Integrals of motion and the shape of the attractor for the Lorenz model

In this paper, we consider three-dimensional dynamical systems, as for example the Lorenz model. For these systems, we introduce a method for obtaining families of two-dimensional surfaces such that trajectories cross each surface of the family in the same direction. For obtaining these surfaces, we are guided by the integrals of motion that exist for particular values of the parameters of the system. Nonetheless families of surfaces are obtained for arbitrary values of these parameters. Only a bounded region of the phase space is not filled by these surfaces. The global attractor of the system must be contained in this region. In this way, we obtain information on the shape and location of the global attractor. These results are more restrictive than similar bounds that have been recently found by the method of Lyapunov functions.Comment: 17 pages,12 figures. PACS numbers : 05.45.+b / 02.30.Hq Accepted for publication in Physics Letters A. e-mails : [email protected] & [email protected]

Variational bound on energy dissipation in turbulent shear flow

We present numerical solutions to the extended Doering-Constantin variational principle for upper bounds on the energy dissipation rate in plane Couette flow, bridging the entire range from low to asymptotically high Reynolds numbers. Our variational bound exhibits structure, namely a pronounced minimum at intermediate Reynolds numbers, and recovers the Busse bound in the asymptotic regime. The most notable feature is a bifurcation of the minimizing wavenumbers, giving rise to simple scaling of the optimized variational parameters, and of the upper bound, with the Reynolds number.Comment: 4 pages, RevTeX, 5 postscript figures are available as one .tar.gz file from [email protected]

THE FEDERAL AGRICULTURE IMPROVEMENT AND REFORM ACT OF 1996: COMMODITY AND CONSERVATION PROGRAMS

The Federal Agriculture Improvement and Reform Act contains major revisions in farm commodity programs. This paper summarizes the major provision of legislation. Because many program implementation rules must be developed, program participants are advised to consult their local office of the USDA Farm Service Agency for final program provisions.Agricultural and Food Policy,

A PREVIEW OF THE 1996 FARM PROGRAM PROVISIONS

The U.S. House of Representatives and Senate have written farm bills that contain major revisions in farm commodity programs. Differences in these bills, House bill HR 2854 and Senate bill S 1541, must now be resolved by a Conference Committee, approved by a final vote of both houses of Congress, and signed by the President. Though differences in the bills do exist, the bills contain many similar provisions that appear likely to be included in the final version of the bill. This paper summarizes the major provisions of these bills and identifies areas where differences must be resolved by the Conference Committee.Agricultural and Food Policy,

Subdiffusion-limited reactions

We consider the coagulation dynamics A+A -> A and A+A A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension. This scenario combines the "anomalous kinetics" and "anomalous diffusion" problems, each of which leads to interesting dynamics separately and to even more interesting dynamics in combination. Our analysis is based on the fractional diffusion equation

A random walker on a ratchet potential: Effect of a non Gaussian noise

We analyze the effect of a colored non Gaussian noise on a model of a random walker moving along a ratchet potential. Such a model was motivated by the transport properties of motor proteins, like kinesin and myosin. Previous studies have been realized assuming white noises. However, for real situations, in general we could expect that those noises be correlated and non Gaussian. Among other aspects, in addition to a maximum in the current as the noise intensity is varied, we have also found another optimal value of the current when departing from Gaussian behavior. We show the relevant effects that arise when departing from Gaussian behavior, particularly related to current's enhancement, and discuss its relevance for both biological and technological situations.Comment: Submitted to Europ.Phys. J. B (LaTex, 16 pgs, 8 figures

Convolutional neural networks applied to high-frequency market microstructure forecasting

Highly sophisticated artificial neural networks have achieved unprecedented performance across a variety of complex real-world problems over the past years, driven by the ability to detect significant patterns autonomously. Modern electronic stock markets produce large volumes of data, which are very suitable for use with these algorithms. This research explores new scientific ground by designing and evaluating a convolutional neural network in predicting future financial outcomes. A visually inspired transformation process translates high-frequency market microstructure data from the London Stock Exchange into four market-event based input channels, which are used to train six deep networks. Primary results indicate that con-volutional networks behave reasonably well on this task and extract interesting microstructure patterns, which are in line with previous theoretical findings. Furthermore, it demonstrates a new approach using modern deep-learning techniques for exploiting and analysing market microstructure behaviour

Magnetization precession due to a spin polarized current in a thin nanoelement: numerical simulation study

In this paper a detailed numerical study (in frames of the Slonczewski formalism) of magnetization oscillations driven by a spin-polarized current through a thin elliptical nanoelement is presented. We show that a sophisticated micromagnetic model, where a polycrystalline structure of a nanoelement is taken into account, can explain qualitatively all most important features of the magnetization oscillation spectra recently observed experimentally (S.I. Kiselev et al., Nature, vol. 425, p. 380 (2003), namely: existence of several equidistant spectral bands, sharp onset and abrupt disappearance of magnetization oscillations with increasing current, absence of the out-of-plane regime predicted by a macrospin model and the relation between frequencies of so called small-angle and quasichaotic oscillations. However, a quantitative agreement with experimental results (especially concerning the frequency of quasichaotic oscillations) could not be achieved in the region of reasonable parameter values, indicating that further model refinement is necessary for a complete understanding of the spin-driven magnetization precession even in this relatively simple experimental situation.Comment: Submitted to Phys. Rev. B; In this revised version figure positions on the page have been changed to ensure correct placements of the figure caption

DNA transport by a micromachined Brownian ratchet device

We have micromachined a silicon-chip device that transports DNA with a Brownian ratchet that rectifies the Brownian motion of microscopic particles. Transport properties for a DNA 50mer agree with theoretical predictions, and the DNA diffusion constant agrees with previous experiments. This type of micromachine could provide a generic pump or separation component for DNA or other charged species as part of a microscale lab-on-a-chip. A device with reduced feature size could produce a size-based separation of DNA molecules, with applications including the detection of single nucleotide polymorphisms.Comment: Latex: 8 pages, 4 figure