Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function

A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of the Helmholtz Green function are split into their half advanced+half retarded and half advanced-half retarded components. Closed form solutions are given for these components in terms of a Horn function and a Kampe de Feriet function, respectively. The systems of partial differential equations associated with these two-dimensional hypergeometric functions are used to construct a fourth-order ordinary differential equation which both components satisfy. A second fourth-order ordinary differential equation for the general Fourier coefficent is derived from an integral representation of the coefficient, and both differential equations are shown to be equivalent. Series solutions for the various Fourier coefficients are also given, mostly in terms of Legendre functions and Bessel/Hankel functions. These are derived from the closed form hypergeometric solutions or an integral representation, or both. Numerical calculations comparing different methods of calculating the Fourier coefficients are presented

A key-formula to compute the gravitational potential of inhomogeneous discs in cylindrical coordinates

We have established the exact expression for the gravitational potential of a homogeneous polar cell - an elementary pattern used in hydrodynamical simulations of gravitating discs. This formula, which is a closed-form, works for any opening angle and radial extension of the cell. It is valid at any point in space, i.e. in the plane of the distribution (inside and outside) as well as off-plane, thereby generalizing the results reported by Durand (1953) for the circular disc. The three components of the gravitational acceleration are given. The mathematical demonstration proceeds from the "incomplete version of Durand's formula" for the potential (based on complete elliptic integrals). We determine first the potential due to the circular sector (i.e. a pie-slice sheet), and then deduce that of the polar cell (from convenient radial scaling and subtraction). As a by-product, we generate an integral theorem stating that "the angular average of the potential of any circular sector along its tangent circle is 2/PI times the value at the corner". A few examples are presented. For numerical resolutions and cell shapes commonly used in disc simulations, we quantify the importance of curvature effects by performing a direct comparison between the potential of the polar cell and that of the Cartesian (i.e. rectangular) cell having the same mass. Edge values are found to deviate roughly like 2E-3 x N/256 in relative (N is the number of grid points in the radial direction), while the agreement is typically four orders of magnitude better for values at the cell's center. We also produce a reliable approximation for the potential, valid in the cell's plane, inside and close to the cell. Its remarkable accuracy, about 5E-4 x N/256 in relative, is sufficient to estimate the cell's self-acceleration.Comment: Accepted for publication in Celestial Mechanics and Dynamical Astronom

A framework for the local information dynamics of distributed computation in complex systems

The nature of distributed computation has often been described in terms of the component operations of universal computation: information storage, transfer and modification. We review the first complete framework that quantifies each of these individual information dynamics on a local scale within a system, and describes the manner in which they interact to create non-trivial computation where "the whole is greater than the sum of the parts". We describe the application of the framework to cellular automata, a simple yet powerful model of distributed computation. This is an important application, because the framework is the first to provide quantitative evidence for several important conjectures about distributed computation in cellular automata: that blinkers embody information storage, particles are information transfer agents, and particle collisions are information modification events. The framework is also shown to contrast the computations conducted by several well-known cellular automata, highlighting the importance of information coherence in complex computation. The results reviewed here provide important quantitative insights into the fundamental nature of distributed computation and the dynamics of complex systems, as well as impetus for the framework to be applied to the analysis and design of other systems.Comment: 44 pages, 8 figure

Optimal low-thrust trajectories to asteroids through an algorithm based on differential dynamic programming

In this paper an optimisation algorithm based on Differential Dynamic Programming is applied to the design of rendezvous and fly-by trajectories to near Earth objects. Differential dynamic programming is a successive approximation technique that computes a feedback control law in correspondence of a fixed number of decision times. In this way the high dimensional problem characteristic of low-thrust optimisation is reduced into a series of small dimensional problems. The proposed method exploits the stage-wise approach to incorporate an adaptive refinement of the discretisation mesh within the optimisation process. A particular interpolation technique was used to preserve the feedback nature of the control law, thus improving robustness against some approximation errors introduced during the adaptation process. The algorithm implements global variations of the control law, which ensure a further increase in robustness. The results presented show how the proposed approach is capable of fully exploiting the multi-body dynamics of the problem; in fact, in one of the study cases, a fly-by of the Earth is scheduled, which was not included in the first guess solution

Kaon-Nucleus Drell-Yan Processes and Kaon Structure Functions

We investigate the information which could be obtained from Drell-Yan processes with sufficiently intense beams of charged kaons on isoscalar targets. It is found that combinations of $K^+$ and $K^-$ Drell-Yan measurements on isoscalar nuclear targets would allow one to extract the kaon sea quark distributions. These cross sections are also sensitive to the strange valence quark distribution in the kaon, although one would need a significant increase over the presently available kaon fluxes in order to extract this quantity with sufficient accuracy.Comment: 9 pages plus 4 figures, on eps

Prediagnostic smoking is associated with binary and quantitative measures of ER protein and ESR1 mRNA expression in breast tumors

Background: Smoking is a possible risk factor for breast cancer and has been linked to increased risk of estrogen receptor-positive (ER+) disease in some epidemiologic studies. It is unknown whether smoking has quantitative effects on ER expression. Methods: We examined relationships between smoking and ER expression from tumors of 1,888 women diagnosed with invasive breast cancer from a population-based study in North Carolina. ER expression was characterized using binary (±) and continuous measures for ER protein, ESR1 mRNA, and a multigene luminal score (LS) that serves as a measure of estrogen signaling in breast tumors. We used logistic and linear regression models to estimate temporal and dose-dependent associations between smoking and ER measures. Results: The odds of ER+, ESR1+, and LS+ tumors among current smokers (at the time of diagnosis), those who smoked 20 or more years, and those who smoked within 5 years of diagnosis were nearly double those of nonsmokers. Quantitative levels of ESR1 were highestamong current smokers compared with never smokers overall [mean (log2) = 9.2 vs. 8.7, P > 0.05] and among ER+ cases; however, we did not observe associations betweensmokingmeasures and continuous ER protein expression. Conclusions: In relationship to breast cancer diagnosis, recent smoking was associated with higher odds of the ER+, ESR1+, and LS+ subtype. Current smoking was associated with elevated ESR1 mRNA levels and an elevated LS, but not with altered ER protein. Impact: A multigene LS and single-gene ESR1 mRNA may capture tumor changes associated with smoking

Valence-quark distributions in the pion

We calculate the pion's valence-quark momentum-fraction probability distribution using a Dyson-Schwinger equation model. Valence-quarks with an active mass of 0.30 GeV carry 71% of the pion's momentum at a resolving scale q_0=0.54 GeV = 1/(0.37 fm). The shape of the calculated distribution is characteristic of a strongly bound system and, evolved from q_0 to q=2 GeV, it yields first, second and third moments in agreement with lattice and phenomenological estimates, and valence-quarks carrying 49% of the pion's momentum. However, pointwise there is a discrepancy between our calculated distribution and that hitherto inferred from parametrisations of extant pion-nucleon Drell-Yan data.Comment: 8 pages, 3 figures, REVTEX, aps.sty, epsfig.sty, minor corrections, version to appear in PR

Comparison of three wet-alkaline methods of digestion of biogenic silica in water

Methods for determination of low levels of biogenic silica (0.2–0.4 mg SiO 2 ) in aqueous samples after digestion with three wetalkaline extraction procedures compared favourably in both precision of replicates and recovery of silica utilized by diatoms in budgeted cultures. Leaching samples with 0.2 M NaOH for 10–15 min at 100°C was the least time consuming procedure. Also interference from silicate minerals was lower for this method than leaching with either 0.5 or 5% Na 2 CO 3 for 2 h at 85°C. The use of filters to concentrate samples enables detection of low levels of biogenic silica with colorimetric procedures. Polycarbonate filters are recommended in preference to cellulose acetate or polyvinyl chloride filters for sample collection. Time-course experiments are recommended for establishing digestion times and determining the presence of mineral silicate interference. Wet-alkaline digestion methods are recommended for routine analysis of biogenic silica in suspended matter in preference to infra-red analysis, alkaline fusion and hydrofluoric acid/nitric acid methods.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74725/1/j.1365-2427.1983.tb00658.x.pd

The PHENIX Experiment at RHIC

The physics emphases of the PHENIX collaboration and the design and current status of the PHENIX detector are discussed. The plan of the collaboration for making the most effective use of the available luminosity in the first years of RHIC operation is also presented.Comment: 5 pages, 1 figure. Further details of the PHENIX physics program available at http://www.rhic.bnl.gov/phenix

Landscape-scale species monitoring of agri-environment schemes (LandSpAES project). Final project report, 2022

In this project, we applied a novel, pseudo-experimental design in order to collect a baseline survey dataset of the responses of mobile taxa to local and landscape AES gradients over four years, from 54 survey squares across six regions (NCAs) in England. This is the first project to monitor the responses of multiple mobile taxa to generalised AES gradients across large spatial extents, which were applied to arable, grassland and upland agricultural systems, in order specifically to address impacts beyond AES option or agreement boundaries. This baseline dataset supported a spatial assessment of relationships between the AES gradients and taxon abundance (or activity), species richness and diversity. Strong evidence for relationships with local and / or landscape AES gradients were found for one or more response variable for butterflies, moths and bats. Little or no evidence of AES gradient relationships were found for either bees or hoverflies and weak evidence for associations with bird metrics. A future resurvey would allow analyses of the longer-term changes in target taxa in response to AES management, against this baseline. The identification of various spatial relationships is encouraging in terms of the likely power to detect AES effects on biodiversity change in the future