A GEOMETRICAL PROPERTY OF SETS OF FRACTIONAL DIMENSION

1950 ◽  
Vol 1 (1) ◽  
pp. 81-85
Author(s):  
H. G. EGGLESTON
Keyword(s):  
Geometrical Property ◽  
Fractional Dimension

scholarly journals Newtonian Fractional-dimension Gravity and Rotationally Supported Galaxies

2021 ◽  
Author(s):  
Gabriele U Varieschi
Keyword(s):  
Fractional Dimension ◽  
Newtonian Gravity ◽  
Axially Symmetric ◽  
Local Dimension ◽  
Radial Acceleration ◽  
Modified Newtonian Dynamics ◽  
Newtonian Dynamics ◽  
The Subject ◽  
Symmetric Structures ◽  
Natural Scale

Abstract We continue our analysis of Newtonian Fractional-Dimension Gravity, an extension of the standard laws of Newtonian gravity to lower dimensional spaces including those with fractional (i.e., non-integer) dimension. We apply our model to three rotationally supported galaxies: NGC 7814 (Bulge-Dominated Spiral), NGC 6503 (Disk-Dominated Spiral), and NGC 3741 (Gas-Dominated Dwarf). As was done in the general cases of spherically-symmetric and axially-symmetric structures, which were studied in previous work on the subject, we examine a possible connection between our model and Modified Newtonian Dynamics, a leading alternative gravity model which explains the observed properties of these galaxies without requiring the Dark Matter hypothesis. In our model, the MOND acceleration constant a0 ≃ 1.2 × 10−10m s−2 can be related to a natural scale length l0, namely $a_{0} \approx GM/l_{0}^{2}$ for a galaxy of mass M. Also, the empirical Radial Acceleration Relation, connecting the observed radial acceleration gobs with the baryonic one gbar, can be explained in terms of a variable local dimension D. As an example of this methodology, we provide detailed rotation curve fits for the three galaxies mentioned above.

scholarly journals Stable and oscillating solitons of $$\pmb {\mathcal {PT}}$$-symmetric couplers with gain and loss in fractional dimension

2021 ◽  
Vol 103 (2) ◽  
pp. 1831-1840
Author(s):  
Liangwei Zeng ◽  
Jincheng Shi ◽  
Xiaowei Lu ◽  
Yi Cai ◽  
Qifan Zhu ◽  
...  
Keyword(s):  
Fractional Dimension ◽  
Gain And Loss

scholarly journals The non-Hermitian geometrical property of 1D Lieb lattice under Majorana’s stellar representation

2020 ◽  
Vol 32 (42) ◽  
pp. 425402
Author(s):  
Xingran Xu ◽  
Haodi Liu ◽  
Zhidong Zhang ◽  
Zhaoxin Liang
Keyword(s):  
Geometrical Property ◽  
Lieb Lattice

scholarly journals Newtonian Fractional-Dimension Gravity and MOND

2020 ◽  
Vol 50 (11) ◽  
pp. 1608-1644 ◽  
Author(s):  
Gabriele U. Varieschi
Keyword(s):  
Fractional Dimension

Transition mechanism design of a hybrid wheel-track-leg based on foldable rims

2019 ◽  
Vol 233 (13) ◽  
pp. 4788-4801 ◽  
Author(s):  
Faliang Zhou ◽  
Xiaojun Xu ◽  
Haijun Xu ◽  
Teng’an Zou ◽  
Lei Zhang
Keyword(s):  
Driving Force ◽  
Geometrical Property ◽  
Screw Theory ◽  
Transition Process ◽  
Performance Comparison ◽  
Dynamic Simulations ◽  
Compact Structure ◽  
Transition Mechanism ◽  
Wheel Rim ◽  
Wheel Track

Hybrid mobile robots with multiple locomotion modes are getting more and more popular in search and rescue (SAR) and explosive object disposal (EOD) missions because of their good terrain adaptability. Present researchers devote themselves to develop efficient and reliable transition method between different locomotion modes to make the hybrid robot more compact and flexible. In this paper, we present a novel transition mechanism for a hybrid wheel-track based on foldable rims. The wheel rim is cut into four segments so that it is foldable. And the transition between wheel and track is achieved by the folding or unfolding of the foldable rim. According to its geometrical property during the transition process, a single-freedom supporting spoke is proposed to drive the foldable rim’s transformation. We analyze the length and angle varying principles of the supporting spoke by utilizing the kinematic mode based on screw theory. According to above results, five different kinds of transition mechanism of the supporting spoke is designed, performance comparison among which is conducted by dynamic simulations. Two of the five candidate transition mechanisms are picked up for their smaller driving force requirements. Their 3D printing prototypes are also fabricated and experiments show that the hybrid wheel-track can switch between wheel and track successfully. Compared to most hybrid robots which have separate wheels, tracks and legs, this transition mechanism makes the robot own both compact structure and multimodal locomotion.

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