PrefaceAn author usually faces the onerous task of justifying the need for his or her treatise, as there are few subjects left where not enough has been written. Fortunately for us, the continuum theory of mixtures is one of the few areas where it is unnecessary to plead the case for a book. While there are many mathematical treatments on the subject matter of this book, their approach is quite different from that which is presented here. A few review articles on mixture theory have come close to providing a comprehensive overview of the theoretical foundations of the topic; however they do not discuss, in any detail, initial and boundary value problems within the context of the theory. It is to this aspect of the subject that our book is primarily devoted. Our bias towards applications can be felt throughout the book, though the last two chapters are devoted to developing new approaches to modelling a mixture of two fluids and a fluid infused with solid particles with a special class of applications in mind.We have tried to inject new ideas or look at old problems within the context of a new perspective, wherever possible in the book. For instance, the exact boundary conditions that are to be prescribed for boundary value problems involving mixtures in general are far from settled. Boundary conditions based on thermodynamic argu ments have been used previously to analyze steady state problems. These boundary conditions are valid when the boundary of the mixture is saturated. However, there are situations when such a condition does not obtain on the boundary. Thus, we have revisited some steady state boundary value problems and solved them within the con text of a new set of boundary conditions that are based on a very different philosophy from that adopted in earlier attempts at resolving these problems. Similarly, in the treatment of a mixture of a fluid infused with solid particles in this book, we present an approach that is markedly different from my earlier treatment of such problems with Johnson and Massoudi. We envisage a different class of problems where we feel our present approach is applicable. The presentation here concerning a. mixture of two fluids also sets forth an approach that might be extended to a turbulent motion of the mixture of two fluids. Here, we recognize that the turbulent motion of a single constituent is as yet not well understood. However, given the fact that mixtures do undergo turbulent motion, it is necessary to address this problem even if the attempt is crude at best.This book is not meant to be a text on the theory of mixtures, as it does not VlllPreface develop the basic frame-work for the study of mixtures in the kind of detail and completeness that a beginning graduate student needs. The book presumes that the reader is quite conversant with continuum mechanics. No exercises or examples are provided, and in many instances, results from papers published recently in the literature are used, without recording them in any detail. Issues that we consider to be unresolved are ...

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Rotated blades are key mechanical components in turbomachinery and high cycle fatigues often induce blade cracks. Accurate detection of small cracks in rotated blades is very significant for safety, reliability, and availability. In nature, a breathing crack model is fit for a small crack in a rotated blade rather than other models. However, traditional vibration displacements-based methods are less sensitive to nonlinear characteristics due to small breathing cracks. In order to solve this problem, vibration power flow analysis (VPFA) is proposed to analyze nonlinear dynamic behaviors of rotated blades with small breathing cracks in this paper. Firstly, local flexibility due to a crack is derived and then time-varying dynamic model of the rotated blade with a small breathing crack is built. Based on it, the corresponding vibration power flow model is presented. Finally, VPFA-based numerical simulations are done to validate nonlinear behaviors of the cracked blade. The results demonstrate that nonlinear behaviors of a crack can be enhanced by power flow analysis and VPFA is more sensitive to a small breathing crack than displacements-based vibration analysis. Bifurcations will occur due to breathing cracks and subharmonic resonance factors can be defined to identify breathing cracks. Thus the proposed method can provide a promising way for detecting and predicting small breathing cracks in rotated blades.

a b s t r a c tIn this paper, we propose a novel force field parameter optimization method based on LSSVR and optimize the torsion energy parameters of ECEPP force field. In this method force field parameter optimization problem is turned into a support vector regression problem. Protein samples for regression model training are chosen from Protein Data Bank. The experiments show that the optimized force-field parameters make both a-helix and b-hairpin structures more consistent with the experimental implications than the original parameters. Crown