Dynamical Problems for Geometrically Exact Theories of Nonlinearly Viscoelastic Rods.- The Limits of Hamiltonian Structures in Three-Dimensional Elasticity, Shells, and Rods.- The Membrane Shell Model in Nonlinear Elasticity: A Variational Asymptotic Derivation.- Gravity Waves on the Surface of the Sphere.- A Nonlinear Extensible 4-Node Shell Element Based on Continuum Theory and Assumed Strain Interpolations.- Multilayer Beams: A Geometrically Exact Formulation.- Obstructions to Quantization.- An Impetus-Striction Simulation of the Dynamics of an Elastica.- A Symplectic Integrator for Riemannian Manifolds.- Time Integration and Discrete Hamiltonian Systems.- Problems and Progress in Microswimming.- Symmetry Methods in Collisionless Many-Body Problems.- Mathematical Analysis of Sideband Instabilities with Application to Rayleigh-Bénard Convection.- KAM Theory Near Multiplicity One Resonant Surfaces in Perturbations of A-Priori Stable Hamiltonian Systems.- Constrained Euler Buckling.- Continuity Properties and Global Attractors of Generalized Semiflows and the Navier-Stokes Equations.- Stacked Lagrange Tops.- On the Bifurcation and Stability of Rigidly Rotating Inviscid Liquid Bridges.
Starting in 1996, a sequence of articles appeared in the Journal of Nonlinear Science dedicated to the memory of one of its original editors, Juan-Carlos Simo, Applied Me chanics, Stanford University. Sadly, Juan-Carlos passed away at an early age in 1994. We lost a brilliant colleague and a wonderful person. These articles are collected in the present volume. Many of them are updated and corrected especially for this occasion. These essays are in areas of scientific interest of Juan-Carlos, including mechanics (particles, rigid bodies, fluids, elasticity, plastic ity, etc.), geometry, applied dynamics, and, of course, computation. His interests were extremely broad-he did not see boundaries between computation, mathematics, me chanics, and dynamics, and, in that sense, he ideally reflected the spirit of the journal and many of the most exciting areas of current scientific interest. Juan-Carlos was one of those select and gifted people who could cross interdisci plinary boundaries with extremely high quality and productive interactions of lasting value. His contributions, ranging from concrete engineering problems to fundamental mathematical theorems in geometric mechanics, are remarkable. In current conferences as well as in scientific books and articles, and over a wide range of subjects, one frequently hears how his ideas as well as specific results are often used and quoted-this is one indication of just how profound and fundamental his work has impacted the community.
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