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.     

An ab initio study of vibration and rotation effects in isocyanatomethane,isothiocyanatomethane and azidomethane

The potential energy surfaces (PESs) for methyl group rotation accompanied by N-atom inversion in isocyanatomethane (MeNCO), isothiocyanatomethane (MeNCS) and azidomethane (MeN₃), have been investigated by Möller-Plesset (MP2), coupled cluster (CCD) and, in part, CCSD(T) ab initio calculations. Analytical forms for these surfaces are represented in terms of the (H₃)CNX (X=N, C) angle (θ°) and the HCNX torsion angle (φ°) using the expression E(θ, φ) = E₀(θ) + ½δE(θ)(1 + cos 3φ), where E₀(θ) and δE(θ) are even polynomials in (180—θ). In contrast to previous works of this nature, here it is shown explicitly that the fitting procedure is sufficiently flexible to provide accurate representations of the PES. It is found that the barrier to linearity and the barrier to internal methyl-group rotation both increase in the order MeNCS < MeNCO < MeN₃. The ratio of harmonic to quartic coefficients in the expansion of E₀(θ) also increases along this same series, and is largely responsible for the geometry of the CNX group becoming increasingly bent. The energetic and structural results compare favourably with data from previous experimental and theoretical studies.     

Low-Dimensional Modelling of Turbulence Using the Proper Orthogonal Decomposition: A Tutorial

The proper orthogonal decomposition identifies basis functions or modes which optimally capture the average energy content from numerical or experimental data. By projecting the Navier–Stokes equations onto these modes and truncating, one can obtain low-dimensional ordinary differential equation models for fluid flows. In this paper we present a tutorial on the construction of such models. In addition to providing a general overview of the procedure, we describe two different ways to numerically calculate the modes, show how symmetry considerations can be exploited to simplify and understand them, comment on how parameter variations are captured naturally in such models, and describe a generalization of the procedure involving projection onto uncoupled modes that allow streamwise and cross-stream components to evolve independently. We illustrate for the example of plane Couette flow in a minimal flow unit – a domain whose spanwise and streamwise extent is just sufficient to maintain turbulence.     

Effective thermal conductivity of condensed polymeric nanofluids (nanosolids) controlled by diffusion and interfacial scattering

Thermal properties of polymeric nanosolids, obtained by condensing the corresponding nanofluids, are investigated using photothermal techniques. The heat transport properties of two sets of polyvinyl alcohol (PVA) based nanosolids, TiO₂/PVA and Cu/PVA, prepared by condensing the respective nanofluids, which are prepared by dispersing nanoparticles of TiO₂ and metallic copper in liquid PVA, are reported. Two photothermal techniques, the photoacoustic and the photopyroelectric techniques, have been employed for measuring thermal diffusivity, thermal conductivity and specific heat capacity of these nanosolids. The experimental results indicate that thermal conduction in these polymer composites is controlled by heat diffusion through the embedded particles and interfacial scattering at matrix–particle boundaries. These two mechanisms are combined to arrive at an expression for their effective thermal conductivity. Analysis of the results reveals the possibility to tune the thermal conductivity of such nanosolids over a wide range using the right types of nanoparticles and right concentration.     

Accurate non-relativistic density functional theory predictions for 77Se NMR shielding parameters

A reoptimized density functional theory (DFT) hybrid functional gives orbitals and energies which when substituted into the uncoupled generalized gradient approximation (GGA) sum-over-states expressions gives NMR shielding constants of high accuracy for first- and second-row nuclei. This procedure is validated further and its performance compared against well established exchange-correlation (XC) functionals for the prediction of the third-row ⁷⁷Se NMR shielding constants, in a series of challenging molecules where both accurate theoretical and experimental data are available. The shielding parameters obtained from this new mixed hybrid GGA scheme provide a significant improvement over conventional XC functionals. and are competitive with the benchmark coupled-cluster singles and doubles (CCSD) methods. From these results together with previous studies it is now apparent that this new GGA shielding scheme provides high accuracy NMR shielding constants for first-, second-and third-row atoms (excluding transition-metal atoms) even in molecules exhibiting large correlation effects.     

Triple-deck Flows over Wavy Surfaces

Sinusoidally perturbed laminar flow over a flat plate is considered,in which the amplitude and wave number bear the triple-deckrelation to the Reynolds number R. To find the resulting flowfield and in particular the surface shear stress and pressureit is necessary to solve the non-linear lower-deck equation.Analytic solutions of the linearized equations are obtainedand the behaviour of the stresses near the leading edge of thewaviness is examined. As regions further downstream are consideredit is found that the linearized results predict the same surfacestress phase shifts as those derived by Benjamin (1959) forboundary-layer flows over wavy surfaces of amplitude and wavenumberindependent of R. For larger amplitudes, the full non-linearequations are solved numerically via a modification of the spectralmethod of Burggraf & Duck (1981). This modification is shownto significantly increase both the speed and accuracy of theoriginal method for lower-deck problems in general. Specialattention is paid to the problems associated with the semi-infiniteextent of the surface perturbation. The results of these non-linearcalculations of the stresses are examined to determine the effectsof increasing amplitude h and of increasing distance downstream.It is found that the surface stress extrema are phase-shifteddownstream with respect to the surface perturbation both asthe amplitude is increased and as regions further downstreamof the leading edge are considered. Moreover, the stress profilesbecome considerably distorted from sinusoidal as h increases.It is found that separation occurs at higher values of h thanpredicted by linear theory. Finally, differences between resultsfor positive and negative h are examined.     

An argumentation-based approach to risk assesment

Reliable quantitative risk assessment requires the use of meaningfulstatistical data and well validated models for their interpretation.In certain domains, neither the data nor the validated modelsare available. Nevertheless, there may still be a requirementto generate a meaningful characterization of risk, presentedin a form which reflects the reliability and accuracy of thedata available. One such domain is the assessment of the potentialcarcinogenic risk in chemical compounds, and there are manyothers. Work is described which is underway to provide a soundframework for the qualitative assessment of risk using a computermodel of 'argumentation'. This work is being applied to thedevelopment of computer-based support for the assessment ofcarcinogenic risk.