Analytical and numerical solutions describing the inward solidification of a binary melt

We present a mathematical model describing the inward solidification of a slab, a circular cylinder and a sphere of binary melt kept below its equilibrium freezing temperature. The thermal and physical properties of the melt and solid are assumed to be identical. An asymptotic method, valid in the limit of large Stefan number is used to decompose the moving boundary problem for a pure substance into a hierarchy of fixed-domain diffusion problems. Approximate, analytical solutions are derived for the inward solidification of a slab and a sphere of a binary melt which are compared with numerical solutions of the unapproximated system. The solutions are found to agree within the appropriate asymptotic regime of large Stefan number and small time. Numerical solutions are used to demonstrate the dependence of the solidification process upon the level of impurity and other parameters. We conclude with a discussion of the solutions obtained, their stability and possible extensions and refinements of our study.

Linear viscoelasticity from molecular dynamics simulation of entangled polymers

The linear viscoelastic (LVE) spectrum is one of the primary fingerprints of polymer solutions and melts, carrying information about most relaxation processes in the system. Many single chain theories and models start with predicting the LVE spectrum to validate their assumptions. However, until now, no reliable linear stress relaxation data were available from simulations of multichain systems. In this work, we propose a new efficient way to calculate a wide variety of correlation functions and mean-square displacements during simulations without significant additional CPU cost. Using this method, we calculate stress−stress autocorrelation functions for a simple bead−spring model of polymer melt for a wide range of chain lengths, densities, temperatures, and chain stiffnesses. The obtained stress−stress autocorrelation functions were compared with the single chain slip−spring model in order to obtain entanglement related parameters, such as the plateau modulus or the molecular weight between entanglements. Then, the dependence of the plateau modulus on the packing length is discussed. We have also identified three different contributions to the stress relaxation:  bond length relaxation, colloidal and polymeric. Their dependence on the density and the temperature is demonstrated for short unentangled systems without inertia.

Living up to the value agenda: the empirical realities of through-life value creation in construction

Current research agendas are increasingly encouraging the construction industry to operate on the basis of 'added value'. Such debates echo the established concept of 'high value manufacturing' and associated trends towards servitization. Within construction, the so-called 'value agenda' draws heavily from the notion of integrated solutions. This is held to be especially appropriate in the context of PFI projects. Also relevant is the concept of service-led projects whereby the project rationale is driven by the client's objectives for delivering an enhanced service to its own customers. Such ideas are contextualized by a consideration of broader trends of privatization and outsourcing within and across the construction industry's client base. The current emphasis on integrated solutions reflects long-term trends within privatized client organizations towards the outsourcing of asset management capabilities. However, such trends are by no means uniform or consistent. An in-depth case study of three operating divisions within a major construction company illustrates that firms are unlikely to reorientate their business in response to the 'value agenda'. In the case of PFI, the tendency has been to establish specialist units for the purposes of winning work. Meanwhile, institutionally embedded operating routines within the rest of the business remain broadly unaffected.

The role of gypsum in the reactions of phosphate with soils

The aim of this study was to examine the mechanisms by which gypsum increases the sorption of fertilizer-P in soils of and and semi-arid regions. Either gypsum or soil (Usher from the UK; pH 7.8, 7% organic matter, 21% CaCO3: Yasouj from Iran; pH 8.2, 1.4% OM, 18% CaCO3: Ghanimeh from Saudi Arabia; pH 7.8, 1% OM, 26% CaCO3, 13% gypsum) was shaken for 24 It with KH2PO4 solutions in 10 mM CaCl2. With gypsum, grinding increased sorption by a factor of about 3, and increase in pH from 5.6 to 7.5 greatly increased sorption. Scanning electron micrographs (SEM) and EDX quantitative analysis showed that small crystals of gypsum disappeared and roughly spherical particles of dicalcium phosphate (DCPD) were formed. Analysis of equilibrium Solutions showed, using GEOCHEM, that octa-calcium phosphate (OCP) coated the DCPD. For the soils, sorption was in the order Ghanimeh > Yasouj > Usher. Removal of gypsum from Ghanimeh reduced sorption, with precipitated gypsum having a greater effect than gypsum mixed physically with the soil. Addition to Usher had no effect. SEM and EDX could not be used in the soil matrix, but solubility analysis again showed that solutions were close to equilibrium with OCP. Usher was unresponsive to added gypsum, presumably because of its small sorption capacity and high organic matter content. In Ghanimeh and Yasouj soils, gypsum increased sorption by being a source of readily available Ca2+ (c) 2005 Elsevier B.V. All rights reserved.

The composition and crystallinity of the near-surface regions of weathered alkali feldspars

Our ability to identify thin non-stoichiometric and amorphous layers beneath mineral surfaces has been tested by undertaking X-ray photoelectron spectroscopy (XPS) and transmission electron microscopy (TEM) work on alkali feldspars from pH 1 dissolution experiments. The outcomes of this work were used to help interpret XPS and TEM results from alkali feldspars weathered for <10,000 years in soils overlying the Shap Granite (north-west England). The chemistry of effluent solutions indicates that silica-rich layers a few nanometers in thickness formed during the pH I experiments. These layers can be successfully identified by XPS and have lower Al/Si, Na/Si, K/Si and Ca/Si values than the outermost similar to 9 nm of unweathered controls. Development of Al-Si non-stoichiometry is coupled with loss of crystal structure to produce amorphous layers that are identifiable by TEM where >similar to 2.5 nm thick, whereas the crystallinity of albite is retained despite leaching of Na to depths of tens to hundreds on nanometers. Integration of XPS data over the outermost 6-9 nm of naturally weathered Shap feldspars shows that they have stoichiometric Al/Si and K/Si ratios, which is consistent with findings of previous TEM work on the same material that they lack amorphous layers. There is some XPS evidence for loss of K from the outermost couple of nanometers of Shap orthoclase, and the possibility of leaching of Na from albite to greater depths cannot be excluded using the XPS or TEM results. This study demonstrates that the leached layer model, as formulated from laboratory experiments, is inapplicable to the weathering of alkali feldspars within acidic soils, which is an essentially stoichiometric reaction. (C) 2008 Elsevier Ltd. All rights reserved.

Laboratory simulation of terrestrial meteorite weathering using the Bensour (LL6) ordinary chondrite

Laboratory dissolution experiments using the LL6 ordinary chondrite Bensour demonstrate that meteoritic minerals readily react with distilled water at low temperatures, liberating ions into solution and forming reaction products. Three experiments were performed, all for 68 days and at atmospheric fO(2) but using a range of water/rock ratios and different ternperatures. Experiments I and 2 were batch experiments and undertaken at room temperature, whereas in experiment 3, condensed boiling water was dripped onto meteorite subsamples within a Soxhlet extractor. Solutions from experiment 1 were chemically analyzed at the end of the experiment, whereas aliquots were extracted from experiments 2 and 3 for analysis at regular intervals. In all three experiments, a very significant proportion of the Na, Cl, and K within the Bensour subsamples entered solution, demonstrating that chlorapatite and feldspar were especially susceptible to dissolution. Concentrations of Mg, Al, Si, Ca, and Fe in solution were strongly affected by the precipitation of reaction products and Mg and Ca may also have been removed by sorption. Calculations predict saturation of experimental solutions with respect to Al hydroxides, Fe oxides, and Fe (oxy)hydroxides, which would have frequently been accompanied by hydrous aluminosilicates. Some reaction products were identified and include silica, a Mg-rich silicate, Fe oxides, and Fe (oxy)hydroxides. The implications of these results are that even very short periods of subaerial exposure of ordinary chondrites will lead to dissolution of primary minerals and crystallization of weathering products that are likely to include aluminosilicates and silicates, Mg-Ca carbonates, and sulfates in addition to the ubiquitous Fe oxides and (oxy)hydroxides.

Who owns the copyright of architectural works and designs?

Copyright protects the rights and interests of authors on their original works of authorship such as literary, dramatic, musical, artistic, and certain other intellectual works including architectural works and designs. It is automatic once a tangible medium of expression in any form of an innovative material, which conforms the Copyright Designs and Patents Act 1988 (CDPA 1988), is created. This includes the building, the architectural plans and drawings. There is no official copyright registry, no requirements on any fees need to be paid and they can be published or unpublished materials. Copyrights owners have the rights to control the reproduction, display, publication, and even derivation of the design. However, there are limitations on the rights of the copyright owners concerning copyrights infringements. Infringement of copyright is an unauthorised violation of the exclusive rights of the copyright author. Architects and engineers depend on copyright law to protect their works and design. Copyrights are protected on the arrangements of spaces and elements as well as the overall form of the architectural design. However, it does not cover the design of functional elements and standard features. Although copyright law provides automatic protection to all original architectural plans, the limitation is that copyright only protects the expression of ideas but not the ideas themselves. It can be argued that architectural drawings and design, including models are recognised categories of artistic works which are protected under the copyright law. This research investigates to what extent copyrights protect the rights and interests of the designers on architectural works and design.

Effect of feeding supplemental fibrolytic enzymes or soluble sugars with malic acid on milk production

Two trials were conducted to evaluate effects of feeding supplemental fibrolytic enzymes or soluble sugars and malic acid on milk production. In trial 1, 257 cows at four sites were fed a basal diet consisting of no more than 60% of forage DM as corn silage and less than 40% as alfalfa hay. Cows were assigned randomly within site, parity, and two stages of lactation to: 1) control; 2) enzyme A; 3) enzyme B; and 4) soluble sugars and malic acid. There was a 14-d pretreatment and an 84-d treatment period. Enzyme solutions were sprayed on either the forage component or the TMR each day while mixing feed. Trial 2 was similar, except 122 cows at one site in the United Kingdom were fed diets containing forage that was 75% corn silage and 25% grass silage, and all cows began the study between 25 to 31 DIM. Mean milk productions for 233 cows that completed trial 1 were 32.9, 32.5, 32.4, and 32.9 kg/d for control, enzyme A, enzyme B, and soluble sugars and malic acid, respectively. Mean milk productions for 116 cows that completed trial 2 were 28.2, 27.9, 28.8, and 28.4 kg/d, respectively. In vitro analyses of the activities of enzyme solutions indicated that all major cellulose and hemicellulose degrading activities were present; however, the pH optima (approximate pH = 4 to 5) were more acidic, and the temperature optimum (approximately 50 C) was greater than normal pH and temperature in the rumen. If fibrolytic activity in the rumen is a major mechanism of action of supplemental fibrolytic enzymes, it appears that considerable activity of these preparations was lost due to conditions in the rumen. In conclusion, feeding supplemental fibrolytic enzymes or malic acid with soluble sugars had no effect on milk production under the conditions used in this study.

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.

Micellar and surface properties of a poly(methyl methacrylate)-block-poly(N-isopropylacrylamide) copolymer in aqueous solution

Critical micelle concentrations (cmc) of aqueous solutions of poly(methyl methacrylate)-block-poly(N-isopropylacrylamide) were determined at several temperatures by surface tensiometry. Below the lower critical solution temperature (LCST), the low Delta(mic) H-0 determined can be assigned to the PMMA block being tightly coiled in the dispersed molecular state, so that the unfavorable interactions of hydrophobic entities with water are minimized. Above the LCST the cmc value was found to increase; an anomalous behavior that can be directly related to the micelle-globule transition of the hydrophilic block. Interestingly, above the LCST the surface tension of relatively concentrated solutions was found to depend weakly on temperature not following the usual strong decrease with temperature expected for aqueous solutions. (C) 2007 Elsevier Inc. All rights reserved.

Design of mucoadhesive polymeric films based on blends of poly(acrylic acid) and (hydroxypropyl)cellulose

Mixing of aqueous solutions of poly(acrylic acid) and (hydroxypropyl) cellulose results in formation of hydrogen-bonded interpolymer complexes, which precipitate and do not allow preparation of homogeneous polymeric films by casting. In the present work the effect of pH on the complexation between poly(acrylic acid) and (hydroxypropyl)cellulose in solutions and miscibility of these polymers in solid state has been studied. The pH-induced complexation-miscibility-immiscibility transitions in the polymer mixtures have been observed. The optimal conditions for preparation of homogeneous polymeric films based on blends of these polymers have been found, and the possibility of radiation cross-linking of these materials has been demonstrated. Although the gamma-radiation treatment of solid polymeric blends was found to be inefficient, successful cross-linking was achieved by addition of N, N'- methylenebis(acrylamide). The mucoadhesive potential of both soluble and cross-linked films toward porcine buccal mucosa is evaluated. Soluble films adhered to mucosal tissues undergo dissolution within 30-110 min depending on the polymer ratio in the blend. Cross-linked films are retained on the mucosal surface for 10-40 min and then detach.

A swarm intelligence method for feature tracking in AMV derivation

Feature tracking is a key step in the derivation of Atmospheric Motion Vectors (AMV). Most operational derivation processes use some template matching technique, such as Euclidean distance or cross-correlation, for the tracking step. As this step is very expensive computationally, often shortrange forecasts generated by Numerical Weather Prediction (NWP) systems are used to reduce the search area. Alternatives, such as optical flow methods, have been explored, with the aim of improving the number and quality of the vectors generated and the computational efficiency of the process. This paper will present the research carried out to apply Stochastic Diffusion Search, a generic search technique in the Swarm Intelligence family, to feature tracking in the context of AMV derivation. The method will be described, and we will present initial results, with Euclidean distance as reference.

Numerical solution of some nonlocal, nonlinear dispersive wave equations

We use a spectral method to solve numerically two nonlocal, nonlinear, dispersive, integrable wave equations, the Benjamin-Ono and the Intermediate Long Wave equations. The proposed numerical method is able to capture well the dynamics of the solutions; we use it to investigate the behaviour of solitary wave solutions of the equations with special attention to those, among the properties usually connected with integrability, for which there is at present no analytic proof. Thus we study in particular the resolution property of arbitrary initial profiles into sequences of solitary waves for both equations and clean interaction of Benjamin-Ono solitary waves. We also verify numerically that the behaviour of the solution of the Intermediate Long Wave equation as the model parameter tends to the infinite depth limit is the one predicted by the theory.

Application of Gaussian multi-scale representation to feature tracking in meteorological satellite imagery

Gaussian multi-scale representation is a mathematical framework that allows to analyse images at different scales in a consistent manner, and to handle derivatives in a way deeply connected to scale. This paper uses Gaussian multi-scale representation to investigate several aspects of the derivation of atmospheric motion vectors (AMVs) from water vapour imagery. The contribution of different spatial frequencies to the tracking is studied, for a range of tracer sizes, and a number of tracer selection methods are presented and compared, using WV 6.2 images from the geostationary satellite MSG-2.

Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth

We study weak solutions for a class of free-boundary problems which includes as a special case the classical problem of travelling gravity waves on water of finite depth. We show that such problems are equivalent to problems in fixed domains and study the regularity of their solutions. We also prove that in very general situations the free boundary is necessarily the graph of a function.