共查询到20条相似文献,搜索用时 234 毫秒
1.
M. Rosati 《Applied Mathematics and Optimization》2000,41(1):51-85
In this paper we consider a class of discrete variational models derived from a theory of Geman and McClure (see [15]) and
study their asymptotic behavior when their stepsize tends to zero. It is shown that a result of Γ -convergence toward a certain functional holds true if a characteristic parameter of these models obeys a well-defined dependence
law upon the stepsize. Under this condition the Γ -limit is a modified form of the Mumford—Shah functional.
Accepted 19 June 1998 相似文献
2.
Summary. The ABC lamellar phase of a triblock copolymer in the strong segregation region is studied on periodic and bounded intervals. In
the periodic case we find a family of local minimizers of the free energy functional all with a fine lamellar structure. Among
these local minimizers we identify the one most favored by the free energy, and hence determine the thickness of lamellar
microdomains. In the bounded interval case we show that perfect lamellar structure does not exist due to the boundary effect.
We view the strong segregation limit as a Γ -limit of the free energy by a proper choice of the material sample size. The key step is the spectral analysis of a large
matrix resulting from the second derivative of the Γ -limit. 相似文献
3.
We study a one-dimensional variational problem with two or more level set constraints. The existence of global and local
minimizers turns out to be dependent on the regularity of the energy density. A complete characterization of local minimizers
and the underlying energy landscape is provided. The Γ -limit when the phases exhaust the whole domain is computed. 相似文献
4.
A Volume Constrained Variational Problem with Lower-Order Terms 总被引:1,自引:0,他引:1
We study a one-dimensional variational problem with two or more level set constraints. The existence of global and local
minimizers turns out to be dependent on the regularity of the energy density. A complete characterization of local minimizers
and the underlying energy landscape is provided. The Γ -limit when the phases exhaust the whole domain is computed. 相似文献
5.
Radu Ignat 《Calculus of Variations and Partial Differential Equations》2009,36(2):285-316
Three reduced models are considered for Néel walls which are dominant transition layers in thin-film micromagnetics. Each
model comes as a nonlocal and nonconvex variational principle for one-dimensional magnetizations and it depends on a small
parameter ε > 0. Our aim is to study the Γ-convergence of these models as eˉ 0{\varepsilon \downarrow 0} . We prove that the limiting magnetization patterns are piecewise constant functions that correspond to a finite number of
walls of the same angle. The Γ-limit energy is proportional to the number of walls of these configurations and the energetic
cost of each wall is quartic for small wall angles. 相似文献
6.
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.
相似文献
7.
María del Mar González 《Calculus of Variations and Partial Differential Equations》2009,36(2):173-210
We prove a Γ-convergence result for an energy functional related to some fractional powers of the Laplacian operator, (−Δ)
s
for 1/2 < s < 1, with two singular perturbations, that leads to a two-phase problem. The case (−Δ)1/2 was considered by Alberti–Bouchitté–Seppecher in relation to a model in capillarity with line tension effect. However, the
proof in our setting requires some new ingredients such as the Caffarelli–Silvestre extension for the fractional Laplacian
and new trace inequalities for weighted Sobolev spaces. 相似文献
8.
9.
A Г-Convergence Result for Thin Curved Films Bonded to a Fixed Substrate with a Noninterpenetration Constraint 下载免费PDF全文
Hamdi ZORGATI 《数学年刊B辑(英文版)》2006,27(6):615-636
Abstract
The behavior of a thin curved hyperelastic film bonded to a fixed substrate is described by an energy composed of a nonlinearly
hyperelastic energy term and a debonding interfacial energy term. The author computes the Γ-limit of this energy under a noninterpenetration
constraint that prohibits penetration of the film into the substrate without excluding contact between them. 相似文献
10.
Marc Briane Juan Casado-Díaz 《Calculus of Variations and Partial Differential Equations》2007,29(4):455-479
In this paper, we study the asymptotic behaviour of a given equicoercive sequence of diffusion energies F
n
, , defined in L
2(Ω), for a bounded open subset Ω of . We prove that, contrary to the dimension three (or greater), the Γ-limit of any convergent subsequence of F
n
is still a diffusion energy. We also provide an explicit representation formula of the Γ-limit when its domains contains
the regular functions with compact support in Ω. This compactness result is based on the uniform convergence satisfied by
some minimizers of the equicoercive sequence F
n
, which is specific to the dimension two. The compactness result is applied to the period framework, when the energy density
is a highly oscillating sequence of equicoercive matrix-valued functions. So, we give a definitive answer to the question
of the asymptotic behaviour of periodic conduction problems under the only assumption of equicoerciveness for the two-dimensional
conductivity. 相似文献
11.
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
12.
This paper describes a spectral representation of solutions of self-adjoint elliptic problems with immersed interfaces. The
interface is assumed to be a simple non-self-intersecting closed curve that obeys some weak regularity conditions. The problem
is decomposed into two problems, one with zero interface data and the other with zero exterior boundary data. The problem
with zero interface data is solved by standard spectral methods. The problem with non-zero interface data is solved by introducing
an interface space H
Γ(Ω) and constructing an orthonormal basis of this space. This basis is constructed using a special class of orthogonal eigenfunctions
analogously to the methods used for standard trace spaces by Auchmuty (SIAM J. Math. Anal. 38, 894–915, 2006). Analytical and numerical approximations of these eigenfunctions are described and some simulations are presented. 相似文献
13.
Alexander Mielke Filip Rindler 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(1):17-40
Energetic solutions to rate-independent processes are usually constructed via time-incremental minimization problems. In this
work we show that all energetic solutions can be approximated by such incremental problems if we allow for approximate minimizers,
where the error in minimization has to be of the order of the time step. Moreover, we study sequences of problems where the
energy functionals have a Γ-limit.
Research partially supported by Deutsche Forschungsgemeinschaft via the MATHEON project C18. 相似文献
14.
15.
Let G be the group of rational points of a split connected reductive group over a p-adic local field, and let Γ be a discrete and cocompact subgroup of G. Motivated by questions on the cohomology of p-adic symmetric spaces, we investigate the homology of Γ with coefficients in locally analytic principal series and related representations of G. The vanishing and finiteness results that we find partially rely on the compactness of certain Banach–Hecke operators. We
also give a new construction of P. Schneider’s reduced Hodge–de Rham spectral sequence and show that the induced filtration
is the Hodge–de Rham filtration. In a previously unknown case, our vanishing theorems then also imply two other of P. Schneider’s
conjectures. 相似文献
16.
Baran Sándor Pap Gyula Van Zuijlen Martien C. A. 《Statistical Inference for Stochastic Processes》2004,7(3):279-304
A shifted Wiener sheet is observed above a decreasing curve Γ. By the help of a direct discrete approach and under weaker
assumptions than in the paper of Arató [Comput. Math. Appl.
33 (1997), 13–25], an explicit formula is derived for the maximum likelihood estimator of the shift parameter. This estimator
is a weighted linear combination of the values at the endpoints of the curve Γ and weighted integrals of the observed process
and its normal derivative along the curve Γ.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
17.
M. A. Berezhnoi 《Ukrainian Mathematical Journal》2009,61(3):361-382
We study the asymptotic behavior of solutions of the problem that describes small motions of a viscous incompressible fluid
filling a domain Ω with a large number of suspended small solid interacting particles concentrated in a small neighborhood
of a certain smooth surface Γ ⊂ Ω. We prove that, under certain conditions, the limit of these solutions satisfies the original equations in the domain Ω\Γ and some averaged boundary conditions (conjugation conditions) on Γ. 相似文献
18.
Iterative Approximation of Statistical Distributions and Relation to Information Geometry 总被引:1,自引:0,他引:1
The optimal control of stochastic processes through sensor estimation of probability density functions is given a geometric
setting via information theory and the information metric. Information theory identifies the exponential distribution as the
maximum entropy distribution if only the mean is known and the Γ distribution if also the mean logarithm is known. The surface
representing Γ models has a natural Riemannian information metric. The exponential distributions form a one-dimensional subspace
of the two-dimensional space of all Γ distributions, so we have an isometric embedding of the random model as a subspace of
the Γ models. This geometry provides an appropriate structure on which to represent the dynamics of a process and algorithms
to control it. This short paper presents a comparative study on the parameter estimation performance between the geodesic
equation and the B-spline function approximations when they are used to optimize the parameters of the Γ family distributions. In this case,
the B-spline functions are first used to approximate the Γ probability density function on a fixed length interval; then the coefficients
of the approximation are related, through mean and variance calculations, to the two parameters (i.e. μ and β) in Γ distributions.
A gradient based parameter tuning method has been used to produce the trajectories for (μ, β) when B-spline functions are used, and desired results have been obtained which are comparable to the trajectories obtained from
the geodesic equation.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
19.
A. N. Starkov 《Mathematical Notes》1999,66(2):233-239
Consider a connected Lie groupG, a lattice Γ inG, a connected subgroupH ofG, and the adjoint representation Ad ofG on its Lie algebra g. Suppose that Ad(H) splits into a semidirect product of a reductive subgroup and the unipotent radical. We prove that the minimality of the
leftH-action onG/Γ then implies its unique ergodicity. Simultaneously, we suggest a reduction of the study of finite ergodic measures for
an arbitrary action (G/Γ,H), where the subgroupH∈G is connected and Γ∈G is discrete, to the case of an Abelian subgroupH.
Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 293–301, August, 1999. 相似文献
20.
Ecaterina Sava 《Monatshefte für Mathematik》2010,124(1):379-396
The main goal of this paper is to determine the Poisson boundary of lamplighter random walks over a general class of discrete
groups Γ endowed with a “rich” boundary. The starting point is the Strip Criterion of identification of the Poisson boundary
for random walks on discrete groups due to Kaimanovich (Ann. Math. 152:659–692, 2000). A geometrical method for constructing
the strip as a subset of the lamplighter group
\mathbb Z2\wr G{\mathbb {Z}_{2}\wr \Gamma} starting with a “smaller” strip in the group Γ is developed. Then, this method is applied to several classes of base groups
Γ: groups with infinitely many ends, hyperbolic groups in the sense of Gromov, and Euclidean lattices. We show that under
suitable hypothesis the Poisson boundary for a class of random walks on lamplighter groups is the space of infinite limit
configurations. 相似文献