Existence and Stability of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem

We extend our previous analytic existence of a symmetric periodic simultaneous binary collision orbit in a regularized fully symmetric equal mass four-body problem to the analytic existence of a symmetric periodic simultaneous binary collision orbit in a regularized planar pairwise symmetric equal mass four-body problem. We then use a continuation method to numerically find symmetric periodic simultaneous binary collision orbits in a regularized planar pairwise symmetric 1, m, 1, m four-body problem for $m$ between 0 and 1. Numerical estimates of the the characteristic multipliers show that these periodic orbits are linearly stability when $0.54\leq m\leq 1$, and are linearly unstable when $0<m\leq0.53$.Comment: 6 figure

Varietal differences in rate of carbohydrate accumulation for tall fescue

Total non-structural carbohydrates (TNC) accumulate during daylight because photosynthesis produces more TNC than are metabolized for plant growth and maintenance. The net balance of leaf photosynthesis, respiration, and carbohydrate export produces a diurnal variation in TNC such that minimum concentrations occur in early morning and maximum in late afternoon. The objectives were to determine variability of TNC concentrations among cultivars, and to investigate daily rates of carbohydrate accumulation in tall fescue (Lolium arundinaceum (Schreb .) S J . Darbyshire= Festuca arundinacea Schreb .

A Survey of the Nutrients Status of Sugarbeets Grown in Idaho and Washington

Sugarbeets are a major irrigated crop in Idaho and Washington. In recent years foliar sprays of several nutrient elements, especially the micronutrients, have been recommended by commercial consultants and applicators. As a result, many acres not only of beets but other crops as well have received foliar sprays containing one or more nutrient elements. Consequently, many questions have arisen concerning the need for such applications, especially when the crop appears to be growing well without them, and since definite responses to Cu, Fe, and Mn have not been documented and responses to Zn and B have been very few

K -> pi pi and a light scalar meson

We explore the Delta-I= 1/2 rule and epsilon'/epsilon in K -> pi pi transitions using a Dyson-Schwinger equation model. Exploiting the feature that QCD penguin operators direct K^0_S transitions through 0^{++} intermediate states, we find an explanation of the enhancement of I=0 K -> pi pi transitions in the contribution of a light sigma-meson. This mechanism also affects epsilon'/epsilon.Comment: 7 pages, REVTE

Disease effects on reproduction can cause population cycles in seasonal environments

Recent studies of rodent populations have demonstrated that certain parasites can cause juveniles to delay maturation until the next reproductive season. Furthermore, a variety of parasites may share the same host, and evidence is beginning to accumulate showing nonindependent effects of different infections.We investigated the consequences for host population dynamics of a disease-induced period of no reproduction, and a chronic reduction in fecundity following recovery from infection (such as may be induced by secondary infections) using a modified SIR (susceptible, infected, recovered) model. We also included a seasonally varying birth rate as recent studies have demonstrated that seasonally varying parameters can have important effects on long-term host–parasite dynamics. We investigated the model predictions using parameters derived from five different cyclic rodent populations.Delayed and reduced fecundity following recovery from infection have no effect on the ability of the disease to regulate the host population in the model as they have no effect on the basic reproductive rate. However, these factors can influence the long-term dynamics including whether or not they exhibit multiyear cycles.The model predicts disease-induced multiyear cycles for a wide range of realistic parameter values. Host populations that recover relatively slowly following a disease-induced population crash are more likely to show multiyear cycles. Diseases for which the period of infection is brief, but full recovery of reproductive function is relatively slow, could generate large amplitude multiyear cycles of several years in length. Chronically reduced fecundity following recovery can also induce multiyear cycles, in support of previous theoretical studies.When parameterized for cowpox virus in the cyclic field vole populations (Microtus agrestis) of Kielder Forest (northern England), the model predicts that the disease must chronically reduce host fecundity by more than 70%, following recovery from infection, for it to induce multiyear cycles. When the model predicts quasi-periodic multiyear cycles it also predicts that seroprevalence and the effective date of onset of the reproductive season are delayed density-dependent, two phenomena that have been recorded in the field

Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities

We examine in detail the relative equilibria in the four-vortex problem where two pairs of vortices have equal strength, that is, \Gamma_1 = \Gamma_2 = 1 and \Gamma_3 = \Gamma_4 = m where m is a nonzero real parameter. One main result is that for m > 0, the convex configurations all contain a line of symmetry, forming a rhombus or an isosceles trapezoid. The rhombus solutions exist for all m but the isosceles trapezoid case exists only when m is positive. In fact, there exist asymmetric convex configurations when m < 0. In contrast to the Newtonian four-body problem with two equal pairs of masses, where the symmetry of all convex central configurations is unproven, the equations in the vortex case are easier to handle, allowing for a complete classification of all solutions. Precise counts on the number and type of solutions (equivalence classes) for different values of m, as well as a description of some of the bifurcations that occur, are provided. Our techniques involve a combination of analysis and modern and computational algebraic geometry

Daily carbohydrate accumulation in eight tall fescue cultivars

Eight cultivars of tall fescue (Loliumarundinaceum Schreb., S.J. Darbyshire = Festuca arundinacea Schreb.), Barcel, Kenhy, Kentucky-31, Missouri-96, Mozark, Stargrazer, C-1 (an experimental selection), and HiMag, were sampled at 2-h intervals during daylight on four cutting dates. Cultivars varied in concentrations of carbohydrate fractions but accumulation rates were not different. Daily mean total non-structural carbohydrate (TNC) concentrations for cutting dates in May, July, August and September declined from 239 to 231, 143 and 120 g TNC kg?1 adjusted dry weight (ADW) respectively. Concentrations of fructans were highest in July but sucrose, glucose and starch concentrations were highest in May. Sucrose was the largest contributor proportionately to TNC daily means across accessions in May (0·33), August (0·30) and September (0·38). Glucose composed an equivalent proportion of TNC in the August harvest. Starch concentration was highest in May at 53 g kg?1 ADW and lowest in August at 23 g kg?1 ADW. The TNC concentration increased by 22·4 (May), 16·8 (July), 21·0 (August) and 30·8 g kg?1 ADW (September) from dawn to dusk. Forage samples taken to estimate preference by ruminants or for TNC analyses should be cut and preserved within 1 h to control the diurnal variation of TNC proportionately within 0·05. Tall fescue should generally be cut between noon and sunset for TNC concentrations to be greater than the daily mean

Probing semiclassical analogue gravity in Bose--Einstein condensates with widely tunable interactions

Bose-Einstein condensates (BEC) have recently been the subject of considerable study as possible analogue models of general relativity. In particular it was shown that the propagation of phase perturbations in a BEC can, under certain conditions, closely mimic the dynamics of scalar quantum fields in curved spacetimes. In two previous articles [gr-qc/0110036, gr-qc/0305061] we noted that a varying scattering length in the BEC corresponds to a varying speed of light in the ``effective metric''. Recent experiments have indeed achieved a controlled tuning of the scattering length in Rubidium 85. In this article we shall discuss the prospects for the use of this particular experimental effect to test some of the predictions of semiclassical quantum gravity, for instance, particle production in an expanding universe. We stress that these effects are generally much larger than the Hawking radiation expected from causal horizons, and so there are much better chances for their detection in the near future.Comment: 18 pages; uses revtex4. V2: Added brief discussion of "Bose-Nova" phenomenon, and appropriate reference

Euler configurations and quasi-polynomial systems

In the Newtonian 3-body problem, for any choice of the three masses, there are exactly three Euler configurations (also known as the three Euler points). In Helmholtz' problem of 3 point vortices in the plane, there are at most three collinear relative equilibria. The "at most three" part is common to both statements, but the respective arguments for it are usually so different that one could think of a casual coincidence. By proving a statement on a quasi-polynomial system, we show that the "at most three" holds in a general context which includes both cases. We indicate some hard conjectures about the configurations of relative equilibrium and suggest they could be attacked within the quasi-polynomial framework.Comment: 21 pages, 6 figure

Streamer Wave Events Observed in Solar Cycle 23

In this paper we conduct a data survey searching for well-defined streamer wave events observed by the Large Angle and Spectrometric Coronagraph (LASCO) on-board the Solar and Heliospheric Observatory (SOHO) throughout Solar Cycle 23. As a result, 8 candidate events are found and presented here. We compare different events and find that in most of them the driving CMEs ejecta are characterized by a high speed and a wide angular span, and the CME-streamer interactions occur generally along the flank of the streamer structure at an altitude no higher than the bottom of the field of view of LASCO C2. In addition, all front-side CMEs have accompanying flares. These common observational features shed light on the excitation conditions of streamer wave events. We also conduct a further analysis on one specific streamer wave event on 5 June 2003. The heliocentric distances of 4 wave troughs/crests at various exposure times are determined; they are then used to deduce the wave properties like period, wavelength, and phase speeds. It is found that both the period and wavelength increase gradually with the wave propagation along the streamer plasma sheet, and the phase speed of the preceding wave is generally faster than that of the trailing ones. The associated coronal seismological study yields the radial profiles of the Alfv\'en speed and magnetic field strength in the region surrounding the streamer plasma sheet. Both quantities show a general declining trend with time. This is interpreted as an observational manifestation of the recovering process of the CME-disturbed corona. It is also found that the Alfv\'enic critical point is at about 10 R$_\odot$ where the flow speed, which equals the Alfv\'en speed, is $\sim$ 200 km s$^{-1}$