Two Welsh surveys of blood lead and blood pressure.

The relationship between blood pressure and blood lead was examined in two population samples. One of these consisted of 1137 men aged 49 to 65 years, the other of 865 men and 856 women aged 18 to 64 years. Neither population had any known important exposure to lead, and the 95% ranges of blood lead levels were 6 to 26 micrograms/100 mL and 6 to 23 micrograms/mL in the men and 5 to 18 micrograms/100 mL in the women. No significant relationship between blood pressure and blood lead was detected in either of the population samples, and the regression coefficients suggest that if there were a real effect, then the mean difference in blood pressure per 10 micrograms difference in blood lead is likely to be 0.7 mm Hg in both systolic and diastolic pressures. In the survey of 1137 men, the rise in blood pressure was measured during the cold pressor test. This test is likely to be affected if lead were to affect neurogenic mediators of blood pressure. The mean change in systolic pressure was 24 mm Hg and the 95% range was -6 to 60 mm Hg, but there was no evidence of any association with blood lead level

Using the fractional interaction law to model the impact dynamics in arbitrary form of multiparticle collisions

Using the molecular dynamics method, we examine a discrete deterministic model for the motion of spherical particles in three-dimensional space. The model takes into account multiparticle collisions in arbitrary forms. Using fractional calculus we proposed an expression for the repulsive force, which is the so called fractional interaction law. We then illustrate and discuss how to control (correlate) the energy dissipation and the collisional time for an individual article within multiparticle collisions. In the multiparticle collisions we included the friction mechanism needed for the transition from coupled torsion-sliding friction through rolling friction to static friction. Analysing simple simulations we found that in the strong repulsive state binary collisions dominate. However, within multiparticle collisions weak repulsion is observed to be much stronger. The presented numerical results can be used to realistically model the impact dynamics of an individual particle in a group of colliding particles.Comment: 17 pages, 8 figures, 1 table; In review process of Physical Review

On-Farm Participatory Research is an Essential Step Towards Achieving Successful Adoption of Innovation: ‘Lifetime Wool’ a Case Study

\u27Lifetime Wool\u27 project (LTW) is a national project that is developing new nutritional guidelines for the management of ewe flocks across Australia funded by farmers through Australian Wool Innovation (AWI EC298; 2001-2008). A large replicated plot-scale experiment was used to define the dose-response of current production (wool and reproduction from the ewe) and future production (survival, growth and wool from progeny over their lifetime) to a range of levels of ewe nutrition (Thompson & Oldham, 2004). However, farmers and research workers have long realised that the difference between the results obtained on experimental plots and those obtained by farmers is of crucial importance if farmers are to be convinced to adopt new technology (Davidson & Martin, 1968). Hence, the LTW was designed from the start to include four distinct phases: (i) plot-scale research (2001 2003; see Oldham et al. 2006); (ii) on-farm paddock-scale research (2003 - 2005); (iii) whole-farm systems modelling (see Young et al. 2004); and (iv) on-farm demonstration or \u27road-testing\u27 of the draft guidelines (2005-2007)

Non-Markovian Levy diffusion in nonhomogeneous media

We study the diffusion equation with a position-dependent, power-law diffusion coefficient. The equation possesses the Riesz-Weyl fractional operator and includes a memory kernel. It is solved in the diffusion limit of small wave numbers. Two kernels are considered in detail: the exponential kernel, for which the problem resolves itself to the telegrapher's equation, and the power-law one. The resulting distributions have the form of the L\'evy process for any kernel. The renormalized fractional moment is introduced to compare different cases with respect to the diffusion properties of the system.Comment: 7 pages, 2 figure

Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives

The classical fields with fractional derivatives are investigated by using the fractional Lagrangian formulation.The fractional Euler-Lagrange equations were obtained and two examples were studied.Comment: 9 page

Transport Equations from Liouville Equations for Fractional Systems

We consider dynamical systems that are described by fractional power of coordinates and momenta. The fractional powers can be considered as a convenient way to describe systems in the fractional dimension space. For the usual space the fractional systems are non-Hamiltonian. Generalized transport equation is derived from Liouville and Bogoliubov equations for fractional systems. Fractional generalization of average values and reduced distribution functions are defined. Hydrodynamic equations for fractional systems are derived from the generalized transport equation.Comment: 11 pages, LaTe

Fractional Hamilton formalism within Caputo's derivative

In this paper we develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives. Expressions for fractional canonical momenta and fractional canonical Hamiltonian are given, and a set of fractional Hamiltonian equations are obtained. Using an example, it is shown that the canonical fractional Hamiltonian and the fractional Euler-Lagrange formulations lead to the same set of equations.Comment: 8 page

Spectral Asymptotics of Eigen-value Problems with Non-linear Dependence on the Spectral Parameter

We study asymptotic distribution of eigen-values $\omega$ of a quadratic operator polynomial of the following form $(\omega^2-L(\omega))\phi_\omega=0$, where $L(\omega)$ is a second order differential positive elliptic operator with quadratic dependence on the spectral parameter $\omega$. We derive asymptotics of the spectral density in this problem and show how to compute coefficients of its asymptotic expansion from coefficients of the asymptotic expansion of the trace of the heat kernel of $L(\omega)$. The leading term in the spectral asymptotics is the same as for a Laplacian in a cavity. The results have a number of physical applications. We illustrate them by examples of field equations in external stationary gravitational and gauge backgrounds.Comment: latex, 20 page

Non-equilibrium Phase Transitions with Long-Range Interactions

This review article gives an overview of recent progress in the field of non-equilibrium phase transitions into absorbing states with long-range interactions. It focuses on two possible types of long-range interactions. The first one is to replace nearest-neighbor couplings by unrestricted Levy flights with a power-law distribution P(r) ~ r^(-d-sigma) controlled by an exponent sigma. Similarly, the temporal evolution can be modified by introducing waiting times Dt between subsequent moves which are distributed algebraically as P(Dt)~ (Dt)^(-1-kappa). It turns out that such systems with Levy-distributed long-range interactions still exhibit a continuous phase transition with critical exponents varying continuously with sigma and/or kappa in certain ranges of the parameter space. In a field-theoretical framework such algebraically distributed long-range interactions can be accounted for by replacing the differential operators nabla^2 and d/dt with fractional derivatives nabla^sigma and (d/dt)^kappa. As another possibility, one may introduce algebraically decaying long-range interactions which cannot exceed the actual distance to the nearest particle. Such interactions are motivated by studies of non-equilibrium growth processes and may be interpreted as Levy flights cut off at the actual distance to the nearest particle. In the continuum limit such truncated Levy flights can be described to leading order by terms involving fractional powers of the density field while the differential operators remain short-ranged.Comment: LaTeX, 39 pages, 13 figures, minor revision

Fractional Dirac Bracket and Quantization for Constrained Systems

So far, it is not well known how to deal with dissipative systems. There are many paths of investigation in the literature and none of them present a systematic and general procedure to tackle the problem. On the other hand, it is well known that the fractional formalism is a powerful alternative when treating dissipative problems. In this paper we propose a detailed way of attacking the issue using fractional calculus to construct an extension of the Dirac brackets in order to carry out the quantization of nonconservative theories through the standard canonical way. We believe that using the extended Dirac bracket definition it will be possible to analyze more deeply gauge theories starting with second-class systems.Comment: Revtex 4.1. 9 pages, two-column. Final version to appear in Physical Review