orbifolded sphere is computed for minimally
coupled scalar fields. The results are presented in terms of derivatives of
Barnes zeta-functions and it is shown how these may be evaluated. Numerical
values are shown. An analytical, heat-kernel derivation of the Ces\`aro-Fedorov
formula for the number of symmetry planes of a regular solid is also presented.Comment: 18 pages, Plain TeX (Mailer oddities possibly corrected.
Graphs and Reflection Groups
It is shown that graphs that generalize the ADE Dynkin diagrams and have
appeared in various contexts of two-dimensional field theory may be regarded in
a natural way as encoding the geometry of a root system. After recalling what
are the conditions satisfied by these graphs, we define a bilinear form on a
root system in terms of the adjacency matrices of these graphs and undertake
the study of the group generated by the reflections in the hyperplanes
orthogonal to these roots. Some ``non integrally laced " graphs are shown to be
associated with subgroups of these reflection groups. The empirical relevance
of these graphs in the classification of conformal field theories or in the
construction of integrable lattice models is recalled, and the connections with
recent developments in the context of supersymmetric theories and
topological field theories are discussed.Comment: 42 pages TEX file, harvmac and epsf macros, AMS fonts optional,
uuencoded, 8 figures include
A Central Partition of Molecular Conformational Space.III. Combinatorial Determination of the Volume Spanned by a Molecular System
In the first work of this series [physics/0204035] it was shown that the
conformational space of a molecule could be described to a fair degree of
accuracy by means of a central hyperplane arrangement. The hyperplanes divide
the espace into a hierarchical set of cells that can be encoded by the face
lattice poset of the arrangement. The model however, lacked explicit rotational
symmetry which made impossible to distinguish rotated structures in
conformational space. This problem was solved in a second work
[physics/0404052] by sorting the elementary 3D components of the molecular
system into a set of morphological classes that can be properly oriented in a
standard 3D reference frame. This also made possible to find a solution to the
problem that is being adressed in the present work: for a molecular system
immersed in a heat bath we want to enumerate the subset of cells in
conformational space that are visited by the molecule in its thermal wandering.
If each visited cell is a vertex on a graph with edges to the adjacent cells,
here it is explained how such graph can be built
A novel generalization of Clifford's classical point-circle configuration. Geometric interpretation of the quaternionic discrete Schwarzian KP equation
The algebraic and geometric properties of a novel generalization of
Clifford's classical C4 point-circle configuration are analysed. A connection
with the integrable quaternionic discrete Schwarzian Kadomtsev-Petviashvili
equation is revealed
Mixing Chiral Polytopes
An abstract polytope of rank n is said to be chiral if its automorphism group
has two orbits on the flags, such that adjacent flags belong to distinct
orbits. Examples of chiral polytopes have been difficult to find. A "mixing"
construction lets us combine polytopes to build new regular and chiral
polytopes. By using the chirality group of a polytope, we are able to give
simple criteria for when the mix of two polytopes is chiral
Flavor Symmetry for Quarks and Leptons
Present data on neutrino masses and mixing favor the highly symmetric
tribimaximal neutrino mixing matrix which suggests an underlying flavor
symmetry. A systematic study of non-abelian finite groups of order
reveals that tribimaximal mixing can be derived not only from the well known
tetrahedral flavor symmetry , but also by using the binary
tetrahedral symmetry which does not contain the
tetrahedral group as a subgroup. has the further advantage that it can
also neatly accommodate the quark masses including a heavy top quark.Comment: 12 pages latex. More typos correcte
A Central Partition of Molecular Conformational Space. IV. Extracting information from the graph of cells
In previous works [physics/0204035, physics/0404052, physics/0509126] a
procedure was described for dividing the -dimensional
conformational space of a molecular system into a number of discrete cells,
this partition allowed the building of a combinatorial structure from data
sampled in molecular dynamics trajectories: the graph of cells, that encodes
the set of cells in conformational space that are visited by the system in its
thermal wandering. Here we outline a set of procedures for extracting useful
information from this structure: 1st) interesting regions in the volume
occupied by the system in conformational space can be bounded by a polyhedral
cone whose faces are determined empirically from a set of relations between the
coordinates of the molecule, 2nd) it is also shown that this cone can be
decomposed into a hierarchical set of smaller cones, 3rd) the set of cells in a
cone can be encoded by a simple combinatorial sequence.Comment: added an intrduction and reference
Multi-triangulations as complexes of star polygons
Maximal -crossing-free graphs on a planar point set in convex
position, that is, -triangulations, have received attention in recent
literature, with motivation coming from several interpretations of them.
We introduce a new way of looking at -triangulations, namely as complexes
of star polygons. With this tool we give new, direct, proofs of the fundamental
properties of -triangulations, as well as some new results. This
interpretation also opens-up new avenues of research, that we briefly explore
in the last section.Comment: 40 pages, 24 figures; added references, update Section
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