For 3D reaction–diffusion equations, we study the problem of existence or nonexistence of an inertial manifold that is normally hyperbolic or absolutely normally hyperbolic. We present a system of two coupled equations with a cubic nonlinearity which does not admit a normally hyperbolic inertial manifold. An example separating the classes of such equations admitting an inertial manifold and a n...

This article presents a technique for modeling and calibrating a camera with integrated low-cost inertial sensors, three gyros and three accelerometers for full 3D sensing. Inertial sensors attached to a camera can provide valuable data about camera pose and movement. In biological vision systems, inertial cues provided by the vestibular system, are fused with vision at an early processing stag...

Cyclists seek to maximize performance during competition, and gross efficiency is an important factor affecting performance. Gross efficiency is itself affected by pedal rate. Thus, it is important to understand factors that affect freely chosen pedal rate. Crank inertial load varies greatly during road cycling based on the selected gear ratio. Nevertheless, the possible influence of crank iner...

An approximate inertial manifold for an évolution équation is a finite dimensional smooth manifold such that the orbits enter, after a transient time, a very thin neighbourhood of the manifold In this paper, we consider the Cahn-Hilliard équation and we present a method which allows to construct several approximate inertial manifolds providing better and better order approximations to the orbit...

Finite-dimensional inertial manifolds attract solutions to a nonlinear parabolic diierential equation at an exponential rate. In this paper inertial manifolds for multistep discretizations of such equations are studied. We provide an existence result for inertial manifolds under multistep discretization and show that these inertial manifolds converge to the inertial manifold of the original equ...

Next generation high anti-jam GPS receivers will take advantage of Ultra-Tightly-Coupled (UTC) GPS/inertial signal processing to improve their anti-jam robustness. UTC signal processing uses the inertial observations to aid the GPS receiver correlation channels and extend the period over which the coherent correlator outputs can be accumulated. For UTC tracking to operate, the residual carrier ...

Because, among other seismological observations, it is important to be able to predict the location of the vibrating pattern of an earthquake, in this chapter we take the first tentative steps towards including "Bryan’s effect" in a mathematical model for the seismic vibration pattern of a layered slowly rotating vibrating planet or moon. Historically, G.H. Bryan observed (in his article (Bryan...