Mechanics and mathematics have been complementary partners since Newton's time and the history of science shows much evidence of the beneficial influence of these disciplines on each other. Driven by increasingly elaborate modern technological applications the symbiotic relationship between mathematics and mechanics is continually growing. However, the increasingly large number of specialist journals has generated a duality gap between the two partners, and this gap is growing wider. This volume is intended to bridge this gap. It should be suitable for scientists, engineers and mathematicians, including advanced students (doctoral and post-doctoral level) at universities and in industry interested in modern mechanics and applied mathematics.