This book covers topics such as seismic and surface wave propagation, nonlinear dynamics, heat and mass transfer, convection phenomena, complex fluid mixing, numerical integration techniques, and crack behaviour in piezoelectric materials. Bringing together analytical, numerical, and theoretical and experimental perspectives, this book serves as a comprehensive reference for understanding cutting-edge developments that shape modern scientific and engineering applications. It is an essential resource for researchers, academicians, and professionals engaged in modelling, simulation, and analysis of sophisticated physical systems. The book features:Comprehensive coverage of advanced wave propagation, including Love-type, Rayleigh-type, and seismic wave scattering in layered, anisotropic, and heterogeneous media. In-depth studies on heat and mass transfer phenomena, featuring thermoconvective behaviour, double-diffusive convection, and fluid–thermal interactions. Robust analytical and numerical methodologies, such as stability analysis, mixed quadrature rules, nonlinear dynamic modelling, and techniques addressing dissipative processes. Focused exploration of modern and complex materials, including piezoelectric composites, orthotropic structures, viscoelastic media, and micro-mechanical systems. It demonstrates interdisciplinary applicability and provides valuable insights for researchers and professionals in applied mathematics, engineering, geophysics, materials science, and computational mechanics. It is primarily written for graduate students and academic researchers in the fields of mechanical engineering, engineering design, civil engineering, materials science, aerospace engineering, and engineering mathematics.