110 research outputs found
On numerical approaches to the analysis of topology of the phase space for dynamical integrability
In this paper we consider the possibility to use numerical simulations for a
computer assisted analysis of integrability of dynamical systems. We formulate
a rather general method of recovering the obstruction to integrability for the
systems with a small number of degrees of freedom. We generalize this method
using the results of KAM theory and stochastic approaches to the families of
parameter depending systems. This permits the localization of possible
integrability regions in the parameter space. We give some examples of
application of this approach to dynamical systems having mechanical origin.Comment: 9 figures, version accepted to CS
Graded geometry in gauge theories and beyond
We study some graded geometric constructions appearing naturally in the
context of gauge theories. Inspired by a known relation of gauging with
equivariant cohomology we generalize the latter notion to the case of arbitrary
Q-manifolds introducing thus the concept of equivariant Q-cohomology. Using
this concept we describe a procedure for analysis of gauge symmetries of given
functionals as well as for constructing functionals (sigma models) invariant
under an action of some gauge group.
As the main example of application of these constructions we consider the
twisted Poisson sigma model. We obtain it by a gauging-type procedure of the
action of an essentially infinite dimensional group and describe its symmetries
in terms of classical differential geometry.
We comment on other possible applications of the described concept including
the analysis of supersymmetric gauge theories and higher structures.Comment: version accepted to Journal of Geometry and Physics, updated
reference
Dirac Sigma Models from Gauging
The G/G WZW model results from the WZW-model by a standard procedure of
gauging. G/G WZW models are members of Dirac sigma models, which also contain
twisted Poisson sigma models as other examples. We show how the general class
of Dirac sigma models can be obtained from a gauging procedure adapted to Lie
algebroids in the form of an equivariantly closed extension. The rigid gauge
groups are generically infinite dimensional and a standard gauging procedure
would give a likewise infinite number of 1-form gauge fields; the proposed
construction yields the requested finite number of them.
Although physics terminology is used, the presentation is kept accessible
also for a mathematical audience.Comment: 20 pages, 3 figure
Effective algorithm of analysis of integrability via the Ziglin's method
In this paper we continue the description of the possibilities to use
numerical simulations for mathematically rigorous computer assisted analysis of
integrability of dynamical systems. We sketch some of the algebraic methods of
studying the integrability and present a constructive algorithm issued from the
Ziglin's approach. We provide some examples of successful applications of the
constructed algorithm to physical systems.Comment: a figure added, version accepted to JDC
Measure of combined effects of morphological parameters of inclusions within composite materials via stochastic homogenization to determine effective mechanical properties
In our previous papers we have described efficient and reliable methods of
generation of representative volume elements (RVE) perfectly suitable for
analysis of composite materials via stochastic homogenization.
In this paper we profit from these methods to analyze the influence of the
morphology on the effective mechanical properties of the samples. More
precisely, we study the dependence of main mechanical characteristics of a
composite medium on various parameters of the mixture of inclusions composed of
spheres and cylinders. On top of that we introduce various imperfections to
inclusions and observe the evolution of effective properties related to that.
The main computational approach used throughout the work is the FFT-based
homogenization technique, validated however by comparison with the direct
finite elements method. We give details on the features of the method and the
validation campaign as well.
Keywords: Composite materials, Cylindrical and spherical reinforcements,
Mechanical properties, Stochastic homogenization.Comment: 23 pages, updated figures, version accepted to Composite Structures
201
Various instances of Harish-Chandra pairs
In this paper we address several algebraic constructions in the context of
groupoids, algebroids and -graded manifolds. We generalize the
results of integration of -graded Lie algebras to the honest
-graded case and provide some examples of application of the
technique based on Harish-Chandra pairs. We extend the construction to the
algebroids setting, the main example being the action Lie algebroid
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