Jeffrey Humpherys

Nonmonotonic twist maps

Abstract We investigate a family of nonmonotonic radial twist maps constructed by unfolding the linear twist function. We find several new modes of reconnection and derive conditions for them to occur. Reconnection and bifurcation of higher order resonances are studied in detail, including vortex pairs and triplets. The structural instability of some of these exotic figures is mitigated by the presence of chaotic separatrix layers. Invariant curves of involution pairs are utilized to locate and chart their often very complex metamorphoses.

Efficient Computation of Analytic Bases in Evans Function Analysis of Large Systems

In Evans function computations of the spectra of asymptotically constant-coefficient linearized operators of large systems, a problem that becomes important is the efficient computation of global analytically varying bases for invariant subspaces of the limiting coefficient matrices. In the case that the invariant subspace is spectrally separated from its complementary invariant subspace, we propose an efficient numerical implementation of a standard projection-based algorithm of Kato, for which the key step is the solution of an associated Sylvester problem. This may be recognized as the analytic cousin of a Ck algorithm developed by Dieci and collaborators based on orthogonal projection rather than eigenprojection as in our case. For a one-dimensional subspace, it reduces essentially to an algorithm of Bridges, Derks and Gottwald based on path-finding and continuation methods.

Fixed Wing UAV Path Following in Wind With Input Constraints

This paper considers the problem of fixed wing unmanned air vehicles following straight lines and orbits. To account for ambient winds, we use a path following approach as opposed to trajectory tracking. The unique feature of this paper is that we explicitly account for roll and flight path angle constraints. The guidance laws are derived using the theory of nested saturations, and explicit flight conditions are derived that guarantee convergence to the path. The method is validated by simulation and flight tests.

Stability of Isentropic Navier–Stokes Shocks in the High-Mach Number Limit

By a combination of asymptotic ODE estimates and numerical Evans function calculations, we establish stability of viscous shock solutions of the isentropic compressible Navier–Stokes equations with γ-law pressure (i) in the limit as Mach number M goes to infinity, for any γ ≥ 1 (proved analytically), and (ii) for M ≥ 2,500,

A dynamic workflow framework for mass customization using web service and autonomous agent techniques

{\gamma\in [1,2.5]}

VISCOUS HYPERSTABILIZATION OF DETONATION WAVES IN ONE SPACE DIMENSION

or M ≥ 13,000,

SPECTRAL STABILITY OF NONCHARACTERISTIC ISENTROPIC NAVIER-STOKES BOUNDARY LAYERS

{\gamma \in [2.5,3]}