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While current sources or sinks are abstract elements used for analysis, generally they have physical counterparts in real-world applications; e.g. the anode or cathode in a battery. In all cases, each of the opposing terms (source or sink) may refer to the same object, depending on the perspective of the observer and the sign convention being ...
where this time is the charge density, is the current density vector, and is the current source-sink term. The current source and current sinks are where the current density emerges > or vanishes <, respectively (for example, the source and sink can represent the two poles of an electrical battery in a closed circuit).
A current source is the dual of a voltage source. The term current sink is sometimes used for sources fed from a negative voltage supply. Figure 1 shows the schematic symbol for an ideal current source driving a resistive load. There are two types. An independent current source (or sink) delivers a constant current.
This problem can be transformed to a maximum flow problem by constructing a network = (,) from , with and being the source and the sink of respectively, and assigning each edge a capacity of . In this network, the maximum flow is k {\displaystyle k} iff there are k {\displaystyle k} edge-disjoint paths.
In a multi-commodity flow problem, you have multiple sources and sinks, and various "commodities" which are to flow from a given source to a given sink. This could be for example various goods that are produced at various factories, and are to be delivered to various given customers through the same transportation network.
Every voltage source connected to the reference node reduces the number of unknowns and equations by one. Mesh analysis: The number of current variables, and hence simultaneous equations to solve, equals the number of meshes. Every current source in a mesh reduces the number of unknowns by one.
The minimum cost variant of the multi-commodity flow problem is a generalization of the minimum cost flow problem (in which there is merely one source and one sink ). Variants of the circulation problem are generalizations of all flow problems. That is, any flow problem can be viewed as a particular circulation problem.
The circulation problem and its variants are a generalisation of network flow problems, with the added constraint of a lower bound on edge flows, and with flow conservation also being required for the source and sink (i.e. there are no special nodes). In variants of the problem, there are multiple commodities flowing through the network, and a ...
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