scholarly journals Modelling Insight to Ball Eyes for Higher Dimensional Hyperspace Vision

2021 ◽  
Vol 5 (2) ◽  
pp. 1-2
Author(s):  
Shaikh S
Keyword(s):  
2018 ◽  
Author(s):  
Peter De Wolf ◽  
Zhuangqun Huang ◽  
Bede Pittenger

Abstract Methods are available to measure conductivity, charge, surface potential, carrier density, piezo-electric and other electrical properties with nanometer scale resolution. One of these methods, scanning microwave impedance microscopy (sMIM), has gained interest due to its capability to measure the full impedance (capacitance and resistive part) with high sensitivity and high spatial resolution. This paper introduces a novel data-cube approach that combines sMIM imaging and sMIM point spectroscopy, producing an integrated and complete 3D data set. This approach replaces the subjective approach of guessing locations of interest (for single point spectroscopy) with a big data approach resulting in higher dimensional data that can be sliced along any axis or plane and is conducive to principal component analysis or other machine learning approaches to data reduction. The data-cube approach is also applicable to other AFM-based electrical characterization modes.


2020 ◽  
Vol 9 (10) ◽  
pp. 8545-8557
Author(s):  
K. P. Singh ◽  
T. A. Singh ◽  
M. Daimary
Keyword(s):  

Author(s):  
Nicholas Mee

Celestial Tapestry places mathematics within a vibrant cultural and historical context, highlighting links to the visual arts and design, and broader areas of artistic creativity. Threads are woven together telling of surprising influences that have passed between the arts and mathematics. The story involves many intriguing characters: Gaston Julia, who laid the foundations for fractals and computer art while recovering in hospital after suffering serious injury in the First World War; Charles Howard, Hinton who was imprisoned for bigamy but whose books had a huge influence on twentieth-century art; Michael Scott, the Scottish necromancer who was the dedicatee of Fibonacci’s Book of Calculation, the most important medieval book of mathematics; Richard of Wallingford, the pioneer clockmaker who suffered from leprosy and who never recovered from a lightning strike on his bedchamber; Alicia Stott Boole, the Victorian housewife who amazed mathematicians with her intuition for higher-dimensional space. The book includes more than 200 colour illustrations, puzzles to engage the reader, and many remarkable tales: the secret message in Hans Holbein’s The Ambassadors; the link between Viking runes, a Milanese banking dynasty, and modern sculpture; the connection between astrology, religion, and the Apocalypse; binary numbers and the I Ching. It also explains topics on the school mathematics curriculum: algorithms; arithmetic progressions; combinations and permutations; number sequences; the axiomatic method; geometrical proof; tessellations and polyhedra, as well as many essential topics for arts and humanities students: single-point perspective; fractals; computer art; the golden section; the higher-dimensional inspiration behind modern art.


1989 ◽  
Vol 16 (1-4) ◽  
pp. 87-101 ◽  
Author(s):  
A. Janner
Keyword(s):  

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Matheus I. N. Rosa ◽  
Massimo Ruzzene ◽  
Emil Prodan

AbstractTwisted bilayered systems such as bilayered graphene exhibit remarkable properties such as superconductivity at magic angles and topological insulating phases. For generic twist angles, the bilayers are truly quasiperiodic, a fact that is often overlooked and that has consequences which are largely unexplored. Herein, we uncover that twisted n-layers host intrinsic higher dimensional topological phases, and that those characterized by second Chern numbers can be found in twisted bi-layers. We employ phononic lattices with interactions modulated by a second twisted lattice and reveal Hofstadter-like spectral butterflies in terms of the twist angle, which acts as a pseudo magnetic field. The phason provided by the sliding of the layers lives on 2n-tori and can be used to access and manipulate the edge states. Our work demonstrates how multi-layered systems are virtual laboratories for studying the physics of higher dimensional quantum Hall effect, and can be employed to engineer topological pumps via simple twisting and sliding.


2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
A. de Giorgi ◽  
S. Vogl

Abstract The Kaluza-Klein (KK) decomposition of higher-dimensional gravity gives rise to a tower of KK-gravitons in the effective four-dimensional (4D) theory. Such massive spin-2 fields are known to be connected with unitarity issues and easily lead to a breakdown of the effective theory well below the naive scale of the interaction. However, the breakdown of the effective 4D theory is expected to be controlled by the parameters of the 5D theory. Working in a simplified Randall-Sundrum model we study the matrix elements for matter annihilations into massive gravitons. We find that truncating the KK-tower leads to an early breakdown of perturbative unitarity. However, by considering the full tower we obtain a set of sum rules for the couplings between the different KK-fields that restore unitarity up to the scale of the 5D theory. We prove analytically that these are fulfilled in the model under consideration and present numerical tests of their convergence. This work complements earlier studies that focused on graviton self-interactions and yields additional sum rules that are required if matter fields are incorporated into warped extra-dimensions.


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