Chaotic Dynamical Conceptual Model To Describe Fluid Flow And Contaminant Transport In A Fractured Vadose Zone 1998 Annual Progress Report

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Chaotic-dynamical Conceptual Model to Describe Fluid Flow and Contaminant Transport in a Fractured Vadose Zone. 1998 Annual Progress Report

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ISBN 13 :
Total Pages : 3 pages
Book Rating : 4.:/5 (683 download)

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Book Synopsis Chaotic-dynamical Conceptual Model to Describe Fluid Flow and Contaminant Transport in a Fractured Vadose Zone. 1998 Annual Progress Report by :

Download or read book Chaotic-dynamical Conceptual Model to Describe Fluid Flow and Contaminant Transport in a Fractured Vadose Zone. 1998 Annual Progress Report written by and published by . This book was released on 1998 with total page 3 pages. Available in PDF, EPUB and Kindle. Book excerpt: DOE faces the remediation of numerous contaminated sites, such as those at Hanford, INEEL, LLNL, and LBNL, where organic and/or radioactive wastes were intentionally or accidentally released to the vadose zone from surface spills, underground tanks, cribs, shallow ponds, and deep wells. Migration of these contaminants through the vadose zone has lead to the contamination of or threatens to contaminate underlying groundwater. A key issue in choosing a corrective action plan to clean up contaminated sites is to determine the location, total mass, mobility and travel time to receptors for contaminants moving in the vadose zone. These problems are difficult to solve in a technically defensible and accurate manner because contaminants travel downward intermittently through narrow pathways driven by variations in environmental conditions. These preferential pathways can be difficult to find and predict. The primary objective of this project is to determine if and when dynamical chaos theory can be used to investigate infiltration of fluid and contaminant transport in heterogeneous soils and fractured rocks. The objective of this project is being achieved through the following Activities (1) Evaluation of chaotic behavior of flow in laboratory and field experiments using methods from non-linear dynamics; (2) Evaluation of the impact these dynamics may have on contaminant transport through heterogeneous fractured rocks and soils, and how it can be used to guide remediation efforts; (3) Development of a conceptual model and mathematical and numerical algorithms for flow and transport, which incorporate both: (a) the spatial variability of heterogeneous porous and fractured media, and (b) the description of the temporal dynamics of flow and transport, which may be chaotic; and (4) Development of appropriate experimental field and laboratory techniques needed to detect diagnostic parameters for chaotic behavior of flow. This approach is based on the assumption that spatial heterogeneity and flow phenomena are affected by non-linear dynamics, and in particular, chaotic processes. The scientific and practical value of this approach is that the authors can predict the range within which the parameters of flow and transport change with time in order to design and manage the remediation, even when the authors can not predict the behavior at any point or time. This progress report summarizes work after 1.5 years of a 3-year project.

A Chaotic-dynamical Conceptual Model to Describe Fluid Flow and Contaminant Transport in a Fractured Vadose Zone. 1997 Annual Progress Report

Download A Chaotic-dynamical Conceptual Model to Describe Fluid Flow and Contaminant Transport in a Fractured Vadose Zone. 1997 Annual Progress Report PDF Online Free

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Total Pages : 16 pages
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Book Synopsis A Chaotic-dynamical Conceptual Model to Describe Fluid Flow and Contaminant Transport in a Fractured Vadose Zone. 1997 Annual Progress Report by :

Download or read book A Chaotic-dynamical Conceptual Model to Describe Fluid Flow and Contaminant Transport in a Fractured Vadose Zone. 1997 Annual Progress Report written by and published by . This book was released on 1997 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding subsurface flow and transport processes is critical for effective assessment, decision-making, and remediation activities for contaminated sites. However, for fluid flow and contaminant transport through fractured vadose zones, traditional hydrogeological approaches are often found to be inadequate. In this project, the authors examine flow and transport through a fractured vadose zone as a deterministic chaotic dynamical process, and develop a model of it in these terms. Initially, they examine separately the geometric model of fractured rock and the flow dynamics model needed to describe chaotic behavior. Ultimately they will put the geometry and flow dynamics together to develop a chaotic-dynamical model of flow and transport in a fractured vadose zone. They investigate water flow and contaminant transport on several scales, ranging from small-scale laboratory experiments in fracture replicas and fractured cores, to field experiments conducted in a single exposed fracture at a basalt outcrop, and finally to a ponded infiltration test using a pond of 7 by 8 m. In the field experiments, the authors measure the time-variation of water flux, moisture content, and hydraulic head at various locations, as well as the total inflow rate to the subsurface. Such variations reflect the changes in the geometry and physics of water flow that display chaotic behavior, which the authors try to reconstruct using the data obtained. In the analysis of experimental data, a chaotic model can be used to predict the long-term bounds on fluid flow and transport behavior, known as the attractor of the system, and to examine the limits of short-term predictability within these bounds. This approach is especially well suited to the need for short-term predictions to support remediation decisions and long-term bounding studies.

A Chaotic-Dynamical Conceptual Model to Describe Fluid Flow and Contaminant Transport in a Fractured Vadose Zone

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ISBN 13 :
Total Pages : 5 pages
Book Rating : 4.:/5 (684 download)

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Book Synopsis A Chaotic-Dynamical Conceptual Model to Describe Fluid Flow and Contaminant Transport in a Fractured Vadose Zone by :

Download or read book A Chaotic-Dynamical Conceptual Model to Describe Fluid Flow and Contaminant Transport in a Fractured Vadose Zone written by and published by . This book was released on 1999 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: (1) To determine if and when dynamical chaos theory can be used to investigate infiltration of fluid and contaminant transport in heterogeneous soils and fractured rocks. (2) To introduce a new approach to the multiscale characterization of flow and transport in fractured basalt vadose zones and to develop physically based conceptual models on a hierarchy of scales. The following activities are indicative of the success in meeting the project s objectives: A series of ponded infiltration tests, including (1) small-scale infiltration tests (ponded area 0.5 m2) conducted at the Hell s Half Acre site near Shelley, Idaho, and (2) intermediate-scale infiltration tests (ponded area 56 m2) conducted at the Box Canyon site near Arco, Idaho. Laboratory investigations and modeling of flow in a fractured basalt core. A series of small-scale dripping experiments in fracture models. Evaluation of chaotic behavior of flow in laboratory and field experiments using methods from nonlinear dynamics; Evaluation of the impact these dynamics may have on contaminant transport through heterogeneous fractured rocks and soils, and how it can be used to guide remediation efforts; Development of a conceptual model and mathematical and numerical algorithms for flow and transport that incorporate (1) the spatial variability of heterogeneous porous and fractured media, and (2) the description of the temporal dynamics of flow and transport, both of which may be chaotic. Development of appropriate experimental field and laboratory techniques needed to detect diagnostic parameters for chaotic behavior of flow. This approach is based on the assumption that spatial heterogeneity and flow phenomena are affected by nonlinear dynamics, and in particular, by chaotic processes. The scientific and practical value of this approach is that we can predict the range within which the parameters of flow and transport change with time in order to design and manage the remediation, even when we can not predict the behavior at any point or time.

Chaotic-Dynamical Conceptual Model to Describe Fluid Flow and Contaminant Transport in a Fractured Vadose Zone

Author :
Publisher :
ISBN 13 :
Total Pages : 5 pages
Book Rating : 4.:/5 (684 download)

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Book Synopsis Chaotic-Dynamical Conceptual Model to Describe Fluid Flow and Contaminant Transport in a Fractured Vadose Zone by :

Download or read book Chaotic-Dynamical Conceptual Model to Describe Fluid Flow and Contaminant Transport in a Fractured Vadose Zone written by and published by . This book was released on 1999 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: DOE faces the remediation of numerous contaminated sites, such as those at Hanford, INEEL, LLNL, and LBNL, where organic and/or radioactive wastes were intentionally or accidentally released to the vadose zone from surface spills, underground tanks, cribs, shallow ponds, and deep wells. Migration of these contaminants through the vadose zone has led to the contamination of (or threatens to contaminate) underlying groundwater. A key issue in choosing a corrective action plan to clean up contaminated sites is the determination of the location, total mass, mobility and travel time to receptors for contaminants moving in the vadose zone. These problems are difficult to solve in a technically defensible and accurate manner because contaminants travel downward intermittently, through narrow pathways, driven by variations in environmental conditions. These preferential flow pathways can be difficult to find and predict. The primary objective of this project is to determine if and when dynamical chaos theory can be used to investigate infiltration of fluid and contaminant transport in heterogeneous soils and fractured rocks. The objective of this project is being achieved through the following activities: Development of multi scale conceptual models and mathematical and numerical algorithms for flow and transport, which incorporate both (a) the spatial variability of heterogeneous porous and fractured media and (b) the temporal dynamics of flow and transport; Development of appropriate experimental field and laboratory techniques needed to detect diagnostic parameters for chaotic behavior of flow; Evaluation of chaotic behavior of flow in laboratory and field experiments using methods from non-linear dynamics; Evaluation of the impact these dynamics may have on contaminant transport through heterogeneous fractured rocks and soils and remediation efforts. This approach is based on the consideration of multi scale spatial heterogeneity and flow phenomena that are affected by nonlinear dynamics, and in particular, chaotic processes. The scientific and practical value of this approach is that we can predict the range within, which the parameters of flow and transport change with time, which allows us to design and manage the remediation even when we cannot predict the behavior at any point or time.

Conceptual Models of Flow and Transport in the Fractured Vadose Zone

Author : National Research Council
Publisher : National Academies Press
ISBN 13 : 0309170990
Total Pages : 398 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Conceptual Models of Flow and Transport in the Fractured Vadose Zone by : National Research Council

Download or read book Conceptual Models of Flow and Transport in the Fractured Vadose Zone written by National Research Council and published by National Academies Press. This book was released on 2001-05-21 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fluid flow and solute transport within the vadose zone, the unsaturated zone between the land surface and the water table, can be the cause of expanded plumes arising from localized contaminant sources. An understanding of vadose zone processes is, therefore, an essential prerequisite for cost-effective contaminant remediation efforts. In addition, because such features are potential avenues for rapid transport of chemicals from contamination sources to the water table, the presence of fractures and other channel-like openings in the vadose zone poses a particularly significant problem, Conceptual Models of Flow and Transport in the Fractured Vadose Zone is based on the work of a panel established under the auspices of the U.S. National Committee for Rock Mechanics. It emphasizes the importance of conceptual models and goes on to review the conceptual model development, testing, and refinement processes. The book examines fluid flow and transport mechanisms, noting the difficulty of modeling solute transport, and identifies geochemical and environmental tracer data as important components of the modeling process. Finally, the book recommends several areas for continued research.

Flow and Transport Through Unsaturated Fractured Rock

Author : Daniel D. Evans
Publisher : American Geophysical Union
ISBN 13 :
Total Pages : 212 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Flow and Transport Through Unsaturated Fractured Rock by : Daniel D. Evans

Download or read book Flow and Transport Through Unsaturated Fractured Rock written by Daniel D. Evans and published by American Geophysical Union. This book was released on 2001-01-09 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Published by the American Geophysical Union as part of the Geophysical Monograph Series, Volume 42. This monograph is an update and revision of the first edition, Geophysical Monograph 42, on ground-water flow and transport through unsaturated, fractured rock, published by AGU in 1987. The first edition evolved from a special symposium held during the American Geophysical Union fall meetings in San Francisco in December 1986. Invited and contributed papers at that AGU session, as well as panel presentations, focused on conceptualizing, measuring and modeling flow and transport through unsaturated fractured rock. As noted in the preface to the first edition, "the expanded interest in the topic (water flow and contaminant transport through unsaturated fractured rock) was initiated when the U.S. Geological Survey proposed that deep unsaturated zones in arid regions be considered in the site selection for the first high-level, commercially generated radioactive waste repository." Much of the research reported in that first edition was motivated by the U.S. Department of Energy's program to investigate Yucca Mountain at the Nevada Test Site as a possible geologic repository for commercially generated, high-level radioactive waste. As noted in the overview paper of the first edition, "characterization methods and modeling are in their developmental stage with the greatest lack of knowledge being the interaction between fracture and matrix flow and transport properties." Although the first edition of this monograph reflected the state-of-the science, laboratory and field experimental programs were novel and limited and, in general, followed from the principles and methods developed in the soil science community.

Conceptual Models of Flow and Transport in the Fractured Vadose Zone

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (16 download)

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Book Synopsis Conceptual Models of Flow and Transport in the Fractured Vadose Zone by :

Download or read book Conceptual Models of Flow and Transport in the Fractured Vadose Zone written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Chaotic Flows

Author : Oleg G. Bakunin
Publisher : Springer
ISBN 13 : 9783642203510
Total Pages : 354 pages
Book Rating : 4.2/5 (35 download)

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Book Synopsis Chaotic Flows by : Oleg G. Bakunin

Download or read book Chaotic Flows written by Oleg G. Bakunin and published by Springer. This book was released on 2011-09-10 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book introduces readers to and summarizes the current ideas and theories about the basic mechanisms for transport in chaotic flows. Typically no single paradigmatic approach exists as this topic is relevant for fields as diverse as plasma physics, geophysical flows and various branches of engineering. Accordingly, the dispersion of matter in chaotic or turbulent flows is analyzed from different perspectives. Partly based on lecture courses given by the author, this book addresses both graduate students and researchers in search of a high-level but approachable and broad introduction to the topic.

A Unifying Conceptual Model to Describe Water, Vapor, and Solute Transport in Deep and Vadose Zones

Author : Michelle A. Walvoord
Publisher :
ISBN 13 :
Total Pages : 594 pages
Book Rating : 4.:/5 (513 download)

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Book Synopsis A Unifying Conceptual Model to Describe Water, Vapor, and Solute Transport in Deep and Vadose Zones by : Michelle A. Walvoord

Download or read book A Unifying Conceptual Model to Describe Water, Vapor, and Solute Transport in Deep and Vadose Zones written by Michelle A. Walvoord and published by . This book was released on 2002 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The DEFUZE Code for Modeling Gaseous Diffusion of Volatile Contaminants in the Vadose Zone

Author :
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ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.:/5 (685 download)

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Book Synopsis The DEFUZE Code for Modeling Gaseous Diffusion of Volatile Contaminants in the Vadose Zone by :

Download or read book The DEFUZE Code for Modeling Gaseous Diffusion of Volatile Contaminants in the Vadose Zone written by and published by . This book was released on 1994 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: The DEFUSE computer model is a convenient and simple tool for calculating the subsurface gaseous diffusion of volatile contaminants in the vadose zone for the purposes of guiding vadose zone characterization and data collection efforts and for determining the need for site remediation. The reader is referred to Nitao (1990) for further details on the conceptual model for contaminant transport in the vadose zone and an application of DEFUZE to a site at the Lawrence Livermore National Laboratory.

Preferential Flow Dynamics in the Vadose Zone of Fractured and Fractured-porous Media: Development of a Parallelized Multi-scale Smoothed Particle Hydrodynamics Model

Download Preferential Flow Dynamics in the Vadose Zone of Fractured and Fractured-porous Media: Development of a Parallelized Multi-scale Smoothed Particle Hydrodynamics Model PDF Online Free

Author : Elena Shigorina
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (118 download)

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Book Synopsis Preferential Flow Dynamics in the Vadose Zone of Fractured and Fractured-porous Media: Development of a Parallelized Multi-scale Smoothed Particle Hydrodynamics Model by : Elena Shigorina

Download or read book Preferential Flow Dynamics in the Vadose Zone of Fractured and Fractured-porous Media: Development of a Parallelized Multi-scale Smoothed Particle Hydrodynamics Model written by Elena Shigorina and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this thesis is the development of a smoothed particle hydrodynamics (SPH) model to study preferential flow dynamics in partially saturated porous-fractured media at core- and micro scale. The research is focused on the numerical investigation of preferential flow in the vadose zone, including the estimation of geometrical and hydraulic properties of the subsurface, such as wettability, surface roughness, hydraulic conductivity, and infiltration rate, which are influencing the infiltration dynamics under saturated, unsaturated and partially saturated conditions. In the ...

CAPTURING UNCERTAINTY IN UNSATURATED-ZONE FLOW USING DIFFERENT CONCEPTUAL MODELS OF FRACTURE-MATRIX INTERACTION.

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (727 download)

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Book Synopsis CAPTURING UNCERTAINTY IN UNSATURATED-ZONE FLOW USING DIFFERENT CONCEPTUAL MODELS OF FRACTURE-MATRIX INTERACTION. by :

Download or read book CAPTURING UNCERTAINTY IN UNSATURATED-ZONE FLOW USING DIFFERENT CONCEPTUAL MODELS OF FRACTURE-MATRIX INTERACTION. written by and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Preliminary calculations show that the two different conceptual models of fracture-matrix interaction presented here yield different results pertinent to the performance of the potential repository at Yucca Mountain. Namely, each model produces different ranges of flow in the fractures, where radionuclide transport is thought to be most important. This method of using different flow models to capture both conceptual model and parameter uncertainty ensures that flow fields used in TSPA calculations will be reasonably calibrated to the available data while still capturing this uncertainty. This method also allows for the use of three-dimensional flow fields for the TSPA-VA calculations.

Simulating radionuclide fate and transport in the unsaturated zone evaluation and sensitivity analyses of select computer models

Author : Jin-Song Chen
Publisher : DIANE Publishing
ISBN 13 : 1428905421
Total Pages : 186 pages
Book Rating : 4.4/5 (289 download)

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Book Synopsis Simulating radionuclide fate and transport in the unsaturated zone evaluation and sensitivity analyses of select computer models by : Jin-Song Chen

Download or read book Simulating radionuclide fate and transport in the unsaturated zone evaluation and sensitivity analyses of select computer models written by Jin-Song Chen and published by DIANE Publishing. This book was released on 2002 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Gas Transport in Porous Media

Author : Clifford K. Ho
Publisher : Springer Science & Business Media
ISBN 13 : 140203962X
Total Pages : 442 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Gas Transport in Porous Media by : Clifford K. Ho

Download or read book Gas Transport in Porous Media written by Clifford K. Ho and published by Springer Science & Business Media. This book was released on 2006-10-07 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: CLIFFORD K. HOAND STEPHEN W. WEBB Sandia National Laboratories, P. O. Box 5800, Albuquerque, NM 87185, USA Gas and vapor transport in porous media occur in a number of important applications includingdryingofindustrialandfoodproducts,oilandgasexploration,environm- tal remediation of contaminated sites, and carbon sequestration. Understanding the fundamental mechanisms and processes of gas and vapor transport in porous media allows models to be used to evaluate and optimize the performance and design of these systems. In this book, gas and vapor are distinguished by their available states at stan- ? dard temperature and pressure (20 C, 101 kPa). If the gas-phase constituent can also exist as a liquid phase at standard temperature and pressure (e. g. , water, ethanol, toluene, trichlorothylene), it is considered a vapor. If the gas-phase constituent is non-condensable at standard temperature and pressure (e. g. , oxygen, carbon di- ide, helium, hydrogen, propane), it is considered a gas. The distinction is important because different processes affect the transport and behavior of gases and vapors in porous media. For example, mechanisms specific to vapors include vapor-pressure lowering and enhanced vapor diffusion, which are caused by the presence of a g- phase constituent interacting with its liquid phase in an unsaturated porous media. In addition, the “heat-pipe” exploits isothermal latent heat exchange during evaporation and condensation to effectively transfer heat in designed and natural systems.

FEFLOW

Author : Hans-Jörg G. Diersch
Publisher : Springer Science & Business Media
ISBN 13 : 364238739X
Total Pages : 1018 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis FEFLOW by : Hans-Jörg G. Diersch

Download or read book FEFLOW written by Hans-Jörg G. Diersch and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 1018 pages. Available in PDF, EPUB and Kindle. Book excerpt: FEFLOW is an acronym of Finite Element subsurface FLOW simulation system and solves the governing flow, mass and heat transport equations in porous and fractured media by a multidimensional finite element method for complex geometric and parametric situations including variable fluid density, variable saturation, free surface(s), multispecies reaction kinetics, non-isothermal flow and multidiffusive effects. FEFLOW comprises theoretical work, modeling experiences and simulation practice from a period of about 40 years. In this light, the main objective of the present book is to share this achieved level of modeling with all required details of the physical and numerical background with the reader. The book is intended to put advanced theoretical and numerical methods into the hands of modeling practitioners and scientists. It starts with a more general theory for all relevant flow and transport phenomena on the basis of the continuum approach, systematically develops the basic framework for important classes of problems (e.g., multiphase/multispecies non-isothermal flow and transport phenomena, discrete features, aquifer-averaged equations, geothermal processes), introduces finite-element techniques for solving the basic balance equations, in detail discusses advanced numerical algorithms for the resulting nonlinear and linear problems and completes with a number of benchmarks, applications and exercises to illustrate the different types of problems and ways to tackle them successfully (e.g., flow and seepage problems, unsaturated-saturated flow, advective-diffusion transport, saltwater intrusion, geothermal and thermohaline flow).

Fractured Porous Media

Author : Pierre M. Adler
Publisher : Oxford University Press, USA
ISBN 13 : 0199666512
Total Pages : 184 pages
Book Rating : 4.1/5 (996 download)

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Book Synopsis Fractured Porous Media by : Pierre M. Adler

Download or read book Fractured Porous Media written by Pierre M. Adler and published by Oxford University Press, USA. This book was released on 2013 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a systematic treatment of the geometrical and transport properties of fractures, fracture networks, and fractured porous media. It is divided into two major parts. The first part deals with geometry of individual fractures and of fracture networks. The use of the dimensionless density rationalizes the results for the percolation threshold of the networks. It presents the crucial advantage of grouping the numerical data for various fracture shapes. The second part deals mainly with permeability under steady conditions of fractures, fracture networks, and fractured porous media. Again the results for various types of networks can be rationalized by means of the dimensionless density. A chapter is dedicated to two phase flow in fractured porous media.

Percolation Theory for Flow in Porous Media

Author : Allen Hunt
Publisher : Springer Science & Business Media
ISBN 13 : 3540897895
Total Pages : 334 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Percolation Theory for Flow in Porous Media by : Allen Hunt

Download or read book Percolation Theory for Flow in Porous Media written by Allen Hunt and published by Springer Science & Business Media. This book was released on 2009-05-05 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why would we wish to start a 2nd edition of “Percolation theory for ?ow in porous media” only two years after the ?rst one was ?nished? There are essentially three reasons: 1) Reviews in the soil physics community have pointed out that the introductory material on percolation theory could have been more accessible. Our additional experience in teaching this material led us to believe that we could improve this aspect of the book. In the context of rewriting the ?rst chapter, however, we also expanded the discussion of Bethe lattices and their relevance for “classical” - ponents of percolation theory, thus giving more of a basis for the discussion of the relevance of hyperscaling. This addition, though it will not tend to make the book more accessible to hydrologists, was useful in making it a more complete reference, and these sections have been marked as being possible to omit in a ?rst reading. It also forced a division of the ?rst chapter into two. We hope that physicists without a background in percolation theory will now also ?nd the - troductory material somewhat more satisfactory. 2) We have done considerable further work on problems of electrical conductivity, thermal conductivity, and electromechanical coupling.