Electronic Sensor Prototype to Detect and Measure Curvature Through Their Curvature Energy

Francisco Bulnes; Isaías Martínez; Omar Zamudio; Gabriel Negrete

doi:doi:10.11648/j.cssp.20150405.12

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Electronic Sensor Prototype to Detect and Measure Curvature Through Their Curvature Energy

Francisco Bulnes, Isaías Martínez, Omar Zamudio, Gabriel Negrete

Published in Science Journal of Circuits, Systems and Signal Processing (Volume 4, Issue 5)

Received: 15 October 2015 Accepted: 23 October 2015 Published: 10 November 2015

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Abstract

Through of the concept of curvature energy, and the curvature theory on homogeneous spaces is designed and constructed an electronic sensor prototype to measure curvature in 2, and 3-dimensional spaces using the programming of shape operators in micro-controllers and the value of their energy integrals along the curves and geodesics in their principal directions. The curvature obtained under the sensor device is their spectral curvature given in voltage in 2- and 3-dimensions and their perception of curvature through electronic signals on a curved surface is the curvature energy that is detected in the displacement of an accelerometer on the curved surface.

Published in	Science Journal of Circuits, Systems and Signal Processing (Volume 4, Issue 5)
DOI	10.11648/j.cssp.20150405.12
Page(s)	41-54
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Curvature Energy, Energy Spectrum of Curvature, Gaussian Curvature, Principal Curvatures, Curvature Accelerometer Detection

References

[1]	Kobayashi, K. Nomizu, “Foundations of Differential Geometry”, Wiley and Sons, New York, 1969.
[2]	V. Kaajakari, “Closed Form Expressions for RF MEMS Switch Actuation and Release Time,” Electronics Letters, Vol. 43, No. 3, 2009, pp149-150.
[3]	V. Kaajakari, A. T. Alastalo, T. Mattila, “Electrostatic Transducers for Micromechanical Resonators: Free Space and Solid Dielectric,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 53, No. 12, 2006, pp. 2484-2489.
[4]	O. Holmgen, K. Kokkonen, T. Veijola, T. Mattila, V. Kaajakari, A. Oja, J. V. Knnuttila, M. Kaivola, “Analysis of Vibration Modes in a Micromechanical Square Plate Resonator,” Journal of Micromechanics and Microengineering, Vol. 19, No. 1, 2009, Article ID: 015028.
[5]	V. Kaajakari, A. Lal, “Micromachined Ultrasonic Motor Based on Parametric Polycrystalline Silicon Plate Excitation,” Sensors and Actuators A: Physical, Vol. 137, No. 1, 2007, pp120-128. Doi:10.1016/j-sna.20.
[6]	A. T. Alastalo, V. Kaajakari, “Intermodulation in Capacitively Coupled Microelectromechanical Filters,” IEEE Electron Device Letters, Vol. 26, 2005, pp189-191.
[7]	Bulnes, F. Martínez, I, Mendoza, A. Landa, M., “Design and Development of an Electronic Sensor to Detect and Measure Curvature of Spaces Using Curvature Energy,” Journal of Sensor Technology, 2012, 2, pp116-126. http://dx.doi.org/10.4236/jst.2012.23017.
[8]	Bulnes, F., Research on Curvature of Homogeneous Spaces, TESCHA, Mexico, 2010, pp. 44-66. http://www.magnamatematica.org.
[9]	F. Bulnes, “Curvature Spectrum to 2-Dimensional Flat and Hyperbolic Spaces through Integral Transforms,” Journal of Mathematics, Vol. 1. No. 1, pp17-24.
[10]	F. Bulnes, Integral Theory of the Universe, Proc. Applied Math 2, IMUNAM, ESIME-IPN, Mexico City, 2006, pp73-122.
[11]	F. Bulnes, “Quantum Gravity Sensor by Curvature Energy: their Encoding and Computational Models, “IEEE Proc., SAI 2014, London, UK, 2014, pp. 855-861.
[12]	Bulnes, F. "Electromagnetic Gauges and Maxwell Lagrangians Applied to the Determination of Curvature in the Space-Time and their Applications," Journal of Electromagnetic Analysis and Applications, Vol. 4 No. 6, 2012, pp. 252-266. doi: 10.4236/jemaa. 2012.46035.
[13]	E. Guivenchy, “Torsion Matter and their Corresponding Dirac Equations on Neutrinos and Matter/anti-Matter Asymmetries (Part I: scattering difference between Neutrinos/anti-Neutrinos),” Journal on Photonics and Spintronics, Vol 3, no. 4, 2014, pp9-18.
[14]	S. Gorbuix, E. Guivenchy, “Torsion Matter and their Corresponding Dirac Equations on Neutrinos and Matter/anti-Matter Asymmetries (Part II: gravitation insights)” Journal on Photonics and Spintronics, Vol. 4 No. 1, pp15-25.
[15]	http://www.mouser.com/ProductDetail/Silicon-Labs/EFM8BB10F2G-A-QFN20/?qs=sGAEpiMZZMu9ReDVvI6ax9sqO0qrXlDW4ZuhKcnb2c%252bQvyUXU1UbuQ%3d%3d.
[16]	Heath, S. (2003). Embedded systems design. EDN series for design engineers (2ed.)., Elsevier Science, Oxford, UK.
[17]	F. Bulnes, E. Hernandez and J. Maya, “Design of Measurement and Detection Devices of Curvature through of the Synergic Integral Operators of the Mechanics on Light Waves,” Proceedings of International Mechanics Engineering Conference and Exposition, Orlando Florida, 16 November 2009, pp. 91-102. doi: 10.1115/IMECE2009-10038.
[18]	F. Bulnes, “Radon Transform and Curvature of an Universe,” UNAM Postgraduate Thesis, 2001.
[19]	F. Bulnes, Detection of finite energy signals to the measurement of the Universe curvature, Iberomet VII, Cancún, Quintana Roo, Mexico, 2002, pp825-843.
[20]	L. J. Van Vliet, P. W. Verbeek, “Curvature and Bending Energy in Digitized 2D and 3D Images”, Proceedings of 8th Scandinavian Conference on Image Analysis, Tromso, 25-28 May 1993, pp. 1403-1410.
[21]	B. Nashelky, “Electronics: Circuit Theory and Electronic Devices,” Pearson Prentice Hall, Upper Saddle River, 2003.
[22]	W. Rudin, Functional Analysis, McGraw-Hill, Inc., USA, 1973.
[23]	J. E. Marsden, A. J. Tromba, Vectorial Calculus, Addison Wesley, 1991.

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APA Style

Francisco Bulnes, Isaías Martínez, Omar Zamudio, Gabriel Negrete. (2015). Electronic Sensor Prototype to Detect and Measure Curvature Through Their Curvature Energy. Science Journal of Circuits, Systems and Signal Processing, 4(5), 41-54. https://doi.org/10.11648/j.cssp.20150405.12

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ACS Style

Francisco Bulnes; Isaías Martínez; Omar Zamudio; Gabriel Negrete. Electronic Sensor Prototype to Detect and Measure Curvature Through Their Curvature Energy. Sci. J. Circuits Syst. Signal Process. 2015, 4(5), 41-54. doi: 10.11648/j.cssp.20150405.12

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AMA Style

Francisco Bulnes, Isaías Martínez, Omar Zamudio, Gabriel Negrete. Electronic Sensor Prototype to Detect and Measure Curvature Through Their Curvature Energy. Sci J Circuits Syst Signal Process. 2015;4(5):41-54. doi: 10.11648/j.cssp.20150405.12

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@article{10.11648/j.cssp.20150405.12,
  author = {Francisco Bulnes and Isaías Martínez and Omar Zamudio and Gabriel Negrete},
  title = {Electronic Sensor Prototype to Detect and Measure Curvature Through Their Curvature Energy},
  journal = {Science Journal of Circuits, Systems and Signal Processing},
  volume = {4},
  number = {5},
  pages = {41-54},
  doi = {10.11648/j.cssp.20150405.12},
  url = {https://doi.org/10.11648/j.cssp.20150405.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cssp.20150405.12},
  abstract = {Through of the concept of curvature energy, and the curvature theory on homogeneous spaces is designed and constructed an electronic sensor prototype to measure curvature in 2, and 3-dimensional spaces using the programming of shape operators in micro-controllers and the value of their energy integrals along the curves and geodesics in their principal directions. The curvature obtained under the sensor device is their spectral curvature given in voltage in 2- and 3-dimensions and their perception of curvature through electronic signals on a curved surface is the curvature energy that is detected in the displacement of an accelerometer on the curved surface.},
 year = {2015}
}

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TY  - JOUR
T1  - Electronic Sensor Prototype to Detect and Measure Curvature Through Their Curvature Energy
AU  - Francisco Bulnes
AU  - Isaías Martínez
AU  - Omar Zamudio
AU  - Gabriel Negrete
Y1  - 2015/11/10
PY  - 2015
N1  - https://doi.org/10.11648/j.cssp.20150405.12
DO  - 10.11648/j.cssp.20150405.12
T2  - Science Journal of Circuits, Systems and Signal Processing
JF  - Science Journal of Circuits, Systems and Signal Processing
JO  - Science Journal of Circuits, Systems and Signal Processing
SP  - 41
EP  - 54
PB  - Science Publishing Group
SN  - 2326-9073
UR  - https://doi.org/10.11648/j.cssp.20150405.12
AB  - Through of the concept of curvature energy, and the curvature theory on homogeneous spaces is designed and constructed an electronic sensor prototype to measure curvature in 2, and 3-dimensional spaces using the programming of shape operators in micro-controllers and the value of their energy integrals along the curves and geodesics in their principal directions. The curvature obtained under the sensor device is their spectral curvature given in voltage in 2- and 3-dimensions and their perception of curvature through electronic signals on a curved surface is the curvature energy that is detected in the displacement of an accelerometer on the curved surface.
VL  - 4
IS  - 5
ER  -

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Author Information

Francisco Bulnes

Research Department in Mathematics and Engineering, TESCHA, and GI, Chalco, Mexico
Isaías Martínez

Electronic Engineering Division TESCHA and GI, Chalco, Mexico
Omar Zamudio

Electronic Engineering Division TESCHA, Chalco, and GI, Chalco, Mexico
Gabriel Negrete

Electronic Engineering Division GI-TESCHA, Chalco, and GI, Chalco Mexico

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Plain Text BibTeX RIS

APA Style

Francisco Bulnes, Isaías Martínez, Omar Zamudio, Gabriel Negrete. (2015). Electronic Sensor Prototype to Detect and Measure Curvature Through Their Curvature Energy. Science Journal of Circuits, Systems and Signal Processing, 4(5), 41-54. https://doi.org/10.11648/j.cssp.20150405.12

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ACS Style

Francisco Bulnes; Isaías Martínez; Omar Zamudio; Gabriel Negrete. Electronic Sensor Prototype to Detect and Measure Curvature Through Their Curvature Energy. Sci. J. Circuits Syst. Signal Process. 2015, 4(5), 41-54. doi: 10.11648/j.cssp.20150405.12

Copy | Download

AMA Style

Francisco Bulnes, Isaías Martínez, Omar Zamudio, Gabriel Negrete. Electronic Sensor Prototype to Detect and Measure Curvature Through Their Curvature Energy. Sci J Circuits Syst Signal Process. 2015;4(5):41-54. doi: 10.11648/j.cssp.20150405.12

Copy | Download

@article{10.11648/j.cssp.20150405.12,
  author = {Francisco Bulnes and Isaías Martínez and Omar Zamudio and Gabriel Negrete},
  title = {Electronic Sensor Prototype to Detect and Measure Curvature Through Their Curvature Energy},
  journal = {Science Journal of Circuits, Systems and Signal Processing},
  volume = {4},
  number = {5},
  pages = {41-54},
  doi = {10.11648/j.cssp.20150405.12},
  url = {https://doi.org/10.11648/j.cssp.20150405.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cssp.20150405.12},
  abstract = {Through of the concept of curvature energy, and the curvature theory on homogeneous spaces is designed and constructed an electronic sensor prototype to measure curvature in 2, and 3-dimensional spaces using the programming of shape operators in micro-controllers and the value of their energy integrals along the curves and geodesics in their principal directions. The curvature obtained under the sensor device is their spectral curvature given in voltage in 2- and 3-dimensions and their perception of curvature through electronic signals on a curved surface is the curvature energy that is detected in the displacement of an accelerometer on the curved surface.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Electronic Sensor Prototype to Detect and Measure Curvature Through Their Curvature Energy
AU  - Francisco Bulnes
AU  - Isaías Martínez
AU  - Omar Zamudio
AU  - Gabriel Negrete
Y1  - 2015/11/10
PY  - 2015
N1  - https://doi.org/10.11648/j.cssp.20150405.12
DO  - 10.11648/j.cssp.20150405.12
T2  - Science Journal of Circuits, Systems and Signal Processing
JF  - Science Journal of Circuits, Systems and Signal Processing
JO  - Science Journal of Circuits, Systems and Signal Processing
SP  - 41
EP  - 54
PB  - Science Publishing Group
SN  - 2326-9073
UR  - https://doi.org/10.11648/j.cssp.20150405.12
AB  - Through of the concept of curvature energy, and the curvature theory on homogeneous spaces is designed and constructed an electronic sensor prototype to measure curvature in 2, and 3-dimensional spaces using the programming of shape operators in micro-controllers and the value of their energy integrals along the curves and geodesics in their principal directions. The curvature obtained under the sensor device is their spectral curvature given in voltage in 2- and 3-dimensions and their perception of curvature through electronic signals on a curved surface is the curvature energy that is detected in the displacement of an accelerometer on the curved surface.
VL  - 4
IS  - 5
ER  -

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