Total Flux Estimates for a Finite-Element Approximation of Elliptic Equations

An elliptic boundary-value problem on a domain with prescribedDirichlet data on _I is approximated using a finite-elementspace of approximation power h^K in the L² norm. It is shownthat the total flux across _I can be approximated with an errorof O(h^K) when is a curved domain in Rⁿ (n = 2 or 3) and isoparametricelements are used. When is a polyhedron, an O(h^2K–2)approximation is given. We use these results to study the finite-elementapproximation of elliptic equations when the prescribed boundarydata on _I is the total flux. Present address: School of Mathematical and Physical Sciences,University of Sussex, Brighton, Sussex BN1 9QH.     

The Stefan Problem with a Non-monotone Constitutive Relation

A finite difference approximation of the non-linear diffusionequation e_t = ((e))_xx' where is non-monotone, is shown to convergeto a measure valued solution. Some numerical results are described.     

Finite Element Approximation of a Rigid Punch Indenting a Membrane

Optimal order H¹ and L error bounds are obtained for a continuouspiecewise linear finite element approximation of an obstacleproblem, where the obstacle's height as well as the contactzone, _c, are a priori unknown. The problem models the indentationof a membrane by a rigid punch. For R², given ,g R⁺ and an obstacle defined over E we consider the minimization of |v|²_1,+gµover (v, µ) H¹₀() x R subject to v+µ on E. In additionwe show under certain nondegeneracy conditions that dist (_c,^h_c)Ch ln 1/h, where ^h_c is the finite element approximation to_c. Finally we show that the resulting algebraic problem canbe solved using a projected SOR algorithm.     

Low-lying energy levels of the FeH molecule

Multireference configuration interaction (MRCI) and complete active space second-order perturbation theory (CASPT2) calculations are performed on Fe₂ and Fe^? ₂. Although it is not possible to definitively identify the ground states of Fe₂ and Fe^? ₂, the calculations suggest that the ground state of Fe^? ₂ in ⁸Σ^? _u derived from 3d¹³4σ² _g4σ² _u and that the states observed in photodetachment are the ⁹Σ^? _g and ⁷Σ^? _g states with a 3d¹³4σ² _g4σ¹ _u occupation, but that the ground state of Fe₂ is ⁷Δ_u(3d¹⁴4σ² _g) and is not observed in the photo-detachment spectra.     

AN INDIVIDUAL‐BASED MODEL FOR FERAL HOGS IN GREAT SMOKY MOUNTAINS NATIONAL PARK

The expansion of feral hog (Sus scrofa) populations in the United States has resulted in increased efforts to develop and implement control strategies designed to minimize the impacts done by this invasive species. We describe an individual‐based model for feral hogs in Great Smoky Mountains National Park (GSMNP). The objectives of the model are to provide an understanding of the population dynamics of this feral hog population and to determine the efficacy of the annual harvest as a population control method. Results suggest that the dynamics of the population are driven by fall hard mast production and the GSMNP harvests currently limit growth of the population, but these control efforts have not reduced the population.     

Chebyshev Approximation by Exponential Ratios

The uniqueness of representation of approximations is examined.Bounds are given on the number of zeros of a difference of approximants.The tangent space of approximants is shown to be a Haar subspace.From these results we characterize best approximation in termsof alternation and obtain uniqueness of best approximations.     

A BIOECONOMIC APPROACH TO THE FAUSTMANN–HARTMAN MODEL: ECOLOGICAL INTERACTIONS IN MANAGED FOREST

Abstract This paper develops a bioeconomic forestry model that makes it possible to take ecosystem services that are independent of the age structure of trees into account. We derive the Faustmann–Hartman optimal harvesting strategy as a special case. The bioeconomic model is then extended to account for the fact that forest harvesting decisions impact on other ecological resources, which provide benefits for the wider community. The paper focuses on impacts associated with disturbance caused by logging operations and habitat destruction due to tree removal. This enables us to explore the interactions between forest management and the dynamics of ecological resources. The optimal rotation rule is obtained as a variation on the traditional Faustmann–Hartman equation, where an additional term captures the potential benefits derived from the growth of the ecological resource valued at its shadow price. The steady‐state solutions to the problem and sensitivity to model parameter are identified using numerical analysis.     

Low field CIDNP of amino acids and proteins: characterization of transient radicals and NMR sensitivity enhancement

A new method for measuring and exploiting the magnetic field dependence of chemically induced dynamic nuclear polarization (CIDNP) is described. A solution of an amino acid or protein together with a flavin photosensitizer is irradiated with laser light at a position in the bore of a superconducting NMR magnet where the field is between 0.1 T and 7.0 T. The polarized sample is then transferred by rapid injection into an NMR tube at the centre of the magnet (at 9.4 T), where the spectrum is recorded. The observed ¹H CIDNP field dependence of tyrosine agrees well with the diffusion model of the radical pair mechanism. The field dependence of histidine, tryptophan and methionine CIDNP allows the g values of the transient radicals responsible for the polarization to be determined. Experiments in which amino acids compete for the photoexcited flavin indicate that methionine residues could be used as probes of surface accessibility, especially if the polarization is generated in low fields (～ 0.7 T) and detected in high fields (≥ 9.4 T). Possible extensions of the technique to study protein folding and the structures of partially denatured states of proteins are discussed.     

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.