Theory of weakly nonlinear self sustained detonations

We propose a theory of weakly nonlinear multi-dimensional self sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced, unsteady, small disturbance, transonic equation and a rate equation for the heat release. In one spatial dimension, the model simplifies to a forced Burgers equation. Through analysis, numerical calculations and comparison with the reactive Euler equations, the model is demonstrated to capture such essential dynamical characteristics of detonations as the steady-state structure, the linear stability spectrum, the period-doubling sequence of bifurcations and chaos in one-dimensional detonations and cellular structures in multi- dimensional detonations

On "jamitons," self-sustained nonlinear traffic waves

"Phantom jams," traffic blockages that arise without apparent cause, have long frustrated transportation scientists. Herein, we draw a novel homology between phantom jams and a related class of self-sustained transonic waves, namely detonations. Through this analogy, we describe the jam structure; favorable agreement with reported measurements from congested highways is observed. Complementary numerical simulations offer insights into the jams' development. Our results identify conditions likely to result in a dangerous concentration of vehicles and thereby lend guidance in traffic control and roadway design.Comment: 6 pages, 4 figure

Feedback Increases the Capacity of Queues with Bounded Service Times

In the "Bits Through Queues" paper, it was conjectured that full feedback always increases the capacity of first-in-first-out queues, except when the service time distribution is memoryless. More recently, a non-explicit sufficient condition on the service time under which feedback increases capacity was provided, along with simple examples of service times satisfying this condition. In this paper, it is shown that full feedback increases the capacity of queues with bounded service times. This result is obtained by investigating a generalized notion of feedback, with full feedback and weak feedback as particular cases.Comment: 10 pages; two-colum

Non-parametric comparison of histogrammed two-dimensional data distributions using the Energy Test

When monitoring complex experiments, comparison is often made between regularly acquired histograms of data and reference histograms which represent the ideal state of the equipment. With the larger HEP experiments now ramping up, there is a need for automation of this task since the volume of comparisons could overwhelm human operators. However, the two-dimensional histogram comparison tools available in ROOT have been noted in the past to exhibit shortcomings. We discuss a newer comparison test for two-dimensional histograms, based on the Energy Test of Aslan and Zech, which provides more conclusive discrimination between histograms of data coming from different distributions than methods provided in a recent ROOT release.The Science and Technology Facilities Council, U

Theory of weakly nonlinear self-sustained detonations

We propose a theory of weakly nonlinear multidimensional self-sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced unsteady small-disturbance transonic equation and a rate equation for the heat release. In one spatial dimension, the model simplifies to a forced Burgers equation. Through analysis, numerical calculations and comparison with the reactive Euler equations, the model is demonstrated to capture such essential dynamical characteristics of detonations as the steady-state structure, the linear stability spectrum, the period-doubling sequence of bifurcations and chaos in one-dimensional detonations and cellular structures in multidimensional detonations

A model for shock wave chaos

We propose the following model equation: $$u_{t}+1/2(u^{2}-uu_{s})_{x}=f(x,u_{s}),$$ that predicts chaotic shock waves. It is given on the half-line $x<0$ and the shock is located at $x=0$ for any $t\ge0$. Here $u_{s}(t)$ is the shock state and the source term $f$ is assumed to satisfy certain integrability constraints as explained in the main text. We demonstrate that this simple equation reproduces many of the properties of detonations in gaseous mixtures, which one finds by solving the reactive Euler equations: existence of steady traveling-wave solutions and their instability, a cascade of period-doubling bifurcations, onset of chaos, and shock formation in the reaction zone.Comment: 4 pages, 4 figure