Existence and approximation of attractors for nonlinear coupled lattice wave equations

<p style='text-indent:20px;'>This paper is concerned with the asymptotic behavior of solutions to a class of nonlinear coupled discrete wave equations defined on the whole integer set. We first establish the well-posedness of the systems in <inline-formula><tex-math id="M1">\begin{document}$ E: = \ell^2\times\ell^2\times\ell^2\times\ell^2 $\end{document}</tex-math></inline-formula>. We then prove that the solution semigroup has a unique global attractor in <inline-formula><tex-math id="M2">\begin{document}$ E $\end{document}</tex-math></inline-formula>. We finally prove that this attractor can be approximated in terms of upper semicontinuity of <inline-formula><tex-math id="M3">\begin{document}$ E $\end{document}</tex-math></inline-formula> by a finite-dimensional global attractor of a <inline-formula><tex-math id="M4">\begin{document}$ 2(2n+1) $\end{document}</tex-math></inline-formula>-dimensional truncation system as <inline-formula><tex-math id="M5">\begin{document}$ n $\end{document}</tex-math></inline-formula> goes to infinity. The idea of uniform tail-estimates developed by Wang (Phys. D, 128 (1999) 41-52) is employed to prove the asymptotic compactness of the solution semigroups in order to overcome the lack of compactness in infinite lattices.</p>

Wave propagation in micromorphic anisotropic continua with an application to tetragonal crystals

We study the coupled macroscopic and lattice wave propagation in anisotropic crystals seen as continua with affine microstructure (or micromorphic). In the general case, we obtain qualitative information on the frequencies and the dispersion relations. These results are then specialized to crystals of the tetragonal point group for various propagation directions: exact representation for the acoustic and optic frequencies and for the coupled vibrations modes are obtained for propagation directions along the tetragonal c-axis.

Scattering of phonon by stacking faults and dislocation cores in plastically deformed LiF crystal: An analysis

The present work studies and analyses the effect of compression on LiF crystal. The compression is of the order that it deforms the LiF crystal plastically. The sequence of closed packed structure of plastically deformed crystal is disturbed and we expect stacking faults i.e., faults in the crystal along a plane. Plastically deformed crystal contains high density of dislocations. The depression of phonon conductivity in plastically deformed crystal is associated with interaction of the phonon with high density of dislocations. Phonon or the quantised lattice wave scatters with these stacking faults and dislocation cores, as a result, there is depression of lattice thermal conductivity near the peak. The number of stacking faults/cm N[Formula: see text] has been calculated which is of the order of 101/cm, and dislocation core size which is of the order of burger vector if dislocation density is of the order of 108/cm2. Separate contributions of relaxation rates for various phonon scattering processes have been calculated for both longitudinal and transverse phonons. Present work strongly supports that phonons are mainly scattered by stacking faults and dislocation cores in plastically deformed LiF crystal.

Design and FPGA implementation of 11th order Efficient IIR Wavelet Filter Banks with Approximate Linear-phase

In this paper. Bireciprocal Lattice Wave Digital Filters (BLWDFs) are utilized in an approximate linear-phase in pass-band design of order IIR wavelet filter banks (FBs). These filter banks are efficiently designed by replacement one of branches for (BLWDFs) by only a unit delay. The coefficients of the designed filter are achieved by simulating the IIR response suggested in [1]. The design is first simulated using Matlab programming in order to investigate the resulting wavelet filter properties and to find the suitable wordlength for the BLWDFs coefficients. FPGA implemtation of the proposed IIR wavelet filter bank is also achived for three levels with less complexity and high operating frequency.