1,474 research outputs found
Static Hopfions in the extended Skyrme-Faddeev model
We construct static soliton solutions with non-zero Hopf topological charges
to a theory which is an extension of the Skyrme-Faddeev model by the addition
of a further quartic term in derivatives. We use an axially symmetric ansatz
based on toroidal coordinates, and solve the resulting two coupled non-linear
partial differential equations in two variables by a successive over-relaxation
(SOR) method. We construct numerical solutions with Hopf charge up to four, and
calculate their analytical behavior in some limiting cases. The solutions
present an interesting behavior under the changes of a special combination of
the coupling constants of the quartic terms. Their energies and sizes tend to
zero as that combination approaches a particular special value. We calculate
the equivalent of the Vakulenko and Kapitanskii energy bound for the theory and
find that it vanishes at that same special value of the coupling constants. In
addition, the model presents an integrable sector with an infinite number of
local conserved currents which apparently are not related to symmetries of the
action. In the intersection of those two special sectors the theory possesses
exact vortex solutions (static and time dependent) which were constructed in a
previous paper by one of the authors. It is believed that such model describes
some aspects of the low energy limit of the pure SU(2) Yang-Mills theory, and
our results may be important in identifying important structures in that strong
coupling regime.Comment: 22 pages, 42 figures, minor correction
The spatial distribution of renewable energy infrastructure in three particular provinces of South Africa
Renewed interest is being shown in South Africa in the promotion of infrastructure for renewable energy (RE) to supplement the country’s current energy- generation capacity and to break loose from its dependency on an unsustainable fossil-fuel-based energy-provision system. The latter system not only has unfavourable consequences for the environment, but is managed by a state-owned institution which since 2008 has been incapable of providing reliable electricity. RE infrastructure - especially for the generation of solar and wind energy - is a relatively new feature in the South African landscape. This paper examines the spatial distribution of the newly commissioned infrastructures for wind and solar energy (operational and under construction) and the role they can play in the diversification of the rural economies of parts of the country’s Northern Cape, Western Cape and Eastern Cape provinces. First, literature on evolutionary economic geography, path dependence and new path creation is reviewed. Second, the role of a single energy provider — embedded in a monopolistic energy policy —in inhibiting the transition from a mainly fossil-fuel-based energy-provision system to a multi-source (multi-owner) provision system is discussed. Third, the reasoning behind the siting of the infrastructures for solar and wind energy in three particular provinces is explained. Fourth, the possible roles these new infrastructures can play in the diversification of the rural economies where they occur are advanced. The paper concludes that solar- and wind-energy projects have the ability to transform the South African energy context and that these projects present some positive socio-economic impacts for rural economies in the three particular provinces. The paper also recommends that future research efforts should be aimed at the evolution of this socio-economic transformation by taking into account the pre-development context of the areas under study
Confinement, solitons and the equivalence between the sine-Gordon and massive Thirring models
We consider a two-dimensional integrable and conformally invariant field
theory possessing two Dirac spinors and three scalar fields. The interaction
couples bilinear terms in the spinors to exponentials of the scalars. Its
integrability properties are based on the sl(2) affine Kac-Moody algebra, and
it is a simple example of the so-called conformal affine Toda theories coupled
to matter fields. We show, using bosonization techniques, that the classical
equivalence between a U(1) Noether current and the topological current holds
true at the quantum level, and then leads to a bag model like mechanism for the
confinement of the spinor fields inside the solitons. By bosonizing the spinors
we show that the theory decouples into a sine-Gordon model and free scalars. We
construct the two-soliton solutions and show that their interactions lead to
the same time delays as those for the sine-Gordon solitons. The model provides
a good laboratory to test duality ideas in the context of the equivalence
between the sine-Gordon and Thirring theories.Comment: LaTeX, 26 page
Connection between the Affine and Conformal Affine Toda Models and their Hirota's Solution
It is shown that the Affine Toda models (AT) constitute a ``gauge fixed''
version of the Conformal Affine Toda model (CAT). This result enables one to
map every solution of the AT models into an infinite number of solutions of the
corresponding CAT models, each one associated to a point of the orbit of the
conformal group. The Hirota's -function are introduced and soliton
solutions for the AT and CAT models associated to and are constructed.Comment: 11 pages, LaTe
Confinement and soliton solutions in the SL(3) Toda model coupled to matter fields
We consider an integrable conformally invariant two dimensional model
associated to the affine Kac-Moody algebra SL(3). It possesses four scalar
fields and six Dirac spinors. The theory does not possesses a local Lagrangian
since the spinor equations of motion present interaction terms which are
bilinear in the spinors. There exists a submodel presenting an equivalence
between a U(1) vector current and a topological current, which leads to a
confinement of the spinors inside the solitons. We calculate the one-soliton
and two-soliton solutions using a procedure which is a hybrid of the dressing
and Hirota methods. The soliton masses and time delays due to the soliton
interactions are also calculated. We give a computer program to calculate the
soliton solutions.Comment: plain LaTeX, 37 page
Toda and Volterra Lattice Equations from Discrete Symmetries of KP Hierarchies
The discrete models of the Toda and Volterra chains are being constructed out
of the continuum two-boson KP hierarchies. The main tool is the discrete
symmetry preserving the Hamiltonian structure of the continuum models. The
two-boson currents of KP hierarchy are being associated with sites of the
corresponding chain by successive actions of discrete symmetry.Comment: 12 pgs, LaTeX, IFT-P.041/9
Some comments on the bi(tri)-Hamiltonian structure of Generalized AKNS and DNLS hierarchies
We give the correct prescriptions for the terms involving the inverse of the
derivative of the delta function, in the Hamiltonian structures of the AKNS and
DNLS systems, in order for the Jacobi identities to hold. We also establish
that the sl(2) AKNS and DNLS systems are tri-Hamiltonians and construct two
compatible Hamiltonian structures for the sl(3) AKNS system. We also give a
derivation of the recursion operator for the sl(n+1) DNLS system.Comment: 10 pages, LaTe
On Non-Linear W-Infinity Symmetry of Generalized Liouville and Conformal Toda Models
Invariance under non-linear algebra is shown for
the two-boson Liouville type of model and its algebraic generalizations, the
extended conformal Toda models. The realization of the corresponding generators
in terms of two boson currents within KP hierarchy is presented.Comment: 10 pgs, LaTeX, IFT-P.038/9
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