The Dynamics Of Modulated Wave Trains

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The Dynamics Of Modulated Wave Trains

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Author : A. Doelman
language : en
Publisher: American Mathematical Soc.
Release Date : 2009

The Dynamics Of Modulated Wave Trains written by A. Doelman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

The authors investigate the dynamics of weakly-modulated nonlinear wave trains. For reaction-diffusion systems and for the complex Ginzburg-Landau equation, they establish rigorously that slowly varying modulations of wave trains are well approximated by solutions to the Burgers equation over the natural time scale. In addition to the validity of the Burgers equation, they show that the viscous shock profiles in the Burgers equation for the wave number can be found as genuine modulated waves in the underlying reaction-diffusion system. In other words, they establish the existence and stability of waves that are time-periodic in appropriately moving coordinate frames which separate regions in physical space that are occupied by wave trains of different, but almost identical, wave number. The speed of these shocks is determined by the Rankine-Hugoniot condition where the flux is given by the nonlinear dispersion relation of the wave trains. The group velocities of the wave trains in a frame moving with the interface are directed toward the interface. Using pulse-interaction theory, the authors also consider similar shock profiles for wave trains with large wave number, that is, for an infinite sequence of widely separated pulses. The results presented here are applied to the FitzHugh-Nagumo equation and to hydrodynamic stability problems.

The Dynamics Of Modulated Wave Trains

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Author : Arjen Doelman
language : en
Publisher:
Release Date : 2005

The Dynamics Of Modulated Wave Trains written by Arjen Doelman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.

The Dynamics Of Modulated Wave Trains

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Author :
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2014-09-11

The Dynamics Of Modulated Wave Trains written by and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with MATHEMATICS categories.

This work examines the dynamics of weakly-modulated nonlinear wave trains. Areas covered by the authors include reaction-diffusion systems, the Ginsburg-Landau equation, Burgers equation, the Rankine-Hugoniot condition, the FitzHugh-Nagumo equation and hydrodynamic stability problems.

Symmetry Phase Modulation And Nonlinear Waves

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Author : Thomas J. Bridges
language : en
Publisher: Cambridge University Press
Release Date : 2017-07-03

Symmetry Phase Modulation And Nonlinear Waves written by Thomas J. Bridges and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-03 with Mathematics categories.

Bridges studies the origin of Korteweg-de Vries equation using phase modulation and its implications in dynamical systems and nonlinear waves.

Ocean Wave Dynamics

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Author : Ian Young
language : en
Publisher: World Scientific
Release Date : 2020-03-20

Ocean Wave Dynamics written by Ian Young and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-20 with Science categories.

Ocean Wave Dynamics is the most up-to-date book of its kind on the three main processes responsible for the generation and evolution of ocean waves: (i) atmospheric input from the wind, (ii) wave breaking and (iii) nonlinear interactions.Ocean waves are important for many reasons. They are the major environmental impact on in the design of coastal or offshore structures. Ocean waves are also fundamental to the processes of coastal flooding and beach erosion. They will play a major role in storm related coastal flooding which will rise in frequency as a result of sea level rise. Ocean waves are also an important part of the coupled ocean-atmosphere system. They determine the roughness of the ocean surface and hence have an impact on winds, fluxes of energy, gases and heat to the ocean and even the stability of ice sheets.Containing the latest research on ocean waves, it is a valuable resource for an overview of knowledge in this important field.Related Link(s)

Topological Automorphic Forms

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Author : Mark Behrens
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-02-22

Topological Automorphic Forms written by Mark Behrens and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-22 with Mathematics categories.

The authors apply a theorem of J. Lurie to produce cohomology theories associated to certain Shimura varieties of type $U(1,n-1)$. These cohomology theories of topological automorphic forms ($\mathit{TAF}$) are related to Shimura varieties in the same way that $\mathit{TMF}$ is related to the moduli space of elliptic curves.

Symplectic Actions Of 2 Tori On 4 Manifolds

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Author : Alvaro Pelayo
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-02-22

Symplectic Actions Of 2 Tori On 4 Manifolds written by Alvaro Pelayo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-22 with Mathematics categories.

In this paper the author classifies symplectic actions of $2$-tori on compact connected symplectic $4$-manifolds, up to equivariant symplectomorphisms. This extends results of Atiyah, Guillemin-Sternberg, Delzant and Benoist. The classification is in terms of a collection of invariants of the topology of the manifold, of the torus action and of the symplectic form. The author constructs explicit models of such symplectic manifolds with torus actions, defined in terms of these invariants.

Holder Sobolev Regularity Of The Solution To The Stochastic Wave Equation In Dimension Three

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Author : Robert C. Dalang
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-04-10

Holder Sobolev Regularity Of The Solution To The Stochastic Wave Equation In Dimension Three written by Robert C. Dalang and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-10 with Mathematics categories.

The authors study the sample path regularity of the solution of a stochastic wave equation in spatial dimension $d=3$. The driving noise is white in time and with a spatially homogeneous covariance defined as a product of a Riesz kernel and a smooth function. The authors prove that at any fixed time, a.s., the sample paths in the spatial variable belong to certain fractional Sobolev spaces. In addition, for any fixed $x\in\mathbb{R}^3$, the sample paths in time are Holder continuous functions. Further, the authors obtain joint Holder continuity in the time and space variables. Their results rely on a detailed analysis of properties of the stochastic integral used in the rigourous formulation of the s.p.d.e., as introduced by Dalang and Mueller (2003). Sharp results on one- and two-dimensional space and time increments of generalized Riesz potentials are a crucial ingredient in the analysis of the problem. For spatial covariances given by Riesz kernels, the authors show that the Holder exponents that they obtain are optimal.

Lectures On The Theory Of Water Waves

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Author : Thomas J. Bridges
language : en
Publisher: Cambridge University Press
Release Date : 2016-02-04

Lectures On The Theory Of Water Waves written by Thomas J. Bridges and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-04 with Mathematics categories.

A range of experts contribute introductory-level lectures on active topics in the theory of water waves.

Numerical Modelling Of Extreme Waves

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Author : Huidong Zhang
language : en
Publisher: Springer Nature
Release Date : 2024-12-18

Numerical Modelling Of Extreme Waves written by Huidong Zhang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-18 with Technology & Engineering categories.

This book describes some approaches for developing the numerical models to efficiently predict the formation of extreme waves which can pose a threat to the safety of marine structures. The numerical algorithms for solving different governing equations and the theoretical probability models for extreme wave predictions are explained in detail. These models can help engineers in the design of marine structures that can withstand extreme waves. With more frequent extreme weather due to climate change, extreme waves have become more common. Extreme waves are an interesting phenomenon, but because of their enormous destructive power, understanding their formation mechanism, properties, and impact, is necessary for the design and safe operation of ships and offshore structures.