共查询到20条相似文献,搜索用时 15 毫秒
1.
Let denote the unit sphere in the Euclidean space . We develop LeVeque type inequalities for the discrepancy between the rotationally invariant probability measure and the normalized counting measures on . We obtain both upper bound and lower bound estimates. We then use these inequalities to estimate the discrepancy of the normalized counting measures associated with minimal energy configurations on . 相似文献
2.
SupposeX is a convex configuration with radius of maximum curvaturer and at most one of the edges joining neighboring points has length strictly greater thanr. We use the variational approach to show the Steiner treeS coincides with the minimal spanning tree and consists of all these edges with a longest edge removed. This generalizes Graham's problem for points on a circle, which we had solved. In addition we describe the minimal spanning tree for certain convex configurations. 相似文献
3.
Luigi Ambrosio 《manuscripta mathematica》1990,68(1):215-228
Summary We prove existence of minimizers of the functional
recently suggested by Ericksen [8] for the statics of nematic liquid crystals. A set of necessary conditions for the minimizers
and a monotonicity formula are also found. 相似文献
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Martin Traizet 《Commentarii Mathematici Helvetici》2004,79(4):798-825
We prove a balancing condition for weak limits of
families of embedded
minimal surfaces of finite total curvature. We use it to
prove compactness theorems for certain families of minimal
surfaces. 相似文献
9.
Bernd Schmidt 《Calculus of Variations and Partial Differential Equations》2007,30(4):477-497
We derive an effective plate theory for internally stressed thin elastic layers as are used, e.g., in the fabrication of nano-
and microscrolls. The shape of the energy minimizers of the effective energy functional is investigated without a priori assumptions
on the geometry. For configurations in two dimensions (corresponding to Euler-Bernoulli theory) we also take into account
a non-interpenetration condition for films of small but non-vanishing thickness.
相似文献
10.
Summary. We derive error bounds for bivariate spline interpolants which are calculated by minimizing certain natural energy norms.
Received March 28, 2000 / Revised version received June 23, 2000 / Published online March 8, 2002
RID="*"
ID="*" Supported by the National Science Foundation under grant DMS-9870187
RID="**"
ID="**" Supported by the National Science Foundation under grant DMS-9803340 and by the Army Research Office under grant DAAD-19-99-1-0160 相似文献
11.
A. B. J. Kuijlaars E. B. Saff 《Transactions of the American Mathematical Society》1998,350(2):523-538
We investigate the energy of arrangements of points on the surface of the unit sphere in that interact through a power law potential where and is Euclidean distance. With denoting the minimal energy for such -point arrangements we obtain bounds (valid for all ) for in the cases when and . For , we determine the precise asymptotic behavior of as . As a corollary, lower bounds are given for the separation of any pair of points in an -point minimal energy configuration, when . For the unit sphere in , we present two conjectures concerning the asymptotic expansion of that relate to the zeta function for a hexagonal lattice in the plane. We prove an asymptotic upper bound that supports the first of these conjectures. Of related interest, we derive an asymptotic formula for the partial sums of when (the divergent case).
12.
Bernardetta Addis Werner Schachinger 《Computational Optimization and Applications》2010,47(1):129-131
We improve lower bounds on the minimal distance between two points of a minimum energy configuration w.r.t. the Morse potential.
This is achieved by generalizing a method that was already applied to the Lennard-Jones potential in Schachinger et al. (Comput.
Optim. Appl. 38:329–349, 2007), resulting in improvements of the currently best bounds known for ρ∈[4.967,15] both for minimal distance and for energy of optimal configurations. 相似文献
13.
K. V. Kostousov 《Algebra and Logic》2008,47(2):118-124
We point out a countable set of pairwise nonisomorphic Cayley graphs of the group ℤ4 that are limit for finite minimal vertex-primitive graphs admitting a vertex-primitive automorphism group containing a regular
Abelian normal subgroup.
Supported by RFBR grant No. 06-01-00378.
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Translated from Algebra i Logika, Vol. 47, No. 2, pp. 203–214, March–April, 2008. 相似文献
14.
In this article we apply a Bochner type formula to show that on a compact conformally flat riemannian manifold (or half-conformally flat in dimension 4) certain types of orthogonal almost-complex structures, if they exist, give the absolute minimum for the energy functional. We give a few examples when such minimizers exist, and in particular, we prove that the standard almost-complex structure on the round S 6 gives the absolute minimum for the energy. We also discuss the uniqueness of this minimum and the extension of these results to other orthogonal G-structures. 相似文献
15.
We show that there exists a metric with positive scalar curvature on S
2 × S
1 and a sequence of embedded minimal cylinders that converges to a minimal lamination that, in a neighborhood of a strictly
stable 2-sphere, is smooth except at two helicoid-like singularities on the 2-sphere. The construction is inspired by a recent
example by D. Hoffman and B. White. 相似文献
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Anders Linné r Joseph W. Jerome 《Transactions of the American Mathematical Society》2007,359(5):2021-2041
Nonlinear functionals that appear as a product of two integrals are considered in the context of elastic curves of variable length. A technique is introduced that exploits the fact that one of the integrals has an integrand independent of the derivative of the unknown. Both the linear and the nonlinear cases are illustrated. By lengthening parameterized curves it is possible to reduce the elastic energy to zero. It is shown here that for graphs this is not the case. Specifically, there is a unique graph of minimal elastic energy among all graphs that have turned 90 degrees after traversing one unit.
19.
Energy minimization has been widely used for constructing curve and surface in the fields such as computer-aided geometric design, computer graphics. However, our testing examples show that energy minimization does not optimize the shape of the curve sometimes. This paper studies the relationship between minimizing strain energy and curve shapes, the study is carried out by constructing a cubic Hermite curve with satisfactory shape. The cubic Hermite curve interpolates the positions and tangent vectors of two given endpoints. Computer simulation technique has become one of the methods of scientific discovery, the study process is carried out by numerical computation and computer simulation technique. Our result shows that: (1) cubic Hermite curves cannot be constructed by solely minimizing the strain energy; (2) by adoption of a local minimum value of the strain energy, the shapes of cubic Hermite curves could be determined for about 60 percent of all cases, some of which have unsatisfactory shapes, however. Based on strain energy model and analysis, a new model is presented for constructing cubic Hermite curves with satisfactory shapes, which is a modification of strain energy model. The new model uses an explicit formula to compute the magnitudes of the two tangent vectors, and has the properties: (1) it is easy to compute; (2) it makes the cubic Hermite curves have satisfactory shapes while holding the good property of minimizing strain energy for some cases in curve construction. The comparison of the new model with the minimum strain energy model is included. 相似文献
20.
S. V. Borodachov D. P. Hardin E. B. Saff 《Transactions of the American Mathematical Society》2008,360(3):1559-1580
Given a closed -rectifiable set embedded in Euclidean space, we investigate minimal weighted Riesz energy points on ; that is, points constrained to and interacting via the weighted power law potential , where is a fixed parameter and is an admissible weight. (In the unweighted case () such points for fixed tend to the solution of the best-packing problem on as the parameter .) Our main results concern the asymptotic behavior as of the minimal energies as well as the corresponding equilibrium configurations. Given a distribution with respect to -dimensional Hausdorff measure on , our results provide a method for generating -point configurations on that are ``well-separated' and have asymptotic distribution as .