The characteristic matrix of the whole multilayer structure is calculated as the product of the elementary matrices obtained at step 7 [Pg.47]

Thus the characteristic matrix for this closedloop system is the 4cl niatrix. Its eigenvalues will be the close oop eigenvalues, and they will be the roots of the closedloop characteristic equation. [Pg.557]

FIGURE 12.1 Characteristic matrix for system of eight reactions in circle. [Pg.304]

The elementary characteristic matrix Mj for each of the — 2 constiment layers in the particular stratified medium is calculated as [Pg.47]

Each structural part (subsystem) has a characteristic matrix of the following form [Pg.253]

The layers in the interface (Figure 9.11) can be represented by a characteristic matrix of the form for an m-layered system [Pg.251]

Each of the stmctmal parts (subsystems) of the system (4.10) have the characteristic matrix V.. [Pg.252]

For each layer zy i

A vector terminating rth of the distance between two characteristic vectors with zero characteristic roots The characteristic matrix for the unperturbed rate constant matrix [Pg.386]

For this approach each layer in the interface as shown in figure 3.3 is represented by a characteristic matrix thus for layer m [Pg.62]

The reflection and transmission coefficients for the whole stack can be extracted from the characteristic matrix of the whole stratified medium using the following relationships [Pg.323]

The Fresnel reflection coefficients r for the overall system can be obtained from the elements m of the characteristic matrix M associated with the overall system [Pg.233]

Upon expansion, an 8th-order polynomial equation in A arises. Eight roots of the polynomial exist. Even if all the values in the characteristic matrix are real, some roots may be complex. When complex roots occur, they appear in pairs. The roots of the polynomial are called eigenvalues of the characteristic matrix. The polynomial equation is called the eigenvalue equation. [Pg.300]

Beyond the simple thin surfactant monolayer, the reflectivity can be interpreted in terms of the internal structure of the layer, and can be used to determine thicker layers and more complex surface structures, and this can be done in two different ways. The first of these uses the optical matrix method [18, 19] developed for thin optical films, and relies on a model of the surface structure being described by a series or stack of thin layers. This assumes that in optical terms, an application of Maxwell s equations and the relationship between the electric vectors in successive layer leads to a characteristic matrix per layer, such that [Pg.92]

See also in sourсe #XX -- [ Pg.5 ]

See also in sourсe #XX -- [ Pg.253 ]

See also in sourсe #XX -- [ Pg.10 , Pg.15 , Pg.16 , Pg.17 , Pg.18 , Pg.19 , Pg.20 , Pg.21 , Pg.25 , Pg.26 , Pg.28 , Pg.30 , Pg.35 , Pg.49 , Pg.127 , Pg.169 ]

© 2019 chempedia.info