- Volumes 84-95 (2024)
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Volumes 72-83 (2023)
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Volume 83
Pages 1-258 (December 2023)
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Volume 82
Pages 1-204 (November 2023)
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Volume 81
Pages 1-188 (October 2023)
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Volume 80
Pages 1-202 (September 2023)
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Volume 79
Pages 1-172 (August 2023)
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Volume 78
Pages 1-146 (July 2023)
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Volume 77
Pages 1-152 (June 2023)
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Volume 76
Pages 1-176 (May 2023)
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Volume 75
Pages 1-228 (April 2023)
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Volume 74
Pages 1-200 (March 2023)
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Volume 73
Pages 1-138 (February 2023)
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Volume 72
Pages 1-144 (January 2023)
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Volume 83
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Volumes 60-71 (2022)
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Volume 71
Pages 1-108 (December 2022)
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Volume 70
Pages 1-106 (November 2022)
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Volume 69
Pages 1-122 (October 2022)
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Volume 68
Pages 1-124 (September 2022)
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Volume 67
Pages 1-102 (August 2022)
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Volume 66
Pages 1-112 (July 2022)
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Volume 65
Pages 1-138 (June 2022)
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Volume 64
Pages 1-186 (May 2022)
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Volume 63
Pages 1-124 (April 2022)
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Volume 62
Pages 1-104 (March 2022)
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Volume 61
Pages 1-120 (February 2022)
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Volume 60
Pages 1-124 (January 2022)
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Volume 71
- Volumes 54-59 (2021)
- Volumes 48-53 (2020)
- Volumes 42-47 (2019)
- Volumes 36-41 (2018)
- Volumes 30-35 (2017)
- Volumes 24-29 (2016)
- Volumes 18-23 (2015)
- Volumes 12-17 (2014)
- Volume 11 (2013)
- Volume 10 (2012)
- Volume 9 (2011)
- Volume 8 (2010)
- Volume 7 (2009)
- Volume 6 (2008)
- Volume 5 (2007)
- Volume 4 (2006)
- Volume 3 (2005)
- Volume 2 (2004)
- Volume 1 (2003)
While science continues to extend to two extremes — micro-scale towards dimensions even smaller than elemental particles and mega-scale even beyond the universe, one recognizes that reductionism is not sufficient to solve many problems we encounter in engineering, which are likely characterized by nonlinearity, nonequilibrium and dissipative multi-scale structures. On the other hand, the common features of these nonlinear systems, such as bifurcation, state multiplicity and self-organization, have attracted much attention, leading to the approaches of the so-called complexity science which has become a focus not only in natural science and engineering science, but also in social science.
However, no effective methodology has been established to understand these complex systems, though noticeable progress has been achieved in studying these systems, such as particle-fluid multi-phase systems. Multi-scale methodology has been considered as a promising methodology to tackle complex systems due to its capability in correlating phenomena at different scales. In this presentation, we shall review the development of the multi-scale methodology and its applications to particle-fluid systems, elucidating the essential relevance of complex systems and the challenging problems in chemical engineering.
Multi-scale structure is considered to be the focus in studying complex systems, particularly, correlation between phenomena at different scales, compromise between different dominant mechanisms, coupling between spatial and temporal structural changes and critical phenomena occurring in these systems — these are the four critical issues in understanding complex systems. We first propose that by analyzing particle-fluid systems complex systems can be formulated as a multi-objective variational problem. Such an analytical multi-scale method will be reviewed in particular by analyzing the above four critical issues and by showing its 20-year development at IPE from a rough idea to modeling approaches, softwares and finally to industrial applications as well as its extension to different chemical and physical systems. The strategy of “from the particular to the general” in developing this multi-scale methodology is emphasized and challenges to mathematicians and physicists are identified to show the necessity of transdisciplinary cooperation. This presentation will be concluded by prospects and suggestions.