Nonlinear Young integrals via fractional calculus

For H\"older continuous functions $W(t,x)$ and $\varphi_t$, we define nonlinear integral $\int_a^b W(dt, \varphi_t)$ via fractional calculus. This nonlinear integral arises naturally in the Feynman-Kac formula for stochastic heat equations with random coefficients. We also define iterated nonlinear integrals.Comment: arXiv admin note: substantial text overlap with arXiv:1404.758

Penta-hepta defect chaos in a model for rotating hexagonal convection

In a model for rotating non-Boussinesq convection with mean flow we identify a regime of spatio-temporal chaos that is based on a hexagonal planform and is sustained by the {\it induced nucleation} of dislocations by penta-hepta defects. The probability distribution function for the number of defects deviates substantially from the usually observed Poisson-type distribution. It implies strong correlations between the defects inthe form of density-dependent creation and annihilation rates of defects. We extract these rates from the distribution function and also directly from the defect dynamics.Comment: 4 pages, 5 figures, submitted to PR

Rattling and freezing in a 1-D transport model

We consider a heat conduction model introduced in \cite{Collet-Eckmann 2009}. This is an open system in which particles exchange momentum with a row of (fixed) scatterers. We assume simplified bath conditions throughout, and give a qualitative description of the dynamics extrapolating from the case of a single particle for which we have a fairly clear understanding. The main phenomenon discussed is {\it freezing}, or the slowing down of particles with time. As particle number is conserved, this means fewer collisions per unit time, and less contact with the baths; in other words, the conductor becomes less effective. Careful numerical documentation of freezing is provided, and a theoretical explanation is proposed. Freezing being an extremely slow process, however, the system behaves as though it is in a steady state for long durations. Quantities such as energy and fluxes are studied, and are found to have curious relationships with particle density

On the miscible Rayleigh-Taylor instability: two and three dimensions

We investigate the miscible Rayleigh-Taylor (RT) instability in both 2 and 3 dimensions using direct numerical simulations, where the working fluid is assumed incompressible under the Boussinesq approximation. We first consider the case of randomly perturbed interfaces. With a variety of diagnostics, we develop a physical picture for the detailed temporal development of the mixed layer: We identify three distinct evolutionary phases in the development of the mixed layer, which can be related to detailed variations in the growth of the mixing zone. Our analysis provides an explanation for the observed differences between two and three-dimensional RT instability; the analysis also leads us to concentrate on the RT models which (1) work equally well for both laminar and turbulent flows, and (2) do not depend on turbulent scaling within the mixing layer between fluids. These candidate RT models are based on point sources within bubbles (or plumes) and interaction with each other (or the background flow). With this motivation, we examine the evolution of single plumes, and relate our numerical results (of single plumes) to a simple analytical model for plume evolution.Comment: 31 pages, 27 figures, to appear in November issue of JFM, 2001. For better figures: http://astro.uchicago.edu/~young/ps/jfmtry08.ps.

Studies of human dynamic space orientation using techniques of control theory

Three-dimensional contact analog display system development for use in surface, subsurface, air, and space vehicle

Studies of human dynamic space orientation using techniques of control theory Status report

Human dynamic space orientation using control theory technique