Numerical methods for steady-state mode interactions

Mock interactions on nontrivial solutions for problems withZ₂ x Z₂ symmetry are considered. It is assumed that a path ofbifurcation points is being followed with two parameters anda mode interaction then corresponds to two separate bifurcationsof an extended system. This view of mode interactions leadsto efficient numerical methods for dealing with such pointsand for swapping onto the new paths of bifurcation points whichoriginate them. The nondegeneracy conditions associated withmode interactions are also interpreted in this context.     

Existence Theory for a Stochastic Bolza Problem

The direct method is used to prove the existence of optimalopen-loop controls for stochastic optimal control problems inBolza form. Instead of requiring the control set to be compact,as previous authors have done, we impose a superquadratic growthcondition on the running cost. Degeneracy of the diffusion coefficientis allowed by this approach—in fact, the main result reducesto a well known deterministic theorem when the diffusion coefficientis zero.     

An ab initio molecular orbital study comparing the bonding of the NH3 and the H2O in the monoammines and the monohydrates of main group and transition metal ions

It is common knowledge that some metal ions prefer to bond to nitrogen atoms, others prefer oxygen and others select sulfur, although the mechanistic origin of this behaviour is not well understood. To provide quantitative data that can illuminate this characteristic difference, we have been performing ab initio molecular orbital calculations on complexes of a wide variety of main group and transition metal ions with simple ligands. In this paper we concentrate on metal ion complexes of NH₃ and compare them with the corresponding complexes with H₂O (Trachtman et al., 1998, Inorg. Chem., 37, 4221). The results reported here show that for each metal ion the bonding to ammonia in monoammines is intrinsically stronger than that to water in monohydrates, but that the enthalpy of formation of the amine complexes has a greater sensitivity to the nature of the metal ion. For both mono- and divalent transition metal cations the ligand-field stabilization energy (LFSE) in the monoammine complexes is larger than that in the monohydrates, although the larger enthalpies of formation, ΔH ⁰ ₂₉₈, for the monoammines are due only in part to the larger LFSE values. The formation of both monoammines and monohydrates is accompanied by a transfer of charge from the ligand hydrogen atoms to the metal ion so that there is relatively little change in the net charge on the oxygen or nitrogen atoms. Hence the increased acidity of the ligand in the metal ion complex is not the result of net electron depletion of the atom that is directly bonded to the metal ion, but rather reflects weakening of the bond of that ligand atom to its proton (O-H or N-H). This characteristic is used by many enzymes to promote catalytic activity.     

CHLOROPHYLL-PROTEINS AND REACTION CENTER PREPARATIONS FROM PHOTOSYNTHETIC BACTERIA,ALGAE AND HIGHER PLANTS*,‡

Abstract— The use of sodium dodecyl sulfate to dissociate photosynthetic membranes followed by standard fractionation techniques yields chlorophyll-proteins and reaction center complexes with molecular weights of 500,000 or less. Much about the structure and function of photo-synthetic units in vivo can be deduced from the properties of the isolated complexes. The Bchl-protein from green bacteria is approximated by an incompletely filled sphere ? 80 Â in diameter consisting of four identical subunits. The five Bchl molecules in each subunit are 14 to 20Â apart. The related Chl a-proteins from a blue-green alga and various eukaryotic plants may have similar structural characteristics. The Chl a-protein from a blue-green alga contains one molecule of P700 per 60–90 Chl a molecules. The quantum requirement for P700 oxidation is 2.6 or less. The midpoint potential in various preparations ranges from 0.38 V to 0.42 V. Green algae and higher plants yield a Chl a-protein similar to that from the blue-green alga; in addition they yield another Chl-protein (mol. wt. = 2–3×10⁴) which contains an equal amount of Chl a and Chl b. These two Chl-proteins account for most of the chlorophyll in these organisms. Two photosynthetic bacteria (Rhodopseudomonas viridis and Chromatium) yield protein complexes containing Bchl, carotenoid, and bound cytochromes. The reaction center complex from R. viridis contains P960 (E_m, ₈= 0.39 to 0.42 V), cytochrome 558 (E_m,8= 0.33 V) and cytochrome 553 (E_m,7=— 0.02 V). Quantum requirements for P960 and C558 oxidation are ?2.2 and 3.0, respectively. Complex A from Chromatium contains Bchl 890, P883, cytochrome 556 (E_m,8= 0.34 V) and cytochrome 552 (E_m,7=?0.04 V). The quantum requirement for C556 oxidation is about 15. Both high- and low-potential cytochromes can donate electrons to the reaction center chlorophyll present in either complex. This fact supports the idea that only one kind of photochemical reaction center functions in photosynthetic bacteria. An hypothesis about the nature of the photosynthetic unit in purple bacteria is outlined.     

Modified Damped Least Squares: An Algorithm for Non-linear Estimation

A new method for non-linear regression is described and comparedto three other well-known methods for the non-linear least squaresproblem. Convergence theorems and computational results aregiven which indicate that the new method is more efficient andreliable than previously published methods.     

The singlet electronic states of pyrrole: a theoretical study by both ab initio multi-reference configuration interaction methods and time-dependent density functional theory and a reconsideration of the experimental VUV spectral data

The singlet electronic excitation spectrum of pyrrole has been reinvestigated by both multi-reference multi-root configuration interaction (CI) calculations and time-dependent density functional theory (DFT) with asymptotically corrected exchange-correlation potentials. The methods used a triple zeta valence + polarization + Rydberg (TZVPR) basis set and a much larger active space than in our previous CI study [Palmer, M. H., Walker, I. C., and Guest, M. F., 1998, Chem. Phys., 238, 179]. Computed vertical excitation energies, oscillator strengths and electronic charge distributions were used to characterize and assign the valence and Rydberg excited states over an energy range of 5–12 eV.

A comparison of the present methods with other high-level ab initio studies has been made, including the effects of basis sets and size of CI, and some statistical relationships determined. The present CI vertical excitation energies are generally in closer agreement with the cluster-type methods, especially CC3, than to the various second-order perturbation-type methods (CASPT2, CASPT2-MS, ADC(2) and MRMP).

The influence on the excitation energies from exact orbital exchange and multiplicative potentials in hybrid functional development has been investigated. Differences between the CI and the DFT methods vary in the order B97-2 < B97-1 < HCTH < LDA. The differences between hybrid DFT and CI excitations are minimized when the fraction of orbital exchange (ξ) lies in the approximate range 0.2–0.3. The Rydberg and valence-type excitations are seen to be less sensitive than the static polarizability to the inclusion of orbital exchange or multiplicative potentials in hybrid functional development.

In order to allow a realistic assessment of the performance of the theoretical studies, the assignment of the experimental electronic spectrum of pyrrole is discussed in detail. Previous conclusions have led to incorrect numbers of Rydberg s- and d-type states, while f-type states have previously been ignored. Some excitations from the second IP, which must occur in the 5–10 eV range, have been reassigned in light of the known small differences between other spectroscopic states and quantum defects. There is an urgent need for higher-resolution studies of pyrrole and related molecules.     

Phase differences in reaction-diffusion-advection systems and applications to morphogenesis

The authors study the effect of advection on reaction-diffusionpatterns. It is shown that the addition of advection to a two-variablereaction–diffusion system with periodic boundary conditionsresults in the appearance of a phase difference between thepatterns of the two variables which depends on the differencebetween the advection coefficients. The spatial patterns movelike a travelling wave with a fixed velocity which depends onthe sum of the advection coefficients. By a suitable choiceof advection coefficients, the solution can be made stationaryin time. In the presence of advection a continuous change inthe diffusion coefficients can result in two Turing-type bifurcationsas the diffusion ratio is varied, and such a bifurcation canoccur even when the inhibitor species does not diffuse. It isalso shown that the initial mode of bifurcation for a givendomain size depends on both the advection and diffusion coefficients.These phenomena are demonstrated in the numerical solution ofa particular reaction–diffusion system, and finally apossible application of the results to pattern formation inDrosophila larvae is discussed.     

UV IRRADIATION OF WILD TYPE AND RADIATION-SENSITIVE MUTANTS OF THE NEMATODE Caenorhabditis elegans: FERTILITIES, SURVIVAL, AND PARENTAL EFFECTS

Abstract— Survival after UV irradiation was examined in wild type and four radiation-sensitive ( rad ) mutants of Caenorhabditis elegans . Synchronous populations were employed to assess radiation sensitivities at different developmental stages. In addition, the effects of irradiation on male and hermaphrodite fertilities were measured. Wild-type sensitivity was maximal early in embryogenesis. Different age-dependent patterns of radiation sensitivity were obtained with the rad mutants. The effects of parental genotype were also tested. A parental wild-type allele was capable of quickly elevating the radiation resistance of embryos derived from homozygous rad hermaphrodites. In a second parental-effect test, homozygous rad embryos displayed greater radiation resistance when derived from heterozygous rather than homozygous hermaphrodites. The results indicate that radiation sensitivity in this metazoan is determined by complex interactions of gene products.     

Dispersion of solid particles in turbulant flow through pipe expansions

Studies of the effects upon gas-liquid two-phase flows of pipefittings such as expansions, contractions, bends, and valveshave usually concentrated upon pressuredrop correlations andhave not attempted to determine changes in the distributionsof the gas and liquid phases caused by the fitting. However,it is known that such information is important if, for example,flow separators, which divide the gas and liquid phases in avariety of industrial processes, are to function efficiently.It is therefore important to gain an understanding of the influenceupon phase distributions of the common pipe fittings mentionedabove, which will be found in almost any industrial pipeworksystem. As a first step, the dispersion of solid particles carriedby turbulent gas flows through a pipe expansion has been modellednumerically. The commercial fluid-flow code CFDS-FLOW{smalltilde}hDas been used to model the gas flow, together with aneddy interaction model for determination of the motion of thesolid particles. Mean particle velocities and root-mean-squarevalues of the particle velocity fluctuations, as well as particleconcentrations, are evaluated and compared with recent experimentalresults. The influence of different eddy-length and eddy-lifetimespecifications upon the dispersion of particles of various sizesis investigated. It is found that the different eddy characteristicshave little effect on predicted mean particle velocities, whereasfluctuations in particle velocities and particle concentrationare sensitive to the changes made. By comparing the resultswith experimental data, it is possible to draw conclusions aboutthe relative merits of the different eddy specifications.     

Biological implications of a discrete mathematical model for collagen deposition and alignment in dermal wound repair

We deveiop a novel mathematical model for collagen depositionand alignment during dermal wound healing. We focus on the interactionsbetween fibroblasts, modelled as discrete entities, and a continuousextracellular matrix composed of collagen and a fibrin basedblood clot. There are four basic interactions assumed in themodel: fibroblasts orient the collagen matrix, fibroblasts produceand degrade collagen and fibrin and the matrix directs the fibroblastsand determines the speed of the cells. Several factors whichinfluence the alignment of collagen are examined and relatedto current anti-scarring therapies using transforming growthfactor ß. The most influential of these factors arecell speed and, more importantly for wound healing, the influxof fibroblasts from surrounding tissue.