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Modal expansion coefficients

This is the propagation equation that is actually solved numerically, but let us express it in terms of field rather than in terms of modal expansion coefficients. From a modal expansion, the transverse part of the electric field is... [Pg.259]

Suppose we have a solution at z = 0, and want to propagate it over a distance corresponding to an integration step Az. Although we wrote the equation in terms of field, it is more natural to solve numerically for the modal expansion coefficients to eliminate fast oscillatory terms. We therefore express the field through the expansion coefficients A which are actually the native solver variables ... [Pg.262]

Let us consider further reasons of pol5rmer chains breaking at so small stresses, which can be on order lower than ftacture macroscopic stress (i.e., at h5rpothetical k = 0.1). The reasons were pointed for the first time in Refs. [1, 26]. Firstly, anharmonicity intensification in fracture center gives the effect, identical to mechanical overloading effect [26]. Quantitatively this effect is expressed by the ratio of thermal expansion coefficient in fracture center and modal thermal expansion coefficient [5]. The second reason is close inter communication of local yielding and fracture processes [ 1]. This allows to identify fracture center for nonoriented polymers as local plasticity zone [27, 28]. The ratio uJ(X in this case can be reached -100 [5]. This effect compensates completely k reduction lower than one. So, for PC ala 70, K- = 0.44, a. = O.IE. 700 MPa and fiien o = o a /K,a 23 MPa, that by order of magnitude corresponds to experimental value Oj. for PC, which is equal approximately to 50 MPa at T= 293 K [7]. [Pg.145]

SOLUTION For the purposes of this calculation we shall assume the drop to be noncirculating. Thus, the matrix of multicomponent mass transfer coefficients [A] may be computed from Eqs. 9.4.18 and 9.4.19 with the help of Sylvester s expansion formula or the modal transformation. At both the long and short contact time limits, however, we may calculate the ratios of mass transfer coefficients ky2/kii and A 21/A 22 without evaluating the series expansions needed in Eq. 9.4.19. [Pg.240]

When an FEA model is run, several elements must be present. These include the CAD data, material properties, loads acting on the part, and the boundary conditions used. Table 4.3 shows the typical input to conduct an analysis through one of the software programs. The minimum input for structural analysis is the modulus of elasticity, Poisson ratio, and density. For thermal predictions, the minimum inputs are coefficient of thermal expansion, specific heat, and thermal conductivity. For modal analysis, the minimum inputs are modulus of elasticity, Poisson ratio, and density. [Pg.56]


See other pages where Modal expansion coefficients is mentioned: [Pg.259]    [Pg.627]    [Pg.23]   
See also in sourсe #XX -- [ Pg.259 , Pg.262 ]




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