721 research outputs found
A study of the Gribov copies in linear covariant gauges in Euclidean Yang-Mills theories
The Gribov copies and their consequences on the infrared behavior of the
gluon propagator are investigated in Euclidean Yang-Mills theories quantized in
linear covariant gauges. Considering small values of the gauge parameter, it
turns out that the transverse component of the gluon propagator is suppressed,
while its longitudinal part is left unchanged. A Green function, G_{tr}, which
displays infrared enhancement and which reduces to the ghost propagator in the
Landau gauge is identified. The inclusion of the dimension two gluon condensate
is also considered. In this case, the transverse component of the gluon
propagator and the Green function G_{tr} remain suppressed and enhanced,
respectively. Moreover, the longitudinal part of the gluon propagator becomes
suppressed. A comparison with the results obtained from the studies of the
Schwinger-Dyson equations and from lattice simulations is provided.Comment: 20 page
Poisson-Lie group of pseudodifferential symbols
We introduce a Lie bialgebra structure on the central extension of the Lie
algebra of differential operators on the line and the circle (with scalar or
matrix coefficients). This defines a Poisson--Lie structure on the dual group
of pseudodifferential symbols of an arbitrary real (or complex) order. We show
that the usual (second) Benney, KdV (or GL_n--Adler--Gelfand--Dickey) and KP
Poisson structures are naturally realized as restrictions of this Poisson
structure to submanifolds of this ``universal'' Poisson--Lie group.
Moreover, the reduced (=SL_n) versions of these manifolds (W_n-algebras in
physical terminology) can be viewed as subspaces of the quotient (or Poisson
reduction) of this Poisson--Lie group by the dressing action of the group of
functions.
Finally, we define an infinite set of functions in involution on the
Poisson--Lie group that give the standard families of Hamiltonians when
restricted to the submanifolds mentioned above. The Poisson structure and
Hamiltonians on the whole group interpolate between the Poisson structures and
Hamiltonians of Benney, KP and KdV flows. We also discuss the geometrical
meaning of W_\infty as a limit of Poisson algebras W_\epsilon as \epsilon goes
to 0.Comment: 64 pages, no figure
Symplectic structures associated to Lie-Poisson groups
The Lie-Poisson analogues of the cotangent bundle and coadjoint orbits of a
Lie group are considered. For the natural Poisson brackets the symplectic
leaves in these manifolds are classified and the corresponding symplectic forms
are described. Thus the construction of the Kirillov symplectic form is
generalized for Lie-Poisson groups.Comment: 30 page
Quantum and Classical Integrable Systems
The key concept discussed in these lectures is the relation between the
Hamiltonians of a quantum integrable system and the Casimir elements in the
underlying hidden symmetry algebra. (In typical applications the latter is
either the universal enveloping algebra of an affine Lie algebra, or its
q-deformation.) A similar relation also holds in the classical case. We discuss
different guises of this very important relation and its implication for the
description of the spectrum and the eigenfunctions of the quantum system.
Parallels between the classical and the quantum cases are thoroughly discussed.Comment: 59 pages, LaTeX2.09 with AMS symbols. Lectures at the CIMPA Winter
School on Nonlinear Systems, Pondicherry, January 199
Dual Isomonodromic Deformations and Moment Maps to Loop Algebras
The Hamiltonian structure of the monodromy preserving deformation equations
of Jimbo {\it et al } is explained in terms of parameter dependent pairs of
moment maps from a symplectic vector space to the dual spaces of two different
loop algebras. The nonautonomous Hamiltonian systems generating the
deformations are obtained by pulling back spectral invariants on Poisson
subspaces consisting of elements that are rational in the loop parameter and
identifying the deformation parameters with those determining the moment maps.
This construction is shown to lead to ``dual'' pairs of matrix differential
operators whose monodromy is preserved under the same family of deformations.
As illustrative examples, involving discrete and continuous reductions, a
higher rank generalization of the Hamiltonian equations governing the
correlation functions for an impenetrable Bose gas is obtained, as well as dual
pairs of isomonodromy representations for the equations of the Painleve
transcendents and .Comment: preprint CRM-1844 (1993), 28 pgs. (Corrected date and abstract.
Dual branes in topological sigma models over Lie groups. BF-theory and non-factorizable Lie bialgebras
We complete the study of the Poisson-Sigma model over Poisson-Lie groups.
Firstly, we solve the models with targets and (the dual group of the
Poisson-Lie group ) corresponding to a triangular -matrix and show that
the model over is always equivalent to BF-theory. Then, given an
arbitrary -matrix, we address the problem of finding D-branes preserving the
duality between the models. We identify a broad class of dual branes which are
subgroups of and , but not necessarily Poisson-Lie subgroups. In
particular, they are not coisotropic submanifolds in the general case and what
is more, we show that by means of duality transformations one can go from
coisotropic to non-coisotropic branes. This fact makes clear that
non-coisotropic branes are natural boundary conditions for the Poisson-Sigma
model.Comment: 24 pages; JHEP style; Final versio
Worldsheet boundary conditions in Poisson-Lie T-duality
We apply canonical Poisson-Lie T-duality transformations to bosonic open
string worldsheet boundary conditions, showing that the form of these
conditions is invariant at the classical level, and therefore they are
compatible with Poisson-Lie T-duality. In particular the conditions for
conformal invariance are automatically preserved, rendering also the dual model
conformal. The boundary conditions are defined in terms of a gluing matrix
which encodes the properties of D-branes, and we derive the duality map for
this matrix. We demonstrate explicitly the implications of this map for
D-branes in two non-Abelian Drinfel'd doubles.Comment: 20 pages, Latex; v2: typos and wording corrected, references added;
v3: three-dimensional example added, reference added, discussion clarified,
published versio
Hysteretic damper based on Bouc-Wen model
In the presented work we consider the dynamics of the mechanical system under internal force with a damper taking into account the hysteretic nature of the damper. As a mathematical model of this hysteretic damper we consider the Bouc-Wen model. The obtained numerical results in the form of the force transfer function demonstrates the efficiency of the hysteretic damper in comparison with the nonlinear viscous damper.This work is supported by the RFBR grant No 16-08-00312, 17-01-00251
Comparison of wheat simulation models under climate change. II. Application of climate change scenarios.
A comparison of the performance of 5 wheat models (AFRCWHEAT2, CERES, NWHEAT, SIRIUS and SOILN) was carried out for 2 sites in Europe Rothamsted, UK, and Seville, Spain. The aims of this study were (1) to compare predictions of wheat models for climate change scenarios, and (2) to investigate the effects of changes in climatic variability in climate change scenarios on model predic-tions. Simulations were run for climate change scenarios derived from a number of 2 × CO2 equilibrium and transient GCM (global circulation model) experiments. For most climate change scenarios the model results were broadly similar. Where results differed, much of the difference could be explained by model sensitivity to climate and differences in initial conditions. Transient scenarios without changes in climatic variability usually resulted in large yield increases for Rothamsted and in nil to large yield increases for Seville. Incorporation of changed climatic variability in the transient scenario had a more profound effect on grain yield and resulted in a substantial decrease in mean yield with a strong increase in yield variation at Seville. This was associated with the changes in the duration of dry spells and a redistribution of precipitation over the vegetation period. The results show that future studies of the effect of climate change on crop yields must consider changes in climatic variability as well as changes in mean climate
Comparison of wheat simulation models under climate change. I. Model calibration and sensitivity analyses.
A comparison of the performance of 5 wheat models was carried out for 2 sites in Europe with considerably different agroclimatic conditions Rothamsted, UK, and Seville, Spain. The models were calibrated against field data sets from both sites. For Rothamsted the measured time courses of crop growth, evapo-transpiration and nitrogen uptake were reproduced reasonably well by the different models, except for leaf area index. For Seville, the experimental data set was insufficient for such a detailed comparison and mainly simulated results were compared. The sensitivity of the model results to stepwise changes in individual weather variables was then determined. In the different model runs a temperature rise generally resulted in lower yields, an increase in precipitation and atmospheric CO2 concentration resulted in higher yields, and increased variability of weather variables often resulted in lower yields with increased yield variability
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