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1.
Sergio Conti Georg Dolzmann 《Calculus of Variations and Partial Differential Equations》2009,34(4):531-551
We derive a two-dimensional model for elastic plates as a Γ-limit of three-dimensional nonlinear elasticity with the constraint
of incompressibility. The resulting model describes plate bending, and is determined from the isochoric elastic moduli of
the three-dimensional problem. Without the constraint of incompressibility, a plate theory was first derived by Friesecke
et al. (Comm Pure Appl Math 55:1461–1506, 2002). We extend their result to the case of p growth at infinity with p ϵ [1, 2), and to the case of incompressible materials. The main difficulty is the construction of a recovery sequence which
satisfies the nonlinear constraint pointwise. One main ingredient is the density of smooth isometries in W
2,2 isometries, which was obtained by Pakzad (J Differ Geom 66:47–69, 2004) for convex domains and by Hornung (Comptes Rendus
Mathematique 346:189–192, 2008) for piecewise C
1 domains. 相似文献
2.
We give an optimal upper bound of the degree of quasi-smooth hypersurfaces which are invariant by a one-dimensional holomorphic foliation on a compact toric orbifold, i.e. on a complete simplicial toric variety. This bound depends only on the degree of the foliation and of the degrees of the toric homogeneous coordinates.
相似文献3.
Alexander Mielke Tomáš Roubíček Ulisse Stefanelli 《Calculus of Variations and Partial Differential Equations》2008,31(3):387-416
This work uses the energetic formulation of rate-independent systems that is based on the stored-energy functionals and the dissipation distance . For sequences and we address the question under which conditions the limits q
∞ of solutions satisfy a suitable limit problem with limit functionals and , which are the corresponding Γ-limits. We derive a sufficient condition, called conditional upper semi-continuity of the stable sets, which is essential to guarantee that q
∞ solves the limit problem. In particular, this condition holds if certain joint recovery sequences exist. Moreover, we show that time-incremental minimization problems can be used to approximate the solutions. A first example
involves the numerical approximation of functionals using finite-element spaces. A second example shows that the stop and
the play operator converge if the yield sets converge in the sense of Mosco. The third example deals with a problem developing
microstructure in the limit k → ∞, which in the limit can be described by an effective macroscopic model.
Research partially supported by LC06052 (MŠMT), MSM21620839 (MŠMT), A1077402 (GAČR), by the Deutsche Forschungsgemeinschaft
under MATHEON C18 and under SFB404 C7, by the European Union under HPRN-CT-2002-00284 Smart Systems, and by the Alexander von Humboldt-Stiftung. Both, TR and US gratefully acknowledge the kind hospitality of the WIAS, where
this research was initiated. 相似文献
4.
Valery V. Kozlov 《Regular and Chaotic Dynamics》2016,21(7-8):821-831
This paper is concerned with the problem of the integrable behavior of geodesics on homogeneous factors of the Lobachevsky plane with respect to Fuchsian groups (orbifolds). Locally the geodesic equations admit three independent Noether integrals linear in velocities (energy is a quadratic form of these integrals). However, when passing along closed cycles the Noether integrals undergo a linear substitution. Thus, the problem of integrability reduces to the search for functions that are invariant under these substitutions. If a Fuchsian group is Abelian, then there is a first integral linear in the velocity (and independent of the energy integral). Conversely, if a Fuchsian group contains noncommuting hyperbolic or parabolic elements, then the geodesic flow does not admit additional integrals in the form of a rational function of Noether integrals. We stress that this result holds also for noncompact orbifolds, when there is no ergodicity of the geodesic flow (since nonrecurrent geodesics can form a set of positive measure). 相似文献
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The Jørgensen, Gehring-Martin-Tan, and Tan numbers are defined for every two-generated subgroup of the group PSL(2,C). These numbers arise in necessary discreteness conditions for two-generated subgroups. The Jørgensen number equals 1 for the figure-eight knot group. We calculate the above numbers or give some two-sided bounds of them for this group and groups of hyperbolic orbifolds with singularities along the figure-eight knot. 相似文献
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For a physical system described by a motion in an energy landscape under holonomic constraints, we study the Γ-convergence
of variational integrators to the corresponding continuum action functional and the convergence properties of solutions of
the discrete Euler–Lagrange equations to stationary points of the continuum problem. This extends the results in Müller and
Ortiz (J. Nonlinear Sci. 14:279–296, 2004) to constrained systems. The convergence result is illustrated with examples of mass point systems and flexible multibody
dynamics.
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The purpose of this paper is to study the Hopf bifurcation property of the non-smooth planar dynamical systemwhere the individual functions K± R2 x I R2 at the right-hand side for some interval I containing 0 are smooth enough and given byThe parameter dependent matrices Aa(A) are assumed to be of the formwhere a 0 and w±() > 0. And the nonlinear terms in equation (??) are assumed to be smooth enough and have the formIn a standard way we extend the system (??) to a differential inclusion … 相似文献
11.
We study complex analytic properties of the augmented Teichmüller spaces [`(T)]g,n{\overline{\mathcal{T}}_{g,n}} obtained by adding to the classical Teichmüller spaces Tg,n{\mathcal{T}_{g,n}} points corresponding to Riemann surfaces with nodal singularities. Unlike Tg,n{\mathcal{T}_{g,n}}, the space [`(T)]g,n{\overline{\mathcal{T}}_{g,n}} is not a complex manifold (it is not even locally compact). We prove, however, that the quotient of the augmented Teichmüller
space by any finite index subgroup of the Teichmüller modular group has a canonical structure of a complex orbifold. Using
this structure, we construct natural maps from [`(T)]{\overline{\mathcal{T}}} to stacks of admissible coverings of stable Riemann surfaces. This result is important for understanding the cup-product
in stringy orbifold cohomology. We also establish some new technical results from the general theory of orbifolds which may
be of independent interest. 相似文献
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Andrija Raguž 《PAMM》2010,10(1):523-524
We use the approach developed in the paper G. Alberti, S. Muller: A new approach to variational problems with multiple scales, Comm. Pure Appl. Math. 54 , 761-825 (2001) to obtain Γ-convergence for a class of Ginzburg-Landau functionals Iε(v), where v = v(s) is appropriate Sobolev function. We generalize results from the paper A. Raguž: Relaxation of Ginzburg-Landau functional with 1-Lipschitz penalizing term in one dimension by Young measures on micropatterns, Asymptotic Anal. 41 ( 3,4 ), 331-361 (2005), where original functional was penalized by 1-Lipschitz function g = g(s). In this note we prove Γ-convergence when g = g(s, v(s), v′(s)) under suitable growth conditions imposed on g. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
14.
Hai Yun Zhou 《数学学报(英文版)》2010,26(4):743-758
In this paper, we continue to discuss the properties of iterates generated by a strict pseudo- contraction or a finite family of strict pseudo-contractions in a real q-uniformly smooth Banach space. The results presented in this paper are interesting extensions and improvements upon those known ones of Marino and Xu [Marino, G., Xu, H. K.: Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces. J. Math. Anal. Appl., 324, 336-349 (2007)]. In order to get a strong convergence theorem, we modify the normal Mann's iterative algorithm by using a suitable convex combination of a fixed vector and a sequence in C. This result extends a recent result of Kim and Xu [Kim, T. H., Xu, H. K.: Strong convergence of modified Mann iterations. Nonl. Anal., 61, 51- 60 (2005)] both from nonexpansive mappings to λ-strict pseudo-contractions and from Hilbert spaces to q-uniformly smooth Banach spaces. 相似文献
15.
Dominic Wright 《Selecta Mathematica, New Series》2011,17(2):281-299
We prove that any asymptotically locally Euclidean scalar-flat K?hler 4-orbifold whose isometry group contains a 2-torus is
isometric, up to an orbifold covering, to a quaternionic-complex quotient of a k-dimensional quaternionic vector space by a (k−1)-torus. In order to do so, we first prove that any compact anti-self-dual 4-orbifold with positive Euler characteristic
whose isometry group contains a 2-torus is conformally equivalent, up to an orbifold covering, to a quaternionic quotient of k-dimensional quaternionic projective space by a (k − 1)-torus. 相似文献
16.
The toric ideals of 3×3 transportation polytopes
Trc\mathsf{T}_{\mathbf{rc}}
are quadratically generated. The only exception is the Birkhoff polytope B
3.
If
Trc\mathsf{T}_{\mathbf{rc}}
is not a multiple of B
3, these ideals even have square-free quadratic initial ideals. This class contains all smooth 3×3 transportation polytopes. 相似文献
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