Modelling the movement and survival of the root-feeding clover weevil, Sitona lepidus, in the root-zone of white clover

White clover (Trifolium repens) is an important pasture legume but is often difficult to sustain in a mixed sward because, among other things, of the damage to roots caused by the soil-dwelling larval stages of S. lepidus. Locating the root nodules on the white clover roots is crucial for the survival of the newly hatched larvae. This paper presents a numerical model to simulate the movement of newly hatched S. lepidus larvae towards the root nodules, guided by a chemical signal released by the nodules. The model is based on the diffusion-chemotaxis equation. Experimental observations showed that the average speed of the larvae remained approximately constant, so the diffusion-chernotaxis model was modified so that the larvae respond only to the gradient direction of the chemical signal but not its magnitude. An individual-based lattice Boltzmann method was used to simulate the movement of individual larvae, and the parameters required for the model were estimated from the measurement of larval movement towards nodules in soil scanned using X-ray microtomography. The model was used to investigate the effects of nodule density, the rate of release of chemical signal, the sensitivity of the larvae to the signal, and the random foraging of the larvae on the movement and subsequent survival of the larvae. The simulations showed that the most significant factors for larval survival were nodule density and the sensitivity of the larvae to the signal. The dependence of larval survival rate on nodule density was well fitted by the Michealis-Menten kinetics. (c) 2005 Elsevier B.V All rights reserved.

Modelling the movement and survival of the root-feeding clover weevil, Sitona lepidus, in the root-zone of white clover

White clover (Trifolium repens) is an important pasture legume but is often difficult to sustain in a mixed sward because, among other things, of the damage to roots caused by the soil-dwelling larval stages of S. lepidus. Locating the root nodules on the white clover roots is crucial for the survival of the newly hatched larvae. This paper presents a numerical model to simulate the movement of newly hatched S. lepidus larvae towards the root nodules, guided by a chemical signal released by the nodules. The model is based on the diffusion-chemotaxis equation. Experimental observations showed that the average speed of the larvae remained approximately constant, so the diffusion-chernotaxis model was modified so that the larvae respond only to the gradient direction of the chemical signal but not its magnitude. An individual-based lattice Boltzmann method was used to simulate the movement of individual larvae, and the parameters required for the model were estimated from the measurement of larval movement towards nodules in soil scanned using X-ray microtomography. The model was used to investigate the effects of nodule density, the rate of release of chemical signal, the sensitivity of the larvae to the signal, and the random foraging of the larvae on the movement and subsequent survival of the larvae. The simulations showed that the most significant factors for larval survival were nodule density and the sensitivity of the larvae to the signal. The dependence of larval survival rate on nodule density was well fitted by the Michealis-Menten kinetics. (c) 2005 Elsevier B.V All rights reserved.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Evaluation of data for atmospheric models: master equation/RRKM calculations on the combination reaction, BrO+NO2 -> BrONO2, a conundrum

Experimental data for the title reaction were modeled using master equation (ME)/RRKM methods based on the Multiwell suite of programs. The starting point for the exercise was the empirical fitting provided by the NASA (Sander, S. P.; Finlayson-Pitts, B. J.; Friedl, R. R.; Golden, D. M.; Huie, R. E.; Kolb, C. E.; Kurylo, M. J.; Molina, M. J.; Moortgat, G. K.; Orkin, V. L.; Ravishankara, A. R. Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies, Evaluation Number 15; Jet Propulsion Laboratory: Pasadena, California, 2006)(1) and IUPAC (Atkinson, R.; Baulch, D. L.; Cox, R. A.: R. F. Hampson, J.; Kerr, J. A.; Rossi, M. J.; Troe, J. J. Phys. Chem. Ref. Data. 2000, 29, 167) 2 data evaluation panels, which represents the data in the experimental pressure ranges rather well. Despite the availability of quite reliable parameters for these calculations (molecular vibrational frequencies (Parthiban, S.; Lee, T. J. J. Chem. Phys. 2000, 113, 145)3 and a. value (Orlando, J. J.; Tyndall, G. S. J. Phys. Chem. 1996, 100,. 19398)4 of the bond dissociation energy, D-298(BrO-NO2) = 118 kJ mol(-1), corresponding to Delta H-0(circle) = 114.3 kJ mol(-1) at 0 K) and the use of RRKM/ME methods, fitting calculations to the reported data or the empirical equations was anything but straightforward. Using these molecular parameters resulted in a discrepancy between the calculations and the database of rate constants of a factor of ca. 4 at, or close to, the low-pressure limit. Agreement between calculation and experiment could be achieved in two ways, either by increasing Delta H-0(circle) to an unrealistically high value (149.3 kJ mol(-1)) or by increasing , the average energy transferred in a downward collision, to an unusually large value (> 5000 cm(-1)). The discrepancy could also be reduced by making all overall rotations fully active. The system was relatively insensitive to changing the moments of inertia in the transition state to increase the centrifugal effect. The possibility of involvement of BrOONO was tested and cannot account for the difficulties of fitting the data.

A traceable physical calibration of the vertical advection-diffusion equation for modelling ocean heat uptake

The classic vertical advection-diffusion (VAD) balance is a central concept in studying the ocean heat budget, in particular in simple climate models (SCMs). Here we present a new framework to calibrate the parameters of the VAD equation to the vertical ocean heat balance of two fully-coupled climate models that is traceable to the models’ circulation as well as to vertical mixing and diffusion processes. Based on temperature diagnostics, we derive an effective vertical velocity w∗ and turbulent diffusivity k∗ for each individual physical process. In steady-state, we find that the residual vertical velocity and diffusivity change sign in mid-depth, highlighting the different regional contributions of isopycnal and diapycnal diffusion in balancing the models’ residual advection and vertical mixing. We quantify the impacts of the time-evolution of the effective quantities under a transient 1%CO2 simulation and make the link to the parameters of currently employed SCMs.

Understanding mixing efficiency in the oceans. Do the nonlinearities of the equation of state matter?

There exist two central measures of turbulent mixing in turbulent stratified fluids that are both caused by molecular diffusion: 1) the dissipation rate D(APE) of available potential energy APE; 2) the turbulent rate of change Wr, turbulent of background gravitational potential energy GPEr. So far, these two quantities have often been regarded as the same energy conversion, namely the irreversible conversion of APE into GPEr, owing to the well known exact equality D(APE)=Wr, turbulent for a Boussinesq fluid with a linear equation of state. Recently, however, Tailleux (2009) pointed out that the above equality no longer holds for a thermally-stratified compressible, with the ratio ξ=Wr, turbulent/D(APE) being generally lower than unity and sometimes even negative for water or seawater, and argued that D(APE) and Wr, turbulent actually represent two distinct types of energy conversion, respectively the dissipation of APE into one particular subcomponent of internal energy called the "dead" internal energy IE0, and the conversion between GPEr and a different subcomponent of internal energy called "exergy" IEexergy. In this paper, the behaviour of the ratio ξ is examined for different stratifications having all the same buoyancy frequency N vertical profile, but different vertical profiles of the parameter Υ=α P/(ρCp), where α is the thermal expansion coefficient, P the hydrostatic pressure, ρ the density, and Cp the specific heat capacity at constant pressure, the equation of state being that for seawater for different particular constant values of salinity. It is found that ξ and Wr, turbulent depend critically on the sign and magnitude of dΥ/dz, in contrast with D(APE), which appears largely unaffected by the latter. These results have important consequences for how the mixing efficiency should be defined and measured in practice, which are discussed.

An investigation of the germylene addition reaction, GeH2+C2H2: Time-resolved gas-phase kinetic studies and quantum chemical calculations of the reaction energy surface

Time resolved studies of germylene, GeH2, generated by laser flash photolysis of 3,4-dimethylgermacyclopentene-3, have been carried out to obtain rate constants for its bimolecular reaction with acetylene, C2H2. The reaction was studied in the gas-phase over the pressure range 1-100 Tort, with SF6 as bath gas, at 5 temperatures in the range 297-553 K. The reaction showed a very slight pressure dependence at higher temperatures. The high pressure rate constants (obtained by extrapolation at the three higher temperatures) gave the Arrhenius equation: log(k(infinity)/cm(3) molecule(-1) s(-1)) (-10.94 +/- 0.05) + (6.10 +/- 0.36 kJ mol(-1))/RTln10. These Arrhenius parameters are consistent with a fast reaction occurring at approximately 30% of the collision rate at 298 K. Quantum chemical calculations (both DFT and ab initio G2//B3LYP and G2//QCISD) of the GeC2H4 potential energy surface (PES), show that GeH2 + C2H2 react initially to form germirene which can isomerise to vinylgermylene with a relatively low barrier. RRKM modelling, based on a loose association transition state, but assuming vinylgermylene is the end product (used in combination with a weak collisional deactivation model) predicts a strong pressure dependence using the calculated energies, in conflict with the experimental evidence. The detailed GeC2H4 PES shows considerable complexity with ten other accessible stable minima (B3LYP level), the three most stable of which are all germylenes. Routes through this complex surface were examined in detail. The only product combination which appears capable of satisfying the (P-3) + C2H4.C2H4 was confirmed as a product by GC observed lack of a strong pressure dependence is Ge(P-3) + C2H4. C2H4 was confirmed as a product by GC analysis. Although the formation of these products are shown to be possible by singlet-triplet curve crossing during dissociation of 1-germiranylidene (1-germacyclopropylidene), it seems more likely (on thermochernical grounds) that the triplet biradical, (GeCH2CH2.)-Ge-., is the immediate product precursor. Comparisons are made with the reaction of SiH2 with C2H2.

Time-resolved gas-phase kinetic and quantum chemical studies of the reaction of silylene with oxygen

Time-resolved kinetic studies of the reaction of silylene, SiH2, generated by laser flash photolysis of phenylsilane, have been carried out to obtain rate constants for its bimolecular reaction with O-2. The reaction was studied in the gas phase over the pressure range 1-100 Torr in SF6 bath gas, at five temperatures in the range 297-600 K. The second order rate constants at 10 Torr were fitted to the Arrhenius equation: log(k/cm(3) molecule(-1) s(-1)) = (-11.08 +/- 0.04) + (1.57 +/- 0.32 kJ mol(-1))/RT ln10 The decrease in rate constant values with increasing temperature, although systematic is very small. The rate constants showed slight increases in value with pressure at each temperature, but this was scarcely beyond experimental uncertainty. From estimates of Lennard-Jones collision rates, this reaction is occurring at ca. 1 in 20 collisions, almost independent of pressure and temperature. Ab initio calculations at the G3 level backed further by multi-configurational (MC) SCF calculations, augmented by second order perturbation theory (MRMP2), support a mechanism in which the initial adduct, H2SiOO, formed in the triplet state (T), undergoes intersystem crossing to the more stable singlet state (S) prior to further low energy isomerisation processes leading, via a sequence of steps, ultimately to dissociation products of which the lowest energy pair are H2O + SiO. The decomposition of the intermediate cyclo-siladioxirane, via O-O bond fission, plays an important role in the overall process. The bottleneck for the overall process appears to be the T -> S process in H2SiOO. This process has a small spin orbit coupling matrix element, consistent with an estimate of its rate constant of 1 x 10(9) s(-1) obtained with the aid of RRKM theory. This interpretation preserves the idea that, as in its reactions in general, SiH2 initially reacts at the encounter rate with O-2. The low values for the secondary reaction barriers on the potential energy surface account for the lack of an observed pressure dependence. Some comparisons are drawn with the reactions of CH2 + O-2 and SiCl2 + O-2.

Time-resolved gas-phase kinetic and quantum chemical studies of the reaction of silylene with nitric oxide

Time-resolved kinetic studies of the reaction of silylene, SiH2, generated by laser flash photolysis of phenylsilane, have been carried out to obtain rate constants for its bimolecular reaction with NO. The reaction was studied in the gas phase over the pressure range 1-100 Torr in SF6 bath gas at five temperatures in the range 299-592 K. The second-order rate constants at 10 Torr fitted the Arrhenius equation log(k/cm(3) molecule(-1) s(-1)) = (- 11.66 +/- 0.01) + (6.20 +/- 0.10 kJ mol(-1))IRT In 10 The rate constants showed a variation with pressure of a factor of ca. 2 over the available range, almost independent of temperature. The data could not be fitted by RRKM calculations to a simple third body assisted association reaction alone. However, a mechanistic model with an additional (pressure independent) side channel gave a reasonable fit to the data. Ab initio calculations at the G3 level supported a mechanism in which the initial adduct, bent H2SiNO, can ring close to form cyclo-H2SiNO, which is partially collisionally stabilized. In addition, bent H2SiNO can undergo a low barrier isomerization reaction leading, via a sequence of steps, ultimately to dissociation products of which the lowest energy pair are NH2 + SiO. The rate controlling barrier for this latter pathway is only 16 kJ mol(-1) below the energy of SiH2 + NO. This is consistent with the kinetic findings. A particular outcome of this work is that, despite the pressure dependence and the effects of the secondary barrier (in the side reaction), the initial encounter of SiH2 with NO occurs at the collision rate. Thus, silylene can be as reactive with odd electron molecules as with many even electron species. Some comparisons are drawn with the reactions of CH2 + NO and SiCl2 + NO.