The 3-dimensional Fourier grid Hamiltonian method

A method to compute the bound state eigenvalues and eigenfunctions of a Schr\"{o}dinger equation or a spinless Salpeter equation with central interaction is presented. This method is the generalization to the three-dimensional case of the Fourier grid Hamiltonian method for one-dimensional Schr\"{o}dinger equation. It requires only the evaluation of the potential at equally spaced grid points and yields the radial part of the eigenfunctions at the same grid points. It can be easily extended to the case of coupled channel equations and to the case of non-local interactions.Comment: 13 pages, 1 figure. RevTeX file. To appear in J. Comput. Phy

Nonadiabatic effects in the H+H_2 exchange reaction: accurate quantum dynamics calculations at a state-to-state level

Real wave packet propagations were carried out on both a single ground electronic state and two-coupled-electronic states of the title reaction to investigate the extent of nonadiabatic effects on the distinguishable-atom reaction cross sections. The latest diabatic potential matrix of Abrol and Kuppermann [J. Chem. Phys. 116, 1035 (2002)] was employed in the present nonadiabatic quantum state-to-state scattering calculations over a total energy range-from threshold (the zero point of the reagent H_2) to 3.0 eV. Based on the assumption that the hydrogen atoms are distinguishable in the collisions where the inelastic and elastic ones are excluded, no significant nonadiabatic effects have been found in the calculations of the full state-to-state integral and differential cross sections up to a total energy of 3.0 eV for product vibrational levels v' = 0, 1, 2, 3. Our results therefore confirm the recent and the previous studies of the geometric phase effects in H+H_2 employing a different diabatic double many-body expansion potential matrix or a different BKMP2 potential energy surface

Southern leaf blight disease severity is correlated with decreased maize leaf epiphytic bacterial species richness and the phyllosphere bacterial diversity decline is enhanced by nitrogen fertilization

Plant leaves are inhabited by a diverse group of microorganisms that are important contributors to optimal growth. Biotic and abiotic effects on plant growth are usually studied in controlled settings examining response to variation in single factors and in field settings with large numbers of variables. Multi-factor experiments with combinations of stresses bridge this gap, increasing our understanding of the genotype-environment-phenotype functional map for the host plant and the affiliated epiphytic community. The maize inbred B73 was exposed to single and combination abiotic and the biotic stress treatments: low nitrogen fertilizer and high levels of infection with southern leaf blight (causal agent Cochliobolus heterostrophus). Microbial epiphyte samples were collected at the vegetative early-season phase and species composition was determined using 16S ribosomal intergenic spacer analysis. Plant traits and level of southern leaf blight disease were measured late-season. Bacterial diversity was different among stress treatment groups (P < 0.001). Lower species richness—alpha diversity—was correlated with increased severity of southern leaf blight disease when disease pressure was high. Nitrogen fertilization intensified the decline in bacterial alpha diversity. While no single bacterial ribotype was consistently associated with disease severity, small sets of ribotypes were good predictors of disease levels. Difference in leaf bacterial-epiphyte diversity early in the season were correlated with plant disease severity, supporting further tests of microbial epiphyte-disease correlations for use in predicting disease progression

Scattering solutions of the spinless Salpeter equation

A method to compute the scattering solutions of a spinless Salpeter equation (or a Schrodinger equation) with a central interaction is presented. This method relies on the 3-dimensional Fourier grid Hamiltonian method used to compute bound states. It requires only the evaluation of the potential at equally spaced grid points and yields the radial part of the scattering solution at the same grid points. It can be easily extended to the case of coupled channel equations and to the case of non-local interactions.Comment: 7 page

Bounds for Hamiltonians with arbitrary kinetic parts

A method is presented to compute approximate solutions for eigenequations in quantum mechanics with an arbitrary kinetic part. In some cases, the approximate eigenvalues can be analytically determined and they can be lower or upper bounds. A semiclassical interpretation of the generic formula obtained for the eigenvalues supports a new definition of the effective particle mass used in solid state physics. An analytical toy model with a Gaussian dependence in the momentum is studied in order to check the validity of the method.Comment: Improved version with new refernce

Quantum reactive scattering calculations of cross sections and rate constants for the N(2D) + O2(X3Σg-) → O(3Π) + NO(X2Π) reaction

Time-dependent quantum wavepacket calculations have been performed on the two lowest adiabatic potential energy surfaces (2 2A´ and 1 2A˝) for the N(2D) + O2(X3Σg-) → O(3Π) + NO(X2Π) reaction. The calculations have been carried out, on these recently published potential energy surfaces, using the real wavepacket method together with a new dispersion fitted finite difference technique for evaluating the action of the radial kinetic energy operator. Reaction probabilities, corresponding to the O2 reactant in its ground vibrational-rotational state, have been calculated for both surfaces and for many different values of the total angular momentum quantum number (J), within the helicity decoupling approximation. The reaction probabilities associated with all other relevant J values have been interpolated, and to a smaller extent extrapolated, using a capture model, to yield probabilities as a function of energy. The probabilities have in turn been summed to yield energy dependent cross sections and then used to compute rate constants. These rate constants are compared with ones obtained from quasiclassical trajectory (QCT) and variational transition state theory (VTST) calculations performed on the same surfaces. There is a good agreement between the wavepacket and QCT cross sections for reaction on both potential energy surfaces considered, with the exception of the near threshold region, where the reaction probability is dominated by tunnelling. Comparison of the predicted rate constants shows that for the 2 2A´ surface, above 300 K, the wavepacket, QCT and VTST results are quite similar. For the 1 2A˝ surface, however, significant differences occur between the wavepacket and the other methods. These differences become smaller with increasing temperature. It is likely that these differences arise, at least in part, from the fact that, when calculating the rate constants, the reactants are restricted to be in their lowest vibrational-rotational state in the wavepacket calculations but are selected from a thermally equilibrated population in the other methods

Coriolis coupling effects in the calculation of state-to-state integral and differential cross sections for the H+D-2 reaction

The quantum wavepacket parallel computational code DIFFREALWAVE is used to calculate state-to-state integral and differential cross sections for the title reaction on the BKMP2 surface in the total energy range of 0.4-1.2 eV with D-2 initially in its ground vibrational-rotational state. The role of Coriolis couplings in the state-to-state quantum calculations is examined in detail. Comparison of the results from calculations including the full Coriolis coupling and those using the centrifugal sudden approximation demonstrates that both the energy dependence and the angular dependence of the calculated cross sections are extremely sensitive to the Coriolis coupling, thus emphasizing the importance of including it correctly in an accurate state-to-state calculation. (c) 2007 American Institute of Physics

Resistance loci affecting distinct stages of fungal pathogenesis: use of introgression lines for QTL mapping and characterization in the maize - Setosphaeria turcica pathosystem

<p>Abstract</p> <p>Background</p> <p>Studies on host-pathogen interactions in a range of pathosystems have revealed an array of mechanisms by which plants reduce the efficiency of pathogenesis. While R-gene mediated resistance confers highly effective defense responses against pathogen invasion, quantitative resistance is associated with intermediate levels of resistance that reduces disease progress. To test the hypothesis that specific loci affect distinct stages of fungal pathogenesis, a set of maize introgression lines was used for mapping and characterization of quantitative trait loci (QTL) conditioning resistance to <it>Setosphaeria turcica</it>, the causal agent of northern leaf blight (NLB). To better understand the nature of quantitative resistance, the identified QTL were further tested for three secondary hypotheses: (1) that disease QTL differ by host developmental stage; (2) that their performance changes across environments; and (3) that they condition broad-spectrum resistance.</p> <p>Results</p> <p>Among a set of 82 introgression lines, seven lines were confirmed as more resistant or susceptible than B73. Two NLB QTL were validated in BC₄F₂segregating populations and advanced introgression lines. These loci, designated <it>qNLB1.02 </it>and <it>qNLB1.06</it>, were investigated in detail by comparing the introgression lines with B73 for a series of macroscopic and microscopic disease components targeting different stages of NLB development. Repeated greenhouse and field trials revealed that <it>qNLB1.06_Tx303</it>(the Tx303 allele at bin 1.06) reduces the efficiency of fungal penetration, while <it>qNLB1.02_B73</it>(the B73 allele at bin 1.02) enhances the accumulation of callose and phenolics surrounding infection sites, reduces hyphal growth into the vascular bundle and impairs the subsequent necrotrophic colonization in the leaves. The QTL were equally effective in both juvenile and adult plants; <it>qNLB1.06_Tx303</it>showed greater effectiveness in the field than in the greenhouse. In addition to NLB resistance, <it>qNLB1.02_B73</it>was associated with resistance to Stewart's wilt and common rust, while <it>qNLB1.06_Tx303</it>conferred resistance to Stewart's wilt. The non-specific resistance may be attributed to pleiotropy or linkage.</p> <p>Conclusions</p> <p>Our research has led to successful identification of two reliably-expressed QTL that can potentially be utilized to protect maize from <it>S. turcica </it>in different environments. This approach to identifying and dissecting quantitative resistance in plants will facilitate the application of quantitative resistance in crop protection.</p