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]

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

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,

Absence of Evidence for the Ultimate Regime in Two-Dimensional Rayleigh-B\'enard Convection

This work is equivalent to that in {\em Phys. Rev. Lett.} {\bf 123}, 259401 (2019), however, Physical Review Letters prohibited reference to the additional two points in the analysis published by Zhu et al., in {\em Phys. Rev. Lett.} {\bf 123}, 259402 (2019).Comment: 1 page, 1 figur

A Comparison of Turbulent Thermal Convection Between Conditions of Constant Temperature and Constant Flux

We report the results of high resolution direct numerical simulations of two-dimensional Rayleigh-B\'enard convection for Rayleigh numbers up to \Ra=10^{10} in order to study the influence of temperature boundary conditions on turbulent heat transport. Specifically, we considered the extreme cases of fixed heat flux (where the top and bottom boundaries are poor thermal conductors) and fixed temperature (perfectly conducting boundaries). Both cases display identical heat transport at high Rayleigh numbers fitting a power law \Nu \approx 0.138 \times \Ra^{.285} with a scaling exponent indistinguishable from $2/7 = .2857...$ above \Ra = 10^{7}. The overall flow dynamics for both scenarios, in particular the time averaged temperature profiles, are also indistinguishable at the highest Rayleigh numbers. The findings are compared and contrasted with results of recent three-dimensional simulations.Comment: 4 page, two column RevTex4 format, 5 figure

Variational bound on energy dissipation in plane Couette flow

We present numerical solutions to the extended Doering-Constantin variational principle for upper bounds on the energy dissipation rate in turbulent plane Couette flow. Using the compound matrix technique in order to reformulate this principle's spectral constraint, we derive a system of equations that is amenable to numerical treatment in the entire range from low to asymptotically high Reynolds numbers. Our variational bound exhibits a minimum at intermediate Reynolds numbers, and reproduces the Busse bound in the asymptotic regime. As a consequence of a bifurcation of the minimizing wavenumbers, there exist two length scales that determine the optimal upper bound: the effective width of the variational profile's boundary segments, and the extension of their flat interior part.Comment: 22 pages, RevTeX, 11 postscript figures are available as one uuencoded .tar.gz file from [email protected]

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