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Related Concept Videos

Polar Equations of Conics01:29

Polar Equations of Conics

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A conic section can be defined in polar coordinates as the set of all points whose distance from a fixed point, known as the focus, bears a constant ratio to their distance from a fixed line, known as the directrix. This constant ratio is called the eccentricity. This definition unifies all types of conic sections—ellipses, parabolas, and hyperbolas—under a single framework. When the focus is positioned at the origin of the polar coordinate system, a single polar equation can...
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Curvilinear Motion: Polar Coordinates01:27

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In polar coordinates, the motion of a particle follows a curvilinear path. The radial coordinate symbolized as 'r,' extends outward from a fixed origin to the particle, while the angular coordinate, 'θ,' measured in radians, represents the counterclockwise angle between a fixed reference line and the radial line connecting the origin to the particle.
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Polar Coordinates01:24

Polar Coordinates

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The polar coordinate system offers an alternative to the Cartesian coordinate system for specifying points in a plane, using a distance and an angle instead of x and y coordinates. This system is particularly advantageous in situations involving circular or rotational symmetry, such as in physics or engineering problems involving waves, oscillations, or orbital paths.Defining Polar CoordinatesIn polar coordinates, a point is represented as P(r, ��), where r is the radial distance...
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The Cartesian coordinate system is a very convenient tool to use when describing the displacements and velocities of objects and the forces acting on them. However, it becomes cumbersome when we need to describe the rotation of objects. So, when describing rotation, the polar coordinate system is generally used.
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Centroid for the Paraboloid of Revolution01:16

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The paraboloid of revolution is an axially symmetric surface generated by rotating a parabola around its axis. This shape has several applications in mechanical engineering due to its advantageous structural properties, such as strength against stress concentration points and rotational symmetry.
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Potential Due to a Polarized Object01:29

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A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...
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Updated: Dec 3, 2025

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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Robust polarimetry via convex optimization.

Jacob M Leamer, Wenlei Zhang, Ravi K Saripalli

    Applied Optics
    |October 26, 2020
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    Summary
    This summary is machine-generated.

    Mathematical methods correct non-physical coherency matrices in polarimetry. These techniques recover polarization degree values from experimental data, enhancing robust polarimetry through post-processing.

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    Area of Science:

    • Optics and Photonics
    • Mathematical Physics

    Background:

    • Polarimetry measurements can yield non-physical coherency matrices.
    • Experimental data often requires correction for accurate analysis.

    Purpose of the Study:

    • To present mathematical methods for correcting non-physical coherency matrices.
    • To develop techniques for recovering specific degree of polarization values.

    Main Methods:

    • Convex optimization algorithms are employed for matrix correction.
    • Methods are developed to find coherency matrices for extremal degree of polarization.

    Main Results:

    • Demonstrated correction of non-physical coherency matrices using experimental data.
    • Successfully recovered coherency matrices corresponding to minimum and maximum polarization degrees.

    Conclusions:

    • The presented post-processing techniques improve the robustness of polarimetry.
    • These mathematical methods offer a valuable complement to experimental polarimetry approaches.