Scattering variable

To further understand the structure of these samples, SAXS experiments were carried out and the resulting profiles are shown in Figure 4. The smeared intensity was plotted against the angular scattering variable, s, which is defined as ... 

In this case, a natural scattering variable is introduced as a = Q2b2/6 so that ... 

For rigid rods, the natural scattering variable is a = Qb, and the conformational averaging becomes an averaging over orientations. Here also, in order to obtain compact analytical results, one has to go to the continuous chain limit (a < 1... 

The above principles are generally valid for materials in all states and for all applications. A priori simplification and the use of unverified values for the scattering variables for individual stages of sampling leads not only to erroneous determination of the magnitude of the quality characteristic but also to limited usefulness of the values determined and economic waste. As the creation of a sampling scheme is a key task, it is advisable to consult a professional for this step and ensure that the scheme is approved in the framework of contractor-customer relations. 

It can be proven by means of a linear transformation of the conjugate variables into so-called scattering variables [9, 10] that all power continuous nodes have constitutive relations with a multiplicative form. This means that the vector of dependent port variables can be written as a product of some operator on the vector of independent port variables. When this operator only relates efforts to efforts and flows to flows, a property called non-mixing [11], the multiport is called a transformer (node label TF). If the operator is a function of one or more additional node inputs, it is called a modulated transformer (node label MTF). When this operator only relates efforts to flows and flows to efforts, a property called mixing [11], the multiport is called a gyrator (node label GY). If the operator is a function of node inputs it is called a modulated gyrator (node label MGY). 

Junction nodes A junction is a node with power ports that is power continuous and of which the ports are mutually exchangeable without changing its nature this property is called port symmetry Scattering variables can also be used to prove that there exist only two types of power continuous, port symmetric nodes, both with linear constitutive relations (i.e., linearity is not assumed a priori) [9] ... 

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