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Related Concept Videos

Mesh Analysis01:20

Mesh Analysis

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Mesh analysis is a valuable method for simplifying circuit analysis using mesh currents as key circuit variables. Unlike nodal analysis, which focuses on determining unknown voltages, mesh analysis applies Kirchhoff's voltage law (KVL) to find unknown currents within a circuit. This method is particularly convenient in reducing the number of simultaneous equations that need to be solved.
A fundamental concept in mesh analysis is the definition of meshes and mesh currents. A mesh is a closed...
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Collisions in Multiple Dimensions: Introduction01:05

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It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a...
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Mesh Analysis with Current Sources01:10

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Mesh analysis becomes simpler when analyzing circuits with current sources, whether independent or dependent. The presence of current sources reduces the number of equations required for analysis. Two cases illustrate this:
Current Source in One Mesh: The analysis process is straightforward when a current source is found in only one mesh within the circuit. Mesh currents are assigned as usual, with the mesh containing the current source excluded from the analysis. Kirchhoff's voltage law...
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Collisions in Multiple Dimensions: Problem Solving01:06

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In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
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The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
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Multicompartment models are mathematical constructs that depict how drugs are distributed and eliminated within the body. They segment the body into several compartments, symbolizing various physiological or anatomical areas connected through drug transfer processes such as absorption, metabolism, distribution, and elimination.
These models offer a more comprehensive representation of drug behavior in the body than one-compartment models. They accommodate the complexity of drug distribution,...
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AMM: Adaptive Multilinear Meshes.

Harsh Bhatia, Duong Hoang, Nate Morrical

    IEEE Transactions on Visualization and Computer Graphics
    |April 8, 2022
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    Summary
    This summary is machine-generated.

    Adaptive Multilinear Meshes (AMM) offer a novel way to reduce large-scale data size by simultaneously adapting resolution and precision. This practical solution enables significant data reduction for visualization and analysis.

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    Area of Science:

    • Computer Science
    • Data Visualization
    • Scientific Computing

    Background:

    • Large-scale data requires efficient in-memory and on-disk storage solutions.
    • Existing methods focus on reducing data precision (compression) or adapting resolution (hierarchies).
    • Combining resolution and precision adaptation offers greater data reduction potential.

    Purpose of the Study:

    • Introduce a practical, scalable solution for combined resolution-precision adaptive data representation.
    • Present Adaptive Multilinear Meshes (AMM) as a novel data structure for hybrid data reduction.
    • Provide an interface for existing tools and algorithms to utilize this new representation.

    Main Methods:

    • Developed Adaptive Multilinear Meshes (AMM) with novel spatial hierarchy for reduced mesh size.
    • AMM creates piecewise multilinear representations of scalar data, allowing flexible adaptation of conformity, continuity, and coverage.
    • Supported mixed-precision values for enhanced data reduction.
    • Demonstrated incremental AMM creation from arbitrary data orderings.

    Main Results:

    • AMM achieves considerable reduction in mesh size compared to traditional methods.
    • Demonstrated AMM's effectiveness on diverse resolution and precision datastreams.
    • Integrated AMM with VTK for practical visualization, showcasing computational advantages.
    • Open-sourced the AMM creation tool for community accessibility.

    Conclusions:

    • AMM provides a flexible and efficient adaptive representation for hybrid data reduction.
    • The practical implementation and open-source release facilitate broader adoption and future research in data reduction techniques.
    • AMM offers significant advantages for large-scale data visualization and analysis.