Traveling waves in a fluid layer submitted to a horizontal temperature gradient

We report experimental observations of traveling waves in a pure fluid with a free surface situated in a long container submitted to a horizontal temperature gradient perpendicular to its large extension. Above a critical value of the gradient and depending on the height of liquid $h,$ a source of waves is created in the container for small value of $h,$ while the system exhibits stationary patterns for larger values of $h.$ The spatio-temporal properties of the waves are studied and compared to theoretical predictions. Email contact: [email protected]: Saclay-S93/017 Email: [email protected]

Fast Basins and Branched Fractal Manifolds of Attractors of Iterated Function Systems

The fast basin of an attractor of an iterated function system (IFS) is the set of points in the domain of the IFS whose orbits under the associated semigroup intersect the attractor. Fast basins can have non-integer dimension and comprise a class of deterministic fractal sets. The relationship between the basin and the fast basin of a point-fibred attractor is analyzed. To better understand the topology and geometry of fast basins, and because of analogies with analytic continuation, branched fractal manifolds are introduced. A branched fractal manifold is a metric space constructed from the extended code space of a point-fibred attractor, by identifying some addresses. Typically, a branched fractal manifold is a union of a nondenumerable collection of nonhomeomorphic objects, isometric copies of generalized fractal blowups of the attractor

Approximation of Rough Functions

For given $p\in\lbrack1,\infty]$ and $g\in L^{p}\mathbb{(R)}$, we establish the existence and uniqueness of solutions $f\in L^{p}(\mathbb{R)}$, to the equation $$f(x)-af(bx)=g(x),$$ where $a\in\mathbb{R}$, $b\in\mathbb{R} \setminus \{0\}$, and $\left\vert a\right\vert \neq\left\vert b\right\vert ^{1/p}$. Solutions include well-known nowhere differentiable functions such as those of Bolzano, Weierstrass, Hardy, and many others. Connections and consequences in the theory of fractal interpolation, approximation theory, and Fourier analysis are established.Comment: 16 pages, 3 figure

Automated sirulated distillation using an articulated laboratory robot system

An automated method, based on the Hewlett-Packard ORCA (Optimized Robot for Chemical Analysis) system, for sample preparation and analysis of petroleum samples by simulated distillation (SIMDIS) is described. Results obtained for the robotically prepared samples show excellent agreement with those obtained from the same samples prepared manually. The application, based on ASTM method D 2887, is the foundation for a more fully automated system that can perform a variety of SIMDIS samples and methods