"Partial Differential Equations: Analytical Methods and Applications covers all the basic topics of a Partial Differential Equations (PDE) course for undergraduate students or a beginners’ course for graduate students. It provides qualitative physical explanation of mathematical results while maintaining the expected level of it rigor. This text introduces and promotes practice of necessary problem-solving skills. The presentation is c ..."
"This book summarizes the main advances in the field of nonlinear evolution and pattern formation caused by longwave instabilities in fluids. It will allow readers to master the multiscale asymptotic methods and become familiar with applications of these methods in a variety of physical problems. Longwave instabilities are inherent to a variety of systems in fluid dynamics, geophysics, electrodynamics, biophysics, and many others. The te ..."
"Ramon M. L., Maza D. M., Mancini H. L., 1999, Patterns in small aspect ratio
Benard-Marangoni convection, Phys. Rev. E 60, 4193–4198. ... Rasenat S.,
Busse F. H., Rehberg I., 1989, A theoretical and experimental study of double-
layer convection, J. Fluid Mech. 199, 519–540. Ratke L., Walter H., Feuerbacher
B. (editors), 1989, Material and Fluid under Low Gravity, Springer-Verlag, Berlin.
Ratulowski J."
"This book contains a systematic investigation of the convection in systems with interfaces. For the first time, it classifies all of the known types of convective instabilities in such systems, and discusses the peculiarities of multilayer systems. The book provides an overview of the wide variety of steady and oscillatory patterns, waves, and other dynamic phenomena characteristic for multilayer fluid systems. Various physical effects, ..."
"... the motion of the gas is neglected, whereas the heat/mass transfer in the gas is
described in a phenomenological way by ... A more accurate approach (the two-
layer model) takes into account the physical processes in fluids on both sides of
the ... Interfacial convection is a striking phenomenon that takes place any time
the interfacial tension is not uniform along ... where it provides a reliable transport
mechanism (Sammarco a ..."
"It provides qualitative physical explanation of mathematical results while maintaining the expected level of it rigor. This text introduces and promotes practice of necessary problem-solving skills."
"... pleasant and made them want to return to this wonderful place again. Also, our
special thanks go to Dr. Denis Melnikov and Ms Jessica Conway for their
invaluable help in translation between French, English and Russian; this was a
bridge that helped connect together people from so many different countries. One
of the editors and ... the NATO ASI was partially supported by the US National
Science Foundation. Lorenz Kramer lecturi ..."
"For an hexagonal planform in a semi-space a > 0, -oo 3 y < co, bounded by a
rigid wall, a = 0, consider that the ... j = 0, 1, 2 in Eqs (4.70) as Ao = F(a, t), A1 =
A2 = G(a, t), where F(a, t) is the complex amplitude of the system of rolls with the ..."
"The book deals with modern methods of nonlinear stability theory applied to problems of continuous media mechanics in the presence of interfaces, with applications to materials science, chemical engineering, heat transfer technologies, as well as in combustion and other reaction-diffusion systems. Interfaces play a dominant role at small scales, and their correct modeling is therefore also crucial in the rapidly expanding fields of micr ..."
"The book deals with modern methods of nonlinear stability theory applied to problems of continuous media mechanics in the presence of interfaces, with applications to materials science, chemical engineering, heat transfer technologies, as well as in combustion and other reaction-diffusion systems. Interfaces play a dominant role at small scales, and their correct modeling is therefore also crucial in the rapidly expanding fields of micr ..."
"Pierre Colinet, Alexander Nepomnyashchy. been summarized in a ... One can
expect development of topological defects and spiral- like waves. aves
propagating in different directions interact with each other in a nonlocal way (
Knobloch and De Luca (1990), Matkowsky and Volpert (1992)). e conclude that
the investigation of the nonlinear development of oscillatory shortwave instability
is a developing field which is beyond the scope of ..."