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
Direction-selective non-reciprocal mechanical energy splitter
A. Rakhimzhanova,Michele Brun +1 more
TL;DR: In this paper , a direction-selective elastic micro-structured medium is proposed, which combines constitutive nonlinearity, a threshold activation displacement and the gyroscopic effect of an isolated spinner to induce a tunable wave deviation on a selected direction.
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Exact solution of a delay difference equation modeling traffic flow and their ultra-discrete limit
Keisuke Matsuya,Masahiro Kanai +1 more
TL;DR: In this article, a car-following model described by a delay difference equation is considered and exact solutions that present propagation of a traffic jam are given for a discrete-time version of the delayed optimal-velocity model.
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Differentiable Hybrid Traffic Simulation
TL;DR: This is the first differentiable traffic simulator for macroscopic and hybrid models that can compute gradients for traffic states across time steps and inhomogeneous lanes and can provide more efficient and scalable solutions for complex learning and control problems posed in traffic engineering than other existing algorithms.
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Multi-mode solitons in a long-short range traffic lattice model with time delay
Xiufang Ren,Shiji Zhao +1 more
TL;DR: The bifurcation lines and surfaces for stable and unstable regions are deduced by analyzing nearest sites’ interactions, time delay, and bumpy effects and it shows that keeping other conditions unchanged, the traffic flow becomes unstable, opposite to when outgoing flow increases, it becomes stable.
Proceedings ArticleDOI
Prediction of traffic density from wireless cellular data
TL;DR: This paper presents a method of estimating traffic density on a highway/freeway from cellular network data, and the model for estimating the density from the speed is developed from the cellular data.
References
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