50 research outputs found
--Geometry and Associated Continuous Toda System
We discuss an infinite--dimensional k\"ahlerian manifold associated with the
area--preserving diffeomorphisms on two--dimensional torus, and,
correspondingly, with a continuous limit of the --Toda system. In
particular, a continuous limit of the --Grassmannians and a related
Pl\"ucker type formula are introduced as relevant notions for
--geometry of the self--dual Einstein space with the rotational
Killing vector.Comment: 6 pages, no figure report\# ETH-TH/93-2
Supersymmetric Black Holes from Toda Theories
On the example of nonabelian Toda type theory associated with the Lie
superalgebra we show that this integrable dynamical system is
relevant to a black hole background metric in the corresponding target space.
In the even sector the model under consideration reduces to the exactly
solvable conformal theory (nonabelian Toda system) in the presence of a
black hole recently proposed in the article "Black holes from non-abelian Toda
theories" by the last two authors (hep-th 9203039).Comment: 4 pages, Late
Lotka--Volterra Type Equations and their Explicit Integration
In the present note we give an explicit integration of some
two--dimensionalised Lotka--Volterra type equations associated with simple Lie
algebras, other than the familiar case, possessing a representation
without branching. This allows us, in particular, to treat the first
fundamental representations of , , , and on the same
footing.Comment: 3 pages LATEX fil
Progress in classically solving ten dimensional supersymmetric reduced Yang-Mills theories
It is shown that there exists an on-shell light cone gauge where half of the
fermionic components of the super vector potential vanish, so that part of the
superspace flatness conditions becomes linear. After reduction to
space-time dimensions, the general solution of this subset of equations is
derived. The remaining non-linear equations are written in a form which is
analogous to Yang equations, albeit with superderivatives involving sixteen
fermionic coordinates. It is shown that this non-linear part may, nevertheless,
be solved by methods similar to powerful technics previously developed for the
(purely bosonic) self-dual Yang Mills equations in four dimensions.Comment: 17 pages Latex non figure
Gauge Conditions for the Constrained-WZNW--Toda Reductions
There is a constrained-WZNW--Toda theory for any simple Lie algebra equipped
with an integral gradation. It is explained how the different approaches to
these dynamical systems are related by gauge transformations. Combining Gauss
decompositions in relevent gauges, we unify formulae already derived, and
explictly determine the holomorphic expansion of the conformally reduced WZNW
solutions - whose restriction gives the solutions of the Toda equations. The
same takes place also for semi-integral gradations. Most of our conclusions are
also applicable to the affine Toda theories.Comment: 12 pages, no figure
Higher Grading Generalisations of the Toda Systems
In the present paper we obtain some integrable generalisations of the Toda
system generated by flat connection forms taking values in higher --grading subspaces of a simple Lie algebra, and construct their general
solutions. One may think of our systems as describing some new fields of the
matter type coupled to the standard Toda systems. This is of special interest
in nonabelian Toda theories where the latter involve black hole target space
metrics. We also give a derivation of our conformal system on the base of the
Hamiltonian reduction of the WZNW model; and discuss a relation between abelian
and nonabelian systems generated by a gauge transformation that maps the first
grading description to the second. The latter involves grades larger than one.Comment: 24 pages, latex, no figures; Expanded version accepted for
publication in Nuclear Physics
--geometry of the Toda systems associated with non-exceptional simple Lie algebras
The present paper describes the --geometry of the Abelian finite
non-periodic (conformal) Toda systems associated with the and series
of the simple Lie algebras endowed with the canonical gradation. The principal
tool here is a generalization of the classical Pl\"ucker embedding of the
-case to the flag manifolds associated with the fundamental representations
of , and , and a direct proof that the corresponding K\"ahler
potentials satisfy the system of two--dimensional finite non-periodic
(conformal) Toda equations. It is shown that the --geometry of the type
mentioned above coincide with the differential geometry of special holomorphic
(W) surfaces in target spaces which are submanifolds (quadrics) of with
appropriate choices of . In addition, these W-surfaces are defined to
satisfy quadratic holomorphic differential conditions that ensure consistency
of the generalized Pl\"ucker embedding. These conditions are automatically
fulfiled when Toda equations hold.Comment: 30 pages, no figur
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Giant extensional strain of magnetoactive elastomeric cylinders in uniform magnetic fields
Elongations of magnetoactive elastomers (MAEs) under ascending-descending uniform magnetic fields were studied experimentally using a laboratory apparatus specifically designed to measure large extensional strains (up to 20%) in compliant MAEs. In the literature, such a phenomenon is usually denoted as giant magnetostriction. The synthesized cylindrical MAE samples were based on polydimethylsiloxane matrices filled with micrometer-sized particles of carbonyl iron. The impact of both the macroscopic shape factor of the samples and their magneto-mechanical characteristics were evaluated. For this purpose, the aspect ratio of the MAE cylindrical samples, the concentration of magnetic particles in MAEs and the effective shear modulus were systematically varied. It was shown that the magnetically induced elongation of MAE cylinders in the maximum magnetic field of about 400 kA/m, applied along the cylinder axis, grew with the increasing aspect ratio. The effect of the sample composition is discussed in terms of magnetic filler rearrangements in magnetic fields and the observed experimental tendencies are rationalized by simple theoretical estimates. The obtained results can be used for the design of new smart materials with magnetic-field-controlled deformation properties, e.g., for soft robotics. © 2020 by the authors