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

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.

Detection and Measurement of Quantum Gravity by a Curvature Energy Sensor: H-States of Curvature Energy

“…Similarly, it was mentioned and considered that the curvature value can be understood as the deformation contour on a surface (initial idea created and developed relative to the understanding of curvature in a space-time [10,15]). …”

“…Similarly, the curvature was obtained initially (using the units of volts on cubic meter, mentioned before) as measure through the corresponding co-cycles as integral transform [2,10]:…”

“…Likewise, considering the representation of curvature in a Hilbert space (energy space) that is to say, given by Λg ðf Þ, ∀υ ∈ V ζ , ∀ζ ∈ K ∧ , and f ∈ C Theoretical sensor of curvature by a wave of light [6,10,11] 3g , is the pseudo-Riemannian metric in G/K, induced by the pseudo-Riemannian metric of the manifold M.…”

Autonomous and Mobile Prototype of Curvature Sensor with Remote Reliable Communication of Spectral Curvature

“…Along several researches and works on integral geometry theory to field observables as curvature and torsion of the space, we have constructed an adequate energy integrals theory obtaining important results to international level of curvature given as smooth embedding of a differential sub-manifold given in co-cycles [1] [2] [3] [4] [5] and their application through electronics and science of specialized sensors obtaining the concept of curvature energy, and their application in a range of energy given by the interval [1] [3] [4 where V, is the applied potential energy of curvature (in this case voltages) 1 ; A, is the area of the surface and h, their mean curvature and the last integral corresponds to the curvature energy employed to measure the roundness in their displacement along a principal direction. Applying certain cycles as Gaussian pulses which are measured invariant of curvature, we obtain the corresponding energy co-cycles that are curvature information "in situs" of the curvature sensor designed to first prototype of this type.…”

“…The autonomy and independence must be two characteristics necessary to the remote development of the prototype considering their stability, mechanical robustness which will be characterized by their traction as continuous function of displacement and of the direction change of the mobile curvature sensor. Our curvature sensor is obtaining a Gaussian curvature through electrical pulses (electrically gauged [2]) that arise of the energy curvature accumulated in the proper space or surface [1] [3] according to field theory.…”