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111.
In this paper we study higher Chow groups of smooth, projective surfaces over a field k of characteristic zero, using some new Hodge theoretic methods which we develop for this purpose. In particular we investigate the subgroup of CH
r+1 (X,r) with r = 1,2 consisting of cycles that are supported over a normal crossing divisor Z on X. In this case, the Hodge theory of the complement forms an interesting variation of mixed Hodge structures in any geometric deformation of the situation. Our main result is a structure theorem in the case where X is a very general hypersurface of degree d in projective 3-space for d sufficiently large and Z is a union of very general hypersurface sections of X. In this case we show that the subgroup of CH
r+1 (X,r) we consider is generated by obvious cycles only arising from rational functions on X with poles along Z. This can be seen as a generalization of the Noether–Lefschetz theorem for r = 0. In the case r = 1 there is a similar generalization by Müller-Stach, but our result is more precise than it, since it is geometric and not only cohomological. The case r = 2 is entirely new and original in this paper. For small d, we construct some explicit examples for r = 1 and 2 where the corresponding higher Chow groups are indecomposable, i.e. not the image of certain products of lower order groups. In an appendix Alberto Collino constructs even more indecomposable examples in CH
3 (X,2) which move in a one-dimensional family on the surface X.Contribution to appendix. 相似文献
112.
We study phase separation in a system of hard-core particles driven by a fluctuating two-dimensional self-affine potential landscape which evolves through Kardar–Parisi–Zhang (KPZ) dynamics. We find that particles tend to cluster together on a length scale which grows in time. The final phase-separated steady state is characterized by an unusual cusp singularity in the scaled correlation function and a broad distribution for the order parameter. Unlike the one-dimensional case studied earlier, the cluster-size distribution is asymmetric between particles and holes, reflecting the broken reflection symmetry of the KPZ dynamics, and has a contribution from an infinite cluster in addition to a power law part. A study of the surface in terms of coarse-grained depth variables helps understand many of these features. 相似文献
113.
M. Dubé C. Daneault V. Vuorinen M. Alava M. Rost 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,56(1):15-26
We investigate the structure and dynamics of the interface between
two immiscible liquids in a three-dimensional disordered porous
medium. We apply a phase-field model that includes explicitly
disorder and discuss both spontaneous and forced imbibition.
The structure of the interface is dominated by a length scale
ξ× which arises from liquid conservation. We further show
that disorder in the capillary and permeability act on different
length scales and give rise to different scalings and
structures of the interface properties. We conclude with a
range of applications. 相似文献
114.
This article focuses on discontinuous Galerkin method for the two‐ or three‐dimensional stationary incompressible Navier‐Stokes equations. The velocity field is approximated by discontinuous locally solenoidal finite element, and the pressure is approximated by the standard conforming finite element. Then, superconvergence of nonconforming finite element approximations is applied by using least‐squares surface fitting for the stationary Navier‐Stokes equations. The method ameliorates the two noticeable disadvantages about the given finite element pair. Finally, the superconvergence result is provided under some regular assumptions. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 421–436, 2007 相似文献
115.
A theoretical study of the electron dynamics in image potential states on Cu(1 0 0) surfaces with different types of adsorbates is presented. Scattering of the image state electron by an adsorbate induces inter-band and intra-band transitions leading respectively to the population decay and to the dephasing of the image state. We compare results obtained with low coverage (typically 1 adsorbate atom per 1000 surface atoms) Cs, Ar, and a model electronegative adsorbates. As follows from our results, Cs adsorbates lead to both appreciable dephasing and decay, while electronegative adsorbates mostly affect the dephasing rate. The effect of low coverage Ar adsorbates is small, consistent with their neutrality. 相似文献
116.
Arman Melkumyan 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(2):330-349
The problem of electric and acoustic waves diffraction by a half-plane crack in a transversal isotropic piezoelectric medium
is investigated. The crack is assumed to be electric permeable and free of tractions. The so-called “quasi-hyperbolic approximation”
[15] is adopted. Applying Laplace transformations and Wiener–Hopf technique a closed form solution is obtained. By the means
of Cagniard–de Hoop method a detailed dynamic full electroacoustic wavefield’s investigation is conducted. Mode conversion
between electric and acoustic waves, effect of electroacoustic head wave, Bleustein–Gulyaev surface wave and the wavefield
structure depending on the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in details.
The dynamic field intensity factors at the crack tip depending on the angle of incidence and on time are derived explicitly.
Numerical analysis is presented. 相似文献
117.
Gaiane Panina 《Central European Journal of Mathematics》2006,4(2):270-293
Hyperbolic virtual polytopes arose originally as polytopal versions of counterexamples to the following A.D.Alexandrov’s uniqueness
conjecture: Let K ⊂ ℝ3
be a smooth convex body. If for a constant C, at every point of ∂K, we have R
1 ≤ C ≤ R
2
then K is a ball. (R
1
and R
2
stand for the principal curvature radii of ∂K.)
This paper gives a new (in comparison with the previous construction by Y.Martinez-Maure and by G.Panina) series of counterexamples
to the conjecture. In particular, a hyperbolic virtual polytope (and therefore, a hyperbolic hérisson) with odd an number
of horns is constructed.
Moreover, various properties of hyperbolic virtual polytopes and their fans are discussed. 相似文献
118.
119.
The paper addresses bivariate surface fitting problems, where data points lie on the vertices of a rectangular grid. Efficient
and stable algorithms can be found in the literature to solve such problems. If data values are missing at some grid points,
there exists a computational method for finding a least squares spline by fixing appropriate values for the missing data.
We extended this technique to arbitrary least squares problems as well as to linear least squares problems with linear equality
constraints. Numerical examples are given to show the effectiveness of the technique presented.
AMS subject classification (2000) 65D05, 65D07, 65D10, 65F05, 65F20 相似文献
120.
We study the Helmholtz equation in the exterior of an infinite perturbed cylinder with a Dirichlet boundary condition. Existence and uniqueness of solutions are established using the variational technique introduced (SIAM J. Math. Anal. 2005; 37 (2):598–618). We also provide stability estimates with explicit dependence of the constants in terms of the frequency and the perturbed cylinder thickness. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献