排序方式: 共有21条查询结果,搜索用时 15 毫秒
1.
G.I. Giannopoulos I.A. Liosatos A.K. Moukanidis 《Physica E: Low-dimensional Systems and Nanostructures》2011,44(1):124-134
The elastic mechanical behavior of different sized zigzag and armchair graphene nanoribbons is numerically investigated and predicted using a new structural mechanic approach. According to the proposed method three dimensional, two nodded spring elements of three degrees of freedom per node, which remain straight when deformed, are combined in order to simulate realistically the interatomic interactions appearing within the graphene nanostructure. The computed variations of mechanical elastic properties are fitted by appropriate size dependent non-linear functions of two independent variables i.e. length and width, in order to express the analytical rules governing the elastic behavior of graphene nanoribbons within specific dimension limits. The numerical results, which are compared with corresponding data given in the open literature, demonstrate thoroughly the important influence of size and chirality of a narrow graphene monolayer on its elastic behavior. 相似文献
2.
M.?FradeliziEmail author M.?Meyer A.?Giannopoulos 《Israel Journal of Mathematics》2003,135(1):157-179
We prove inequalities about the quermassintegralsV
k
(K) of a convex bodyK in ℝ
n
(here,V
k
(K) is the mixed volumeV((K, k), (B
n
,n − k)) whereB
n
is the Euclidean unit ball). (i) The inequality
holds for every pair of convex bodiesK andL in ℝ
n
if and only ifk=2 ork=1. (ii) Let 0≤k≤p≤n. Then, for everyp-dimensional subspaceE of ℝ
n
,
whereP
E
K denotes the orthogonal projection ofK ontoE. The proof is based on a sharp upper estimate for the volume ratio |K|/|L| in terms ofV
n−k
(K)/V
n−k
(L), wheneverL andK are two convex bodies in ℝ
n
such thatK ⊆L. 相似文献
3.
A. A. Giannopoulos 《Proceedings of the American Mathematical Society》1996,124(1):233-241
If is an -dimensional normed space and , there exists , such that the formal identity can be written as , with . This is proved as a consequence of a Sauer-Shelah type theorem for ellipsoids.
4.
Let K and L be two convex bodies in Rn. The volume ratio vr(K,L) of K and L is defined by vr(K, L = inf(|K|/|T(L)|)1/n, wherethe infimum is over all affine transformations T of Rn for whichT(L) K. It is shown in this paper that vr(K, L) , where c > 0 is an absolute constant. This isoptimal up to the logarithmic term. 2000 Mathematics SubjectClassification 52A40, 46B07 (primary); 52A21, 52A20 (secondary). 相似文献
5.
Dimitris Gatzouras Giannopoulos Apostolos Nikolaos Markoulakis 《Discrete and Computational Geometry》2005,34(2):331-349
Let $f_{n-1}(P)$ denote the number of facets of a
polytope $P$ in ${\Bbb R}^n$. We show that there exist 0/1
polytopes $P$ with $$f_{n-1}(P)\geq\left (\frac{cn}{\log^2
n}\right )^{n/2},$$ where $c>0$ is an absolute constant. This
improves earlier work of Barany and Por on a question
of Fukuda and Ziegler. 相似文献
6.
We provide a generalization of John's representation of the identity for the maximal volume position of L inside K, where K and L are arbitrary smooth convex bodies in
n
. From this representation we obtain Banach–Mazur distance and volume ratio estimates. 相似文献
7.
Silouanos Brazitikos Susanna Dann Apostolos Giannopoulos Alexander Koldbosky 《Israel Journal of Mathematics》2017,222(2):921-947
The average section functional as(K) of a star body in Rn is the average volume of its central hyperplane sections: \(as\left( k \right) = \int_{{S^{n - 1}}} {\left| {K \cap {\xi ^ \bot }} \right|} d\sigma \left( \xi \right)\). We study the question whether there exists an absolute constantC > 0 such that for every n, for every centered convex body K in R n and for every 1 ≤ k ≤ n ? 2, . We observe that the case k = 1 is equivalent to the hyperplane conjecture. We show that this inequality holds true in full generality if one replaces C by CL K orCdovr(K, BP k n ), where L K is the isotropic constant of K and dovr(K, BP k n ) is the outer volume ratio distance of K to the class BP k n of generalized k-intersection bodies. We also compare as(K) to the average of as(K ∩ E) over all k-codimensional sections of K. We examine separately the dependence of the constants on the dimension when K is in some classical position. Moreover, we study the natural lower dimensional analogue of the average section functional.
相似文献
$$as\left( K \right) \leqslant {C^k}{\left| K \right|^{\frac{k}{n}}}\mathop {\max }\limits_{|E \in G{r_{n - k}}} {\kern 1pt} as\left( {K \cap E} \right)$$
8.
A. Giannopoulos A. Pajor G. Paouris 《Proceedings of the American Mathematical Society》2007,135(8):2599-2606
We give an alternative proof of a recent result of Klartag on the existence of almost subgaussian linear functionals on convex bodies. If is a convex body in with volume one and center of mass at the origin, there exists such that for all , where is an absolute constant. The proof is based on the study of the -centroid bodies of . Analogous results hold true for general log-concave measures.
9.
Sotirios G. Siampanis Georgios I. Giannopoulos Nikos D. Lagaros Antonios Hatziefremidis Stelios K. Georgantzinos 《Molecules (Basel, Switzerland)》2022,27(5)
In this study, a nonlinear, spring-based finite element approach is employed in order to predict the nonlinear mechanical response of graphyne structures under shear loading. Based on Morse potential functions, suitable nonlinear spring finite elements are formulated simulating the interatomic interactions of different graphyne types. Specifically, the four well-known types of γ-graphyne, i.e., graphyne-1 also known as graphyne, graphyne-2 also known as graphdiyne, graphyne-3, and graphyne-4 rectangular sheets are numerically investigated applying appropriate boundary conditions representing shear load. The obtained finite element analysis results are employed to calculate the in-plane shear stress–strain behaviour, as well as the corresponding mechanical properties as shear modulus and shear strength. Comparisons of the present graphyne shearing response predictions with other corresponding estimations are performed to validate the present research results. 相似文献
10.