548 research outputs found
Lie Superalgebra Stability and Branes
The algebra of the generators of translations in superspace is unstable, in
the sense that infinitesimal perturbations of its structure constants lead to
non-isomorphic algebras. We show how superspace extensions remedy this
situation (after arguing that remedy is indeed needed) and review the benefits
reaped in the description of branes of all kinds in the presence of the extra
dimensions.Comment: Talk given at the conference ``Brane New World and Non-commutative
Geometry'', held in Torino, October 2000. To appear in the proceedings by
World Scientific. 10 pages, 1 figur
Do Killing-Yano tensors form a Lie Algebra?
Killing-Yano tensors are natural generalizations of Killing vectors. We
investigate whether Killing-Yano tensors form a graded Lie algebra with respect
to the Schouten-Nijenhuis bracket. We find that this proposition does not hold
in general, but that it does hold for constant curvature spacetimes. We also
show that Minkowski and (anti)-deSitter spacetimes have the maximal number of
Killing-Yano tensors of each rank and that the algebras of these tensors under
the SN bracket are relatively simple extensions of the Poincare and (A)dS
symmetry algebras.Comment: 17 page
Protein-templated reactions using DNA-antibody conjugates
DNA-templated chemical reactions have found wide applications in drug discovery, programmed multistep synthesis, nucleic acid detection, and targeted drug delivery. The control of these reactions has, however, been limited to nucleic acid hybridization as a means to direct the proximity between reactants. In this work a system capable of translating protein-protein binding events into a DNA-templated reaction which leads to the covalent formation of a product is introduced. Protein-templated reactions by employing two DNA-antibody conjugates that are both able to recognize the same target protein and to colocalize a pair of reactant DNA strands able to undergo a click reaction are achieved. Two individual systems, each responsive to human serum albumin (HSA) and human IgG, are engineered and it is demonstrated that, while no reaction occurs in the absence of proteins, both protein-templated reactions can occur simultaneously in the same solution without any inter-system crosstalk
Double bracket dissipation in kinetic theory for particles with anisotropic interactions
We derive equations of motion for the dynamics of anisotropic particles
directly from the dissipative Vlasov kinetic equations, with the dissipation
given by the double bracket approach (Double Bracket Vlasov, or DBV). The
moments of the DBV equation lead to a nonlocal form of Darcy's law for the mass
density. Next, kinetic equations for particles with anisotropic interaction are
considered and also cast into the DBV form. The moment dynamics for these
double bracket kinetic equations is expressed as Lie-Darcy continuum equations
for densities of mass and orientation. We also show how to obtain a
Smoluchowski model from a cold plasma-like moment closure of DBV. Thus, the
double bracket kinetic framework serves as a unifying method for deriving
different types of dynamics, from density--orientation to Smoluchowski
equations. Extensions for more general physical systems are also discussed.Comment: 19 pages; no figures. Submitted to Proc. Roy. Soc.
Jacobi structures revisited
Jacobi algebroids, that is graded Lie brackets on the Grassmann algebra
associated with a vector bundle which satisfy a property similar to that of the
Jacobi brackets, are introduced. They turn out to be equivalent to generalized
Lie algebroids in the sense of Iglesias and Marrero and can be viewed also as
odd Jacobi brackets on the supermanifolds associated with the vector bundles.
Jacobi bialgebroids are defined in the same manner. A lifting procedure of
elements of this Grassmann algebra to multivector fields on the total space of
the vector bundle which preserves the corresponding brackets is developed. This
gives the possibility of associating canonically a Lie algebroid with any local
Lie algebra in the sense of Kirillov.Comment: 20 page
Classical field theory on Lie algebroids: Variational aspects
The variational formalism for classical field theories is extended to the
setting of Lie algebroids. Given a Lagrangian function we study the problem of
finding critical points of the action functional when we restrict the fields to
be morphisms of Lie algebroids. In addition to the standard case, our formalism
includes as particular examples the case of systems with symmetry (covariant
Euler-Poincare and Lagrange Poincare cases), Sigma models or Chern-Simons
theories.Comment: Talk deliverd at the 9th International Conference on Differential
Geometry and its Applications, Prague, September 2004. References adde
Counting Complex Disordered States by Efficient Pattern Matching: Chromatic Polynomials and Potts Partition Functions
Counting problems, determining the number of possible states of a large
system under certain constraints, play an important role in many areas of
science. They naturally arise for complex disordered systems in physics and
chemistry, in mathematical graph theory, and in computer science. Counting
problems, however, are among the hardest problems to access computationally.
Here, we suggest a novel method to access a benchmark counting problem, finding
chromatic polynomials of graphs. We develop a vertex-oriented symbolic pattern
matching algorithm that exploits the equivalence between the chromatic
polynomial and the zero-temperature partition function of the Potts
antiferromagnet on the same graph. Implementing this bottom-up algorithm using
appropriate computer algebra, the new method outperforms standard top-down
methods by several orders of magnitude, already for moderately sized graphs. As
a first application, we compute chromatic polynomials of samples of the simple
cubic lattice, for the first time computationally accessing three-dimensional
lattices of physical relevance. The method offers straightforward
generalizations to several other counting problems.Comment: 7 pages, 4 figure
Generalized Jacobi structures
Jacobi brackets (a generalization of standard Poisson brackets in which
Leibniz's rule is replaced by a weaker condition) are extended to brackets
involving an arbitrary (even) number of functions. This new structure includes,
as a particular case, the recently introduced generalized Poisson structures.
The linear case on simple group manifolds is also studied and non-trivial
examples (different from those coming from generalized Poisson structures) of
this new construction are found by using the cohomology ring of the given
group.Comment: Latex2e file. 11 pages. To appear in J. Phys.
Bose-Einstein Correlations of Pion Wavepackets
A wavepacket model for a system of free pions, which takes into account the
full permutation symmetry of the wavefunction and which is suitable for any
phase space parametrization is developed. The properties of the resulting mixed
ensembles and the two-particle correlation function are discussed. A physical
interpretation of the chaoticity lambda as localizat of the pions in the source
is presented.
Two techniques to generate test-particles, which satisfy the probability
densities of the wavepacket state, are studied:
1. A Monte Carlo procedure in momentum space based on the standard Metropolis
technique.
2. A molecular dynamic procedure using Bohm's quantum theory of motion.
In order to reduce the numerical complexity, the separation of the
wavefunction into momentum space clusters is discussed. In this context th
influence of an unauthorized factorization of the state, i. e. the omissio of
interference terms, is investigated. It is shown that the correlation radius
remains almost uneffected, but the chaoticity parameter decreases
substantially. A similar effect is observed in systems with high multiplic
where the omission of higher order corrections in the analysis of two-part
correlations causes a reduction of the chaoticity and the radius.
The approximative treatment of the Coulomb interaction between pions and
source is investigated. The results suggest that Coulomb effects on the co
radii are not symmetric for pion pairs of different charges. For negative the
radius, integrated over the whole momentum spectrum, increases substan while
for positive pions the radius remains almost unchanged.Comment: 15 pages, 8 figures, 0.8 Mb, uses ljour2-macro, Submitted to Z. Phys.
A (1997
Manin products, Koszul duality, Loday algebras and Deligne conjecture
In this article we give a conceptual definition of Manin products in any
category endowed with two coherent monoidal products. This construction can be
applied to associative algebras, non-symmetric operads, operads, colored
operads, and properads presented by generators and relations. These two
products, called black and white, are dual to each other under Koszul duality
functor. We study their properties and compute several examples of black and
white products for operads. These products allow us to define natural
operations on the chain complex defining cohomology theories. With these
operations, we are able to prove that Deligne's conjecture holds for a general
class of operads and is not specific to the case of associative algebras.
Finally, we prove generalized versions of a few conjectures raised by M. Aguiar
and J.-L. Loday related to the Koszul property of operads defined by black
products. These operads provide infinitely many examples for this generalized
Deligne's conjecture.Comment: Final version, a few references adde
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