4,560 research outputs found
generalizations of superconformal Galilei algebras and their representations
We introduce two classes of novel color superalgebras of grading. This is done by realizing members of each in the
universal enveloping algebra of the supersymmetric extension of
the conformal Galilei algebra. This allows us to upgrade any representation of
the super conformal Galilei algebras to a representation of the graded algebra. As an example, boson-fermion Fock space
representation of one class is given. We also provide a vector field
realization of members of the other class by using a generalization of the
Grassmann calculus to graded setting.Comment: 17 pages, no figur
Representations of the quantum doubles of finite group algebras and solutions of the Yang--Baxter equation
Quantum doubles of finite group algebras form a class of quasi-triangular
Hopf algebras which algebraically solve the Yang--Baxter equation. Each
representation of the quantum double then gives a matrix solution of the
Yang--Baxter equation. Such solutions do not depend on a spectral parameter,
and to date there has been little investigation into extending these solutions
such that they do depend on a spectral parameter. Here we first explicitly
construct the matrix elements of the generators for all irreducible
representations of quantum doubles of the dihedral groups . These results
may be used to determine constant solutions of the Yang--Baxter equation. We
then discuss Baxterisation ans\"atze to obtain solutions of the Yang--Baxter
equation with spectral parameter and give several examples, including a new
21-vertex model. We also describe this approach in terms of minimal-dimensional
representations of the quantum doubles of the alternating group and the
symmetric group .Comment: 19 pages, no figures, changed introduction, added reference
Solutions of the Yang-Baxter equation: descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras
The representation theory of the Drinfeld doubles of dihedral groups is used
to solve the Yang-Baxter equation. Use of the 2-dimensional representations
recovers the six-vertex model solution. Solutions in arbitrary dimensions,
which are viewed as descendants of the six-vertex model case, are then obtained
using tensor product graph methods which were originally formulated for quantum
algebras. Connections with the Fateev-Zamolodchikov model are discussed.Comment: 34 pages, 2 figure
Bethe ansatz solution of an integrable, non-Abelian anyon chain with D(D_3) symmetry
The exact solution for the energy spectrum of a one-dimensional Hamiltonian
with local two-site interactions and periodic boundary conditions is
determined. The two-site Hamiltonians commute with the symmetry algebra given
by the Drinfeld double D(D_3) of the dihedral group D_3. As such the model
describes local interactions between non-Abelian anyons, with fusion rules
given by the tensor product decompositions of the irreducible representations
of D(D_3). The Bethe ansatz equations which characterise the exact solution are
found through the use of functional relations satisfied by a set of mutually
commuting transfer matrices.Comment: 19 page
Modeling the dynamics of a tracer particle in an elastic active gel
The internal dynamics of active gels, both in artificial (in-vitro) model
systems and inside the cytoskeleton of living cells, has been extensively
studied by experiments of recent years. These dynamics are probed using tracer
particles embedded in the network of biopolymers together with molecular
motors, and distinct non-thermal behavior is observed. We present a theoretical
model of the dynamics of a trapped active particle, which allows us to quantify
the deviations from equilibrium behavior, using both analytic and numerical
calculations. We map the different regimes of dynamics in this system, and
highlight the different manifestations of activity: breakdown of the virial
theorem and equipartition, different elasticity-dependent "effective
temperatures" and distinct non-Gaussian distributions. Our results shed light
on puzzling observations in active gel experiments, and provide physical
interpretation of existing observations, as well as predictions for future
studies.Comment: 11 pages, 6 figure
The influence of clearance on friction, lubrication and squeaking in large diameter metal-on-metal hip replacements
Large diameter metal-on-metal bearings (MOM) are becoming increasingly popular, addressing the needs of young and more active patients. Clinical data has shown excellent short-to-mid-term results, though incidences of transient squeaking have been noted between implantation and up to 2 years post-operative. Geometric design features, such as clearance, have been significant in influencing the performance of the bearings. Sets of MOM bearings with different clearances were investigated in this study using a hip friction simulator to examine the influence of clearance on friction, lubrication and squeaking. The friction factor was found to be highest in the largest clearance bearings under all test conditions. The incidence of squeaking was also highest in the large clearance bearings, with all bearings in this group squeaking throughout the study. A very low incidence of squeaking was observed in the other two clearance groups. The measured lubricating film was found to be lowest in the large clearance bearings. This study suggests that increasing the bearing clearance results in reduced lubricant film thickness, increased friction and an increased incidence of squeaking
generalizations of infinite dimensional Lie superalgebra of conformal type with complete classification of central extensions
We introduce a class of novel -graded color
superalgebras of infinite dimension. It is done by realizing each member of the
class in the universal enveloping algebra of a Lie superalgebra which is a
module extension of the Virasoro algebra. Then the complete classification of
central extensions of the -graded color
superalgebras is presented. It turns out that infinitely many members of the
class have non-trivial extensions. We also demonstrate that the color
superalgebras (with and without central extensions) have adjoint and
superadjoint operations.Comment: 19 pages, no figure, Revision in Section 2 and 3. Some new reference
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