Collaborative Research: Computational Framework for Non-asymptotic Homogenization with Applications to Metamaterials
合作研究:非渐近均质化计算框架及其在超材料中的应用
基本信息
- 批准号:1216970
- 负责人:
- 金额:$ 14.84万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2012
- 资助国家:美国
- 起止时间:2012-07-15 至 2015-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The project is aimed at developing a non-asymptotic homogenizationtheory of Maxwell's equations in artificial periodic composites(metamaterials). Currently, there is a consensus that sufficientlylarge lattice cell sizes are necessary for some nontrivial physicaleffects to occur in such structures. (The most intriguing of theseeffects is high-frequency magnetism.) Classical homogenizationtheories work well in the zero-cell-size limit but are difficult toapply to large metamaterial cells. In contrast, the proposed theory isnon-asymptotic and does not involve any series expansions with respectto the cell size. The electromagnetic field in the material isapproximated by a finite set of functions (modes) usually but notnecessarily Trefftz functions such as Bloch waves. The coarse-grainedfields and flux densities are defined via curl-conforming anddiv-conforming interpolations, respectively. A linear map betweenthese interpolants is established and defines an extended materialtensor. In a certain canonical basis, this extended tensor has aclassical block of 36 local parameters and a novel block quantifyingnonlocal effects. From the differential-geometric perspective, thisconstitutive relationship can be viewed as a realization ofBossavit-Hiptmair's discrete Hodge operators (linear maps betweendiscretized 1-forms that correspond to vector fields and 2-forms thatcorrespond to fluxes).Over the last decade, metamaterials have attracted unprecedentedattention due to a variety of potential applications that includesuperlensing, electromagnetic cloaking, electromagnetically-inducedtransparency, efficient antennas, and more. Experimentaldemonstrations of these effects have been limited to proofs ofprinciple and at optical frequencies have so far been incomplete.Subwavelength optical imaging has been achieved only in thequasi-static (near-field) regime, standard for the more conventionalnear-field optics; the so-called "carpet cloak" conceals surface bumpsrather than 3D objects, and so on. Moreover, applications that do notdepend critically on the effective medium description of metamaterialsappear to be more easily achievable than the ones that do. The lattergroup includes, notably, superlensing and cloaking. This suggeststhat, to make further progress, theoretical and mathematical issues atthe heart of metamaterial science must be unambiguously resolved. Themain problem can be stated as follows. Given the composition of ametamaterial cell and the operating frequency, determine whether thismetamaterial can be reasonably described as a continuous medium withsome effective parameters, just like any natural optical material; ifthe answer is positive, develop a rigorous methodology for such adescription. The proposed research is aimed at solving this problem inthe most difficult case when the cell size of the composite is anappreciable fraction of the wavelength of light. The methodology, oncedeveloped, will allow the scientific community to delineate thepossible from the impossible in the field of metamaterials.The intellectual merit of the proposed research is in the developmentof a new paradigm of non-asymptotic homogenization, of newcomputational methods related to it, and in the application of theproposed methodology to electromagnetic metamaterials, allowing one togain a much deeper understanding of their properties and limitations.As a new area of research, non-asymptotic homogenization will alsohave a broader technical impact in other areas of applied physics andengineering, such as acoustics, heat transfer and possibly elasticity.
该项目旨在在人工周期性复合材料(超材料)中开发麦克斯韦方程的非反应匀浆理论。当前,有一个共识,即某些非平凡的物理效应在此类结构中发生足够的晶格细胞大小是必要的。 (最吸引人的表面是高频磁性。)经典匀浆理论在零细胞尺寸的极限方面很好地工作,但很难与大型超材料细胞相关。相比之下,提出的理论是无反应的,与细胞大小相对于细胞大小不涉及任何串联膨胀。材料中的电磁场通常由有限的函数集(模式)集合而成,但通常不必要的trefftz函数,例如bloch波。粗粒状的田地和通量密度分别通过卷曲构造和符合符合性的插值来定义。建立了一个线性地图,并定义了扩展的材料传感器。在某个规范的基础上,该扩展张量具有36个局部参数的巨型块和一个新颖的块量化nonlocal效应。从微分几何的角度来看,这种结构的关系可以看作是实现Bossavit-ihiptmair的离散Hodge操作员的实现(线性映射的1形,对应于矢量领域和对应于磁通量的1形,对应于磁通量)。由于多种潜在应用,包括植物,电磁套制,电磁诱导的放射性,有效的天线等引起的,史无前例的。这些效果的实验示意图仅限于原理的证明,到目前为止,在光学频率下是不完整的。仅在thequasi static(近场)方向上实现了subbobbemengt Optical成像,这是更常规的nearnear-field光学光学的标准。所谓的“地毯斗篷”比3D物体掩盖了表面凹痕,依此类推。此外,与超材料应用的有效介质描述相比,与那些做法更容易实现的应用程序相比,应用程序的应用非常容易。 LASTERGROUP包括超级镜和掩饰。这表明为了进一步进步,必须明确解决超材料科学核心的理论和数学问题。他们的问题可以说明如下。鉴于氨基材料细胞的组成和工作频率,请确定是否可以合理地描述出该材料的连续培养基具有有效参数,就像任何天然光学材料一样;如果答案是积极的,请为这种适当的方法开发一种严格的方法。提出的研究旨在在最困难的情况下解决此问题,当时复合材料的细胞大小是光的波长的隔离部分。该方法是由占主导地开发的,它将使科学界能够从超材料领域的不可能中划定可能的问题。拟议的研究的智力优点在于开发了非反应均质化的新范式,该范式是与其与之相关的新合作方法以及其以及其及其与其相关的新范围的范式。在将该方法应用于电磁材料的材料中,使人们对其性质和局限性有更深入的了解。作为一个新的研究领域,非反应性均质化还将在应用物理学和革新的其他领域(例如声学,传热和可能的弹性。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Vadim Markel其他文献
Vadim Markel的其他文献
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Standard Grant
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