By Andreas Mandelis
From the reports of the 1st edition:
"A necessary, good balanced, e-book at the eco-friendly functionality technique utilized to options of diverse difficulties concerning diffusion and wave procedures less than a number of actual stipulations in Cartesian, cylindrical and round geometries. Mathematical systems are played in a single, and 3 dimensions. it's a textbook at the graduate point appropriate for college kids however it may also function a reference literature to complex researchers." (Vladimir Cadež, Zentralblatt MATH, Vol. 976, 2002)
"This publication develops a unified mathematical framework for treating a large choice of diffusion-related periodic phenomena in such parts as warmth move, electric conduction, and lightweight scattering. … The presentation, mostly within the type of case experiences without delay appropriate in quite a lot of experimental methodologies, is meant for graduate scholars, specialist scientists and engineers … ." (Applied Mechanics reports, Vol. fifty four (5), 2001)
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Extra resources for Diffusion-Wave Fields: Mathematical Methods and Green Functions
18. Amplitude (a) and phase (b) of the frequency dependence of the finite-domain improper Green function Eq. 38), with thickness, L, as a parameter. The impulse response represents the air-steel-air system. 1. 6 Green Functions for Composite Solids I This category includes one-layer solids of finite thickness on a semi-infinite substrate. The geometry is shown in Fig. 20. An impulsive TW source is located at x = Xo. The thermal conductivities and diffusivities of the solid and the substrate are (kl' ad and (k2' (2), respectively.
E -- y~=·0 . =O ...... \, A:, . c: 405 205 -50 / / ·z·~: ,- / -70 / ! ",,,, " 1 -80 " .. ::. -. _ ,. Q. 1005 b) ~ ---------- -60 805 605 5 I / 205 405 805 605 1005 Frequency [Hz] Fig. Amplitude (a) and phase (b) of the frequency dependence of the finite-domain improper Green function Eq. 38), with the boundary thermalwave reflection coefficient, 1'50, as a parameter.
2). s. reduces to zero. s. is equal to 2E and it also reduces to zero. 3) This condition can readily incorporate the time-modulation factor implicitly through a simple multiplication of both sides by e- iwto , and without any further change. These two interfacial conditions, Eqs. 3), prove that the one-dimensional TW Green function is continuous at the location of the spatially impulsive source, whereas its derivative is discontinuous across the source coordinate. These conditions are much more general than this specific example and will be subsequently used (often without proof) throughout this book.
Diffusion-Wave Fields: Mathematical Methods and Green Functions by Andreas Mandelis