Gradient Extension of Classical Material Models: From Nuclear & Condensed Matter Scales to Earth & Cosmological Scales
Gradient Extension of Classical Material Models: From Nuclear & Condensed Matter Scales to Earth & Cosmological Scales
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经典材料模型的梯度扩展：来自核
DOI：
10.1007/978-3-030-63050-8_15
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
E. Aifantis
中科院分区：
文献类型：
--
作者：
E. Aifantis
过去开发的解释自然和人造材料行为的各种数学模型都是基于当时的观察和实验。经典定律（如牛顿的引力定律、胡克的弹性定律、纳维尔-斯托克斯的流动性定律、菲克/傅立叶的扩散/传热定律、库仑的电学定律、麦克斯韦的电磁学定律和爱因斯坦的相对论定律）构成了当前技术的基础和我们文明的形成。借助最近开发的实验探测器发现的新现象导致了这些定律在各个学科和尺度谱上的各种修改：从亚原子和基本粒子物理学到宇宙学，从原子和纳米/微米到宏观/千兆尺度。纳米技术的出现和空间技术的进一步发展最终与设计新的观测和测量工具以及开发新的量化和理解方法和途径有关。本文首先回顾了作者以前开发的弱非局部或梯度模型的弹性，扩散和塑性统一内部长度梯度（ILG）框架内。然后，它提出了一个类似的扩展流体和麦克斯韦的电磁方程。最后，它冒险牛顿引力定律的梯度修正，并研究其对基本粒子物理学的一些问题的影响，也与宇宙学有关。沿着类似的思路，它提出了伦敦量子力学势的类似扩展，包括“吸引”和“排斥”分支。它的结论与一些意见的ILG框架的分数推广。
The various mathematical models developed in the past to interpret the behavior of natural and manmade materials were based on observations and experiments made at that time. Classical laws (such as Newton's for gravity, Hooke's for elasticity, Navier-Stokes for fluidity, Fick's/Fourier's for diffusion/heat transfer, Coulomb's for electricity, as well as Maxwell's for electromagnetism and Einstein's for relativity) formed the basis of current technology and shaping of our civilization. The discovery of new phenomena with the aid of recently developed experimental probes have led to various modifications of these laws across disciplines and the scale spectrum: from subatomic and elementary particle physics to cosmology and from atomistic and nano/micro to macro/giga scales. The emergence of nanotechnology and the further advancement of space technology are ultimately connected with the design of novel tools for observation and measurements, as well as the development of new methods and approaches for quantification and understanding. The paper first reviews the author's previously developed weakly nonlocal or gradient models for elasticity, diffusion and plasticity within a unifying internal length gradient (ILG) framework. It then proposes a similar extension for fluids and Maxwell's equations of electromagnetism. Finally, it ventures a gradient modification of Newton's law of gravity and examines its implications to some problems of elementary particle physics, also relevant to cosmology. Along similar lines, it suggests an analogous extension of London's quantum mechanical potential to include both an "attractive" and a "repulsive" branch. It concludes with some comments on a fractional generalization of the ILG framework.
DOI：
10.1016/j.ijsolstr.2011.03.006
发表时间：
2011-06-15
影响因子：
3.6
作者：
Askes, Harm;Aifantis, Elias C.
通讯作者：
Aifantis, Elias C.