This book explains the aspiring vision of a sustainable hydrogen generating system which employs nanotechnology one way or the other and presents a detailed update on research activities, achievements and challenges. It explores how nanotechnology is reshaping science in general and how this can be applied to the generation and storage of hydrogen energy. This book begins by highlighting the importance of hydrogen a source of sustainable energy and its impact on the technical advances of fuel cells, internal combustion engines, batteries and power plants. The book depicts the role of nanotechnology in the development of sustainable hydrogen. Comprehensive studies on various nanotechnologies involved in hydrogen generation are discussed in separate chapters, representing a complete picture of hydrogen generation utilizing nanotechnology. This book serves as a useful research tool for academics and practitioners looking towards new ways to develop and consume energy, without conceding our environment. Providing the advantages and disadvantages of each technology discussed, this book shows the benefits of utilizing nanotechnology in this field.

This edited volume presents research results of the PPP European Green Vehicle Initiative (EGVI), focusing on electric vehicle batteries. Electrification is one road towards sustainable road transportation, and battery technology is one of the key enabling technologies. However, at the same time, battery technology is one of the main obstacles for a broad commercial launch of electric vehicles. This book includes research contributions which try to bridge the gap between research and innovation in the field of battery technology for electric vehicles. The target audience primarily comprises researchers and experts in the field.

This book details state-of-the-art fuel cell systems incorporating methanol reformers as the source of purified hydrogen (rather than compressed hydrogen). Beginning with an overview of PEM fuel cells, the book discusses the various technical approaches to methanol reforming and hydrogen purification. A unique theme carried throughout the discussion is the practical aspects of commercial applications that favor one technical approach over another. The reader gains an understanding of the chemistry, engineering, economics, and agency certification requirements that ultimately shape the optimal approach for methanol fuel cell systems targeting commercial applications.

PEM Fuel Cell Diagnostic Tools presents various tools for diagnosing PEM fuel cells and stacks, including in situ and ex situ diagnostic tools, electrochemical techniques, and physical/chemical methods. The text outlines the principles, experimental implementation, data processing, and application of each technique, along with its capabilities and weaknesses. The book covers many diagnostics employed in the characterization and determination of fuel cell performance. It discusses commonly used conventional tools, such as cyclic voltammetry, electrochemical impedance spectroscopy, scanning electron microscopy, and transmission electron microscopy. It also examines special tools developed specifically for PEM fuel cells, including transparent cells, cathode discharge, and current mapping, as well as recent advanced tools for diagnosis, such as magnetic resonance imaging and atomic force microscopy. For clarity, the book splits these diagnostic methodologies into two parts-in situ and ex situ. To better understand the tools, PEM fuel cell testing is also discussed. Each self-contained chapter provides cross-references to other chapters. Written by international scientists active in PEM fuel cell research, this volume incorporates state-of-the-art technical advances in PEM fuel cell diagnosis. The diagnostic tools presented help readers to understand the physical and chemical phenomena involved in PEM fuel cells.

Next-Generation Batteries with Sulfur Cathodes provides a comprehensive review of a modern class of batteries with sulfur cathodes, particularly lithium-sulfur cathodes. The book covers recent trends, advantages and disadvantages in Li-S, Na-S, Al-S and Mg-S batteries and why these batteries are very promising for applications in hybrid and electric vehicles. Battery materials and modelling are also dealt with, as is their design, the physical phenomena existing in batteries, and a comparison of batteries between commonly used lithium-ion batteries and the new class of batteries with sulfur cathodes that are useful for devices like vehicles, wind power aggregates, computers and measurement units.

A top-down approach that enables readers to master and apply core principles Using an innovative top-down approach, this text makes it possible for readers to master and apply the principles of contemporary power electronics and electromechanic power conversion, exploring both systems and individual components. First, the text introduces the role and system context of power conversion functions. Then the authors examine the building blocks of power conversion systems, describing how the components exchange power. Lastly, readers learn the principles of static and electromechanic power conversion. The Principles of Electronic and Electromechanic Power Conversion opens with a chapter that introduces core concepts in electrical systems and power conversion, followed by a chapter dedicated to electrical power sources and energy storage. Next, the book covers: * Power, reactive power, and power factor * Magnetically coupled networks * Dynamics of rotational systems * Power electronic converters * DC machines * AC machines The text offers readers a concise treatise on the basic concepts of magnetic circuits. Its simple approach to machines makes the principles of field-oriented control and space vector theory highly accessible. In order to help readers fully grasp power electronics, the authors focus on topologies that use a series transistor and diode combination connected to a DC source, a standard building block of today s power conversion systems. Problem sets at the end of each chapter enable readers to fully master each topic as they progress through the text. In summary, The Principles of Electronic and Electromechanic Power Conversion provides the most up-to-date, relevant tools needed by today s power engineers, making it an ideal undergraduate textbook as well as a self-study guide for practicing engineers.

Ten years ago, D.M. Rowe introduced the bestselling CRC Handbook of Thermoelectrics to wide acclaim. Since then, increasing environmental concerns, desire for long-life electrical power sources, and continued progress in miniaturization of electronics has led to a substantial increase in research activity involving thermoelectrics. Reflecting the latest trends and developments, the Thermoelectrics Handbook: Macro to Nano is an extension of the earlier work and covers the entire range of thermoelectrics disciplines. Serving as a convenient reference as well as a thorough introduction to thermoelectrics, this book includes contributions from 99 leading authorities from around the world. Its coverage spans from general principles and theoretical concepts to material preparation and measurements; thermoelectric materials; thermoelements, modules, and devices; and thermoelectric systems and applications. Reflecting the enormous impact of nanotechnology on the field-as the thermoelectric properties of nanostructured materials far surpass the performance of conventional materials-each section progresses systematically from macro-scale to micro/nano-scale topics. In addition, the book contains an appendix listing major manufacturers and suppliers of thermoelectric modules. There is no longer any need to spend hours plodding through the journal literature for information. The Thermoelectrics Handbook: Macro to Nano offers a timely, comprehensive treatment of all areas of thermoelectrics in a single, unified reference.

Designing with Solar Power is the result of international collaborative research and development work carried out within the framework of the International Energy Agency's Photovoltaic Power Systems Programme (PVPS) and performed within its Task 7 on 'Photovoltaic power systems in the built environment'. Each chapter of this precisely detailed and informative book has been prepared by an international expert in a specific area related to the development, use and application of building-integrated photovoltaics (BiPV). Chapters not only cover the basics of solar power and electrical concepts, but also investigate the ways in which photovoltaics can be integrated into the design and creation of buildings equipped for the demands of the 21st century. The potential for BiPV, in both buildings and other structures, is explored together with broader issues such as market deployment, and international marketing and government strategies. In addition, more than 20 contemporary international case studies describe in detail how building-integrated photovoltaics have been applied to new and existing buildings, and discuss the architectural and technical quality, and the success of various strategies. Packed with photographs and illustrations, this book is an invaluable companion for architects, builders, designers, engineers, students and all involved with the exciting possibilities of building-integrated photovoltaics.

The first comprehensive book on thin-film solar cells, potentially a key technology for solving the energy production problem in the 21st century in an environmentally friendly way. It covers a wide range of scientific and technological aspects of thin film semiconductors - deposition technologies, growth mechanisms and the basic properties of amorphous and nano-crystalline silicon - as well as the optimum design theory and device physics of high-efficiency solar cells, especially of single-junction and multi-junction solar cells. The development of large-area solar cell modules using single and multi-junction solar cells is also considered. Examples of recent photovoltaic systems are presented and analysed.

The why, what and how of the electric vehicle powertrain Empowers engineering professionals and students with the knowledge and skills required to engineer electric vehicle powertrain architectures, energy storage systems, power electronics converters and electric drives. The modern electric powertrain is relatively new for the automotive industry, and engineers are challenged with designing affordable, efficient and high-performance electric powertrains as the industry undergoes a technological evolution. Co-authored by two electric vehicle (EV) engineers with decades of experience designing and putting into production all of the powertrain technologies presented, this book provides readers with the hands-on knowledge, skills and expertise they need to rise to that challenge. This four-part practical guide provides a comprehensive review of battery, hybrid and fuel cell EV systems and the associated energy sources, power electronics, machines, and drives. The first part of the book begins with a historical overview of electromobility and the related environmental impacts motivating the development of the electric powertrain. Vehicular requirements for electromechanical propulsion are then presented. Battery electric vehicles (BEV), fuel cell electric vehicles (FCEV), and conventional and hybrid electric vehicles (HEV) are then described, contrasted and compared for vehicle propulsion. The second part of the book features in-depth analysis of the electric powertrain traction machines, with a particular focus on the induction machine and the surface- and interior-permanent magnet ac machines. The brushed dc machine is also considered due to its ease of operation and understanding, and its historical place, especially as the traction machine on NASA's Mars rovers. The third part of the book features the theory and applications for the propulsion, charging, accessory, and auxiliary power electronics converters. Chapters are presented on isolated and non-isolated dc-dc converters, traction inverters, and battery charging. The fourth part presents the introductory and applied electromagnetism required as a foundation throughout the book. - Introduces and holistically integrates the key EV powertrain technologies. - Provides a comprehensive overview of existing and emerging automotive solutions. - Provides experience-based expertise for vehicular and powertrain system and sub-system level study, design, and optimization. - Presents many examples of powertrain technologies from leading manufacturers. - Discusses the dc traction machines of the Mars rovers, the ultimate EVs from NASA. - Investigates the environmental motivating factors and impacts of electromobility. - Presents a structured university teaching stream from introductory undergraduate to postgraduate. - Includes real-world problems and assignments of use to design engineers, researchers, and students alike. - Features a companion website with numerous references, problems, solutions, and practical assignments. - Includes introductory material throughout the book for the general scientific reader. - Contains essential reading for government regulators and policy makers. Electric Powertrain: Energy Systems, Power Electronics and Drives for Hybrid, Electric and Fuel Cell Vehicles is an important professional resource for practitioners and researchers in the battery, hybrid, and fuel cell EV transportation industry. The book is a structured holistic textbook for the teaching of the fundamental theories and applications of energy sources, power electronics, and electric machines and drives to engineering undergraduate and postgraduate students. Textbook Structure and Suggested Teaching Curriculum This is primarily an engineering textbook covering the automotive powertrain, energy storage and energy conversion, power electronics, and electrical machines. A significant additional focus is placed on the engineering design, the energy for transportation, and the related environmental impacts. This textbook is an educational tool for practicing engineers and others, such as transportation policy planners and regulators. The modern automobile is used as the vehicle upon which to base the theory and applications, which makes the book a useful educational reference for our industry colleagues, from chemists to engineers. This material is also written to be of interest to the general reader, who may have little or no interest in the power electronics and machines. Introductory science, mathematics, and an inquiring mind suffice for some chapters. The general reader can read the introduction to each of the chapters and move to the next as soon as the material gets too advanced for him or her. Part I Vehicles and Energy Sources Chapter 1 Electromobility and the Environment Chapter 2 Vehicle Dynamics Chapter 3 Batteries Chapter 4 Fuel Cells Chapter 5 Conventional and Hybrid Powertrains Part II Electrical Machines Chapter 6 Introduction to Traction Machines Chapter 7 The Brushed DC Machine Chapter 8 Induction Machines Chapter 9 Surface-permanent-magnet AC Machines Chapter 10: Interior-permanent-magnet AC Machines Part III Power Electronics Chapter 11 DC-DC Converters Chapter 12 Isolated DC-DC Converters Chapter 13 Traction Drives and Three-phase Inverters Chapter 14 Battery Charging Chapter 15 Control of the Electric Drive Part IV Basics Chapter 16 Introduction to Electromagnetism, Ferromagnetism, and Electromechanical Energy Conversion The first third of the book (Chapters 1 to 6), plus parts of Chapters 14 and 16, can be taught to the general science or engineering student in the second or third year. It covers the introductory automotive material using basic concepts from mechanical, electrical, environmental, and electrochemical engineering. Chapter 14 on electrical charging and Chapter 16 on electromagnetism can also be used as a general introduction to electrical engineering. The basics of electromagnetism, ferromagnetism and electromechanical energy conversion (Chapter 16) and dc machines (Chapter 7) can be taught to second year (sophomore) engineering students who have completed introductory electrical circuits and physics. The third year (junior) students typically have covered ac circuit analysis, and so they can cover ac machines, such as the induction machine (Chapter 8) and the surface permanent-magnet ac machine (Chapter 9). As the students typically have studied control theory, they can investigate the control of the speed and torque loops of the motor drive (Chapter 15). Power electronics, featuring non-isolated buck and boost converters (Chapter 11), can also be introduced in the third year. The final-year (senior) students can then go on to cover the more advanced technologies of the interior-permanent-magnet ac machine (Chapter 10). Isolated power converters (Chapter 12), such as the full-bridge and resonant converters, inverters (Chapter 13), and power-factor-corrected battery chargers (Chapter 14), are covered in the power electronics section. This material can also be covered at the introductory postgraduate level. Various homework, simulation, and research exercises are presented throughout the textbook. The reader is encouraged to attempt these exercises as part of the learning experience. Instructors are encouraged to contact the author, John Hayes, direct to discuss course content or structure.

This book covers a significant number of R&D projects, performed mostly after 2000, devoted to the understanding and prevention of performance degradation processes in polymer electrolyte fuel cells (PEFCs). The extent and severity of performance degradation processes in PEFCs were recognized rather gradually. Indeed, the recognition overlapped with a significant number of industrial dem- strations of fuel cell powered vehicles, which would suggest a degree of technology maturity beyond the resaolution of fundamental failure mechanisms. An intriguing question, therefore, is why has there been this apparent delay in addressing fun- mental performance stability requirements. The apparent answer is that testing of the power system under fully realistic operation conditions was one prerequisite for revealing the nature and extent of some key modes of PEFC stack failure. Such modes of failure were not exposed to a similar degree, or not at all, in earlier tests of PEFC stacks which were not performed under fully relevant conditions, parti- larly such tests which did not include multiple on-off and/or high power-low power cycles typical for transportation and mobile power applications of PEFCs. Long-term testing of PEFCs reported in the early 1990s by both Los Alamos National Laboratory and Ballard Power was performed under conditions of c- stant cell voltage, typically near the maximum power point of the PEFC.

Including chemical, synthetic, and cross-disciplinary approaches; this book includes the necessary techniques and technologies to help readers better understand polymers for polymer electrolyte membrane (PEM) fuel cells. The methods in the book are essential to researchers and scientists in the field and will lead to further development in polymer and fuel cell technologies.- Provides complete, essential, and comprehensive overview of polymer applications for PEM fuel cells- Emphasizes state-of-the-art developments and methods, like PEMs for novel fuel cells and polymers for fuel cell catalysts- Includes detailed chapters on major topics, like PEM for direct liquid fuel cells and fluoropolymers and non-fluorinated polymers for PEM- Has relevance to a range of industries - like polymer engineering, materials, and green technology - involved with fuel cell technologies and R&D

'Comprehensive and authoritative.' - RIBA Journal

'An invaluable primer for any architect or client considering integrated photovoltaics.' - Architecture Today

'This book is a concise and useful guide to building-integrated photovoltaics.' - Architectural Review

'It is tempting to suggest that a copy of this excellent book should be sent to George W Bush!' - Building Engineer

This book analyzes the economic and technical effects of demand response programs in smart grids. A variety of operational and financial benefits are offered by demand response programs (DRPs) for load-serving entities, grid operators, and electricity consumers. The most notable advantages of DRPs are presented in this book, including decreased electricity prices, risk management, market power mitigation, and flexibility of market operations. In-depth chapters discuss the integration of demand response programs for the planning and operation of smart grids and explore the uncertainties of market prices, renewable resources and intermittent load management, making this a useful reference for a variety of different organizations and players in the electricity market, such as reliability organizations, distribution companies, transmission companies, and electric end-users.

"…warmly recommended as a comprehensive, introductory text on a subject which should become increasingly important." (Review of the First Edition in Contemporary Physics) The rapid evolution of photovoltaic technology has highlighted the increasing capabilities of solar electricity as a power source for distributed energy generation. Building on the success of the first edition, Solar Electricity presents a balanced introduction to all aspects of solar energy conversion, from cell types to environmental impact and applications. Now fully revised to incorporate the latest industry achievements and featuring: New sections on the role of dye sensitised solar cells, photovoltaics in buildings, diesel hybrid systems, and photovoltaic markets and funding. Solar cell design and manufacturing technology including crystalline silicon and thin film devices. Introduction to a range of photovoltaic applications including rural electrification, grid connection issues, and the supply of electrical power to satellites in space. Illustrative case studies and self-assessment questions and answers at the end of each chapter. Undergraduate and postgraduate science and engineering students, practising mechanical and power engineers and those with a general interest in renewable energy will find this comprehensive text on invaluable reference. Solar Electricity, Second Edition forms part of the Energy Engineering Learning Package. Organised by UNESCO, this distance learning package has been established to train engineers to meet the challengs of today and tomorrow in this exciting field of energy engineering. It has been developed by an international team of distinguished academics, coordinated by Dr Boris Berkovski. This modular course will appeal to advanced undergraduates and post graduate students, as well as practising power engineers in industry. World Solar Summit Process Visit Our Web Page! http://www.wiley.com/

The book is a comprehensive view of all electromembrane processes, including electromembrane processes for energy conversion - a currently very significant problem. The necessary theory and basic information needed for understanding the technology are explained in Part I. Materials used for ion-selective membranes and seoaration processes are described in Part II, and the applications for synthesis and energy conversion in Part III.

High-temperature Solid Oxide Fuel Cells, Second Edition, explores the growing interest in fuel cells as a sustainable source of energy. The text brings the topic of green energy front and center, illustrating the need for new books that provide comprehensive and practical information on specific types of fuel cells and their applications. This landmark volume on solid oxide fuel cells contains contributions from experts of international repute, and provides a single source of the latest knowledge on this topic.

This book provides the short history, current state, main problems and historical perspective for the development of electrical power engineering. The focus of the textbook is on the two most important issues related to meeting of the growing needs of humanity in electricity: "Hunger for energy" and "Ecological infarct". In the book are discussed the methods of their solution: optimization of energy balance, use of renewable energy resources, new methods of electricity production, increase of the efficiency of production, accumulation, transmission, distribution and consumption electricity. The third issue - social and geopolitical threats due to the increasing need for energy - in the textbook is not considered inasmuch it details in non-stop regime discussed in the mass media. Choosing the structure and content of the textbook is based on the ten years of the author experience of giving lectures to Tomsk Polytechnic University students who study according to the program Electric Power Engineering. This textbook is addresed to students, masters and post-graduates. It can be interesting for everyone who is thinking about the future of our civilization, in general, and meeting of human needs in electric power, in particular.

Energy Storage for Sustainable Microgrid addresses the issues related to modelling, operation and control, steady-state and dynamic analysis of microgrids with ESS. This book discusses major electricity storage technologies in depth along with their efficiency, lifetime cycles, environmental benefits and capacity, so that readers can envisage which type of storage technology is best for a particular microgrid application. This book offers solutions to numerous difficulties such as choosing the right ESS for the particular microgrid application, proper sizing of ESS for microgrid, as well as design of ESS control systems for proper interfacing with the microgrid.

The Handbook of Lithium-Ion Battery Pack Design: Chemistry, Components, Types and Terminology offers to the reader a clear and concise explanation of how Li-ion batteries are designed from the perspective of a manager, sales person, product manager or entry level engineer who is not already an expert in Li-ion battery design. It will offer a layman's explanation of the history of vehicle electrification, what the various terminology means, and how to do some simple calculations that can be used in determining basic battery sizing, capacity, voltage and energy. By the end of this book the reader has a solid understanding of all of the terminology around Li-ion batteries and is able to do some simple battery calculations. The book is immensely useful to beginning and experienced engineer alike who are moving into the battery field. Li-ion batteries are one of the most unique systems in automobiles today in that they combine multiple engineering disciplines, yet most engineering programs focus on only a single engineering field. This book provides you with a reference to the history, terminology and design criteria needed to understand the Li-ion battery and to successfully lay out a new battery concept. Whether you are an electrical engineer, a mechanical engineer or a chemist this book helps you better appreciate the inter-relationships between the various battery engineering fields that are required to understand the battery as an Energy Storage System.

Advances in Battery Technologies for Electric Vehicles provides an in-depth look into the research being conducted on the development of more efficient batteries capable of long distance travel. The text contains an introductory section on the market for battery and hybrid electric vehicles, then thoroughly presents the latest on lithium-ion battery technology. Readers will find sections on battery pack design and management, a discussion of the infrastructure required for the creation of a battery powered transport network, and coverage of the issues involved with end-of-life management for these types of batteries.

Conducting polymers are organic polymers which contain conjugation along the polymer backbone that conduct electricity. Conducting polymers are promising materials for energy storage applications because of their fast charge-discharge kinetics, high charge density, fast redox reaction, low-cost, ease of synthesis, tunable morphology, high power capability and excellent intrinsic conductivity compared with inorganic-based materials. Conducting Polymers-Based Energy Storage Materials surveys recent advances in conducting polymers and their composites addressing the execution of these materials as electrodes in electrochemical power sources. Key Features: Provides an overview on the conducting polymer material properties, fundamentals and their role in energy storage applications. Deliberates cutting-edge energy storage technology based on synthetic metals (conducting polymers) Covers current applications in next-generation energy storage devices. Explores the new aspects of conducting polymers with processing, tunable properties, nanostructures and engineering strategies of conducting polymers for energy storage. Presents up-to-date coverage of a large, rapidly growing and complex conducting polymer literature on all-types electrochemical power sources. This book is an invaluable guide for students, professors, scientists, and R&D industrial specialists working in the field of advanced science, nanodevices, flexible electronics, and energy science.

This book is unique to be the only one completely dedicated for battery modeling for all components of battery management system (BMS) applications. The contents of this book compliment the multitude of research publications in this domain by providing coherent fundamentals. An explosive market of Li ion batteries has led to aggressive demand for mathematical models for battery management systems (BMS). Researchers from multi-various backgrounds contribute from their respective background, leading to a lateral growth. Risk of this runaway situation is that researchers tend to use an existing method or algorithm without in depth knowledge of the cohesive fundamentals-often misinterpreting the outcome. It is worthy to note that the guiding principles are similar and the lack of clarity impedes a significant advancement. A repeat or even a synopsis of all the applications of battery modeling albeit redundant, would hence be a mammoth task, and cannot be done in a single offering. The authors believe that a pivotal contribution can be made by explaining the fundamentals in a coherent manner. Such an offering would enable researchers from multiple domains appreciate the bedrock principles and forward the frontier. Battery is an electrochemical system, and any level of understanding cannot ellipse this premise. The common thread that needs to run across-from detailed electrochemical models to algorithms used for real time estimation on a microchip-is that it be physics based. Build on this theme, this book has three parts. Each part starts with developing a framework-often invoking basic principles of thermodynamics or transport phenomena-and ends with certain verified real time applications. The first part deals with electrochemical modeling and the second with model order reduction. Objective of a BMS is estimation of state and health, and the third part is dedicated for that. Rules for state observers are derived from a generic Bayesian framework, and health estimation is pursued using machine learning (ML) tools. A distinct component of this book is thorough derivations of the learning rules for the novel ML algorithms. Given the large-scale application of ML in various domains, this segment can be relevant to researchers outside BMS domain as well. The authors hope this offering would satisfy a practicing engineer with a basic perspective, and a budding researcher with essential tools on a comprehensive understanding of BMS models.

Carbon dioxide (CO2) capture and storage (CCS) is the one advanced technology that conventional power generation cannot do without. CCS technology reduces the carbon footprint of power plants by capturing and storing the CO2 emissions from burning fossil-fuels and biomass. Volume one provides a comprehensive reference on the state of the art research, development and demonstration of carbon capture technology in the power sector and in industry. It critically reviews the range of post- and pre-combustion capture and combustion-based capture processes and technology applicable to fossil-fuel power plants, as well as applications of CCS in other high carbon footprint industries.
Volume two provides a comprehensive reference on the state of the art research, development and demonstration of carbon storage and utilisation, covering all the storage options and their environmental impacts. It critically reviews geological, terrestrial and ocean sequestration, including enhanced oil and gas recovery, as well as other advanced concepts such as industrial utilisation, mineral carbonation, biofixation and photocatalytic reduction.
Foreword written by Lord Oxburgh, Climate Science PeerReviews the economics, regulation and planning of carbon capture and storage for power plants and industryComprehensively examines the different methods of storage of carbon dioxide (CO2) and the various concepts for utilisation

Applications oriented, it contains all the pertinent and comprehensive information necessary to meet the growing demands placed upon solid-state power conversion equipment. These demands include improved reliability, increased efficiency, higher packing density, improved performance plus meeting safety and EMC regulations. Features a thorough assessment of basic electrical and magnetic aspects of power conversion as well as thermal, protection, radiation and reliability considerations. Stresses semiconductor and magnetic components and gives an analysis of diverse topologies.