The Equilibrium Measure for a Nonlocal Dislocation Energy
The Equilibrium Measure for a Nonlocal Dislocation Energy
复制标题
非局域位错能的平衡测度
DOI：
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发表时间：
2016
影响因子：
3
通讯作者：
L. Scardia
中科院分区：
文献类型：
--
作者：
M. G. Mora;L. Rondi;L. Scardia
本文刻画了描述平面内正位错相互作用的非局域各向异性加权能量的平衡测度。我们证明了能量的最小值是由垂直轴上支承的、按照半圆定律分布的度量来获得的，该度量也是作为一维纯对数相互作用的最小化而产生的。通过这种方式，我们给出了正位错倾向于形成垂直壁的猜想的肯定答案。这个结果是少数几个显式计算非局部能量的极小值的例子之一，也是唯一一个在各向异性核的情况下的例子。©2018威利期刊公司。
In this paper we characterize the equilibrium measure for a nonlocal and anisotropic weighted energy describing the interaction of positive dislocations in the plane. We prove that the minimum value of the energy is attained by a measure supported on the vertical axis and distributed according to the semicircle law, a well‐known measure that also arises as the minimizer of purely logarithmic interactions in one dimension. In this way we give a positive answer to the conjecture that positive dislocations tend to form vertical walls. This result is one of the few examples where the minimizer of a nonlocal energy is explicitly computed and the only one in the case of anisotropic kernels. © 2018 Wiley Periodicals, Inc.
影响因子：
3.1
作者：
Carrillo, J. A.;Hittmeir, S.;Yao, Y.
通讯作者：
Yao, Y.
影响因子：
2.5
作者：
Balague, D.;Carrillo, J. A.;Raoul, G.
通讯作者：
Raoul, G.