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A Meshless Regularization Method for a Two-Dimensional Two-Phase Linear Inverse Stefan Problem
- B. Tomas Johansson, Daniel Lesnic, Thomas Reeve
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- Journal:
- Advances in Applied Mathematics and Mechanics / Volume 5 / Issue 6 / December 2013
- Published online by Cambridge University Press:
- 03 June 2015, pp. 825-845
- Print publication:
- December 2013
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In this paper, a meshless regularization method of fundamental solutions is proposed for a two-dimensional, two-phase linear inverse Stefan problem. The numerical implementation and analysis are challenging since one needs to handle composite materials in higher dimensions. Furthermore, the inverse Stefan problem is ill-posed since small errors in the input data cause large errors in the desired output solution. Therefore, regularization is necessary in order to obtain a stable solution. Numerical results for several benchmark test examples are presented and discussed.
Summary for Policy Makers
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- By Thomas B. Johansson, Lund University, Nebojsa Nakicenovic, International Institute for Applied Systems Analysis and Vienna University of Technology, Anand Patwardhan, Indian Institute of Technology-Bombay), Luis Gomez-Echeverri, International Institute for Applied Systems Analysis, Rangan Banerjee, Indian Institute of Technology, Sally M. Benson, Stanford University, Daniel H. Bouille, Bariloche Foundation, Abeeku Brew-Hammond, Kwame Nkrumah University of Science and Technology, Aleh Cherp, Central European University, Suani T. Coelho, National Reference Center on Biomass, University of São Paulo, Lisa Emberson, Stockholm Environment Institute, University of York, Maria Josefina Figueroa, Technical University, Arnulf Grubler, International Institute for Applied Systems Analysis, Austria and Yale University, Kebin He, Tsinghua University, Mark Jaccard, Simon Fraser University, Suzana Kahn Ribeiro, Federal University of Rio de Janeiro, Stephen Karekezi, AFREPREN/FWD, Eric D. Larson, Princeton University and Climate Central, Zheng Li, Tsinghua University, Susan McDade, United Nations Development Programme), Lynn K. Mytelka, United Nations University-MERIT, Shonali Pachauri, International Institute for Applied Systems Analysis, Keywan Riahi, International Institute for Applied Systems Analysis, Johan Rockström, Stockholm Environment Institute, Stockholm University, Hans-Holger Rogner, International Atomic Energy Agency, Joyashree Roy, Jadavpur University, Robert N. Schock, World Energy Council, UK and Center for Global Security Research, Ralph Sims, Massey University, Kirk R. Smith, University of California, Wim C. Turkenburg, Utrecht University, Diana Ürge-Vorsatz, Central European University, Frank von Hippel, Princeton University, Kurt Yeager, Electric Power Research Institute and Galvin Electricity Initiative
- Global Energy Assessment Writing Team
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- Book:
- Global Energy Assessment
- Published online:
- 05 September 2012
- Print publication:
- 27 August 2012, pp 3-30
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Summary
Introduction
Energy is essential for human development and energy systems are a crucial entry point for addressing the most pressing global challenges of the 21st century, including sustainable economic and social development, poverty eradication, adequate food production and food security, health for all, climate protection, conservation of ecosystems, peace and security. Yet, more than a decade into the 21st century, current energy systems do not meet these challenges.
A major transformation is therefore required to address these challenges and to avoid potentially catastrophic future consequences for human and planetary systems. The Global Energy Assessment (GEA) demonstrates that energy system change is the key for addressing and resolving these challenges. The GEA identifies strategies that could help resolve the multiple challenges simultaneously and bring multiple benefits. Their successful implementation requires determined, sustained and immediate action.
Transformative change in the energy system may not be internally generated; due to institutional inertia, incumbency and lack of capacity and agility of existing organizations to respond effectively to changing conditions. In such situations clear and consistent external policy signals may be required to initiate and sustain the transformative change needed to meet the sustainability challenges of the 21st century.
The industrial revolution catapulted humanity onto an explosive development path, whereby, reliance on muscle power and traditional biomass was replaced mostly by fossil fuels. In 2005, some 78% of global energy was based on fossil energy sources that provided abundant and ever cheaper energy services to more than half the people in the world.
Chapter 1 - Energy Primer
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- By Arnulf Grubler, International Institute for Applied Systems Analysis, Austria and Yale University, Thomas B. Johansson, Lund University, Luis Mundaca, Lund University, Nebojsa Nakicenovic, International Institute for Applied Systems Analysis and Vienna University of Technology, Shonali Pachauri, International Institute for Applied Systems Analysis, Keywan Riahi, International Institute for Applied Systems Analysis, Hans-Holger Rogner, International Atomic Energy Agency, Lars Strupeit, Lund University, Peter Kolp, International Institute for Applied Systems Analysis, Volker Krey, International Institute for Applied Systems Analysis, Jordan Macknick, National Renewable Energy Laboratory, Yu Nagai, Vienna University of Technology, Mathis L. Rogner, International Institute for Applied Systems Analysis, Kirk R. Smith, University of California, Kjartan Steen-Olsen, Norwegian University of Science and Technology, Jan Weinzettel, Norwegian University of Science and Technology), Ogunlade Davidson, Ministry of Energy and Water Resources
- Global Energy Assessment Writing Team
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- Book:
- Global Energy Assessment
- Published online:
- 05 September 2012
- Print publication:
- 27 August 2012, pp 99-150
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Summary
Introduction and Roadmap
Life is but a continuous process of energy conversion and transformation. The accomplishments of civilization have largely been achieved through the increasingly efficient and extensive harnessing of various forms of energy to extend human capabilities and ingenuity. Energy is similarly indispensable for continued human development and economic growth. Providing adequate, affordable energy is a necessary (even if by itself insufficient) prerequisite for eradicating poverty, improving human welfare, and raising living standards worldwide. Without economic growth, it will also be difficult to address social and environmental challenges, especially those associated with poverty. Without continued institutional, social, and technological innovation, it will be impossible to address planetary challenges such as climate change. Energy extraction, conversion, and use always generate undesirable by-products and emissions – at a minimum in the form of dissipated heat. Energy cannot be created or destroyed – it can only be converted from one form to another, along a one-way street from higher to lower grades (qualities) of energy. Although it is common to discuss energy “consumption,” energy is actually transformed rather than consumed.
This Energy Primer 1 aims at a basic-level introduction to fundamental concepts and data that help to understand energy systems holistically and to provide a common conceptual and terminological framework before examining in greater detail the various aspects of energy systems from challenges and options to integrated solutions, as done in the different chapters of the Global Energy Assessment (GEA).
Technical Summary
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- By Thomas B. Johansson, Lund University, Nebojsa Nakicenovic, International Institute for Applied Systems Analysis and Vienna University of Technology, Anand Patwardhan, Indian Institute of Technology, Luis Gomez-Echeverri, International Institute for Applied Systems Analysis, Doug J. Arent, National Renewable Energy Laboratory, Rangan Banerjee, Indian Institute of Technology, Sally M. Benson, Stanford University, Daniel H. Bouille, Bariloche Foundation, Abeeku Brew-Hammond, Kwame Nkrumah University of Science and Technology, Aleh Cherp, Central European University, Suani T. Coelho, National Reference Center on Biomass, University of São Paulo, Lisa Emberson, Stockholm Environment Institute, University of York, Maria Josefina Figueroa, Technical University, Arnulf Grubler, International Institute for Applied Systems Analysis, Austria and Yale University, Kebin He, Tsinghua University, Mark Jaccard, Simon Fraser University, Suzana Kahn Ribeiro, Federal University of Rio de Janeiro, Stephen Karekezi, AFREPREN/FWD, Eric D. Larson, Princeton University and Climate Central, Zheng Li, Tsinghua University, Susan McDade, United Nations Development Programme, Lynn K. Mytelka, United Nations University-MERIT, Shonali Pachauri, International Institute for Applied Systems Analysis, Keywan Riahi, International Institute for Applied Systems Analysis, Johan Rockström, Stockholm Environment Institute, Stockholm University, Hans-Holger Rogner, International Atomic Energy Agency, Joyashree Roy, Jadavpur University, Robert N. Schock, World Energy Council, UK and Center for Global Security Research, Ralph Sims, Massey University, Kirk R. Smith, University of California, Wim C. Turkenburg, Utrecht University, Diana Ürge-Vorsatz, Central European University, Frank von Hippel, Princeton University, Kurt Yeager, Electric Power Research Institute and Galvin Electricity Initiative
- Global Energy Assessment Writing Team
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- Book:
- Global Energy Assessment
- Published online:
- 05 September 2012
- Print publication:
- 27 August 2012, pp 31-94
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Summary
Introduction
Energy is essential for human development and energy systems are a crucial entry point for addressing the most pressing global challenges of the 21st century, including sustainable economic, and social development, poverty eradication, adequate food production and food security, health for all, climate protection, conservation of ecosystems, peace, and security. Yet, more than a decade into the 21st century, current energy systems do not meet these challenges.
In this context, two considerations are important. The first is the capacity and agility of the players within the energy system to seize opportunities in response to these challenges. The second is the response capacity of the energy system itself, as the investments are long-term and tend to follow standard financial patterns, mainly avoiding risks and price instabilities. This traditional approach does not embrace the transformation needed to respond properly to the economic, environmental, and social sustainability challenges of the 21st century.
A major transformation is required to address these challenges and to avoid potentially catastrophic consequences for human and planetary systems. The GEA identifies strategies that could help resolve the multiple challenges simultaneously and bring multiple benefits. Their successful implementation requires determined, sustained, and immediate action.
The industrial revolution catapulted humanity onto an explosive development path, whereby reliance on muscle power and traditional biomass was replaced mostly by fossil fuels. In 2005, approximately 78% of global energy was based on fossil energy sources that provided abundant and ever cheaper energy services to more than half the world's population.
Contributors
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- By DeAnna L. Adkins, Samir Belagaje, S. Thomas Carmichael, Alex R. Carter, John Chae, François Chollet, Michael Chopp, Leonardo G. Cohen, Maurizio Corbetta, Steven C. Cramer, Rick M. Dijkhuizen, Megan Farrell, Seth P. Finklestein, Leigh R. Hochberg, Barbro B Johansson, Theresa A. Jones, Brett Kissela, Jeffrey A. Kleim, Bryan Kolb, J. Leigh Leasure, Yi Li, Isabelle Loubinoux, Andreas Luft, Randolph J. Nudo, Stephen J. Page, Thomas Platz, Valerie M. Pomeroy, David J. Reinkensmeyer, JingMei Ren, J. C. Rothwell, Dorothee Saur, Timothy Schallert, Gottfried Schlaug, Susan Schwerin, Rüdiger J. Seitz, Gordon L. Shulman, O. Swayne, P. Talelli, G. Campbell Teskey, Maurits P. A. van Meer, Nick S. Ward, Cornelius Weiller, Carolee J. Winstein, Steven L. Wolf
- Edited by Steven C. Cramer, University of California, Irvine, Randolph J. Nudo, Kansas University Medical Center
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- Book:
- Brain Repair After Stroke
- Published online:
- 10 November 2010
- Print publication:
- 28 October 2010, pp viii-x
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2 - The Imperatives of Energy for Sustainable Development
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- By Thomas B. Johansson, Sweden
- Edited by Adrian J. Bradbrook, University of Adelaide, Rosemary Lyster, University of Sydney, Richard L. Ottinger, Pace University, New York, Wang Xi, Shanghai Jiao Tong University, China
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- Book:
- The Law of Energy for Sustainable Development
- Published online:
- 10 August 2009
- Print publication:
- 24 January 2005, pp 46-52
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Summary
Many challenges threaten the movement toward sustainable development. The most significant of these objectives include the simultaneous (i) social development and poverty alleviation, and (ii) economic growth, while (iii) protecting the environment. Past and present forms of economic growth have created a very uneven distribution of wealth between and within nations, and placed severe strains on the environment, resulting in urban air pollution, regional acidification, and global climate change, to name but a few.
Current trends in energy systems development, and several of the linkages between these systems and current unsustainable global socioeconomic development patterns shall be discussed here. The main finding is that strong links exist between sustainable development challenges and the energy systems in the world, and that major changes in energy systems are required to achieve sustainability at large.
CURRENT ENERGY SUPPLY AND DEMAND
During the last century, the use of fossil fuel resources – oil, natural gas, and coal – dominated world primary energy. In 2001, fossil energy use made up seventy-nine percent of world primary energy consumption. In comparison, renewables (including large hydro, traditional biomass, and new renewable like solar, wind, geothermal) made up fourteen percent and nuclear seven percent of world primary energy use. Furthermore, demand for energy services continues to increase with growing economies and population size. For example, between 1960 and 1997 in the OECD countries, primary energy use and electricity use increased by a factor of 2 and 4.5 respectively, to support a three-fold increase in the economies and an increase in population size of fifty percent.