Falling Liquid Films gives a detailed review of state-of-the-art theoretical, analytical and numerical methodologies, for the analysis of dissipative wave dynamics and pattern formation on the surface of a film falling down a planar inclined substrate. This prototype is an open-flow hydrodynamic instability, that represents an excellent paradigm for the study of complexity in active nonlinear media with energy supply, dissipation and dispersion. It will also be of use for a more general understanding of specific events characterizing the transition to spatio-temporal chaos and weak/dissipative turbulence. Particular emphasis is given to low- dimensional approximations for such flows through a hierarchy of modeling approaches, including equations of the boundary-layer type, averaged formulations based on weighted residuals approaches and long-wave expansions. Whenever possible the link between theory and experiment is illustrated, and, as a further bridge between the two, the development of order-of-magnitude estimates and scaling arguments is used to facilitate the understanding of basic, underlying physics. This monograph will appeal to advanced graduate students in applied mathematics, science or engineering undertaking research on interfacial fluid mechanics or studying fluid mechanics as part of their program. It will also be of use to researchers working on both applied, fundamental theoretical and experimental aspects of thin film flows, as well as engineers and technologists dealing with processes involving isothermal or heated films. This monograph is largely self-contained and no background on interfacial fluid mechanics is assumed.

Within nonlinear spatio-temporal dynamics, active lattice systems are of relevance to the study of multi-dimensional dynamical systems and the theory of nonlinear waves and dis- sipative structures of extended systems. In this book, the authors deal with basic concepts and models, with methodolo- gies for studying the existence and stability of motions, understanding the mechanisms of formation of patterns and waves, their propagation and interactions in active lattice systems, and about how much cooperation or competition bet- ween order and chaos is crucial for synergetic behavior and evolution. The results described in the book have both in- ter- and trans-disciplinary features and a fundamental cha- racter. It is a textbook for graduate courses in nonlinear sciences, including physics, biophysics, biomathematics, bioengineering, neurodynamics, electrical and electronic engineering, mathematical economics, and computer sciences.

This monograph provides a detailed review of the state-of-the-art theoretical (analytical and numerical) methodologies for the analysis of dissipative wave dynamics and pattern formation on the surface of a film falling down a planar, inclined substrate. Particular emphasis is given to low-dimensional approximations for such flows through a hierarchy of modeling approaches, including equations of the boundary-layer type, averaged formulations based on weighted residuals approaches, and long-wave expansions.

Whenever possible, the link between theory and experiments is illustrated and, as a further bridge between the two, the development of order-of-magnitude estimates and scaling arguments is used to facilitate the understanding of the underlying basic physics.

The book will be of particular interest to advanced graduate students in applied mathematics, science or engineering undertaking research on interfacial fluid mechanics or studying fluid mechanics as part of their program; researchers working on both applied and fundamental theoretical and experimental aspects of thin film flows; and engineers and technologists dealing with processes involving thin films, either isothermal or heated.

Topics covered include:

Detailed derivations of governing equations and wall and free-surface boundary conditions for free-surface thin film flows in the presence of thermocapillary Marangoni effect; linear stability including Orr-Sommerfeld, absolute/convective instability and Floquet analysis of periodic waves; strongly nonlinear analysis including construction of bifurcation diagrams of periodic and solitary waves; weakly nonlinear prototypes such as Kuramoto-Sivashinsky equation; validity domain of the long-wave expansions; kinematic/dynamic waves, connection with shallow water and river flows/hydraulic jumps; dynamical systems approach, local and global bifurcations, homoclinicity and conditions for periodic, subsidiary and secondary homoclinic orbits; modulation instability of solitary waves to transverse perturbations; transition to two-dimensional solitary waves and interaction of two-dimensional solitary waves; and substrate heating and competition between solitary waves and rivulet formation in free-surface flows over heated substrates.

Tutorials and details of computational methodologies including computer programs:

Solution of the Orr-Sommerfeld eigenvalue problem; computational search via continuation for traveling wave solutions and their bifurcations; computation of systems of nonlinear pde s using finite differences; spectral representation and aliasing.

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This volume contains the lectures and invited seminars pre sented at the NATO Advanced Study Institute on NON-EQUILIBRIUM COOPERATIVE PHENOMENA IN PHYSICS AND RELATED FIELDS that was held at EL ESCORIAL (MADRID), SPAIN, on August 1-11, 1983. Most nonlinear problems in dissipative systems, i . e . , most mathematical models in SYNERGETICS are highly trans disciplinary in practice and the list of lecturers and participants at the ASI reflects this di versi ty both in background and interest. The presentation of the material fell into two main categories: tutopia~ Zectures on some basic ideas and methods, both experimental and theoretical, intended to lay a common base for all participants, and a series of more specific lectures and seminars, serving the purpose of exemplying selected but typical applications in their current state of development. Topics were chosen for their basic interest as well as for their potential for applications (laser, hydrodynamics, liquid crystals, EHD, combustion, thermoelasticity, etc. ). We had more seminars and some of the oral presentations were supported or complemented with 16 mm films and on occasion with experimental demonstrations including a special seminar, a social one on broken symmetries in Art and Music. There is here no record of these non-standard acti vi ties. We had, indeed, quite a heavy load for which I was fully responsible. However, the reader and, above all, the participants at the ASI ought to be aware of the fact that in Spain, with.

In this book, the authors deal with basic concepts and models, with methodologies for studying the existence and stability of motions, understanding the mechanisms of formation of patterns and waves, their propagation and interactions in active lattice systems, and about how much cooperation or competition between order and chaos is crucial for synergetic behavior and evolution.