Studying the Perturbative Reggeon

We consider the flavour non-singlet Reggeon within the context of perturbative QCD. This consists of ladders built out of ``reggeized'' quarks. We propose a method for the numerical solution of the integro-differential equation for the amplitude describing the exchange of such a Reggeon. The solution is known to have a sharp rise at low values of Bjorken-x when applied to non-singlet quantities in deep-inelastic scattering. We show that when the running of the coupling is taken into account this sharp rise is further enhanced, although the Q^2 dependence is suppressed by the introduction of the running coupling. We also investigate the effects of simulating non-perturbative physics by introducing a constituent mass for the soft quarks and an effective mass for the soft gluons exchanged in the t-channel.Comment: LaTeX, 21 pages, 16 figure

Reply to "Comment(s) on `Preacceleration without radiation: The non-existence of preradiation phenomenon," by J. D. Jackson [Am. J. Phys. 75, 844-845 (2007)] and V. Hnizdo [Am. J. Phys. 75, 845-846 (2007)

This paper replies the comments by J. D. Jackson [Am. J. Phys. 75, 844-845 (2007)] and V. Hnizdo [Am. J. Phys. 75, 845-846 (2007)].Comment: 9 pages. See also the related paper: "E. Eriksen and O. Gron, Does preradiation exist? [Phys. Scr. 76, 60-63 (2007)].

Preacceleration without radiation: the non-existence of preradiation phenomenon

An unexpected prediction of classical electrodynamics is that a charge can accelerate before a force is applied. We would expect that a preaccelerated charge would radiate so that there would be spontaneous preradiation, an acausal phenomenon. We reexamine the subtle relation between the Larmor formula for the power radiated by a point charge and the Abraham-Lorentz equation and find that for well-behaved external forces acting for finite times, the charge does not radiate in time intervals where there is preacceleration. That is, for these forces preradiation does not exist even though the charge is preaccelerated. The radiative energy is emitted only in time intervals when the external force acts on the charge.Comment: Equation (37) of the published paper in AJP has been correcte

Plant root proliferation in nitrogen-rich patches confers competitive advantage

Plants respond to environmental heterogeneity, particularly below ground, where spectacular root proliferations in nutrient-rich patches may occur. Such 'foraging' responses apparently maximize nutrient uptake and are now prominent in plant ecological theory. Proliferations in nitrogen-rich patches are difficult to explain adaptively, however. The high mobility of soil nitrate should limit the contribution of proliferation to N capture. Many experiments on isolated plants show only a weak relation between proliferation and N uptake. We show that N capture is associated strongly with proliferation during interspecific competition for finite, locally available, mixed N sources, precisely the conditions under which N becomes available to plants on generally infertile soils. This explains why N-induced root proliferation is an important resource-capture mechanism in N-limited plant communities and suggests that increasing proliferation by crop breeding or genetic manipulation will have a limited impact on N capture by well-fertilized monocultures

A cross sectional study investigating the association between exposure to food outlets and childhood obesity in Leeds, UK.

Background: Current UK policy in relation to the influence of the ‘food environment’ on childhood obesity appears to be driven largely on assumptions or speculations because empirical evidence is lacking and findings from studies are inconsistent. The aim of this study was to investigate the number of food outlets and the proximity of food outlets in the same sample of children, without solely focusing on fast food. Methods: Cross sectional study over 3 years (n = 13,291 data aggregated). Body mass index (BMI) was calculated for each participant, overweight and obesity were defined as having a BMI >85th (sBMI 1.04) and 95th (sBMI 1.64) percentiles respectively (UK90 growth charts). Home and school neighbourhoods were defined as circular buffers with a 2 km Euclidean radius, centred on these locations. Commuting routes were calculated using the shortest straight line distance, with a 2 km buffer to capture varying routes. Data on food outlet locations was sourced from Leeds City Council covering the study area and mapped against postcode. Food outlets were categorised into three groups, supermarkets, takeaway and retail. Proximity to the nearest food outlet in the home and school environmental domain was also investigated. Age, gender, ethnicity and deprivation (IDACI) were included as covariates in all models. Results: There is no evidence of an association between the number of food outlets and childhood obesity in any of these environments; Home Q4 vs. Q1 OR = 1.11 (95% CI = 0.95-1.30); School Q4 vs. Q1 OR = 1.00 (95% CI 0.87 – 1.16); commute Q4 vs. Q1 OR = 0.1.00 (95% CI 0.83 – 1.20). Similarly there is no evidence of an association between the proximity to the nearest food outlet and childhood obesity in the home (OR = 0.77 [95% CI = 0.61 – 0.98]) or the school (OR = 1.01 [95% CI 0.84 – 1.23]) environment. Conclusions: This study provides little support for the notion that exposure to food outlets in the home, school and commuting neighbourhoods increase the risk of obesity in children. It seems that the evidence is not well placed to support Governmental interventions/recommendations currently being proposed and that policy makers should approach policies designed to limit food outlets with caution

Cosmic microwave background constraints on the epoch of reionization

We use a compilation of cosmic microwave anisotropy data to constrain the epoch of reionization in the Universe, as a function of cosmological parameters. We consider spatially-flat cosmologies, varying the matter density $\Omega_0$ (the flatness being restored by a cosmological constant), the Hubble parameter $h$ and the spectral index $n$ of the primordial power spectrum. Our results are quoted both in terms of the maximum permitted optical depth to the last-scattering surface, and in terms of the highest allowed reionization redshift assuming instantaneous reionization. For critical-density models, significantly-tilted power spectra are excluded as they cannot fit the current data for any amount of reionization, and even scale-invariant models must have an optical depth to last scattering of below 0.3. For the currently-favoured low-density model with $\Omega_0 = 0.3$ and a cosmological constant, the earliest reionization permitted to occur is at around redshift 35, which roughly coincides with the highest estimate in the literature. We provide general fitting functions for the maximum permitted optical depth, as a function of cosmological parameters. We do not consider the inclusion of tensor perturbations, but if present they would strengthen the upper limits we quote.Comment: 9 pages LaTeX file with ten figures incorporated (uses mn.sty and epsf). Corrects some equation typos, superseding published versio

An experimental and theoretical investigation of particle–wall impacts in a T-junction

Understanding the behaviour of particles entrained in a fluid flow upon changes in flow direction is crucial in problems where particle inertia is important, such as the erosion process in pipe bends.We present results on the impact of particles in a T-shaped channel in the laminar-turbulent transitional regime. The impacting event for a given system is described in terms of the Reynolds number and the particle Stokes number. Experimental results for the impact are compared with the trajectories predicted by theoretical particle tracing models for a range of configurations to determine the role of the viscous boundary layer in retarding the particles and reducing the rate of collision with the substrate. In particular a 2D model based on a stagnation point flow is used together with 3D numerical simulations. We show how the simple 2D model provides a tractable way of understanding the general collision behaviour, while more advanced 3D simulation can be helpful in understanding the details of the flow

Correlation inequalities for noninteracting Bose gases

For a noninteracting Bose gas with a fixed one-body Hamiltonian H^0 independent of the number of particles we derive the inequalities _N < _{N+1}, _N _N _N for i\neq j, \partial _N/\partial \beta >0 and ^+_N _N. Here N_i is the occupation number of the ith eigenstate of H^0, \beta is the inverse temperature and the superscript + refers to adding an extra level to those of H^0. The results follow from the convexity of the N-particle free energy as a function of N.Comment: a further inequality adde