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Applied Hyperspace Structures (HYPER)

应用超空间结构（HYPER）

基本信息

批准号：
EP/X011984/1
负责人：
金额：
$ 69.53万
依托单位：
University of Liverpool
依托单位国家：
英国
项目类别：
Fellowship
财政年份：
2023
资助国家：
英国
起止时间：
2023 至无数据
项目状态：
未结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FX011984%2F1
关键词：
Applied Hyperspace Structures HYPER

项目摘要

Imagine shining a torch onto a cube: the cube is 3D, and its shadow is 2D. Depending on the angle and position of the torch, the shape of the shadow will change. We can call the shadow of the cube its 'projection', and define specific projections depending on the direction we point the torch, or the position of the cube. Projections of 3D cubes are simple, but what happens when we add an extra dimension? The human brain can't imagine what a fourth dimension looks like, but we can project a 4D structure onto dimensional spaces we can understand, for example, 2D. If we carry on this way, we can also visualize 5D cubes by projecting onto a 2D and 3D space, or 6D cubes by projecting onto two 3D spaces.The extra dimensions can be called higher-dimensional spaces, or hyperspaces. The dimensions we can visualize (2D and 3D) are called real-space. Changing the dimension of the cube or the angle of projection in hyperspace changes the real-space structure we obtain. By projecting hyperspace structures, we can produce simple or complex repeating patterns, or create examples which have no repeating units, but still have long-range order. These special arrangements are called aperiodic, or quasicrystalline structures. Therefore, unlike a 3D cube projection, projected hyperspace structures can produce a huge variety of structures in real-space. Importantly, we have not even begun to explore all the possible structures and uses hidden in projections of hyperspace. Applied Hyperspace Structures (HYPER) aims to exploit and apply new hyperspace structures in novel fashions, demonstrating their power and utilization in three new ways. The first will be to help understand the stability of physical quasicrystals. Quasicrystals are typically found as intermetallic alloys, and again, they have no repeating unit (unlike crystals) but retain perfect order. Their structure is very complex but can be understood using hyperspace projections. However, we still do not know exactly why such materials are stable - a fundamental question which is important to understand their existence in nature. Current theories argue between the relative ratio of energetic and entropic contributions of phasons, which are atomic movements in the quasicrystal structure. HYPER will take the novel approach of applying hyperspace projections to analyse phasonic motion at the surfaces of physical quasicrystals, measuring at the atomic level using Scanning Tunnelling Microscopy. In doing so, we can understand their precise energetic or entropic contribution to the surface structure, and therefore find the key to understanding quasicrystal stability. The second focus of HYPER will be to investigate theoretical hybrid materials which have unique structures designed by hyperspace projections. These hybrids will consist of periodic and aperiodic sections which share rotational symmetry - an avenue of aperiodic research which has so far been relatively overlooked. Such hybrid materials have therefore never been imagined before, let alone explored. We will investigate how waves propagate through such structures and study their effective properties, which, hopefully, can be tuned in future manufactured materials for a range of applications.Finally, HYPER will produce a piece of easy-to-use software which will allow anyone to generate their own hyperspace structures - even if they're not experts on the subject. This software package will allow users to pick their hyperspace dimension, choose between aperiodic and periodic structures, and visualize their resultant projections.The proposed research is therefore both fundamental and applied in its nature, with the potential to influence and introduce an interdisciplinary audience to the possibilities of exploring hyperstructures.

想象一下，用手电筒照一个立方体：立方体是3D的，而它的影子是2D的。根据火炬的角度和位置，阴影的形状会发生变化。我们可以称立方体的阴影为“投影”，并根据我们指向火炬的方向或立方体的位置来定义特定的投影。三维立方体的投影很简单，但是当我们增加一个额外的维度时会发生什么呢？人类的大脑无法想象四维空间是什么样子，但我们可以将四维结构投射到我们可以理解的维度空间上，比如二维空间。如果我们继续这样做，我们也可以通过投影到2D和3D空间来可视化5D立方体，或者通过投影到两个3D空间来可视化6D立方体。额外的维度可以称为高维空间或超空间。我们可以可视化的维度（2D和3D）被称为实空间。在超空间中改变立方体的维数或投影角度会改变我们得到的实空间结构。通过投射超空间结构，我们可以生成简单或复杂的重复模式，或者创建没有重复单元但仍然具有长程顺序的示例。这些特殊的排列被称为非周期或准晶体结构。因此，与三维立方体投影不同，投影的超空间结构可以在实际空间中产生各种各样的结构。重要的是，我们甚至还没有开始探索隐藏在超空间投影中的所有可能的结构和用途。应用超空间结构（Hyperspace Structures， HYPER）旨在以新颖的方式开发和应用新的超空间结构，以三种新的方式展示它们的功能和用途。首先是帮助理解物理准晶体的稳定性。准晶体通常是金属间合金，它们没有重复单元（不像晶体），但保持完美的顺序。它们的结构非常复杂，但可以用超空间投影来理解。然而，我们仍然不知道为什么这些材料是稳定的——这是一个基本的问题，对理解它们在自然界的存在很重要。目前的理论在准晶体结构中的原子运动相的能量和熵贡献的相对比例之间争论不休。HYPER将采用应用超空间投影的新方法来分析物理准晶体表面的相位运动，使用扫描隧道显微镜在原子水平上进行测量。通过这样做，我们可以了解它们对表面结构的精确能量或熵贡献，从而找到理解准晶体稳定性的关键。HYPER的第二个重点将是研究理论混合材料，这些材料具有由超空间投影设计的独特结构。这些杂化将由周期和非周期部分组成，它们共享旋转对称——这是迄今为止相对被忽视的非周期研究途径。因此，这种混合材料以前从未被想象过，更不用说探索了。我们将研究波是如何通过这种结构传播的，并研究它们的有效特性，这些特性有望在未来的制造材料中得到广泛的应用。最后，HYPER将生产一个易于使用的软件，允许任何人生成自己的超空间结构-即使他们不是这方面的专家。这个软件包将允许用户选择他们的超空间维度，在非周期和周期结构之间进行选择，并可视化他们的结果投影。因此，拟议的研究在本质上既是基础的，也是应用的，有可能影响并向跨学科的观众介绍探索超结构的可能性。