Stability Problems in Applied Mechanics starts with the stability problems in statics. The example of buckling of columns is studed through Euler method followed by the Energy method, based on Lagrange-Dirichlet theorem. Snap buckling, instability of shape, buckling due to follower load are also discussed. Insufficiency of static analysis for instability is clearly brought out and buckling problems are revisited from the point of view of dynamics. The theory of Dynamical System and the foundations of bifurcation theory and Floquet theory are developed and used to revisit the stability problems in the light of these unified mathematical concepts. This mathematical basis is then applied to investigate the stability problems encountered in dynamics of particle, rigid and flexible bodies. Finally the emergence of length scale and pattern formation as a consequence of instability in fluid, thermal and diffusion systems are discussed through a number of real-life problems. Different notions of stability and the analysis of nonlinear states are briefly included in two appendices."--BOOK JACKET.
The book describes the progress made in understanding the phenomena of various hydrodynamic instabilities over the last thirty years. Exact results for the onset of Rayleigh-Benard convection in different systems are presented and approximation techniques like amplitude equations and few-mode truncations are treated at length. Routes to chaos and the characteristics of the chaotic state are reviewed. Certain features of the Taylor-Couette flow and the effect of parametric modulation on hydrodynamic instabilities are discussed. The theory is supplemented by experimental results.
In this new textbook, a number of unusual applications are discussed in addition to the usual topics covered in a course on Statistical Physics. Examples are: statistical mechanics of powders, Peierls instability, graphene, Bose-Einstein condensates in a trap, Casimir effect and the quantum Hall effect. Superfluidity and super-conductivity (including the physics of high-temperature superconductors) have also been discussed extensively.The emphasis on the treatment of these topics is pedagogic, introducing the basic tenets of statistical mechanics, with extensive and thorough discussion of the postulates, ensembles, and the relevant statistics. Many standard examples illustrate the microcanonical, canonical and grand canonical ensembles, as well as the Bose-Einstein and Fermi-Dirac statistics.A special feature of this text is the detailed presentation of the theory of second-order phase transitions and the renormalization group, emphasizing the role of disorder. Non-equilibrium statistical physics is introduced via the Boltzmann transport equation. Additional topics covered here include metastability, glassy systems, the Langevin equation, Brownian motion, and the Fokker-Planck equation.Graduate students will find the presentation readily accessible, since the topics have been treated with great deal of care and attention to detail.
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