Physical laws are for the most part expressed in terms of differential equations, and natural classes of these are in the form of conservation laws or of problems of the calculus of variations for an action functional. These problems can generally be posed as Hamiltonian systems, whether dynamical systems on finite dimensional phase space as in classical mechanics, or partial differential equations (PDE) which are naturally of infinitely many degrees of freedom. This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that...
Physical laws are for the most part expressed in terms of differential equations, and natural classes of these are in the form of conservation laws...
This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems. Applications are also presented to several important areas of research, including problems in classical mechanics, continuum mechanics, and partial differential equations.
This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NA...
Sorasak Danworaphong Gerald J. Diebold Walter Craig
When two phase coherent laser beams are crossed at an angle, the electric fields of the beams produce a sinusoidal interference pattern. Partial absorption of the electric fields in a colloidal sample creates a sinusoidal temperature field. The temperature gradient then causes production of concentration gradient in the sample, known as the Ludwig-Soret effect or thermal diffusion. Solutions to nonlinear partial differential equations that describe the effect show that shock waves analogous to fluid shock waves are produced. A mathematical relation between the shock speed and the density...
When two phase coherent laser beams are crossed at an angle, the electric fields of the beams produce a sinusoidal interference pattern. Partial absor...
