J. Parisi

Near-field heat transfer in a scanning thermal microscope

We present measurements of the near-field heat transfer between the tip of a thermal profiler and planar material surfaces under ultrahigh vacuum conditions. For tip-sample distances below 10(-8) m, our results differ markedly from the prediction of fluctuating electrodynamics. We argue that these differences are due to the existence of a material-dependent small length scale below which the macroscopic description of the dielectric properties fails, and discuss a heuristic model which yields fair agreement with the available data. These results are of importance for the quantitative interpretation of signals obtained by scanning thermal microscopes capable of detecting local temperature variations on surfaces.

Tool to recover scalar time-delay systems from experimental time series.

We propose a method that is able to analyze chaotic time series, gained from exp erimental data. The method allows to identify scalar time-delay systems. If the dynamics of the system under investigation is governed by a scalar time-delay differential equation of the form

Instability of the Mandelbrot Set

dy(t)/dt = h(y(t),y(t-tau_0))

Hyperchaos and Julia Sets

, the delay time

Dynamics of current filaments in p-type germanium under the influence of a transverse magnetic field

tau_0

Delayed Feedback Control of Chaos in an Electronic Double-Scroll Oscillator

and the functi on

Smooth Decomposition of Generalized Fatou Set Explains Smooth Structure in Generalized Mandelbrot Set

h

Impact ionization avalanche breakdown in short crystal regions of p‐Ge

can be recovered. There are no restrictions to the dimensionality of the chaotic attractor. The method turns out to be insensitive to noise. We successfully apply the method to various time series taken from a computer experiment and two different electronic oscillators.

Notizen: Comparison Between a Generic Reaction- Diffusion Model and a Synergetic Semiconductor System

Numerical evidence is presented that perturbations away from analyticity change the qualitative structure of the Mandelbrot set. The changes affect both the form and the surface structure. Most characteristically, the infinitely thin “necks” disappear. At at least one place, the surface structure becomes smooth.

Non-Differentiable Structure in the Generalized Mandelbrot Set

Julia sets are self-similar separatrices of the coast-line type found in noninvertible 2-D maps. The same class of maps also generates hyperchaos (chaos with two mixing directions). Smale’s notion of a “nontrivial basic set” provides a connection. These sets arise when a chaotic (or hyperchaotic) attractor “explodes”. In the case of more than one escape route, this set becomes a “fuzzy boundary” (Mira). Its projection as the map becomes noninvertible (1-D ) is a “Julia set in 1 D ”. In the analogous hyperchaos case the 2-D limiting map contains a classical Julia set of the continuous type. An identically looking set can also be obtained within a non-exploded hyperchaotic attractor, however, as a “cloud”. Julia-like attractors therefore exist. The theory also predicts Mandelbrot sets for 4-D flows. Julia-like behavior is a new, numerically easy-to-test for property o f most nontrivial dynamical systems.