The area of computation called artificial intelligence (AI) is falsified by describing a previous 1972 falsification of AI by British applied mathematician James Lighthill. It is explained how Lighthill’s arguments continue to apply to current AI. It is argued that AI should use the Popperian scientific method in which it is the duty of every scientist to attempt to falsify theories and if theo...

A mathematical macroscopic traffic flow model known as Lighthill, Whitham and Richards (LWR) model appended with a closure nonlinear velocity-density relationship yielding a quasilinear first order (hyperbolic) partial differential equation as an initial boundary value problem (IBVP) was considered. The traffic model IBVP by finite difference method which leads to a first order explicit upwind ...

It is shown that the anelastic Oberbeck-Boussinesq system is a small Mach, small Péclet and small Froude number limit of the complete Navier-Stokes-Fourier system for gases with large specific heat at constant volume. This result is obtained on an arbitrary large time interval. The proof allows an intrinsic view into the process of separation of fast oscillating acoustic waves, governed by a Li...

This paper studies the convergence of the Finite Element Method for predicting the noise generated by turbulent flows through the Lighthill model. The model’s derivation is given in an intuitive and physical manner. The model gives a non-homogeneous wave equation for the acoustic pressure where the right-hand side depends on the divergence of the nonlinear term of the NSE and external force. Th...

Increasing noise regulation at urban airports force jet engine manufactures to develop and build quieter engines. Over the last 10-15 years, a significant reduction in fan and mechanical noise has been achieved. However, the reduction in jet noise over the same time period is fairly small and a major reduction in acoustic emissions of jet engines has to come from a reduction in jet noise. Tradi...

The choice of title of this presentation comes from two papers that James Lighthill published in the issue of Journal of Engineering Mathematics commemorating H. A. Lorentz’s famous 1896 paper on 0uid mechanics [1]. This paper will discuss Lighthill’s signi)cant contribution to microbiological 0uid mechanics, both through his own work and his postgraduate and postdoctoral students, of which thi...

A Mach 0.9 jet at Reynolds number 3600 is simulated along with its radiated sound by direct numerical solution of the flow equations. The numerical simulation is shown to be in excellent agreement with experimental measurements at the same flow conditions. Basic turbulence and sound statistics are presented and analyzed. Pressure data is Fourier transformed in the streamwise direction and in ti...

First order traffic flow models have been studied for long time, since they represent the simplest way to begin with the understanding of such a complex system. To our knowledge the Lighthill-Whitham-Richards (LWR) model was the first model to describe unidirectional, one-dimensional traffic flow in a highway [1], [2]. This model considers the continuity equation for the density of vehicles (nu...

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