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1838 map of pre-railroad cargo traffic in Ireland, one of the first thematic maps to use proportional symbols. The earliest known map to visually represent the volume of flow were two maps by engineer Henry Drury Harness, published in 1838 as part of a report on the potential for railroad construction in Ireland, showing the quantity of cargo traffic by road and canal.
Informally, a flow may be viewed as a continuous motion of points over time. More formally, a flow is a group action of the real numbers on a set. The idea of a vector flow, that is, the flow determined by a vector field, occurs in the areas of differential topology, Riemannian geometry and Lie groups.
You are free: to share – to copy, distribute and transmit the work; to remix – to adapt the work; Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses ...
Example of a Sankey diagram Sankey's original 1898 diagram showing energy efficiency of a steam engine. Sankey diagrams are a data visualisation technique or flow diagram that emphasizes flow/movement/change from one state to another or one time to another, [1] in which the width of the arrows is proportional to the flow rate of the depicted extensive property.
Alluvial diagrams are a type of flow diagram originally developed to represent changes in network structure over time. In allusion to both their visual appearance and their emphasis on flow, alluvial diagrams are named after alluvial fans that are naturally formed by the soil deposited from streaming water.
There is a unique maximal flow D → M whose infinitesimal generator is V. Here D ⊆ R × M is the flow domain. For each p ∈ M the map D p → M is the unique maximal integral curve of V starting at p. A global flow is one whose flow domain is all of R × M. Global flows define smooth actions of R on M. A vector field is complete if it ...
A harmonic map heat flow on an interval (a, b) assigns to each t in (a, b) a twice-differentiable map f t : M → N in such a way that, for each p in M, the map (a, b) → N given by t ↦ f t (p) is differentiable, and its derivative at a given value of t is, as a vector in T f t (p) N, equal to (∆ f t ) p. This is usually abbreviated as:
A map is a function, as in the association of any of the four colored shapes in X to its color in Y. In mathematics, a map or mapping is a function in its general sense. [1] These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper. [2]
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