Double Compton effect with high intensity radiation

Double Compton effect with high intensity radiatio

Numerical equilibrium analysis for structured consumer resource models

In this paper, we present methods for a numerical equilibrium and stability analysis for models of a size structured population competing for an unstructured resource. We concentrate on cases where two model parameters are free, and thus existence boundaries for equilibria and stability boundaries can be defined in the (two-parameter) plane. We numerically trace these implicitly defined curves using alternatingly tangent prediction and Newton correction. Evaluation of the maps defining the curves involves integration over individual size and individual survival probability (and their derivatives) as functions of individual age. Such ingredients are often defined as solutions of ODE, i.e., in general only implicitly. In our case, the right-hand sides of these ODE feature discontinuities that are caused by an abrupt change of behavior at the size where juveniles are assumed to turn adult. So, we combine the numerical solution of these ODE with curve tracing methods. We have implemented the algorithms for “Daphnia consuming algae” models in C-code. The results obtained by way of this implementation are shown in the form of graphs

Weighted Bergman kernels and virtual Bergman kernels

We introduce the notion of "virtual Bergman kernel" and apply it to the computation of the Bergman kernel of "domains inflated by Hermitian balls", in particular when the base domain is a bounded symmetric domain.Comment: 12 pages. One-hour lecture for graduate students, SCV 2004, August 2004, Beijing, P.R. China. V2: typo correcte

Multireference Correlation in Long Molecules with the Quadratic Scaling Density Matrix Renormalization Group

We have devised and implemented a local ab initio Density Matrix Renormalization Group (DMRG) algorithm to describe multireference nondynamic correlations in large systems. For long molecules that are extended in one of their spatial dimensions, this method allows us to obtain an exact characterisation of correlation, in the given basis, with a cost that scales only quadratically with the size of the system. The reduced scaling is achieved solely through integral screening and without the construction of correlation domains. We demonstrate the scaling, convergence, and robustness of the algorithm in polyenes and hydrogen chains. We converge to exact correlation energies (with 1-10 microhartree precision) in all cases and correlate up to 100 electrons in 100 active orbitals. We further use our algorithm to obtain exact energies for the metal-insulator transition in hydrogen chains and compare and contrast our results with those from conventional quantum chemical methods.Comment: 14 pages, 12 figures, tciLaTeX, aip-BibTeX styl

Theoretical calculations for solid oxygen under high pressure

The crystal structure of solid oxygen at low temperatures and at pressures up to 7 GPa is studied by theoretical calculations. In the calculations, the adiabatic potential of the crystal is approximated by a superposition of pair-potentials between oxygen molecules calculated by an ab-initio method. The monoclinic alpha structure is stable up to 6 GPa and calculated lattice parameters agree well with experiments. The origin of a distortion and that of an anisotropic lattice compressibility of the basal plane of alpha-O2 are clearly demonstrated. In the pressure range from 6 to 7 GPa, two kinds of structures are proposed by X-ray diffraction experiments: the alpha and orthorhombic delta structures. It is found that the energy difference between these structures becomes very small in this pressure range. The relation between this trend and the incompatible results of X-ray diffraction experiments is discussed.Comment: 12 pages, 6 figure

Computation of conical intersections by using perturbation techniques

Multiconfigurational second-order perturbation theory, both in its single-state multiconfigurational second-order perturbation theory (CASPT2) and multistate (MS-CASPT2) formulations, is used to search for minima on the crossing seams between different potential energy hypersurfaces of electronic states in several molecular systems. The performance of the procedures is tested and discussed, focusing on the problem of the nonorthogonality of the single-state perturbative solutions. In different cases the obtained structures and energy differences are compared with available complete active space self-consistent field and multireference configuration interaction solutions. Calculations on different state crossings in LiF, formaldehyde, the ethene dimer, and the penta-2,4-dieniminium cation illustrate the discussions. Practical procedures to validate the CASPT2 solutions in polyatomic systems are explored, while it is shown that the application of the MS-CASPT2 procedure is not straightforward and requires a careful analysis of the stability of the results with the quality of the reference wave functions, that is, the size of the active [email protected] [email protected] [email protected]

Orbital Optimization in the Density Matrix Renormalization Group, with applications to polyenes and \beta-carotene

In previous work we have shown that the Density Matrix Renormalization Group (DMRG) enables near-exact calculations in active spaces much larger than are possible with traditional Complete Active Space algorithms. Here, we implement orbital optimisation with the Density Matrix Renormalization Group to further allow the self-consistent improvement of the active orbitals, as is done in the Complete Active Space Self-Consistent Field (CASSCF) method. We use our resulting DMRGCASSCF method to study the low-lying excited states of the all-trans polyenes up to C24H26 as well as \beta-carotene, correlating with near-exact accuracy the optimised complete \pi-valence space with up to 24 active electrons and orbitals, and analyse our results in the light of the recent discovery from Resonance Raman experiments of new optically dark states in the spectrum.Comment: 16 pages, 8 figure