Fourier integrals), variational methods, and the like. On those occasions when further development of a topic is beyond the limits of such an approach the author furnishes appropriate references to the literature. The author has a "pet" concept which he pushes in what I would regard as an inoffensive manner, namely his two-surface model of a shell. There is an "S" (for stretching) surface and a "B" (for bending) surface with appropriate distributions of certain internal loads required to ensure that they deform together. The reader can take this or leave it; I happen to leave it. This is definitely an engineer's book on the subject, but one that those with a very mathematical view of structural mechanics could well read with profit.A wide variety of topics is included. Throughout the text there is ample discussion of the practical implications of the results. The historical background of a problem is occasionally given, and there are numerous references to the literature. The list of topics is more or less as follows: the membrane theory, its advantages and limitations; analysis of cylindrical shells, the influence of length, boundary conditions, and type of loading; the analysis and design of cylindrical shell roofs, including the effects of edge beams; pressure vessels and junction problems, i.e., torispherical heads, etc.; flexibility of axially symmetric bellows, mostly by energy methods; curved tubes and pipe bends including the effects of reinforcing rings; buckling of cylindrical shells under various loadings and with various boundary conditions by the classical bifurcation analysis including the effect of stiffening elements; post-buckling analysis and imperfection sensitivity, the Brazier effect in the buckling of bent tubes; vibrations of cylindrical shells; plastic analysis, generalized yield surfaces, plastic collapse, upper and lower bound methods applied to limit analysis of pressure vessels.
In this article, the authors consider optimal decision making in two-alternative forced-choice (TAFC) tasks. They begin by analyzing 6 models of TAFC decision making and show that all but one can be reduced to the drift diffusion model, implementing the statistically optimal algorithm (most accurate for a given speed or fastest for a given accuracy). They prove further that there is always an optimal trade-off between speed and accuracy that maximizes various reward functions, including reward rate (percentage of correct responses per unit time), as well as several other objective functions, including ones weighted for accuracy. They use these findings to address empirical data and make novel predictions about performance under optimality.
For turbulent flows at relatively low speeds there exists an excellent mathematical model in the incompressible Navier–Stokes equations. Why then is the 'problem of turbulence' so difficult? One reason is that these nonlinear partial differential equations appear to be insoluble, except through numerical simulations, which offer useful approximations but little direct understanding. Three recent developments offer new hope. First, the discovery by experimentalists of coherent structures in certain turbulent flows. Secondly, the suggestion that strange attractors and other ideas from finite-dimensional dynamical systems theory might play a role in the analysis of the governing equations. And, finally, the introduction of the Karhunen-Loève or proper orthogonal decomposition. This book introduces these developments and describes how they may be combined to create low-dimensional models of turbulence, resolving only the coherent structures. This book will interest engineers, especially in the aerospace, chemical, civil, environmental and geophysical areas, as well as physicists and applied mathematicians concerned with turbulence.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.