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Related Concept Videos

Spherical Coordinates01:23

Spherical Coordinates

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Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
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Support reactions in three dimensions help maintain the stability and equilibrium of various structures and systems. These reactions prevent the system from translating and rotating, ensuring the design can withstand external forces and perform its intended function efficiently and safely. Some of the supports providing support reactions in three dimensions are discussed below:
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The understanding of the concept of reference frames is essential to discuss relative motion in one or more dimensions. When we say that an object has a certain velocity, we must state the velocity with respect to a given reference frame. In most examples, this reference frame has been Earth. For instance, if a statement reads that a person is sitting in a train moving at 10 m/s east, then it implies that the person on the train is moving relative to the surface of Earth at this velocity,...
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Gravity between Spherical Bodies01:27

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A spherical capacitor consists of two concentric conducting spherical shells of radii R1 (inner shell) and R2 (outer shell). The shells have  equal and opposite charges of +Q and −Q, respectively. For an isolated conducting spherical capacitor, the radius of the outer shell can be considered to be infinite.
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Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
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Related Experiment Video

Updated: Jan 30, 2026

Ultrasonic Assessment of Myocardial Microstructure
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Spherical coupling probe for measuring inner dimensions of microstructures.

Yuanzheng Chen, Jiwen Cui, Jiubin Tan

    Optics Express
    |January 18, 2019
    PubMed
    Summary
    This summary is machine-generated.

    A new probe design enhances microstructure measurement accuracy by improving signal-to-noise ratio and spot stability. This advanced fiber probe achieves a 66% resolution increase for high aspect ratio microstructures.

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    Area of Science:

    • Optical Engineering
    • Metrology
    • Materials Science

    Background:

    • Spherical coupling fiber probes are essential for measuring high aspect ratio microstructures.
    • Current probes suffer from limited measurement accuracy due to low signal-to-noise ratio and spot instability.

    Purpose of the Study:

    • To develop and experimentally validate a novel fiber probe design for enhanced microstructure measurement.
    • To overcome the limitations of conventional spherical coupling probes.

    Main Methods:

    • Design of a specialized probe incorporating a polished spherical coupler.
    • Integration of a micro-axicon lensed output fiber.
    • Experimental verification of the probe's performance.

    Main Results:

    • The proposed probe demonstrated a 42.95% improvement in signal-to-noise ratio.
    • Spot stability was enhanced by 36% compared to common probes.
    • Measurement resolution was improved from 30 nm to 10 nm, a 66% increase.

    Conclusions:

    • The novel probe design significantly enhances measurement accuracy for high aspect ratio microstructures.
    • The micro-axicon lensed fiber and polished spherical coupler effectively improve probe performance.
    • This advancement offers superior resolution and stability in microstructural analysis.