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Record Nr. |
UNISA996466495503316 |
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Autore |
Berger Mitchell A |
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Titolo |
Lectures on Topological Fluid Mechanics [[electronic resource] ] : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 2 - 10, 2001 / / by Mitchell A. Berger, Louis H. Kauffman, Boris Khesin, H. Keith Moffatt, Renzo L. Ricca, De Witt Sumners ; edited by Renzo L. Ricca |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2009 |
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ISBN |
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1-280-38431-X |
9786613562234 |
3-642-00837-2 |
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Edizione |
[1st ed. 2009.] |
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Descrizione fisica |
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1 online resource (XII, 223 p.) |
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Collana |
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C.I.M.E. Foundation Subseries ; ; 1973 |
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Classificazione |
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Disciplina |
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Soggetti |
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Continuum physics |
Topology |
Dynamics |
Ergodic theory |
Functions of complex variables |
Classical and Continuum Physics |
Dynamical Systems and Ergodic Theory |
Several Complex Variables and Analytic Spaces |
Kongress. |
Cetraro <2001> |
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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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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Braids and Knots -- Topological Quantities: Calculating Winding, Writhing, Linking, and Higher Order Invariants -- Tangles, Rational Knots and DNA -- The Group and Hamiltonian Descriptions of Hydrodynamical Systems -- Singularities in Fluid Dynamics and their Resolution -- Structural Complexity and Dynamical Systems -- Random Knotting: Theorems, Simulations and Applications. |
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Sommario/riassunto |
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Helmholtz's seminal paper on vortex motion (1858) marks the |
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beginning of what is now called topological fluid mechanics.After 150 years of work, the field has grown considerably. In the last several decades unexpected developments have given topological fluid mechanics new impetus, benefiting from the impressive progress in knot theory and geometric topology on the one hand, and in mathematical and computational fluid dynamics on the other. This volume contains a wide-ranging collection of up-to-date, valuable research papers written by some of the most eminent experts in the field. Topics range from fundamental aspects of mathematical fluid mechanics, including topological vortex dynamics and magnetohydrodynamics, integrability issues, Hamiltonian structures and singularity formation, to DNA tangles and knotted DNAs in sedimentation. A substantial introductory chapter on knots and links, covering elements of modern braid theory and knot polynomials, as well as more advanced topics in knot classification, provides an invaluable addition to this material. |
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2. |
Record Nr. |
UNINA9911047653403321 |
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Autore |
Schmerr Jr., Lester W |
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Titolo |
MATLAB Essentials: Symbolic and Numeric Problem-Solving in Engineering / / by Lester W. Schmerr, Jr |
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Pubbl/distr/stampa |
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Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2025 |
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ISBN |
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9783031993084 |
9783031993077 |
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Edizione |
[1st ed. 2025.] |
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Descrizione fisica |
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1 online resource (237 pages) |
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Collana |
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Disciplina |
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Soggetti |
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Engineering mathematics |
Engineering - Data processing |
Mathematics - Data processing |
Statics |
Algebras, Linear |
Differential equations |
Mathematical and Computational Engineering Applications |
Computational Science and Engineering |
Mechanical Statics and Structures |
Linear Algebra |
Differential Equations |
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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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Nota di contenuto |
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Introduction -- Vectors and Vector Operations -- Matrices and Matrix Operations -- Linear Equations -- Ordinary Differential Equations -- Nonlinear Problems -- Advanced Plotting -- Appendix A MATLAB Resources -- Appendix B Supplemental Material. |
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Sommario/riassunto |
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This book introduces MATLAB as a direct problem-solving tool, where the many built-in functions and commands of MATLAB can be used to perform even complex tasks. In this mode MATLAB acts as a very advanced scientific calculator. The primary purpose of this book is to teach the reader how to use the functions and commands of this calculator and, when necessary, how to save the problem-solving steps so that the solution obtained can be re-used or re-evaluated under different conditions. The book also introduces symbolic calculations extensively in addition to the traditional numerical methods found in other texts. MATLAB was initially introduced as a numerical tool for linear algebra problems and over the years has extended those numerical capabilities significantly to many areas of science and engineering. Consequently, it is not surprising that most books retain a strong emphasis on numerical solutions and treat symbolic calculations only briefly, if at all. A key point is that while symbolic algebra can be used to solve problems symbolically, it can also be used to make the formulation of problems much simpler, even if the ultimate solution is found numerically. Recognizing and demonstrating this important property of symbolic calculations is unique to this book. Examines symbolic and numeric MATLAB tools with examples: linear/ nonlinear/ differential equations, eigenvalue problems; Provides the reader with the MATLAB background needed to use MATLAB interactively (without traditional programming); Targets engineering students with examples and exercises taken from problems found in the engineering curriculum. |
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