William G. Gray – författare

Learn the fundamental concepts that underlie the physics of multiphase flow and transport in porous media with the information in Essentials of Multiphase Flow in Porous Media, which demonstrates the mathematical-physical ways to express and address multiphase flow problems. Find a logical, step-by-step introduction to everything from the simple concepts to the advanced equations useful for addressing real-world problems like infiltration, groundwater contamination, and movement of non-aqueous phase liquids. Discover and apply the governing equations for application to these and other problems in light of the physics that influence system behavior.

Learn the fundamental concepts that underlie the physics of multiphase flow and transport in porous media with the information in Essentials of Multiphase Flow in Porous Media, which demonstrates the mathematical-physical ways to express and address multiphase flow problems. Find a logical, step-by-step introduction to everything from the simple concepts to the advanced equations useful for addressing real-world problems like infiltration, groundwater contamination, and movement of non-aqueous phase liquids. Discover and apply the governing equations for application to these and other problems in light of the physics that influence system behavior.

The Tree of Life is growing, flexible and adaptable life pattern capable of indefinite extensions throughout all states of existence. The Qabalah, or "received teachings," is the outcome of experiences of those who have climbed the ladder of the Tree by arranging their lives according to its pattern of perfection. The Tree provides the means of receiving inner world contacts with types of consciuosness normally inaccessible to the ordinary human mindit is from and through these sources that the "teaching" comes. Here William Gray has presented a step by step guide to the Tree of Life and the Four Worlds of the Qabalahsthe worlds of contemplation, meditation, magic and daily action. The Tree of Life is a means and not an end. It is a map for helping you attain the single objective common to all systems, mysteries and religionsnamely, the mystical union of humanity and divinity. This revised edition includes an index.

This is not just another book about the tarot. It can be used with any deck of cards, for it looks at the symbols of the tarot from the Sangreal viewpoint to teach you a new way of meditation that will enhance your pursuit of the Western Mystery Tradition. Gray combines the symbolism of the Quabbalistic Tree of Life with the symbolism inherent in the traot so you can learn the secret language of the tarot while looking at it through the lens of the mystical path. The ten fundamental types of consciousness will be explored using the four worlds of the qabbalah that also appear in the four suits in the tarot, and Mr. Gray will explain how he workds with the meanings of the major and minor arcana. Also included is the Journey of the Fool, that mystical journey of the soul that each person who quests for the Holy Grail must take. Mr. Gray does recommend that you use the cards for fortunetelling, but rather that you use them to help your spiritual growth. By working with the cards, they will begin to talk to you, and as you better understand the symbolism, you will learn the true value of what you hold within yourself.

Mathematical Tools for Changing Scale in the Analysis of Physical Systems presents a new systematic approach to changing the spatial scale of the differential equations describing science and engineering problems. It defines vectors, tensors, and differential operators in arbitrary orthogonal coordinate systems without resorting to conceptually difficult Riemmann-Christoffel tensor and contravariant and covariant base vectors. It reveals the usefulness of generalized functions for indicating curvilineal, surficial, or spatial regions of integration and for transforming among these integration regions. These powerful mathematical tools are harnessed to provide 128 theorems in tabular format (most not previously available in the literature) that transform time-derivative and del operators of a function at one scale to the corresponding operators acting on the function at a larger scale.Mathematical Tools for Changing Scale in the Analysis of Physical Systems also provides sample applications of the theorems to obtain continuum balance relations for arbitrary surfaces, multiphase systems, and problems of reduced dimensionality. The mathematical techniques and tabulated theorems ensure the book will be an invaluable analysis tool for practitioners and researchers studying balance equations for systems encountered in the fields of hydraulics, hydrology, porous media physics, structural analysis, chemical transport, heat transfer, and continuum mechanics.

Mathematical Tools for Changing Scale in the Analysis of Physical Systems presents a new systematic approach to changing the spatial scale of the differential equations describing science and engineering problems. It defines vectors, tensors, and differential operators in arbitrary orthogonal coordinate systems without resorting to conceptually difficult Riemmann-Christoffel tensor and contravariant and covariant base vectors. It reveals the usefulness of generalized functions for indicating curvilineal, surficial, or spatial regions of integration and for transforming among these integration regions. These powerful mathematical tools are harnessed to provide 128 theorems in tabular format (most not previously available in the literature) that transform time-derivative and del operators of a function at one scale to the corresponding operators acting on the function at a larger scale.Mathematical Tools for Changing Scale in the Analysis of Physical Systems also provides sample applications of the theorems to obtain continuum balance relations for arbitrary surfaces, multiphase systems, and problems of reduced dimensionality. The mathematical techniques and tabulated theorems ensure the book will be an invaluable analysis tool for practitioners and researchers studying balance equations for systems encountered in the fields of hydraulics, hydrology, porous media physics, structural analysis, chemical transport, heat transfer, and continuum mechanics.

This textbook presents an understanding of how basic physical descriptions can be translated into mathematical analogues that provide an opportunity to investigate environmental processes. Examples come from a range of hydrologic, atmospheric, and geophysical problems. The emphasis is on simple examples and calculations that add to understanding. The book provides a sense for the meaning of mathematical expressions, a physical feel for their relations to processes, and confidence in working with mathematical solutions. The goal of this book, in essence, is to present the timeless basic physical and mathematical principles and philosophy of environmental modeling, often to students who need to be taught how to think in a different way than they would for more narrowly-defined engineering or physics problems. Minimum prerequisites for the student reader include a knowledge of calculus through differential equations, but the book provides the mathematical and physical tools needed as the occasion arises.

This textbook presents an understanding of how basic physical descriptions can be translated into mathematical analogues that provide an opportunity to investigate environmental processes. Examples come from a range of hydrologic, atmospheric, and geophysical problems. The emphasis is on simple examples and calculations that add to understanding. The book provides a sense for the meaning of mathematical expressions, a physical feel for their relations to processes, and confidence in working with mathematical solutions. The goal of this book, in essence, is to present the timeless basic physical and mathematical principles and philosophy of environmental modeling, often to students who need to be taught how to think in a different way than they would for more narrowly-defined engineering or physics problems. Minimum prerequisites for the student reader include a knowledge of calculus through differential equations, but the book provides the mathematical and physical tools needed as the occasion arises.

This textbook presents an understanding of how basic physical descriptions can be translated into mathematical analogues that provide an opportunity to investigate environmental processes. Examples come from a range of hydrologic, atmospheric, and geophysical problems. The emphasis is on simple examples and calculations that add to understanding. The book provides a sense for the meaning of mathematical expressions, a physical feel for their relations to processes, and confidence in working with mathematical solutions. The goal of this book, in essence, is to present the timeless basic physical and mathematical principles and philosophy of environmental modeling, often to students who need to be taught how to think in a different way than they would for more narrowly-defined engineering or physics problems. Minimum prerequisites for the student reader include a knowledge of calculus through differential equations, but the book provides the mathematical and physical tools needed as the occasion arises.

Finite Element Simulation in Surface and Subsurface Hydrology provides an introduction to the finite element method and how the method is applied to problems in surface and subsurface hydrology. The book presents the basic concepts of the numerical methods and the finite element approach; applications to problems on groundwater flow and mass and energy transport; and applications to problems that involve surface water dynamics. Computational methods for the solution of differential equations; classification of partial differential equations; finite difference and weighted residual integral techniques; and The Galerkin finite element method are discussed as well. The text will be of value to engineers, hydrologists, and students in the field of engineering.

1965-1967 ...As the New Age seemed to explode into being, everything spiritual had to be Eastern. Psychedelic artwork showed Glastonbury Tor overshadowed by the Maharishi Mahesh Yogi, or Stonehenge sending its energies up to Lord Krishna - imagery which William G. Gray summed up quite simply as "Balls." He was working hard to make sure that our weakened (or slumbering) Western Traditions would survive. Among his endeavours at the time was this guide to the inner and outer practicalities of ritual magic, which includes instruction on god-forms, words of power, magic circles, initiation, extension of consciousness and raising power through ritual. Previously unpublished, Working with Inner Light is the first new book by William G. Gray since the author's death in 1992. Written in the form of a journal or magical diary, it includes his original sketches, and forms a detailed course in modern Qabalistic magic which will be of immense value to esoteric students and practitioners working within the Western Mysteries today.

In the early 1970s the redoubtable old occultist William G. Gray bicycled from his Gloucestershire home to the Rollright stone circle in Oxfordshire on a clear and full-mooned summer night. The visionary experiences he encountered on that night and in other similar visits resulted in the writing of this book, originally published by Helios Books in 1975 and now a classic among pagan and craft traditions. The text of the ritual is given in full, along with a discussion of its pattern and purpose. The Rollright Ritual is a powerful initiatory rite for attuning oneself to a personal and communal path of spiritual growth, presented here with an explanatory text and a discussion of the spiritual lives and practices of the stone circle builders of Great Britain. "Somehow, we ought to get away from ideas that a Standing Stone is only an outworn sign of our past, and see it as an upraised Finger of Fate beckoning us ahead toward our future. The Stone is not merely a memorial of bygone beliefs, but a pointer that should raise our highest hopes of finding faith in all the Life that lies ahead of us."

As an "omniscient and obnoxious" teenager in 1969, Alan Richardson wrote to the occult author William G. Gray in pursuit of instant magical enlightenment. It was the beginning of a correspondence lasting many years in which Gray generously shared his magical knowledge and experience.

Thermodynamically constrained averaging theory provides a consistent method for upscaling conservation and thermodynamic equations for application in the study of porous medium systems. The method provides dynamic equations for phases, interfaces, and common curves that are closely based on insights from the entropy inequality. All larger scale variables in the equations are explicitly defined in terms of their microscale precursors, facilitating the determination of important parameters and macroscale state equations based on microscale experimental and computational analysis. The method requires that all assumptions that lead to a particular equation form be explicitly indicated, a restriction which is useful in ascertaining the range of applicability of a model as well as potential sources of error and opportunities to improve the analysis.

Thermodynamically constrained averaging theory provides a consistent method for upscaling conservation and thermodynamic equations for application in the study of porous medium systems. The method provides dynamic equations for phases, interfaces, and common curves that are closely based on insights from the entropy inequality. All larger scale variables in the equations are explicitly defined in terms of their microscale precursors, facilitating the determination of important parameters and macroscale state equations based on microscale experimental and computational analysis. The method requires that all assumptions that lead to a particular equation form be explicitly indicated, a restriction which is useful in ascertaining the range of applicability of a model as well as potential sources of error and opportunities to improve the analysis.

Thermodynamically constrained averaging theory provides a consistent method for upscaling conservation and thermodynamic equations for application in the study of porous medium systems. The method provides dynamic equations for phases, interfaces, and common curves that are closely based on insights from the entropy inequality. All larger scale variables in the equations are explicitly defined in terms of their microscale precursors, facilitating the determination of important parameters and macroscale state equations based on microscale experimental and computational analysis. The method requires that all assumptions that lead to a particular equation form be explicitly indicated, a restriction which is useful in ascertaining the range of applicability of a model as well as potential sources of error and opportunities to improve the analysis.

This two-volume work constitutes the edited proceedings of the Tenth International Conference on Computational Methods in Water Resources (formerly Finite Elements in Water Resources), held at Heidelberg University, Germany in July 1994, organized jointly by Interdisziplinäres Zentrum für Wissenschaftliches Rechnen (Interdisciplinary Center for Scientific Computing) and Sonderforschungsbereich 359 of Heidelberg University and the Institute of Supercomputing and Applied Mathematics of IBM Heidelberg. The 1994 proceedings present the work of authors from 23 countries. Numerical methods, mathematical modeling and applications to subsurface and surface hydrology are covered by a wide variety of papers. Issues of formation description and modeling, including parameter estimation, heterogeneity, and scaling up continue to attract the attention of a large number of researchers. Several papers edited in this book concern the solution of the Navier--Stokes equations. For applied mathematicians, engineers and geoscientists working in the fields of numerical methods, hydrology, ecology, water resources planning and management, remediation design, porous media research, petroleum engineering and coastal engineering.