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Graded geometry in gauge theories Salnikov, Vladimir Presentation (2015) Detailed reference viewed: 26 (3 UL)Graded geometry in gauge theories and beyond Salnikov, Vladimir in Journal of Geometry & Physics (2015) 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 61 (3 UL)Measure of combined effects of morphological parameters of inclusions within composite materials via stochastic homogenization to determine effective mechanical properties Salnikov, Vladimir ; ; et al in Composite Structures (2015) Detailed reference viewed: 54 (0 UL)Workshop on Higher Geometry and Field Theory Kwok, Stephen ; Poncin, Norbert ; Salnikov, Vladimir Report (2015) Detailed reference viewed: 95 (14 UL)Approche par la dynamique moléculaire pour la conception de VER 3D et variations autour de la pixellisation. Salnikov, Vladimir ; ; et al in Approche par la dynamique moléculaire pour la conception de VER 3D et variations autour de la pixellisation. (2015) Detailed reference viewed: 54 (1 UL)Graded geometry in gauge theories: above and beyond Salnikov, Vladimir Presentation (2015) Detailed reference viewed: 42 (2 UL)On efficient and reliable stochastic generation of RVEs for analysis of composites within the framework of homogenization Salnikov, Vladimir ; ; in Computational Mechanics (2014) Detailed reference viewed: 54 (0 UL)2d gauge theories and generalized geometry ; Salnikov, Vladimir ; in Journal of High Energy Physics [=JHEP] (2014) We show that in the context of two-dimensional sigma models minimal coupling of an ordinary rigid symmetry Lie algebra g leads naturally to the appearance of the “generalized tangent bundle” TM ≡ T M ⊕ T ... [more ▼] We show that in the context of two-dimensional sigma models minimal coupling of an ordinary rigid symmetry Lie algebra g leads naturally to the appearance of the “generalized tangent bundle” TM ≡ T M ⊕ T ∗ M by means of composite fields. Gauge transformations of the composite fields follow the Courant bracket, closing upon the choice of a Dirac structure D ⊂ TM (or, more generally, the choide of a “small Dirac-Rinehart sheaf” D), in which the fields as well as the symmetry parameters are to take values. In these new variables, the gauge theory takes the form of a (non-topological) Dirac sigma model, which is applicable in a more general context and proves to be universal in two space-time dimensions: a gauging of g of a standard sigma model with Wess-Zumino term exists, iff there is a prolongation of the rigid symmetry to a Lie algebroid morphism from the action Lie algebroid M × g → M into D → M (or the algebraic analogue of the morphism in the case of D). The gauged sigma model results from a pullback by this morphism from the Dirac sigma model, which proves to be universal in two-spacetime dimensions in this sense. [less ▲] Detailed reference viewed: 67 (1 UL)Effective Algorithm of Analysis of Integrability via the Ziglin’s Method Salnikov, Vladimir in Journal of Dynamical & Control Systems (2014) 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 64 (2 UL)Dirac sigma models from gauging Salnikov, Vladimir ; in Journal of High Energy Physics [=JHEP] (2013) 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 52 (0 UL)On numerical approaches to the analysis of topology of the phase space for dynamical integrability Salnikov, Vladimir in Chaos, Solitons & Fractals (2013) In this paper we consider the possibility to use numerical simulations for a computer assisted qualitative analysis of dynamical systems. We formulate a rather general method of recovering the ... [more ▼] In this paper we consider the possibility to use numerical simulations for a computer assisted qualitative analysis of dynamical systems. We formulate a rather general method of recovering the obstructions to dynamical integrability for the systems that after reduction have 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 to localize possible integrability regions in the parameter space. We give some examples of application of this approach to dynamical systems having a mechanical origin. [less ▲] Detailed reference viewed: 38 (1 UL) |
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