Transfer-matrix methods have been critical for many exact solutions of problems in statistical mechanics, including the helix-coil transition, transfer matrix models for protein-DNA binding, as well as the famous exact solution of the two-dimensional Ising model by Lars Onsager.
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However, it has proven to be unwieldy for the analysis of transfer matrix can be always obtained for any linear system, in order to analyze its dynamics and other properties : each element of a transfer matrix is a transfer function relating a particular input variable to an output variable.
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However, it has proven to be unwieldy for the analysis of transfer matrix can be always obtained for any linear system, in order to analyze its dynamics and other properties : each element of a transfer matrix is a transfer function relating a particular input variable to an output variable.
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Expressing the behaviour of a mechanical component as a two-port or multi-port with a transfer matrix is a useful thing to do because, like electrical circuits, the component can often be operated in reverse and its behaviour is dependent on the loads at the inputs and outputs.
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Given the initial beam parameter, " q " i, one can use the ray transfer matrix of an optical system, \ begin { pmatrix } A & B \ \ C & D \ end { pmatrix }, to find the resulting beam parameter, " q " f, after the beam has traversed the system:
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