Linear and nonlinear waves
TLDR
The study of waves can be traced back to antiquity where philosophers, such as Pythagoras, studied the relation of pitch and length of string in musical instruments and the subject of classical acoustics was laid down and presented as a coherent whole by John William Strutt in his treatise Theory of Sound.Abstract:
The study of waves can be traced back to antiquity where philosophers, such as Pythagoras (c.560-480 BC), studied the relation of pitch and length of string in musical instruments. However, it was not until the work of Giovani Benedetti (1530-90), Isaac Beeckman (1588-1637) and Galileo (1564-1642) that the relationship between pitch and frequency was discovered. This started the science of acoustics, a term coined by Joseph Sauveur (1653-1716) who showed that strings can vibrate simultaneously at a fundamental frequency and at integral multiples that he called harmonics. Isaac Newton (1642-1727) was the first to calculate the speed of sound in his Principia. However, he assumed isothermal conditions so his value was too low compared with measured values. This discrepancy was resolved by Laplace (1749-1827) when he included adiabatic heating and cooling effects. The first analytical solution for a vibrating string was given by Brook Taylor (1685-1731). After this, advances were made by Daniel Bernoulli (1700-82), Leonard Euler (1707-83) and Jean d’Alembert (1717-83) who found the first solution to the linear wave equation, see section (3.2). Whilst others had shown that a wave can be represented as a sum of simple harmonic oscillations, it was Joseph Fourier (1768-1830) who conjectured that arbitrary functions can be represented by the superposition of an infinite sum of sines and cosines now known as the Fourier series. However, whilst his conjecture was controversial and not widely accepted at the time, Dirichlet subsequently provided a proof, in 1828, that all functions satisfying Dirichlet’s conditions (i.e. non-pathological piecewise continuous) could be represented by a convergent Fourier series. Finally, the subject of classical acoustics was laid down and presented as a coherent whole by John William Strutt (Lord Rayleigh, 1832-1901) in his treatise Theory of Sound. The science of modern acoustics has now moved into such diverse areas as sonar, auditoria, electronic amplifiers, etc.read more
Citations
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Focused ultrasound actuation of shape memory polymers; acoustic-thermoelastic modeling and testing
TL;DR: An experimentally-validated acoustic-thermoelastic mathematical framework for modeling the focused ultrasound (FU)-induced thermal actuation of shape memory polymers (SMPs) and the feasibility of using SMPs stimulated by FU for designing CDD systems is investigated.
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Results of a numerical study of currents in the vicinity of a damless water intake
TL;DR: In this paper, the conditions of flow spreading (vectors of depth-average velocities) were studied in the specific time intervals and crossings in the water intake area, and the results of the study confirmed that without special engineering measures it is practically impossible to assure stable water diversion into the canal.
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Focusing of unidirectional wave groups on deep water: an approximate nonlinear Schrödinger equation-based model
TL;DR: In this article, the amplitude-to-wavenumber bandwidth ratio is used to model the nonlinear evolution of a Gaussian wave group in deep water, and the model is derived using the conserved quantities of the cubic nonlinear Schrodinger equation (NLSE).
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On n-point amplitudes in N = 4 SYM
TL;DR: In this article, a multi-parameter (moduli) family of solutions for planar amplitudes in N = 4 SYM at strong coupling is constructed, which all correspond to the same s and t and some are related by SO(4,2) transformations.
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Breaking of Galilean invariance in the hydrodynamic formulation of ferromagnetic thin films
TL;DR: By reinterpreting the governing Landau-Lifshitz equation of motion, an exact set of equations of dispersive hydrodynamic form are derived that are amenable to analytical study even when full nonlinearity and exchange dispersion are included.
References
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Linear and Nonlinear Waves
TL;DR: In this paper, a general overview of the nonlinear theory of water wave dynamics is presented, including the Wave Equation, the Wave Hierarchies, and the Variational Method of Wave Dispersion.
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Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
TL;DR: In this article, a second-order extension of the Lagrangean method is proposed to integrate the equations of ideal compressible flow, which is based on the integral conservation laws and is dissipative, so that it can be used across shocks.
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Finite Volume Methods for Hyperbolic Problems
TL;DR: The CLAWPACK software as discussed by the authors is a popular tool for solving high-resolution hyperbolic problems with conservation laws and conservation laws of nonlinear scalar scalar conservation laws.