7,107 research outputs found
Insights and Puzzles from Branes: 4d SUSY Yang-Mills from 6d Models
5-branes of nontrivial topology are associated in the
Diaconescu-Hanany-Witten-Witten (DHWW) approach with the Seiberg-Witten (SW)
theory of low-energy effective actions. There are two different "pictures",
related to the IIA and IIB phases of M-theory. They differ by the choice of
theory on the 5-brane world volume. In the IIB picture it is just the 6d
SUSY Yang-Mills, while in the IIA picture it is a theory of SUSY self-dual
2-form. These two pictures appear capable to describe the (non-abelian) Lax
operator and (abelian) low-energy effective action respectively. Thus IIB-IIA
duality is related to the duality between Hitchin and Whitham integrable
structures.Comment: LaTeX, 12pp, 4 figs in ps-format requiring psfig.te
Molecular Motors Interacting with Their Own Tracks
Dynamics of molecular motors that move along linear lattices and interact
with them via reversible destruction of specific lattice bonds is investigated
theoretically by analyzing exactly solvable discrete-state ``burnt-bridge''
models. Molecular motors are viewed as diffusing particles that can
asymmetrically break or rebuild periodically distributed weak links when
passing over them. Our explicit calculations of dynamic properties show that
coupling the transport of the unbiased molecular motor with the bridge-burning
mechanism leads to a directed motion that lowers fluctuations and produces a
dynamic transition in the limit of low concentration of weak links. Interaction
between the backward biased molecular motor and the bridge-burning mechanism
yields a complex dynamic behavior. For the reversible dissociation the backward
motion of the molecular motor is slowed down. There is a change in the
direction of the molecular motor's motion for some range of parameters. The
molecular motor also experiences non-monotonic fluctuations due to the action
of two opposing mechanisms: the reduced activity after the burned sites and
locking of large fluctuations. Large spatial fluctuations are observed when two
mechanisms are comparable. The properties of the molecular motor are different
for the irreversible burning of bridges where the velocity and fluctuations are
suppressed for some concentration range, and the dynamic transition is also
observed. Dynamics of the system is discussed in terms of the effective driving
forces and transitions between different diffusional regimes
Phase behaviour of block copolymer melts with arbitrary architecture
The Leibler theory [L. Leibler, Macromolecules, v.13, 1602 (1980)] for
microphase separation in AB block copolymer melts is generalized for systems
with arbitrary topology of molecules. A diagrammatic technique for calculation
of the monomeric correlation functions is developed. The free energies of
various mesophases are calculated within the second-harmonic approximation.
Model highly-branched tree-like structures are considered as an example and
their phase diagrams are obtained. The topology of molecules is found to
influence the spinodal temperature and asymmetry of the phase diagrams, but not
the types of phases and their order. We suggest that all model AB
block-copolymer systems will exhibit the typical phase behaviour.Comment: Submitted to J. Chem. Phys., see also
http://rugmd4.chem.rug.nl/~morozov/research.htm
Liouville Type Models in Group Theory Framework. I. Finite-Dimensional Algebras
In the series of papers we represent the ``Whittaker'' wave functional of
-dimensional Liouville model as a correlator in -dimensional theory
of the sine-Gordon type (for and ). Asypmtotics of this wave function
is characterized by the Harish-Chandra function, which is shown to be a product
of simple -function factors over all positive roots of the
corresponding algebras (finite-dimensional for and affine for ).
This is in nice correspondence with the recent results on 2- and 3-point
correlators in Liouville model, where emergence of peculiar
double-periodicity is observed. The Whittaker wave functions of
-dimensional non-affine ("conformal") Toda type models are given by simple
averages in the dimensional theories of the affine Toda type. This
phenomenon is in obvious parallel with representation of the free-field wave
functional, which is originally a Gaussian integral over interior of a
-dimensional disk with given boundary conditions, as a (non-local)
quadratic integral over the -dimensional boundary itself. In the present
paper we mostly concentrate on the finite-dimensional case. The results for
finite-dimensional "Iwasawa" Whittaker functions were known, and we present
their survey. We also construct new "Gauss" Whittaker functions.Comment: 47 pages, LaTe
Theories of -Gravity: The Set of Observables as a Model of Simply Laced
We propose to study a generalization of the Klebanov-Polyakov-Witten (KPW)
construction for the algebra of observables in the string model to
theories with . We emphasize the algebraic meaning of the KPW
construction for related to occurrence of a {\it model} of {\it SU}(2)
as original structure on the algebra of observables. The attempts to preserve
this structure in generalizations naturally leads to consideration of
-gravities. As a first step in the study of these generalized KPW
constructions we design explicitly the subsector of the space of observables in
appropriate -string theory, which forms the {\it model} of for any
simply laced {\it G}. The {\it model} structure is confirmed by the fact that
corresponding one-loop Kac-Rocha-Caridi -characters for sum into
a chiral (open string) -WZW partition function.Comment: 36
Faces of matrix models
Partition functions of eigenvalue matrix models possess a number of very
different descriptions: as matrix integrals, as solutions to linear and
non-linear equations, as tau-functions of integrable hierarchies and as
special-geometry prepotentials, as result of the action of W-operators and of
various recursions on elementary input data, as gluing of certain elementary
building blocks. All this explains the central role of such matrix models in
modern mathematical physics: they provide the basic "special functions" to
express the answers and relations between them, and they serve as a dream model
of what one should try to achieve in any other field.Comment: 10 page
New matrix model solutions to the Kac-Schwarz problem
We examine the Kac-Schwarz problem of specification of point in Grassmannian
in the restricted case of gap-one first-order differential Kac-Schwarz
operators. While the pair of constraints satisfying always
leads to Kontsevich type models, in the case of the
corresponding KP -functions are represented as more sophisticated matrix
integrals.Comment: 19 pages, latex, no figures, contribution to the proceedings of the
29th International Symposium Ahrenshoop on the Theory of Elementary
Particles, Buckow, German
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