The Application of Mathematics to Physics and Nonlinear Science
Nonlinear science is the science of, among other exotic phenomena, unexpected and unpredictable behavior, catastrophes, complex interactions, and significant perturbations. Ocean and atmosphere dynamics, weather, many bodies in interaction, ultra-high intensity excitations, life, formation of natura...
में बचाया:
| मुख्य लेखक: | |
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| स्वरूप: | Online |
| भाषा: | अंग्रेज़ी |
| प्रकाशित: |
MDPI - Multidisciplinary Digital Publishing Institute
2021
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| विषय: | |
| ऑनलाइन पहुंच: | 46022 |
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कोई टैग नहीं, इस रिकॉर्ड को टैग करने वाले पहले व्यक्ति बनें!
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| _version_ | 1869514441084633088 |
|---|---|
| author | Ludu, Andrei |
| author_browse | Ludu, Andrei |
| author_facet | Ludu, Andrei |
| author_sort | Ludu, Andrei |
| collection | Directory of Open Access Books |
| description | Nonlinear science is the science of, among other exotic phenomena, unexpected and unpredictable behavior, catastrophes, complex interactions, and significant perturbations. Ocean and atmosphere dynamics, weather, many bodies in interaction, ultra-high intensity excitations, life, formation of natural patterns, and coupled interactions between components or different scales are only a few examples of systems where nonlinear science is necessary. All outstanding, self-sustained, and stable structures in space and time exist and protrude out of a regular linear background of states mainly because they identify themselves from the rest by being highly localized in range, time, configuration, states, and phase spaces. Guessing how high up you drive toward the top of the mountain by compiling your speed, road slope, and trip duration is a linear model, but predicting the occurrence around a turn of a boulder fallen on the road is a nonlinear phenomenon. In an effort to grasp and understand nonlinear phenomena, scientists have developed several mathematical approaches including inverse scattering theory, Backlund and groups of transformations, bilinear method, and several other detailed technical procedures. In this Special Issue, we introduce a few very recent approaches together with their physical meaning and applications. We present here five important papers on waves, unsteady flows, phases separation, ocean dynamics, nonlinear optic, viral dynamics, and the self-appearance of patterns for spatially extended systems, which are problems that have aroused scientists’ interest for decades, yet still cannot be predicted and have their generating mechanism and stability open to debate. The aim of this Special Issue was to present these most debated and interesting topics from nonlinear science for which, despite the existence of highly developed mathematical tools of investigation, there are still fundamental open questions. |
| format | Online |
| id | doab-20.500.12854ir-41047 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | MDPI - Multidisciplinary Digital Publishing Institute |
| publisherStr | MDPI - Multidisciplinary Digital Publishing Institute |
| record_format | ojs |
| spelling | doab-20.500.12854ir-410472023-12-20T18:40:38Z The Application of Mathematics to Physics and Nonlinear Science Ludu, Andrei QA1-939 Q1-390 diffusion viral infection non-Newtonian fluid convergence Navier–Stokes–Voigt equations existence Lyapunov functional Faedo–Galerkin approximations probability distribution strong solutions stability multigrid method parabolic equations long-time behavior Fokker–Planck equation viscoelastic models Cauchy problem unconditionally gradient stable scheme uniqueness existence and uniqueness theorem continuum spectrum pulse equation Stokes operator Lagrangian scheme Cahn–Hilliard equation Feller equation bic Book Industry Communication::P Mathematics & science Nonlinear science is the science of, among other exotic phenomena, unexpected and unpredictable behavior, catastrophes, complex interactions, and significant perturbations. Ocean and atmosphere dynamics, weather, many bodies in interaction, ultra-high intensity excitations, life, formation of natural patterns, and coupled interactions between components or different scales are only a few examples of systems where nonlinear science is necessary. All outstanding, self-sustained, and stable structures in space and time exist and protrude out of a regular linear background of states mainly because they identify themselves from the rest by being highly localized in range, time, configuration, states, and phase spaces. Guessing how high up you drive toward the top of the mountain by compiling your speed, road slope, and trip duration is a linear model, but predicting the occurrence around a turn of a boulder fallen on the road is a nonlinear phenomenon. In an effort to grasp and understand nonlinear phenomena, scientists have developed several mathematical approaches including inverse scattering theory, Backlund and groups of transformations, bilinear method, and several other detailed technical procedures. In this Special Issue, we introduce a few very recent approaches together with their physical meaning and applications. We present here five important papers on waves, unsteady flows, phases separation, ocean dynamics, nonlinear optic, viral dynamics, and the self-appearance of patterns for spatially extended systems, which are problems that have aroused scientists’ interest for decades, yet still cannot be predicted and have their generating mechanism and stability open to debate. The aim of this Special Issue was to present these most debated and interesting topics from nonlinear science for which, despite the existence of highly developed mathematical tools of investigation, there are still fundamental open questions. 2021-02-11T08:18:48Z 2021-02-11T08:18:48Z 2020-06-09 16:38:57 2020 book 46022 9783039287277 9783039287260 https://directory.doabooks.org/handle/20.500.12854/41047 eng application/octet-stream Attribution-NonCommercial-NoDerivatives 4.0 International https://mdpi.com/books/pdfview/book/2197 MDPI - Multidisciplinary Digital Publishing Institute 10.3390/books978-3-03928-727-7 10.3390/books978-3-03928-727-7 46cabcaa-dd94-4bfe-87b4-55023c1b36d0 9783039287277 9783039287260 122 open access |
| spellingShingle | QA1-939 Q1-390 diffusion viral infection non-Newtonian fluid convergence Navier–Stokes–Voigt equations existence Lyapunov functional Faedo–Galerkin approximations probability distribution strong solutions stability multigrid method parabolic equations long-time behavior Fokker–Planck equation viscoelastic models Cauchy problem unconditionally gradient stable scheme uniqueness existence and uniqueness theorem continuum spectrum pulse equation Stokes operator Lagrangian scheme Cahn–Hilliard equation Feller equation bic Book Industry Communication::P Mathematics & science Ludu, Andrei The Application of Mathematics to Physics and Nonlinear Science |
| title | The Application of Mathematics to Physics and Nonlinear Science |
| title_full | The Application of Mathematics to Physics and Nonlinear Science |
| title_fullStr | The Application of Mathematics to Physics and Nonlinear Science |
| title_full_unstemmed | The Application of Mathematics to Physics and Nonlinear Science |
| title_short | The Application of Mathematics to Physics and Nonlinear Science |
| title_sort | application of mathematics to physics and nonlinear science |
| topic | QA1-939 Q1-390 diffusion viral infection non-Newtonian fluid convergence Navier–Stokes–Voigt equations existence Lyapunov functional Faedo–Galerkin approximations probability distribution strong solutions stability multigrid method parabolic equations long-time behavior Fokker–Planck equation viscoelastic models Cauchy problem unconditionally gradient stable scheme uniqueness existence and uniqueness theorem continuum spectrum pulse equation Stokes operator Lagrangian scheme Cahn–Hilliard equation Feller equation bic Book Industry Communication::P Mathematics & science |
| topic_facet | QA1-939 Q1-390 diffusion viral infection non-Newtonian fluid convergence Navier–Stokes–Voigt equations existence Lyapunov functional Faedo–Galerkin approximations probability distribution strong solutions stability multigrid method parabolic equations long-time behavior Fokker–Planck equation viscoelastic models Cauchy problem unconditionally gradient stable scheme uniqueness existence and uniqueness theorem continuum spectrum pulse equation Stokes operator Lagrangian scheme Cahn–Hilliard equation Feller equation bic Book Industry Communication::P Mathematics & science |
| url | 46022 |
| work_keys_str_mv | AT luduandrei theapplicationofmathematicstophysicsandnonlinearscience AT luduandrei applicationofmathematicstophysicsandnonlinearscience |