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.     

TEMPORAL AGGREGATION AND TESTING FOR TIMBER PRICE BEHAVIOR

ABSTRACT. Different harvest timing models make different assumptions about timber price behavior. Those seeking to optimize harvest timing are thus first faced with a decision regarding which assumption of price behavior is appropriate for their market, particularly regarding the presence of a unit root in the timber price time series. Unfortunately for landowners and investors, the literature provides conflicting guidance on this subject. One source for the ambiguous results of unit root tests of timber prices may involve data problems. We used Monte Carlo simulations to show that aggregating observations below their observed rate resulted in similar power reductions and empirical size distortions across three classes of unit root tests. Moving‐average error structures can also affect power and sizes of tests on period‐averaged data. Such error structures can also be created by the kind of temporal averaging common in reported timber prices. If we take timber prices at their face value and therefore ignore these sampling error and temporal aggregation complications, we find that unit root tests on southern timber prices support a unit root in 158 out of 208 product‐deflation combinations tested, random walks in 38 of the series found to be nonsta‐tionary, and stationarity in none. However, if we recognize temporal aggregation errors, unit root tests more commonly favor stationarity, especially for pulpwood stumpage. Because price trends for sawtimber and pulpwood products may behave differently even in the same region, stochastic harvest timing models must be developed that allow their multiple products to follow different price paths.     

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.     

Effect of Solvents on the Fluorescence Emission Spectra of 1-Anilino-8-Naphthalene Sulfonic Acid: A Physical Chemistry Experiment

This article describes an experiment that can be conducted to cover basic fluorescence concepts and study the effects of solvent polarity. It introduces students to fluorescence spectrophotometry and illustrates the effects of the solvents dielectric constant and hydrogen bonding capability on fluorescence-emmision spectra.     

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.