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1. |
Record Nr. |
UNINA9910457717203321 |
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Autore |
Hirota Ryōgo <1932-> |
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Titolo |
The direct method in soliton theory / / Ryogo Hirota ; translated from Japanese and edited by Atsushi Nagai, Jon Nimmo, and Claire Gilson [[electronic resource]] |
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Pubbl/distr/stampa |
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Cambridge : , : Cambridge University Press, , 2004 |
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ISBN |
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1-107-15013-2 |
1-280-54012-5 |
9786610540129 |
0-511-21484-7 |
0-511-21663-7 |
0-511-21126-0 |
0-511-31541-4 |
0-511-54304-2 |
0-511-21303-4 |
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Descrizione fisica |
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1 online resource (xi, 200 pages) : digital, PDF file(s) |
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Collana |
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Cambridge tracts in mathematics ; ; 155 |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
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Nota di bibliografia |
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Includes bibliographical references (p. 195-197) and index. |
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Nota di contenuto |
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1. Bilinearization of soliton equations -- 2. Determinants and pfaffians -- 3. Structure of soliton equations -- 4. Backlund transformations -- Afterword -- References -- Index. |
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Sommario/riassunto |
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The bilinear, or Hirota's direct, method was invented in the early 1970s as an elementary means of constructing soliton solutions that avoided the use of the heavy machinery of the inverse scattering transform and was successfully used to construct the multisoliton solutions of many new equations. In the 1980s the deeper significance of the tools used in this method - Hirota derivatives and the bilinear form - came to be understood as a key ingredient in Sato's theory and the connections with affine Lie algebras. The main part of this book concerns the more modern version of the method in which solutions are expressed in the form of determinants and pfaffians. While maintaining the original |
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philosophy of using relatively simple mathematics, it has, nevertheless, been influenced by the deeper understanding that came out of the work of the Kyoto school. The book will be essential for all those working in soliton theory. |
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2. |
Record Nr. |
UNINA9910464960403321 |
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Autore |
Marchisio Daniele L. |
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Titolo |
Computational models for polydisperse particulate and multiphase systems / / Daniele L. Marchisio, Rodney O. Fox [[electronic resource]] |
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Pubbl/distr/stampa |
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Cambridge : , : Cambridge University Press, , 2013 |
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ISBN |
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1-107-23354-2 |
1-68015-991-7 |
1-107-33627-9 |
1-139-01659-8 |
1-107-33295-8 |
1-107-33227-3 |
1-107-33461-6 |
1-299-40321-2 |
1-107-33544-2 |
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Descrizione fisica |
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1 online resource (xxxviii, 508 pages) : digital, PDF file(s) |
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Collana |
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Cambridge series in chemical engineering |
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Disciplina |
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Soggetti |
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Multiphase flow - Mathematical models |
Chemical reactions - Mathematical models |
Transport theory |
Dispersion - Mathematical models |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
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Nota di contenuto |
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""Cover""; ""Contents""; ""Preface""; ""Notation""; ""1 Introduction""; ""1.1 Disperse multiphase flows""; ""1.2 Two example systems""; ""1.2.1 The population-balance equation for fine particles""; ""1.2.2 The kinetic equation for gas--particle flow""; ""1.3 The mesoscale modeling approach""; ""1.3.1 Relation to microscale models""; ""1.3.2 Number- |
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density functions""; ""1.3.3 The kinetic equation for the disperse phase""; ""1.3.4 Closure at the mesoscale level""; ""1.3.5 Relation to macroscale models""; ""1.4 Closure methods for moment-transport equations""; ""1.4.1 Hydrodynamic models"" |
""1.4.2 Moment methods""""1.5 A road map to Chapters 2--8""; ""2 Mesoscale description of polydisperse systems""; ""2.1 Number-density functions (NDF)""; ""2.1.1 Length-based NDF""; ""2.1.2 Volume-based NDF""; ""2.1.3 Mass-based NDF""; ""2.1.4 Velocity-based NDF""; ""2.2 The NDF transport equation""; ""2.2.1 The population-balance equation (PBE)""; ""2.2.2 The generalized population-balance equation (GPBE)""; ""2.2.3 The closure problem""; ""2.3 Moment-transport equations""; ""2.3.1 Moment-transport equations for a PBE""; ""2.3.2 Moment-transport equations for a GPBE"" |
""2.4 Flow regimes for the PBE""""2.4.1 Laminar PBE""; ""2.4.2 Turbulent PBE""; ""2.5 The moment-closure problem""; ""3 Quadrature-based moment methods""; ""3.1 Univariate distributions""; ""3.1.1 Gaussian quadrature""; ""3.1.2 The product--difference (PD) algorithm""; ""3.1.3 The Wheeler algorithm""; ""3.1.4 Consistency of a moment set""; ""3.2 Multivariate distributions""; ""3.2.1 Brute-force QMOM""; ""3.2.2 Tensor-product QMOM""; ""3.2.3 Conditional QMOM""; ""3.3 The extended quadrature method of moments (EQMOM)""; ""3.3.1 Relationship to orthogonal polynomials"" |
""3.3.2 Univariate EQMOM""""3.3.3 Evaluation of integrals with the EQMOM""; ""3.3.4 Multivariate EQMOM""; ""3.4 The direct quadrature method of moments (DQMOM)""; ""4 The generalized population-balance equation""; ""4.1 Particle-based definition of the NDF""; ""4.1.1 Definition of the NDF for granular systems""; ""4.1.2 NDF estimation methods""; ""4.1.3 Definition of the NDF for fluid--particle systems""; ""4.2 From the multi-particle--fluid joint PDF to the GPBE""; ""4.2.1 The transport equation for the multi-particle joint PDF"" |
""4.2.2 The transport equation for the single-particle joint PDF""""4.2.3 The transport equation for the NDF""; ""4.2.4 The closure problem""; ""4.3 Moment-transport equations""; ""4.3.1 A few words about phase-space integration""; ""4.3.2 Disperse-phase number transport""; ""4.3.3 Disperse-phase volume transport""; ""4.3.4 Fluid-phase volume transport""; ""4.3.5 Disperse-phase mass transport""; ""4.3.6 Fluid-phase mass transport""; ""4.3.7 Disperse-phase momentum transport""; ""4.3.8 Fluid-phase momentum transport""; ""4.3.9 Higher-order moment transport"" |
""4.4 Moment closures for the GPBE"" |
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Sommario/riassunto |
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Providing a clear description of the theory of polydisperse multiphase flows, with emphasis on the mesoscale modelling approach and its relationship with microscale and macroscale models, this all-inclusive introduction is ideal whether you are working in industry or academia. Theory is linked to practice through discussions of key real-world cases (particle/droplet/bubble coalescence, break-up, nucleation, advection and diffusion and physical- and phase-space), providing valuable experience in simulating systems that can be applied to your own applications. Practical cases of QMOM, DQMOM, CQMOM, EQMOM and ECQMOM are also discussed and compared, as are realizable finite-volume methods. This provides the tools you need to use quadrature-based moment methods, choose from the many available options, and design high-order numerical methods that guarantee realizable moment sets. In addition to the numerous practical examples, MATLAB scripts for several algorithms are also provided, so you can apply the methods described to practical problems straight away. |
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