On the geometry of classically integrable two-dimensional non-linear sigma models

A master equation expressing the zero curvature representation of the equations of motion of a two-dimensional non-linear sigma models is found. The geometrical properties of this equation are outlined. Special attention is paid to those representations possessing a spectral parameter. Furthermore, a closer connection between integrability and T-duality transformations is emphasised. Finally, new integrable non-linear sigma models are found and all their corresponding Lax pairs depend on a spectral parameter.     

Implicitly restarted projection algorithm for solving optimization problems

An algorithm for solving the problem of minimizing a quadratic function subject to ellipsoidal constraints is introduced. This algorithm is based on the impHcitly restarted Lanczos method to construct a basis for the Krylov subspace in conjunction with a model trust region strategy to choose the step. The trial step is computed on the small dimensional subspace that lies inside the trust region.

One of the main advantages of this algorithm is the way that the Krylov subspace is terminated. We introduce a terminationcondition that allows the gradient to be decreased on that subspace.

A convergence theory for this algorithm is presented. It is shown that this algorithm is globally convergent and it shouldcope quite well with large scale minimization problems. This theory is sufficiently general that it holds for any algorithm that projects the problem on a lower dimensional subspace.     

Sensitivity analysis of the largest dependent eigenvalue functions of eigensystems

This paper presents and discusses the first order sensitivity of the largest eigenvalue functions of eigensystems. The analysis is based on investigating the entries of the matrices associated with the finite element formulations. These entries are continuously differentiable functions, but the dependent eigenvalue functions may be continuous nondifferentiable. The main emphasis of this contribution is the derivation and the investigation of this analysis under the assumption that the generalized dependent eigenvalue functions are continuous nondifferentiable.     

A dual description of the four dimensional non-linear sigma model

The dual of the four dimensional non-linear sigma model is constructed using techniques familiar to string theory. This construction necessitates the introduction of a rank two antisymmetric tensor field whose properties are examined. The physics of the dual theory and that of the original model are compared. As an illustration we study in detail the SU(2}) chiral model. We find that the scattering amplitudes of the charged Goldstone bosons in the two theories are in complete agreement at the one loop level.     

Ultraviolet properties of noncommutative nonlinear σ-models in two dimensions

We discuss the ultra-violet properties of bosonic and supersymmetric noncommutative nonlinear σ-models in two dimensions, both with and without a Wess–Zumino–Witten term.     

On mirror symmetry in Wess-Zumino-Novikov-Witten models

We examine the problem of constructing N=2 superconformal algebras out of N=1 non-semi-simple affine Lie algebras. These N=2 superconformal theories share the property that the super Virasoro central charge depends only on the dimension of the Lie algebra. We find, in particular, a construction having a central charge c=9. This provides a possible internal space for string compactification and where mirror symmetry might be explored.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 1, pp. 55–63, July, 1995.     

CO-processing conception of a quenching plasma reactor associated to a fluidized bed designed to hydrogen radical production at low temperatures

The aim of this paper is to present a new way to produce a high flow of hydrogen radical, at low temperatures. Thirst, an atmospheric pressure plasma of an argon-hydrogen mixture generates a high flow of hydrogen radical at temperatures up to 5 000 K. The applications of these radicals, in such conditions, are limited by thermal aspects which are obviously different from classical reactions of hydropyrolysis or other treatment processings of organic molecules. Our approach is to quench the plasma by a fluidized bed reactor which transport properties are compatible with plasma phase. From this point of view, the plasma/fluidized bed system is qualified in terms of its thermodynamic and hydrodynamical properties and its quenching velocity. The atomic hydrogen flow generated within such conditions is calculated and then experimentally measured.