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

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.

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

Studies of human dynamic space orientation using techniques of control theory Status report, Jun. 1967 - Jun. 1968

Human dynamic space orientation using techniques of control theor

Hawking temperature from scattering off the charged 2D black hole

The charged 2D black hole is visualized as presenting an potential barrier $V^{OUT}(r^*)$ to on-coming tachyon wave. Since this takes the complicated form, an approximate form $V^{APP}(r^*)$ is used for scattering analysis. We calculate the reflection and transmission coefficients for scattering of tachyon off the charged 2D black hole. The Hawking temperature is also derived from the reflection coefficient by Bogoliubov transformation. In the limit of $Q \to 0$, we recover the Hawking temperature of the 2D dilaton black hole.Comment: 12 pages 3 figures, RevTeX, to obtain figures contact author ([email protected]

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

Human dynamic space orientation using control theory technique

Symmetric-Gapped Surface States of Fractional Topological Insulators

We construct the symmetric-gapped surface states of a fractional topological insulator with electromagnetic $\theta$-angle $\theta_{em} = \frac{\pi}{3}$ and a discrete $\mathbb{Z}_3$ gauge field. They are the proper generalizations of the T-pfaffian state and pfaffian/anti-semion state and feature an extended periodicity compared with their of "integer" topological band insulators counterparts. We demonstrate that the surface states have the correct anomalies associated with time-reversal symmetry and charge conservation.Comment: 5 pages, 33 references and 2 pages of supplemental materia

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