Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

State-resolved gas-surface reactivity of methane in the symmetric C-H stretch vibration on Ni(100)

The state-resolved reactivity of CH4 in its totally symmetric C-H stretch vibration (�1) has been measured on a Ni(100) surface. Methane molecules were accelerated to kinetic energies of 49 and 63:5 kJ=mol in a molecular beam and vibrationally excited to �1 by stimulated Raman pumping before surface impact at normal incidence. The reactivity of the symmetric-stretch excited CH4 is about an order of magnitude higher than that of methane excited to the antisymmetric stretch (�3) reported by Juurlink et al. [Phys. Rev. Lett. 83, 868 (1999)] and is similar to that we have previously observed for the excitation of the first overtone (2�3). The difference between the state-resolved reactivity for �1 and �3 is consistent with predictions of a vibrationally adiabatic model of the methane reaction dynamics and indicates that statistical models cannot correctly describe the chemisorption of CH4 on nickel.

House price dynamics and their reaction to macroeconomic changes

This article applies a three-regime Markov switching model to investigate the impact of the macroeconomy on the dynamics of the residential real estate market in the US. Focusing on the period between 1960 and 2011, the methodology implemented allows for a clearer understanding of the drivers of the real estate market in “boom”, “steady-state” and “crash” regimes. Our results show that the sensitivity of the real estate market to economic changes is regime-dependent. The paper then proceeds to examine whether policymakers are able to influence a regime switch away from the crash regime. We find that a decrease in interest rate spreads could be an effective catalyst to precipitate such a change of state.

Mechanisms and dynamics of protein clustering on a solid surface

A methodology for discovering the mechanisms and dynamics of protein clustering on solid surfaces is presented. In situ atomic force microscopy images are quantitatively compared to Monte Carlo simulations using cluster statistics to differentiate various models. We study lysozyme adsorption on mica as a model system and find that all surface-supported clusters are mobile, not just the monomers, with diffusion constant inversely related to cluster size. The surface monomer diffusion constant is measured to be D1∼9×10-16  cm2 s-1, such a low value being difficult to measure using other techniques.

Is the Indian Ocean SST variability a homogeneous diffusion process.

Whereas the predominance of El Niño Southern Oscillation (ENSO) mode in the tropical Pacific sea surface temperature (SST) variability is well established, no such consensus seems to have been reached by climate scientists regarding the Indian Ocean. While a number of researchers think that the Indian Ocean SST variability is dominated by an active dipolar-type mode of variability, similar to ENSO, others suggest that the variability is mostly passive and behaves like an autocorrelated noise. For example, it is suggested recently that the Indian Ocean SST variability is consistent with the null hypothesis of a homogeneous diffusion process. However, the existence of the basin-wide warming trend represents a deviation from a homogeneous diffusion process, which needs to be considered. An efficient way of detrending, based on differencing, is introduced and applied to the Hadley Centre ice and SST. The filtered SST anomalies over the basin (23.5N-29.5S, 30.5E-119.5E) are then analysed and found to be inconsistent with the null hypothesis on intraseasonal and interannual timescales. The same differencing method is then applied to the smaller tropical Indian Ocean domain. This smaller domain is also inconsistent with the null hypothesis on intraseasonal and interannual timescales. In particular, it is found that the leading mode of variability yields the Indian Ocean dipole, and departs significantly from the null hypothesis only in the autumn season.

From a discrete to a continuum model of cell dynamics in one dimension

Multiscale modeling is emerging as one of the key challenges in mathematical biology. However, the recent rapid increase in the number of modeling methodologies being used to describe cell populations has raised a number of interesting questions. For example, at the cellular scale, how can the appropriate discrete cell-level model be identified in a given context? Additionally, how can the many phenomenological assumptions used in the derivation of models at the continuum scale be related to individual cell behavior? In order to begin to address such questions, we consider a discrete one-dimensional cell-based model in which cells are assumed to interact via linear springs. From the discrete equations of motion, the continuous Rouse [P. E. Rouse, J. Chem. Phys. 21, 1272 (1953)] model is obtained. This formalism readily allows the definition of a cell number density for which a nonlinear "fast" diffusion equation is derived. Excellent agreement is demonstrated between the continuum and discrete models. Subsequently, via the incorporation of cell division, we demonstrate that the derived nonlinear diffusion model is robust to the inclusion of more realistic biological detail. In the limit of stiff springs, where cells can be considered to be incompressible, we show that cell velocity can be directly related to cell production. This assumption is frequently made in the literature but our derivation places limits on its validity. Finally, the model is compared with a model of a similar form recently derived for a different discrete cell-based model and it is shown how the different diffusion coefficients can be understood in terms of the underlying assumptions about cell behavior in the respective discrete models.

Dynamics of QoI sensitivity in Mycosphaerella fijiensis in Costa Rica during 2000 to 2003

From 1997 onward, the strobilurin fungicide azoxystrobin was widely used in the main banana-production zone in Costa Rica against Mycosphaerella fijiensis var. difformis causing black Sigatoka of banana. By 2000, isolates of M. fijiensis with resistance to the quinolene oxidase inhibitor fungicides were common on some farms in the area. The cause was a single point mutation from glycine to alanine in the fungal target protein, cytochrome b gene. An amplification refractory mutation system Scorpion quantitative polymerase chain reaction assay was developed and used to determine the frequency of G 143A allele in samples of M. fijiensis. Two hierarchical surveys of spatial variability, in 2001 and 2002,found no significant variation in frequency on spatial scales <10 in. This allowed the frequency of G143A alleles on a farm to be estimated efficiently by averaging single samples taken at two fixed locations. The frequency of G 143A allele in bulk samples from I I farms throughout Costa Rica was determined at 2-month intervals. There was no direct relationship between the number of spray applications and the frequency of G143A on individual farms. Instead, the frequency converged toward regional averages, presumably due to the large-scale mixing of ascospores dispersed by wind. Using trap plants in an area remote from the main producing area, immigration of resistant ascospores was detected as far as 6 km away both with and against the prevailing wind.

Gas-solid reactions of single crystals: a study of the reaction of bromine with single crystals of trans-cinnamic acid and a range of its derivatives by infrared and Raman microspectroscopy

Single crystals of trans-cinnamic acid and of a range of derivatives of this compound containing halogen substituents on the aromatic ring have been reacted with 165 Torr pressure of bromine vapour in a sealed desiccator at 20 degrees C for 1 week. Infrared and Raman microspectroscopic examination of the crystals shows that bromination of the aliphatic double bond, but not of the aromatic ring, has occurred. It is demonstrated also that the reaction is truly gas-solid in nature. A time-dependent study of these reactions shows that they do not follow a smooth diffusion-controlled pathway. Rather the reactions appear to be inhomogeneous and to occur at defects within the crystal. The reaction products are seen to flake from the surface of the crystal. It is shown, therefore, that these are not single crystal to single crystal transitions, as have been observed previously for the photodimerisation of trans-cinnamic acid and several of its derivatives. It is shown that there are no by-products of the reaction and that finely ground samples react to form the same products as single crystals.

A reaction surface Hamiltonian study of malonaldehyde

We report calculations using a reaction surface Hamiltonian for which the vibrations of a molecule are represented by 3N-8 normal coordinates, Q, and two large amplitude motions, s(1) and s(2). The exact form of the kinetic energy operator is derived in these coordinates. The potential surface is first represented as a quadratic in Q, the coefficients of which depend upon the values of s(1),s(2) and then extended to include up to Q(6) diagonal anharmonic terms. The vibrational energy levels are evaluated by solving the variational secular equations, using a basis of products of Hermite polynomials and appropriate functions of s(1),s(2). Our selected example is malonaldehyde (N=9) and we choose as surface parameters two OH distances of the migrating H in the internal hydrogen transfer. The reaction surface Hamiltonian is ideally suited to the study of the kind of tunneling dynamics present in malonaldehyde. Our results are in good agreement with previous calculations of the zero point tunneling splitting and in general agreement with observed data. Interpretation of our two-dimensional reaction surface states suggests that the OH stretching fundamental is incorrectly assigned in the infrared spectrum. This mode appears at a much lower frequency in our calculations due to substantial transition state character. (c) 2006 American Institute of Physics.