Peculiar Velocity in Action

Peculiar Velocity in Action addresses both the small and the large: both atoms and galaxies. It also addresses money and economics. It describes the random motion of objects using what is both a classical and quantum mechanical theory of peculiar velocity fields. A peculiar velocity is that directed rate of change of position of some object, contained within a collection of similar such objects, residing within some positional field that is occupied by the collection of objects, which...
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Peculiar Velocity in Action addresses both the small and the large: both atoms and galaxies. It also addresses money and economics. It describes the random motion of objects using what is both a classical and quantum mechanical theory of peculiar velocity fields. A peculiar velocity is that directed rate of change of position of some object, contained within a collection of similar such objects, residing within some positional field that is occupied by the collection of objects, which possesses some aggregate collective motion. The objects can be any abstract entity that can be described as bearing motions within some field possessing any sort of hierarchical structure. As so broadly defined, the theory of peculiar velocity fields can be applied to numerous dynamical systems that can be measured unambiguously using statistical methods. This implies that the rates of change of location of the elements composing any such dynamical system are measurable within some identifiable field which describes some property relevant to the collection. Although placed within this layer of abstraction, the theory of peculiar velocity fields still retains its simple formulation that asserts the peculiar velocity of any one object from a collection to be the difference of its velocity from that of the aggregate velocity of the collection. As such, this is simple vector addition upon an abstract field pertinent to a dynamical system. Then, in fulfillment of the theory, all that remains is the assertion that the peculiar velocity fields are solenoidal. That is, they are both source and sink free. Within the book Peculiar Velocity in Action the reader will find applications of the theory well beyond its original development within the Kinetic Theory of Gases to such diverse subjects as astronomy, atomic nuclei, and economics. While the theory requires a level of high mathematical maturity, this is not a mathematics book. The exposition is entirely applied mathematics with emphasis upon applications of engineering and applied science significance. The application of the theory to astronomy corrects a misunderstanding regarding the dark matter content of star clusters and galaxies. When applied to atomic nuclei the theory demonstrates how the inverse square law of electrostatics and gravitation is a consequence, not an assertion, of quantum mechanics. Advancing beyond the realm of physical science into economics, the book shows how to define price fields and their concomitant properties, such as the price Lagrangean, for the use of the methods of analytical mechanics as applied to finance. The book lays the foundation for the author's further application of the theory to economics and its consequent development as the theory of finance rheology. Peculiar Velocity in Action is the book to begin one's education for an understanding of the principles of finance rheology. With an appreciation for the theory of peculiar velocity fields, the reader is likely to find many other applications of the theory to endeavors of significance to one's self interests.