Acoustical Impedance and the Theory of Horns and of the by Webster A. G.

By Webster A. G.

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10) the displacement current density e @E @t is neglected with respect to the other two terms of the right-hand side, then Eqs. 19) and respectively; they are the differential equations governing the electromagnetic field under quasi-static conditions (diffusion equations). Again, given appropriate boundary and initial conditions, vectors H (or B) and E (or D) are uniquely defined. More generally, let a linear, homogeneous and isotropic material, characterized by conductivity s, permeability m and permittivity e, be considered, where a driving current density J 0 is present, the time variations of which are small.

Static approximation or quasi-static approximation for the field analysis are usual assumptions in electricity and magnetism; both the approximations will be referred to throughout the book, as far as field analysis is concerned. 3 Wave, Diffusion and Steady-State Equations in Terms of Potentials Despite the field is the quantity of main physical interest, suitable potentials can be introduced to transform vector equations into scalar ones, so reducing the problem complexity. 29) associated to a suitable gauge condition on r Á A to be specified later on.

1. It should be noted that the concept of indifference does not apply under the frame of single-objective optimisation. In fact, given an objective cðxÞ and two feasible vectors x1 and x2 with x1 6¼ x2 , if cðx1 Þ 6¼ cðx2 Þ, either cðx1 Þ < cðx2 Þ or cðx2 Þ < cðx1 Þ holds. Moreover, in the case of nf ¼2 objectives, there is a straightforward geometric representation of dominance relationships (Fig. 2). In the Y space, any point y ¼ FðxÞ can be considered as the vertex of a dominance dihedral. The latter is defined as the orthogonal sector having its centre just at the given point y 2 Y, and containing all and only the points dominating y.

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