The value alignment problem: a geometric approach

2018 ◽  
Vol 21 (1) ◽  
pp. 19-28
Author(s):  
Martin Peterson
Keyword(s):  
Geometric Approach ◽  
Alignment Problem

A Geometric Approach to Homology Theory

1976 ◽  
Author(s):  
S. Buonchristiano ◽  
C. P. Rourke ◽  
B. J. Sanderson
Keyword(s):  
Geometric Approach ◽  
Homology Theory

A GEOMETRIC APPROACH TO DISSIPATION AND ITS APPLICATION TO DISSIPATIVE NUCLEAR DYNAMICS

1984 ◽  
Vol 45 (C6) ◽  
pp. C6-87-C6-94
Author(s):  
H. Reinhardt ◽  
R. Balian ◽  
Y. Alhassid
Keyword(s):  
Geometric Approach ◽  
Nuclear Dynamics

Computer Modeling of a Tire under Cornering Loads

1989 ◽  
Vol 17 (2) ◽  
pp. 86-99 ◽  
Author(s):  
I. Gardner ◽  
M. Theves
Keyword(s):  
Finite Element Analysis ◽  
Geometric Approach ◽  
Lateral Force ◽  
Slip Angle ◽  
Element Analysis ◽  
Pressure Distributions ◽  
Slip Effects ◽  
Improved Accuracy ◽  
Nonlinear Geometric ◽  
Good Agreement

Abstract During a cornering maneuver by a vehicle, high forces are exerted on the tire's footprint and in the contact zone between the tire and the rim. To optimize the design of these components, a method is presented whereby the forces at the tire-rim interface and between the tire and roadway may be predicted using finite element analysis. The cornering tire is modeled quasi-statically using a nonlinear geometric approach, with a lateral force and a slip angle applied to the spindle of the wheel to simulate the cornering loads. These values were obtained experimentally from a force and moment machine. This procedure avoids the need for a costly dynamic analysis. Good agreement was obtained with experimental results for self-aligning torque, giving confidence in the results obtained in the tire footprint and at the rim. The model allows prediction of the geometry and of the pressure distributions in the footprint, since friction and slip effects in this area were considered. The model lends itself to further refinement for improved accuracy and additional applications.

scholarly journals Integrated Double-Sided Random Microlens Array Used for Laser Beam Homogenization

Micromachines ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 673
Author(s):  
Wei Yuan ◽  
Cheng Xu ◽  
Li Xue ◽  
Hui Pang ◽  
Axiu Cao ◽  
...  
Keyword(s):  
Laser Beam ◽  
Microlens Array ◽  
Energy Utilization ◽  
Utilization Rate ◽  
Periodic Lattice ◽  
Lattice Distribution ◽  
Speckle Field ◽  
High Laser ◽  
Alignment Problem ◽  
In Series

Double microlens arrays (MLAs) in series can be used to divide and superpose laser beam so as to achieve a homogenized spot. However, for laser beam homogenization with high coherence, the periodic lattice distribution in the homogenized spot will be generated due to the periodicity of the traditional MLA, which greatly reduces the uniformity of the homogenized spot. To solve this problem, a monolithic and highly integrated double-sided random microlens array (D-rMLA) is proposed for the purpose of achieving laser beam homogenization. The periodicity of the MLA is disturbed by the closely arranged microlens structures with random apertures. And the random speckle field is achieved to improve the uniformity of the homogenized spot by the superposition of the divided sub-beams. In addition, the double-sided exposure technique is proposed to prepare the rMLA on both sides of the same substrate with high precision alignment to form an integrated D-rMLA structure, which avoids the strict alignment problem in the installation process of traditional discrete MLAs. Then the laser beam homogenization experiments have been carried out by using the prepared D-rMLA structure. The laser beam homogenized spots of different wavelengths have been tested, including the wavelengths of 650 nm (R), 532 nm (G), and 405 nm (B). The experimental results show that the uniformity of the RGB homogenized spots is about 91%, 89%, and 90%. And the energy utilization rate is about 89%, 87%, 86%, respectively. Hence, the prepared structure has high laser beam homogenization ability and energy utilization rate, which is suitable for wide wavelength regime.

scholarly journals Geometric Approach to Sampling and Communication

2012 ◽  
Vol 11 (1) ◽  
pp. 1-24
Author(s):  
Emil Saucan ◽  
Eli Appleboim ◽  
Yehoshua Y. Zeevi
Keyword(s):  
Geometric Approach

Kinodynamic Model Identification: A Unified Geometric Approach

2021 ◽  
pp. 1-15
Author(s):  
Jaewoon Kwon ◽  
Keunjun Choi ◽  
Frank C. Park
Keyword(s):  
Model Identification ◽  
Geometric Approach

scholarly journals Quantum Polar Duality and the Symplectic Camel: A New Geometric Approach to Quantization

2021 ◽  
Vol 51 (3) ◽  
Author(s):  
Maurice A. de Gosson
Keyword(s):  
Uncertainty Principle ◽  
Convex Geometry ◽  
Geometric Approach ◽  
Point Of View ◽  
Reconstruction Problem ◽  
Orthogonal Projections ◽  
Topological Version ◽  
Mahler Conjecture ◽  
Quantum Indeterminacy ◽  
Dual Quantum

AbstractWe define and study the notion of quantum polarity, which is a kind of geometric Fourier transform between sets of positions and sets of momenta. Extending previous work of ours, we show that the orthogonal projections of the covariance ellipsoid of a quantum state on the configuration and momentum spaces form what we call a dual quantum pair. We thereafter show that quantum polarity allows solving the Pauli reconstruction problem for Gaussian wavefunctions. The notion of quantum polarity exhibits a strong interplay between the uncertainty principle and symplectic and convex geometry and our approach could therefore pave the way for a geometric and topological version of quantum indeterminacy. We relate our results to the Blaschke–Santaló inequality and to the Mahler conjecture. We also discuss the Hardy uncertainty principle and the less-known Donoho–Stark principle from the point of view of quantum polarity.

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