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  2. Line integral convolution - Wikipedia

    en.wikipedia.org/wiki/Line_integral_convolution

    Texture-based methods, like LIC, avoid these problems since they depict the entire vector field at point-like (pixel) resolution. [ 1 ] Compared to other integration-based techniques that compute field lines of the input vector field, LIC has the advantage that all structural features of the vector field are displayed, without the need to adapt ...

  3. Scientific visualization - Wikipedia

    en.wikipedia.org/wiki/Scientific_visualization

    The primary methods for visualizing two-dimensional (2D) scalar fields are color mapping and drawing contour lines. 2D vector fields are visualized using glyphs and streamlines or line integral convolution methods. 2D tensor fields are often resolved to a vector field by using one of the two eigenvectors to represent the tensor each point in ...

  4. Phase plane - Wikipedia

    en.wikipedia.org/wiki/Phase_plane

    The phase plane method refers to graphically determining the existence of limit cycles in the solutions of the differential equation. The solutions to the differential equation are a family of functions. Graphically, this can be plotted in the phase plane like a two-dimensional vector field.

  5. Method of averaging - Wikipedia

    en.wikipedia.org/wiki/Method_of_averaging

    The advantage of this method is the extension to more general settings such as infinite-dimensional systems - partial differential equation or delay differential equations. J. Hale presents generalizations to almost periodic vector-fields. [4]

  6. Sources and sinks - Wikipedia

    en.wikipedia.org/wiki/Sources_and_sinks

    In physics, a vector field (,,) is a function that returns a vector and is defined for each point (with coordinates ,,) in a region of space. The idea of sources and sinks applies to b {\displaystyle \mathbf {b} } if it follows a continuity equation of the form

  7. Vector calculus - Wikipedia

    en.wikipedia.org/wiki/Vector_calculus

    Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, . [1] The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration.

  8. Curl (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Curl_(mathematics)

    Interchanging the vector field v and ∇ operator, we arrive at the cross product of a vector field with curl of a vector field: = () , where ∇ F is the Feynman subscript notation, which considers only the variation due to the vector field F (i.e., in this case, v is treated as being constant in space).

  9. Leray projection - Wikipedia

    en.wikipedia.org/wiki/Leray_projection

    The Leray projection, named after Jean Leray, is a linear operator used in the theory of partial differential equations, specifically in the fields of fluid dynamics. Informally, it can be seen as the projection on the divergence-free vector fields.