Linear and fractal diffusion coefficients in a family of one dimensional chaotic maps

We analyse deterministic diffusion in a simple, one-dimensional setting consisting of a family of four parameter dependent, chaotic maps defined over the real line. When iterated under these maps, a probability density function spreads out and one can define a diffusion coefficient. We look at how the diffusion coefficient varies across the family of maps and under parameter variation. Using a technique by which Taylor-Green-Kubo formulae are evaluated in terms of generalised Takagi functions, we derive exact, fully analytical expressions for the diffusion coefficients. Typically, for simple maps these quantities are fractal functions of control parameters. However, our family of four maps exhibits both fractal and linear behavior. We explain these different structures by looking at the topology of the Markov partitions and the ergodic properties of the maps.Comment: 21 pages, 19 figure

Disentanglement and Decoherence without dissipation at non-zero temperatures

Decoherence is well understood, in contrast to disentanglement. According to common lore, irreversible coupling to a dissipative environment is the mechanism for loss of entanglement. Here, we show that, on the contrary, disentanglement can in fact occur at large enough temperatures $T$ even for vanishingly small dissipation (as we have shown previously for decoherence). However, whereas the effect of $T$ on decoherence increases exponentially with time, the effect of $T$ on disentanglement is constant for all times, reflecting a fundamental difference between the two phenomena. Also, the possibility of disentanglement at a particular $T$ increases with decreasing initial entanglement.Comment: 3 page

Force-directed scheduling in automatic data path synthesis

The HAL system performs data path synthesis using a new scheduling algorithm that 1s part Of an interdependent scheduling and allocation scheme. This scheme uses an BStl-mate of the hardware allocation to guide and optimiza the scheduling subtask. The allocation information includes the number. type. speed and cost of hardware modules as well as the associated multiplexer and interconnect costs. The iterative force-directed scheduling algorithm attempts to balance the distribution of operations that make use Of the same hardware resources:. Every feasible control step assignment is evaluated at each iteration, for a11 operations.. The associated side-effects on all the predecessor and successor operations are taken Into account.. All the decisions are global.. The algorithm has O(n*) complexity. We review and compare existing scheduling techniques. Mod-erate and difficult examples are used to illustrate the ef-fectiveness of the approach. 1

Capturing correlations in chaotic diffusion by approximation methods

We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line which contains dynamical correlations that change irregularly under parameter variation. Capturing these correlations by incorporating higher order terms, all schemes converge to the analytically exact result. Two of these methods are based on expanding the Taylor-Green-Kubo formula for diffusion, whilst the third method approximates Markov partitions and transition matrices by using the escape rate theory of chaotic diffusion. We check the practicability of the different methods by working them out analytically and numerically for a simple one-dimensional map, study their convergence and critically discuss their usefulness in identifying a possible fractal instability of parameter-dependent diffusion, in case of dynamics where exact results for the diffusion coefficient are not available.Comment: 11 pages, 5 figure

The Impacts of Retail Promotions on the Demand for Orange Juice: A Study of a Retail Chain

This study examined the impacts of retail promotions on the demand for five brands of orange juices for a retail chain (referred to as Retailer X) and its competitors using the Rotterdam model. Results show that the combination of feature ads and displays had the largest impacts on retail revenue among the four promotional tactics considered, while temporary price reductions had no additional advertising impacts other than price impacts on retail revenues. Results also show that when Retailer X promotes an OJ brand using any of the tactics studied, a larger portion of the increased demand for the promoted brand came from reduced demand for other brands of OJ in the same store and a smaller portion came from the decreased demand in competing stores in the same trading area.Demand and Price Analysis, Marketing,

An Economic analysis of the potential for precision farming in UK cereal production

The results from alternative spatial nitrogen application studies are analysed in economic terms and compared to the costs of precision farming hardware, software and other services for cereal crops in the UK. At current prices, the benefits of variable rate application of nitrogen exceed the returns from a uniform application by an average of £22 ha−1 The cost of the precision farming systems range from £5 to £18 ha−1 depending upon the system chosen for an area of 250 ha. The benefits outweigh the associated costs for cereal farms in excess of 80 ha for the lowest price system to 200–300 ha for the more sophisticated systems. The scale of benefits obtained depends upon the magnitude of the response to the treatment and the proportion of the field that will respond. To be cost effective, a farmed area of 250 ha of cereals, where 30% of the area will respond to variable treatment, requires an increase in crop yield in the responsive areas of between 0·25 and 1.00 t ha−1 (at £65 t−1) for the basic and most expensive precision farming systems, respectively

TB81: Investigations on the Life History and Habits of Pityokteines sparsus (Coleoptera: Scolytidae)

The primary objectives of this study are (1) to investigate the life history of Pityokteines sparsus (LeConte) in the Oxbow area of northern Maine; (2) to study the seasonal and daily flight behavior of the insect; (3) to investigate the food energy relations of the species.https://digitalcommons.library.umaine.edu/aes_techbulletin/1110/thumbnail.jp

Reply to the comments of M. S. Uberoi

We do not accept Uberoi’s grounds for his statement that turbulent line vortices do not exist. They are based on experiments on a trailing vortex.(1) In Ref. 2, we have presented the conditions under which a turbulent trailing vortex may be approximated by a turbulent line vortex. These conditions are not satisfied by Uberoi’s experiment