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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Journal ArticleDOI
A Survey on Visual Traffic Simulation: Models, Evaluations, and Applications in Autonomous Driving
Qianwen Chao,Qianwen Chao,Huikun Bi,Huikun Bi,Weizi Li,Tianlu Mao,Zhaoqi Wang,Ming C. Lin,Zhigang Deng +8 more
TL;DR: A comprehensive review on the state‐of‐the‐art techniques for traffic simulation and animation, including various data‐driven animation techniques, and the validation and evaluation of simulated traffic flows is provided.
Journal ArticleDOI
Nonlinear dynamics of ion concentration polarization in porous media: The leaky membrane model
TL;DR: In this article, a simple leaky membrane model is formulated, based on macroscopic electroneutrality and Nernst-Planck ionic fluxes, and solved in cases of unsupported binary electrolytes.
Proceedings ArticleDOI
Interactive hybrid simulation of large-scale traffic
TL;DR: A novel, real-time algorithm for modeling large-scale, realistic traffic using a hybrid model of both continuum and agent-based methods for traffic simulation, which demonstrates the flexibility and scalability of the interactive visual simulation technique on extensive road networks.
Journal ArticleDOI
Plasma dynamics in PF-1000 device under full-scale energy storage: I. Pinch dynamics, shock-wave diffraction, and inertial electrode
Vladimir A. Gribkov,Barbara Bienkowska,M. Borowiecki,A. V. Dubrovsky,Irena Ivanova-Stanik,Leslaw Karpinski,Ryszard Miklaszewski,Marian Paduch,Marek Scholz,K. Tomaszewski +9 more
TL;DR: In this paper, the first part of results obtained with the PF-1000 facility for the first time at its upper energy limit (≈ 1 MJ) were presented with the help of a number of diagnostics, both time-integrated and with nanosecond temporal resolution.
Journal ArticleDOI
Virtualized Traffic: Reconstructing Traffic Flows from Discrete Spatiotemporal Data
TL;DR: This work presents a novel concept, Virtualized Traffic, to reconstruct and visualize continuous traffic flows from discrete spatio-temporal data provided by traffic sensors or generated artificially to enhance a sense of immersion in a dynamic virtual world.
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.