Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Harmonic Wave Systems: Partial Differential Equations of the Helmholtz Decomposition
View through CrossRef
<p style="background:white;">
<i><span style="font-size:11.5pt;font-family:;" "=""> </span></i>
</p>
<p class="MsoNormal" style="margin-top:3.4pt;margin-right:0cm;margin-bottom:3.4pt;margin-left:0cm;line-height:normal;background:white;">
<i><i><span lang="EN-US" style="font-size:11.5pt;font-family:;" "=""></span></i></i>
</p>
<p class="MsoNormal" style="margin-top:3.4pt;margin-right:0cm;margin-bottom:3.4pt;margin-left:0cm;line-height:normal;background:white;">
<i><i><span lang="EN-US" style="font-size:12pt;font-family:;" "=""></span></i></i>
</p>
<p class="MsoNormal" style="margin-top:3.4pt;margin-right:0cm;margin-bottom:3.4pt;margin-left:0cm;line-height:normal;background:white;">
<span lang="EN-US" font-size:14px;"="" style="font-family: " times="" new="" roman";"=""><em>Harmonic Wave Systems</em> </span><span lang="EN-US" "="" style="font-family:;"><span font-size:14px;"="" style="font-family: " times="" new="" roman";"="">is the first
textbook about the computational method of Decomposition in Invariant
Structures (DIS) that generalizes the analytical methods of separation of
variables, undetermined coefficients, asymptotic expansions, and series
expansions. In recent years, there has been a boom in publications on
propagation of nonlinear waves described by a fascinating list of partial
differential equations (PDEs). The vast majority of wave problems are reducible
to one-dimensional ones in propagation variables. However, a list of
publications with two- and three-dimensional applications of the DIS method is
brief.</span></span>
</p>
<p class="MsoNormal" style="margin-top:3.4pt;margin-right:0cm;margin-bottom:3.4pt;margin-left:0cm;line-height:normal;background:white;">
<br />
</p>
<p class="MsoNormal" style="margin-top:3.4pt;margin-right:0cm;margin-bottom:3.4pt;margin-left:0cm;line-height:normal;background:white;">
<span lang="EN-US" style="font-family:;" "=""><span style="font-family: " times="" new="" roman";"="" font-size:14px;"="">The book
offers a comprehensive and rigorous treatment of the DIS method in two and
three dimensions using the PDE approach to the Helmholtz decomposition that
provides the most general background for mathematical modelling of harmonic
waves in fluid dynamics, electrodynamics, heat transfer, and other numerous
areas of science and engineering, which are dealing with propagation and
interaction of N internal
waves.</span></span>
</p>
Title: Harmonic Wave Systems: Partial Differential Equations of the Helmholtz Decomposition
Description:
<p style="background:white;">
<i><span style="font-size:11.
5pt;font-family:;" "=""> </span></i>
</p>
<p class="MsoNormal" style="margin-top:3.
4pt;margin-right:0cm;margin-bottom:3.
4pt;margin-left:0cm;line-height:normal;background:white;">
<i><i><span lang="EN-US" style="font-size:11.
5pt;font-family:;" "=""></span></i></i>
</p>
<p class="MsoNormal" style="margin-top:3.
4pt;margin-right:0cm;margin-bottom:3.
4pt;margin-left:0cm;line-height:normal;background:white;">
<i><i><span lang="EN-US" style="font-size:12pt;font-family:;" "=""></span></i></i>
</p>
<p class="MsoNormal" style="margin-top:3.
4pt;margin-right:0cm;margin-bottom:3.
4pt;margin-left:0cm;line-height:normal;background:white;">
<span lang="EN-US" font-size:14px;"="" style="font-family: " times="" new="" roman";"=""><em>Harmonic Wave Systems</em> </span><span lang="EN-US" "="" style="font-family:;"><span font-size:14px;"="" style="font-family: " times="" new="" roman";"="">is the first
textbook about the computational method of Decomposition in Invariant
Structures (DIS) that generalizes the analytical methods of separation of
variables, undetermined coefficients, asymptotic expansions, and series
expansions.
In recent years, there has been a boom in publications on
propagation of nonlinear waves described by a fascinating list of partial
differential equations (PDEs).
The vast majority of wave problems are reducible
to one-dimensional ones in propagation variables.
However, a list of
publications with two- and three-dimensional applications of the DIS method is
brief.
</span></span>
</p>
<p class="MsoNormal" style="margin-top:3.
4pt;margin-right:0cm;margin-bottom:3.
4pt;margin-left:0cm;line-height:normal;background:white;">
<br />
</p>
<p class="MsoNormal" style="margin-top:3.
4pt;margin-right:0cm;margin-bottom:3.
4pt;margin-left:0cm;line-height:normal;background:white;">
<span lang="EN-US" style="font-family:;" "=""><span style="font-family: " times="" new="" roman";"="" font-size:14px;"="">The book
offers a comprehensive and rigorous treatment of the DIS method in two and
three dimensions using the PDE approach to the Helmholtz decomposition that
provides the most general background for mathematical modelling of harmonic
waves in fluid dynamics, electrodynamics, heat transfer, and other numerous
areas of science and engineering, which are dealing with propagation and
interaction of N internal
waves.
</span></span>
</p>.
Related Results
Applications of Partial Differential Equations in Fluid Physics
Applications of Partial Differential Equations in Fluid Physics
Partial differential equations, or PDEs, assume a critical part in grasping and outlining different fluid physics peculiarities. They have an expansive scope of utilizations, from ...
Exploring Large Language Models Integration in the Histopathologic Diagnosis of Skin Diseases: A Comparative Study
Exploring Large Language Models Integration in the Histopathologic Diagnosis of Skin Diseases: A Comparative Study
Abstract
Introduction
The exact manner in which large language models (LLMs) will be integrated into pathology is not yet fully comprehended. This study examines the accuracy, bene...
Helmholtz and the Conservation of Energy
Helmholtz and the Conservation of Energy
An examination of the sources Helmholtz drew upon for his formulation of the conservation of energy and the impact of his work on nineteenth-century physics.
In 1847...
Wave Force Calculations for Stokes and Non-Stokes Waves
Wave Force Calculations for Stokes and Non-Stokes Waves
ABSTRACT
A new wave particle velocity procedure permits calculation of forces from regular wave profiles of more or less arbitrary wave crest to height ratios, as...
Hurricane Eloise Directional Wave Energy Spectra
Hurricane Eloise Directional Wave Energy Spectra
ABSTRACT
Directiona1 wave energy spectra, calculated from data recorded during Hurricane Eloise (Gulf of Mexico, 1975), are presented. The spectra, based on an en...
Fast Numerical Methods for Non-local Operators
Fast Numerical Methods for Non-local Operators
The fast numerical treatment of non-local operators is an important challenge in many fields of mathematics and its applications. This includes classical Fredholm integral operator...
Multivariate characterization of wave storms in coastal areas
Multivariate characterization of wave storms in coastal areas
Wave-storms are the responsible of the main changes in the Coast. Their detailed characterization results in a better design of any marine structure. The most common approach to de...
Mathematics in Chemical Engineering
Mathematics in Chemical Engineering
Abstract
The article contains sections titled:
...