Lyapunov vs. Geometrical Stability Analysis of the Kepler and the Restricted Three Body Problem

In this letter we show that although the application of standard Lyapunov analysis predicts that completely integrable Kepler motion is unstable, the geometrical analysis of Horwitz et al [1] predicts the observed stability. This seems to us to provide evidence for both the incompleteness of the standard Lyapunov analysis and the strength of the geometrical analysis. Moreover, we apply this approach to the three body problem in which the third body is restricted to move on a circle of large radius which induces an adiabatic time dependent potential on the second body. This causes the second body to move in a very interesting and intricate but periodic trajectory; however, the standard Lyapunov analysis, as well as methods based on the parametric variation of curvature associated with the Jacobi metric, incorrectly predict chaotic behavior. The geometric approach predicts the correct stable motion in this case as well.Comment: 9 pages, 14 figure

Discrimination of the Healthy and Sick Cardiac Autonomic Nervous System by a New Wavelet Analysis of Heartbeat Intervals

We demonstrate that it is possible to distinguish with a complete certainty between healthy subjects and patients with various dysfunctions of the cardiac nervous system by way of multiresolutional wavelet transform of RR intervals. We repeated the study of Thurner et al on different ensemble of subjects. We show that reconstructed series using a filter which discards wavelet coefficients related with higher scales enables one to classify individuals for which the method otherwise is inconclusive. We suggest a delimiting diagnostic value of the standard deviation of the filtered, reconstructed RR interval time series in the range of $\sim 0.035$ (for the above mentioned filter), below which individuals are at risk.Comment: 5 latex pages (including 6 figures). Accepted in Fractal

Ballistic transport, chiral anomaly and emergence of the neutral electron - hole plasma in graphene

The process of coherent creation of particle - hole excitations by an electric field in graphene is quantitatively described using a dynamic "first quantized" approach. We calculate the evolution of current density, number of pairs and energy in ballistic regime using the tight binding model. The series in electric field strength $E$ up to third order in both DC and AC are calculated. We show how the physics far from the two Dirac points enters various physical quantities in linear response and how it is related to the chiral anomaly. The third harmonic generation and the imaginary part of conductivity are obtained. It is shown that at certain time scale $t_{nl}\propto E^{-1/2}$ the physical behaviour dramatically changes and the perturbation theory breaks down. Beyond the linear response physics is explored using an exact solution of the first quantized equations. While for small electric fields the I-V curve is linear characterized by the universal minimal resistivity $\sigma =\pi /2(e^{2}/h)$%, at $t>t_{nl}$ the conductivity grows fast. The copious pair creation (with rate $E^{3/2}$), analogous to Schwinger's electron - positron pair creation from vacuum in QED, leads to creation of the electron - hole plasma at ballistic times of order $t_{nl}$. This process is terminated by a relaxational recombination.Comment: 15 pages, 5 figures

Ballistic transport in graphene beyond linear response

The process of coherent creation of particle - hole excitations by an electric field in graphene is quantitatively described beyond linear response. We calculate the evolution of current density, number of pairs and energy in ballistic regime for electric field E using the tight binding model. While for small ballistic flight times the current is linear in E and independent of time, for larger ballistic times the current increases and finally at yet larger times Bloch oscillations set in. It is shown that the number of pairs follows the 2D generalization of the Schwinger's creation rate only on certain time segments with a prefactor different from that obtained using the asymptotic formula.Comment: 5 pages, 2 figure

The Necessity for a Time Local Dimension in Systems with Time Varying Attractors

We show that a simple non-linear system of ordinary differential equations may possess a time varying attractor dimension. This indicates that it is infeasible to characterize EEG and MEG time series with a single time global dimension. We suggest another measure for the description of non-stationary attractors.Comment: 13 Postscript pages, 12 Postscript figures (figures 3b and 4 by request from Y. Ashkenazy: [email protected]

Sediment and nutrient delivery from thermokarst features in the foothills of the North Slope, Alaska : potential impacts on headwater stream ecosystems

Author Posting. © American Geophysical Union, 2008. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 113 (2008): G02026, doi:10.1029/2007JG000470.Permafrost is a defining characteristic of the Arctic environment. However, climate warming is thawing permafrost in many areas leading to failures in soil structure called thermokarst. An extensive survey of a 600 km2 area in and around the Toolik Lake Natural Research Area (TLNRA) revealed at least 34 thermokarst features, two thirds of which were new since ∼1980 when a high resolution aerial survey of the area was done. Most of these thermokarst features were associated with headwater streams or lakes. We have measured significantly increased sediment and nutrient loading from thermokarst features to streams in two well-studied locations near the TLNRA. One small thermokarst gully that formed in 2003 on the Toolik River in a 0.9 km2 subcatchment delivered more sediment to the river than is normally delivered in 18 years from 132 km2 in the adjacent upper Kuparuk River basin (a long-term monitoring reference site). Ammonium, nitrate, and phosphate concentrations downstream from a thermokarst feature on Imnavait Creek increased significantly compared to upstream reference concentrations and the increased concentrations persisted over the period of sampling (1999–2005). The downstream concentrations were similar to those we have used in a long-term experimental manipulation of the Kuparuk River and that have significantly altered the structure and function of that river. A subsampling of other thermokarst features from the extensive regional survey showed that concentrations of ammonium, nitrate, and phosphate were always higher downstream of the thermokarst features. Our previous research has shown that even minor increases in nutrient loading stimulate primary and secondary production. However, increased sediment loading could interfere with benthic communities and change the responses to increased nutrient delivery. Although the terrestrial area impacted by thermokarsts is limited, the aquatic habitat altered by these failures can be extensive. If warming in the Arctic foothills accelerates thermokarst formation, there may be substantial and wide-spread impacts on arctic stream ecosystems that are currently poorly understood.The results presented in this report are based upon work supported by the U.S. National Science Foundation under grants to the Arctic Hyporheic project (OPP- 0327440) and the Arctic Long-Term Ecological Research Program (DEB- 9810222)