Starting from the eight vertex types in the Penrose tiling, we investigate the configurations beyond the nearest neighbors. The detailed structure of configurations and their concentrations in the whole pattern are ob...Starting from the eight vertex types in the Penrose tiling, we investigate the configurations beyond the nearest neighbors. The detailed structure of configurations and their concentrations in the whole pattern are obtained. It is found that the number of configuration types increases greatly when the observed clusters are becoming larger, which indicates that it is difficult to generate a perfect Penrose tiling according to the local matching rules.展开更多
In the electronic information and intelligent era, microwave absorption materials have been focused on the issue of electromagnetic(EM) pollution, but high-performance absorbers with thin thickness are highly desirabl...In the electronic information and intelligent era, microwave absorption materials have been focused on the issue of electromagnetic(EM) pollution, but high-performance absorbers with thin thickness are highly desirable. The positive action between structural design and component selection can be regarded as a function to optimize the microwave loss capacity, which contributes to understanding the response mechanisms from the micro and macro. Therefore, we designed the absorber with quasiperiodic structures of Penrose tiling that has finely engineered the location of maximum absorption peak, the spherical carbonyl iron in thin rhombus, and flakey carbonyl iron in fat rhombus, the effective absorption bandwidth(Reflection Loss ≤ –10 d B) was realized from 6.46 GHz to 15.78 GHz in the 2 mm thickness. The unique arrangement of Penrose tiling can respond alternatingly to EM waves at large scales, and multicomponent coupling is distinctly in the neighboring unit cells. In addition, spraying aluminum pigment as the upper layer, the infrared emissivity is less than 0.35 to meet the complex application environment.This work opens up novel ideas on quasiperiodic structure combined multicomponent and injects infinite vitality to provide prospects for broadband responsive and high-efciency EM absorbers.展开更多
Starting from Witten’s eleven dimensional M-theory, the present work develops in an analogous way a corresponding dimensional fractal version where . Subsequently, the new fractal formalism is utilized to determine t...Starting from Witten’s eleven dimensional M-theory, the present work develops in an analogous way a corresponding dimensional fractal version where . Subsequently, the new fractal formalism is utilized to determine the measured ordinary energy density of the cosmos which turns out to be intimately linked to the new theory’s fractal dimension via non-integer irrational Lorentzian-like factor: where is Hardy’s probability of quantum entanglement. Consequently, the energy density is found from a limiting classical kinetic energy to be Here, is ‘tHooft’s renormalon of dimensional regularization. The immediate logical, mathematical and physical implication of this result is that the dark energy density of the cosmos must be in astounding agreement with cosmic measurements and observations.展开更多
As starting point for patterns with seven-fold symmetry, we investigate the basic possibility to construct the regular heptagon by bicompasses and ruler. To cover the whole plane with elements of sevenfold symmetry is...As starting point for patterns with seven-fold symmetry, we investigate the basic possibility to construct the regular heptagon by bicompasses and ruler. To cover the whole plane with elements of sevenfold symmetry is only possible by overlaps and (or) gaps between the building stones. Resecting small parts of overlaps and filling gaps between the heptagons, one may come to simple parqueting with only a few kinds of basic tiles related to sevenfold symmetry. This is appropriate for parqueting with a center of seven-fold symmetry that is illustrated by figures. Choosing from the basic patterns with sevenfold symmetry small parts as elementary stripes or elementary cells, one may form by their discrete translation in one or two different directions periodic bordures or tessellation of the whole plane but the sevenfold point-group symmetry of the whole plane is then lost and there remains only such symmetry in small neighborhoods around one or more centers. From periodic tiling, we make the transition to aperiodic tiling of the plane. This is analogous to Penrose tiling which is mostly demonstrated with basic elements of fivefold symmetry and we show that this is also possible with elements of sevenfold symmetry. The two possible regular star-heptagons and a semi-regular star-heptagon play here a basic role.展开更多
文摘Starting from the eight vertex types in the Penrose tiling, we investigate the configurations beyond the nearest neighbors. The detailed structure of configurations and their concentrations in the whole pattern are obtained. It is found that the number of configuration types increases greatly when the observed clusters are becoming larger, which indicates that it is difficult to generate a perfect Penrose tiling according to the local matching rules.
基金Supported by Program for the National Natural Science Foundation of China (Nos.52103334,52071053,U1704253)the China Postdoctoral Science Foundation(Nos.2020M680946,2020M670748)the Fundamental Research Funds for the Central Universities (No.DUT20GF111)。
文摘In the electronic information and intelligent era, microwave absorption materials have been focused on the issue of electromagnetic(EM) pollution, but high-performance absorbers with thin thickness are highly desirable. The positive action between structural design and component selection can be regarded as a function to optimize the microwave loss capacity, which contributes to understanding the response mechanisms from the micro and macro. Therefore, we designed the absorber with quasiperiodic structures of Penrose tiling that has finely engineered the location of maximum absorption peak, the spherical carbonyl iron in thin rhombus, and flakey carbonyl iron in fat rhombus, the effective absorption bandwidth(Reflection Loss ≤ –10 d B) was realized from 6.46 GHz to 15.78 GHz in the 2 mm thickness. The unique arrangement of Penrose tiling can respond alternatingly to EM waves at large scales, and multicomponent coupling is distinctly in the neighboring unit cells. In addition, spraying aluminum pigment as the upper layer, the infrared emissivity is less than 0.35 to meet the complex application environment.This work opens up novel ideas on quasiperiodic structure combined multicomponent and injects infinite vitality to provide prospects for broadband responsive and high-efciency EM absorbers.
文摘Starting from Witten’s eleven dimensional M-theory, the present work develops in an analogous way a corresponding dimensional fractal version where . Subsequently, the new fractal formalism is utilized to determine the measured ordinary energy density of the cosmos which turns out to be intimately linked to the new theory’s fractal dimension via non-integer irrational Lorentzian-like factor: where is Hardy’s probability of quantum entanglement. Consequently, the energy density is found from a limiting classical kinetic energy to be Here, is ‘tHooft’s renormalon of dimensional regularization. The immediate logical, mathematical and physical implication of this result is that the dark energy density of the cosmos must be in astounding agreement with cosmic measurements and observations.
文摘As starting point for patterns with seven-fold symmetry, we investigate the basic possibility to construct the regular heptagon by bicompasses and ruler. To cover the whole plane with elements of sevenfold symmetry is only possible by overlaps and (or) gaps between the building stones. Resecting small parts of overlaps and filling gaps between the heptagons, one may come to simple parqueting with only a few kinds of basic tiles related to sevenfold symmetry. This is appropriate for parqueting with a center of seven-fold symmetry that is illustrated by figures. Choosing from the basic patterns with sevenfold symmetry small parts as elementary stripes or elementary cells, one may form by their discrete translation in one or two different directions periodic bordures or tessellation of the whole plane but the sevenfold point-group symmetry of the whole plane is then lost and there remains only such symmetry in small neighborhoods around one or more centers. From periodic tiling, we make the transition to aperiodic tiling of the plane. This is analogous to Penrose tiling which is mostly demonstrated with basic elements of fivefold symmetry and we show that this is also possible with elements of sevenfold symmetry. The two possible regular star-heptagons and a semi-regular star-heptagon play here a basic role.
