Memòria justificativa de l'estada de recerca

Estudi elaborat a partir d’una estada a l’Associação para o Desenvolvimento da Aerodinânica Industrial (ADAI) de la Universitat de Coimbra, Portugal, entre març i juliol de 2006. Aquesta disposa d'un laboratori d'assaigs i té medis suficients per a cremar de manera controlada parcel•les prèviament delimitades en terreny forestal. Això permet observar el fenomen dels incendis forestals a dues escales de treball diferents. L’objectiu ha estat l’obtenció de dades experimentals sobre la propagació de fronts de flames que avancen sobre combustible tractat amb retardants sota l’efecte del pendent o el vent. S’ha participat en proves experimentals de camp i se n’han realitzat dues en instal•lacions de laboratori en què l’efecte del pendent o de la velocitat del vent podia ser variat. Degut a l’elevat nombre de variables que entren en joc l’anàlisi acurada de les dades encara està en procés.

Ab initio modeling and molecular dynamics simulation of the alpha 1b-adrenergic receptor activation.

This work describes the ab initio procedure employed to build an activation model for the alpha 1b-adrenergic receptor (alpha 1b-AR). The first version of the model was progressively modified and complicated by means of a many-step iterative procedure characterized by the employment of experimental validations of the model in each upgrading step. A combined simulated (molecular dynamics) and experimental mutagenesis approach was used to determine the structural and dynamic features characterizing the inactive and active states of alpha 1b-AR. The latest version of the model has been successfully challenged with respect to its ability to interpret and predict the functional properties of a large number of mutants. The iterative approach employed to describe alpha 1b-AR activation in terms of molecular structure and dynamics allows further complications of the model to allow prediction and interpretation of an ever-increasing number of experimental data.

Exercice physique et athérosclérose : quels sont les mécanismes physiologiques et moléculaires de l'exercice qui préviennent et protègent de l'athérosclérose? : approche chez un modèle expérimental d'athérosclérose : la souris génétiquement dépourvue en apolipoprotéine E (apoE-/-)

RESUME : L'athérosclérose, pathologie inflammatoire artérielle chronique, est à l'origine de la plupart des maladies cardiovasculaires qui constituent l'une des premières causes de morbidité et mortalité en France. Les études observationnelles et expérimentales montrent que l'exercice physique prévient la mortalité cardiovasculaire. Cependant, les mécanismes précisant les bénéfices cliniques de l'exercice sur l'athérosclérose sont encore largement inconnus. Le but général de ce travail a donc été d'explorer, en utilisant un modèle expérimental d'athérosclérose, la souris hypercholestérolémique génétiquement dépourvue en apolipoprotéine E (apoE-/-), les mécanismes athéroprotecteurs de l'exercice. La dysfonction endothéliale, généralement associée aux facteurs de risque cardiovasculaire, serait l'une des étapes précoces majeures de l'athérogenèse. Elle est caractérisée par une diminution de la biodisponibilité en monoxyde d'azote (NO) avec la perte de ses propriétés vasculo-protectrices, ce qui favorise un climat pro-athérogène (stress oxydatif, adhésion et infiltration des cellules inflammatoires dans la paroi artérielle...) conduisant à la formation de la plaque athéromateuse. L'objectif de notre premier travail a donc été d'explorer les effets de l'exercice d'une part, sur le développement des plaques athéromateuses et d'autre part, sur la fonction endothéliale de la souris apoE-/-. Nos résultats montrent que l'exercice réduit significativement l'extension de l'athérosclérose et prévient la dysfonction endothéliale. L'explication pharmacologique montre que l'exercice stimule la fonction endothéliale via, notamment, une plus grande sensibilité des récepteurs endothéliaux muscariniques, ce qui active les événements signalétiques cellulaires récepteurs-dépendants à l'origine d'une bioactivité accrue de NO. Les complications cliniques graves de l'athérosclérose sont induites par la rupture de la plaque instable provoquant la formation d'un thrombus occlusif et l'ischémie du territoire tissulaire en aval. L'objectif de notre deuxième travail a été d'examiner l'effet de l'exercice sur la qualité/stabilité de la plaque. Nos résultats indiquent que l'exercice de longue durée stabilise la plaque en augmentant le nombre de cellules musculaires lisses et en diminuant le nombre de macrophages intra-plaques. Nos résultats montrent aussi que la phosphorylation de la eNOS (NO Synthase endothéliale) Akt-dépendante n'est pas le mécanisme moléculaire majeur à l'origine de ce bénéfice. Enfin, dans notre troisième travail, nous avons investigué l'effet de l'exercice sur le développement de la plaque vulnérable. Nos résultats montrent, chez un modèle murin de plaque instable (modèle d'hypertension rénovasculaire à rénine et angiotensine II élevés) que l'exercice prévient l'apparition de la plaque vulnérable indépendamment d'un effet hémodynamique. Ce bénéfice serait associé à une diminution de l'expression vasculaire des récepteurs AT1 de l'Angiotensine II. Nos résultats justifient l'importance de l'exercice comme outil préventif des maladies cardiovasculaires. ABSTRACT : Atherosclerosis, a chronic inflammatory disease, is one of the main causes of morbidity and mortality in France. Observational and experimental data indicate that regular physical exercise has a positive impact on cardiovascular mortality. However, the mechanisms by which exercise exerts clinical benefits on atherosclerosis are still unknown. The general aim of this work was to elucidate the anti-atherosclerotic effects of exercise, using a mouse model of atherosclerosis: the apolipoprotein E-deficient mice (apoE-/- mice). Endothelial dysfunction, generally associated with cardiovascular risk factors, has been recognized to be a major and early step in atherogenesis. Endothelial dysfunction is characterized by Nitric Oxide (NO) biodisponibility reduction with loss of NO-mediated vasculoprotective actions. This leads to vascular effects such as increased oxidative stress and increased adhesion of inflammatory cells into arterial wall thus playing a role in atherosclerotic plaque development. Therefore, one of the objective of our study was to explore the effects of exercise on atherosclerotic plaque extension and on endothelial function in apoE-/- mice. Results show that exercise significantly reduces plaque progression and prevents endothelial dysfunction. Pharmacological explanation indicates that exercise stimulates endothelial function by increasing muscarinic receptors sensitivity which in turn activates intracellular signalling receptor-dependent events leading to increased NO bioactivity. The clinical manifestations of atherosclerosis are the consequences of unstable plaque rupture with thrombus formation leading to tissue ischemia. The second aim of our work was to determine the effect of exercise on plaque stability. We demonstrate that long-term exercise stabilizes atherosclerotic plaques as shown by decreased macrophage and increased Smooth Muscle Cells plaque content. Our results also suggest that the Akt-dependent eNOS phosphorylation pathway is not the primary molecular mechanism mediating these beneficial effects. Finally, we assessed a putative beneficial effect of exercise on vulnerable plaque development. In a mouse model of Angiotensine II (Ang II)-mediated vulnerable atherosclerotic plaques, we provide fist evidence that exercise prevents atherosclerosis progression and plaque vulnerability. The beneficial effect of swimming was associated with decreased aortic Ang II AT1 receptor expression independently from any hemodynamic change. These findings suggest clinical benefit of exercise in terms of cardiovascular event protection.

Model based fault diagnosis with application to an automotive engine

Report for the scientific sojourn at the University of Linköping between April to July 2007. Monitoring of the air intake system of an automotive engine is important to meet emission related legislative diagnosis requirements. During the research the problem of fault detection in the air intake system was stated as a constraint satisfaction problem over continuous domains with a big number of variables and constraints. This problem was solved using Interval-based Consistency Techniques. Interval-based consistency techniques are shown to be particularly efficient for checking the consistency of the Analytical Redundancy Relations (ARRs), dealing with uncertain measurements and parameters, and using experimental data. All experiments were performed on a four-cylinder turbo-charged spark-ignited SAAB engine located in the research laboratory at Vehicular System Group - University of Linköping.

Experimentació amb un receptor software GPS-Galileo d'alta sensibilitat per a entorns interiors

Este proyecto se centra en el análisis de señales GPS, utilizando un receptor software desarrollado con Matlab en un proyecto de investigación para la Agencia Espacial Europea (ESA), llevado a cabo por parte del departamento de Telecomunicaciones e Ingeniería de Sistemas de la ETSE. Este software utiliza técnicas de procesado de señal de alta sensibilidad (HS-GNSS) que permite al usuario determinar su posición en entornos de difícil propagación como puede ser el caso de los escenarios interiores. Los datos experimentales se analizan en función del nivel de multipath que afecta a la señal de cada uno de los satélites, y la degradación que los escenarios interiores provocan en las señales, a causa del mobiliario, paredes, personas, etc. Para analizar los datos experimentales, se ha utilizado una métrica presentada en el congreso internacional EuCAP 2009, con la que es posible caracterizar las señales en función del nivel de multipath.

Comment on "Streaming potential dependence on water-content in Fontainebleau sand" by V. Allegre, L. Jouniaux, F. Lehmann and P. Sailhac

Allegre et al. recently presented new experimental data regarding the dependence of the streaming potential coupling coefficient with the saturation of the water phase. Such experiments are important to model the self-potential response associated with the flow of water in the vadose zone and the electroseismic/seismoelectric conversions in unsaturated porous media. However, the approach used to interpret the data is questionable and the conclusions reached by Allegre et al. likely incorrect

Commentary on: Berger-Karin C, Hendricks U, Geyer-Lippmann J. Comparison of natural and artificial aging of ballpoint inks

We would like to comment this study recently published in JFS. It is a short technical note proposing an artificial aging technique for the dating of ballpoint pen inks. This is a very difficult and controversial topic, and we are worried about the nature of this paper. The authors propose several ideas to differentiate fast aging and slow aging inks, but their experimental data is not validly represented and/or discussed. The data is insufficient to draw any conclusions about any potential of the method for ink dating purposes. This lack of information on the subject must be filled before proposing such methods for practical caseworks. These are preliminary and unconvincing results from development research performed in a laboratory on controlled samples without due warnings about potential shortcomings. They cannot be used or even compared to results obtained in real situations on uncontrolled specimens of limited size, unknown composition and undefined storage conditions. This can leave an undeserved feeling that these methods are ready for implementation when the task of ensuring their scientific validity is still far away.

Radiocarbon dating of modern groundwater: the role of the unsaturated zone

Biological and physical processes occurring in soils may lead to significant isotopic changes between the isotopic compositions of atmospheric CO2 and of soil CO2. Also, during water and gas transport from the soil surface to the water table, isotopic changes likely occur due to numerous physical processes such as gas production and diffusion, water advection, and gas-water-rock interactions. In most cases, these changes are not included in the correction models developed for groundwater dating, whereas they can significantly impact the calculation of the 14C age. We explore the role of these processes using: i) experimental data from two aquifer sites (Fontainebleau sands and Astian sands, France), ii) a distributed model to simulate the 14C activities of soil CO2, and iii) numerical simulations in order to highlight the role of the physical processes.¦The 13C content in soil CO2 showed seasonal variations and highlighted the competition between CO2 production and CO2 diffusion. Their respective contributions played a significant role in defining the isotopic composition of CO2 at the water table. On both study sites, variations of the 14C activity in soil CO2 reflect the competition between the fluxes of root derived-CO2 and organic matter derived-CO2. Since the nuclear weapon tests in the fifties and sixties, soil CO2 became significantly depleted in 14C compared to modern atmospheric CO2. Models that take into account this 14C depletion in soil CO2 for dating modern groundwater would lead to apparent younger 14C ages than models that only consider the 14C activity in atmospheric CO2. Moreover, since 2000-2005, the inverse effect is observed as soil CO2 is enriched in 14C compared to atmospheric CO2.¦Therefore, we conclude that the isotopic composition of CO2 at the water table have to be taken into account for the dating of modern groundwater. This requires a systematic sampling of soil CO2 and the measurement of its 13C and 14C contents. We used this information in a numerical simulation to calculate the evolution of isotopic composition of CO2 from the soil surface to the water table. This simulation integrated physical processes in the unsaturated zone (e.g. CO2 production and diffusion, water advection, etc.) and gas-water-rock interactions.

New developments and applications in modelling occupational exposure to airborne contaminants

Résumé: L'évaluation de l'exposition aux nuisances professionnelles représente une étape importante dans l'analyse de poste de travail. Les mesures directes sont rarement utilisées sur les lieux même du travail et l'exposition est souvent estimée sur base de jugements d'experts. Il y a donc un besoin important de développer des outils simples et transparents, qui puissent aider les spécialistes en hygiène industrielle dans leur prise de décision quant aux niveaux d'exposition. L'objectif de cette recherche est de développer et d'améliorer les outils de modélisation destinés à prévoir l'exposition. Dans un premier temps, une enquête a été entreprise en Suisse parmi les hygiénistes du travail afin d'identifier les besoins (types des résultats, de modèles et de paramètres observables potentiels). Il a été constaté que les modèles d'exposition ne sont guère employés dans la pratique en Suisse, l'exposition étant principalement estimée sur la base de l'expérience de l'expert. De plus, l'émissions de polluants ainsi que leur dispersion autour de la source ont été considérés comme des paramètres fondamentaux. Pour tester la flexibilité et la précision des modèles d'exposition classiques, des expériences de modélisations ont été effectuées dans des situations concrètes. En particulier, des modèles prédictifs ont été utilisés pour évaluer l'exposition professionnelle au monoxyde de carbone et la comparer aux niveaux d'exposition répertoriés dans la littérature pour des situations similaires. De même, l'exposition aux sprays imperméabilisants a été appréciée dans le contexte d'une étude épidémiologique sur une cohorte suisse. Dans ce cas, certains expériences ont été entreprises pour caractériser le taux de d'émission des sprays imperméabilisants. Ensuite un modèle classique à deux-zone a été employé pour évaluer la dispersion d'aérosol dans le champ proche et lointain pendant l'activité de sprayage. D'autres expériences ont également été effectuées pour acquérir une meilleure compréhension des processus d'émission et de dispersion d'un traceur, en se concentrant sur la caractérisation de l'exposition du champ proche. Un design expérimental a été développé pour effectuer des mesures simultanées dans plusieurs points d'une cabine d'exposition, par des instruments à lecture directe. Il a été constaté que d'un point de vue statistique, la théorie basée sur les compartiments est sensée, bien que l'attribution à un compartiment donné ne pourrait pas se faire sur la base des simples considérations géométriques. Dans une étape suivante, des données expérimentales ont été collectées sur la base des observations faites dans environ 100 lieux de travail différents: des informations sur les déterminants observés ont été associées aux mesures d'exposition des informations sur les déterminants observés ont été associé. Ces différentes données ont été employées pour améliorer le modèle d'exposition à deux zones. Un outil a donc été développé pour inclure des déterminants spécifiques dans le choix du compartiment, renforçant ainsi la fiabilité des prévisions. Toutes ces investigations ont servi à améliorer notre compréhension des outils des modélisations ainsi que leurs limitations. L'intégration de déterminants mieux adaptés aux besoins des experts devrait les inciter à employer cet outil dans leur pratique. D'ailleurs, en augmentant la qualité des outils des modélisations, cette recherche permettra non seulement d'encourager leur utilisation systématique, mais elle pourra également améliorer l'évaluation de l'exposition basée sur les jugements d'experts et, par conséquent, la protection de la santé des travailleurs. Abstract Occupational exposure assessment is an important stage in the management of chemical exposures. Few direct measurements are carried out in workplaces, and exposures are often estimated based on expert judgements. There is therefore a major requirement for simple transparent tools to help occupational health specialists to define exposure levels. The aim of the present research is to develop and improve modelling tools in order to predict exposure levels. In a first step a survey was made among professionals to define their expectations about modelling tools (what types of results, models and potential observable parameters). It was found that models are rarely used in Switzerland and that exposures are mainly estimated from past experiences of the expert. Moreover chemical emissions and their dispersion near the source have also been considered as key parameters. Experimental and modelling studies were also performed in some specific cases in order to test the flexibility and drawbacks of existing tools. In particular, models were applied to assess professional exposure to CO for different situations and compared with the exposure levels found in the literature for similar situations. Further, exposure to waterproofing sprays was studied as part of an epidemiological study on a Swiss cohort. In this case, some laboratory investigation have been undertaken to characterize the waterproofing overspray emission rate. A classical two-zone model was used to assess the aerosol dispersion in the near and far field during spraying. Experiments were also carried out to better understand the processes of emission and dispersion for tracer compounds, focusing on the characterization of near field exposure. An experimental set-up has been developed to perform simultaneous measurements through direct reading instruments in several points. It was mainly found that from a statistical point of view, the compartmental theory makes sense but the attribution to a given compartment could ñó~be done by simple geometric consideration. In a further step the experimental data were completed by observations made in about 100 different workplaces, including exposure measurements and observation of predefined determinants. The various data obtained have been used to improve an existing twocompartment exposure model. A tool was developed to include specific determinants in the choice of the compartment, thus largely improving the reliability of the predictions. All these investigations helped improving our understanding of modelling tools and identify their limitations. The integration of more accessible determinants, which are in accordance with experts needs, may indeed enhance model application for field practice. Moreover, while increasing the quality of modelling tool, this research will not only encourage their systematic use, but might also improve the conditions in which the expert judgments take place, and therefore the workers `health protection.

As the world turns: short-term human spatial memory in egocentric and allocentric coordinates

We aimed to determine whether human subjects' reliance on different sources of spatial information encoded in different frames of reference (i.e., egocentric versus allocentric) affects their performance, decision time and memory capacity in a short-term spatial memory task performed in the real world. Subjects were asked to play the Memory game (a.k.a. the Concentration game) without an opponent, in four different conditions that controlled for the subjects' reliance on egocentric and/or allocentric frames of reference for the elaboration of a spatial representation of the image locations enabling maximal efficiency. We report experimental data from young adult men and women, and describe a mathematical model to estimate human short-term spatial memory capacity. We found that short-term spatial memory capacity was greatest when an egocentric spatial frame of reference enabled subjects to encode and remember the image locations. However, when egocentric information was not reliable, short-term spatial memory capacity was greater and decision time shorter when an allocentric representation of the image locations with respect to distant objects in the surrounding environment was available, as compared to when only a spatial representation encoding the relationships between the individual images, independent of the surrounding environment, was available. Our findings thus further demonstrate that changes in viewpoint produced by the movement of images placed in front of a stationary subject is not equivalent to the movement of the subject around stationary images. We discuss possible limitations of classical neuropsychological and virtual reality experiments of spatial memory, which typically restrict the sensory information normally available to human subjects in the real world.

Time-Course In Vivo Trafficking Pattern and Effector Function of Donor-Specific Regulatory T Cells in Response to an Allograft.

Background: Experimental data have suggested that adoptive transfer of CD4+CD25+Foxp3+ regulatory T cells (Tregs), capable of controlling immune responses to specifi c auto- or alloantigens, could be used as a therapeutic strategy to promote specifi c tolerance in T-cell mediated diseases and in organ transplantation (Tx). However, before advocating the application of immunotherapy with Tregs in Tx, we need to improve our understanding of their in vivo homeostasis, traffi cking pattern and effector function in response to alloantigens. Methods : Donor-antigen specifi c murine Tregs were generated and characterized in vitro following our described protocols. Using an adoptive transfer and skin allotransplantation model, we have analyzed the in vivo expansion and homing of fl uorescent-labeled effector T cells (Teff) and Tregs, at different time-points after Tx, using fl ow-cytometry as well as fl uorescence microscopy techniques. Results: Tregs expressed CD62L, CCR7 and CD103 allowing their homing into lymphoid and non-lymphoid tissues (gut, skin) after intravenous injection. While hyporesponsive to TCR stimulation in vitro, transferred Tregs survived, migrated to secondary lymphoid organs and preferentially expanded within the allograft draining lymph nodes. Furthermore, Foxp3+ cells could be detected inside the allograft as early as day 3-5 after Tx. At a much later time-point (day 60 after Tx), graft-infi ltrating Foxp3+ cells were also detectable in tolerant recipients. When transferred alone, CD4+CD25- Teff cells expanded within secondary lymphoid organs and infi ltrated the allograft by day 3-5 after Tx. The co-transfer of Tregs limited the expansion of alloreactive Teff cells as well as their recruitment into the allograft. The promotion of graft survival observed in the presence of Tregs was in part mediated by the inhibition of the production of effector cytokines by CD4+CD25- T cells. Conclusion: Taken together, our results suggest that the suppression of allograft rejection and the induction of Tx tolerance are in part dependant on the alloantigendriven homing and expansion of Tregs. Thus, the appropriate localization of Tregs may be critical for their suppressive function in vivo.

Schistosoma mansoni: reinfections and concomitant immunity in mice: importance of perfusion time after challenge infection for evaluation of immunoprotection

The concomitant immunity in the presence of repeated infections (with 15 cercariae) was studied in mice sacrificed on the 20th day after each infection. The comparison of the averages of immature worms, recovered from mice submitted to reinfection, with those of their respective controls (previously uninfected) showed a significantly lower worm recovery rate in the animals with previous infections (concomitant immunity). However, statiscally significant differences could not be detected among the various groups of animals, when the mice that accumulated worms in this mature stage were perfused. The theoretical projection based on the accumulation of young worms which developed to adult ones indicates a lower recovery rate of adult worms in the animals with concomitant immunity, but this projection was not corroborated by the experimental data. The visceral hemodynamic alterations that occurred in reinfections due to the pathogeny, favouring recirculation of the recent arriving worms to the other organs on the occasion of perfusion of the portal system. These results suggest that special care should be taken when one wants to investigate concomitant immunity in mice based on the distinction of the immature worms from challenge infection and the mature ones from primary infection.

Sleep EEG changes after middle cerebral artery infarcts in mice: different effects of striatal and cortical lesions.

STUDY OBJECTIVES: Hemispheric stroke in humans is associated with sleep-wake disturbances and sleep electroencephalogram (EEG) changes. The correlation between these changes and stroke extent remains unclear. In the absence of experimental data, we assessed sleep EEG changes after focal cerebral ischemia of different extensions in mice. DESIGN: Following electrode implantation and baseline sleep-wake EEG recordings, mice were submitted to sham surgery (control group), 30 minutes of intraluminal middle cerebral artery (MCA) occlusion (striatal stroke), or distal MCA electrocoagulation (cortical stroke). One and 12 days after stroke, sleep-wake EEG recordings were repeated. The EEG recorded from the healthy hemisphere was analyzed visually and automatically (fast Fourier analysis) according to established criteria. MEASUREMENTS AND RESULTS: Striatal stroke induced an increase in non-rapid eye movement (NREM) sleep and a reduction of rapid eye movement sleep. These changes were detectable both during the light and the dark phase at day 1 and persisted until day 12 after stroke. Cortical stroke induced a less-marked increase in NREM sleep, which was present only at day 1 and during the dark phase. In cortical stroke, the increase in NREM sleep was associated in the wake EEG power spectra, with an increase in the theta and a reduction in the beta activity. CONCLUSION: Cortical and striatal stroke lead to different sleep-wake EEG changes in mice, which probably reflect variable effects on sleep-promoting and wakefulness-maintaining neuronal networks.

Warming experiments underpredict plant phenological responses to climate change.

Warming experiments are increasingly relied on to estimate plant responses to global climate change. For experiments to provide meaningful predictions of future responses, they should reflect the empirical record of responses to temperature variability and recent warming, including advances in the timing of flowering and leafing. We compared phenology (the timing of recurring life history events) in observational studies and warming experiments spanning four continents and 1,634 plant species using a common measure of temperature sensitivity (change in days per degree Celsius). We show that warming experiments underpredict advances in the timing of flowering and leafing by 8.5-fold and 4.0-fold, respectively, compared with long-term observations. For species that were common to both study types, the experimental results did not match the observational data in sign or magnitude. The observational data also showed that species that flower earliest in the spring have the highest temperature sensitivities, but this trend was not reflected in the experimental data. These significant mismatches seem to be unrelated to the study length or to the degree of manipulated warming in experiments. The discrepancy between experiments and observations, however, could arise from complex interactions among multiple drivers in the observational data, or it could arise from remediable artefacts in the experiments that result in lower irradiance and drier soils, thus dampening the phenological responses to manipulated warming. Our results introduce uncertainty into ecosystem models that are informed solely by experiments and suggest that responses to climate change that are predicted using such models should be re-evaluated.

Contact melting of a three-dimensional phase change material on a flat substrate

In this paper a model is developed to describe the three dimensional contact melting process of a cuboid on a heated surface. The mathematical description involves two heat equations (one in the solid and one in the melt), the Navier-Stokes equations for the flow in the melt, a Stefan condition at the phase change interface and a force balance between the weight of the solid and the countering pressure in the melt. In the solid an optimised heat balance integral method is used to approximate the temperature. In the liquid the small aspect ratio allows the Navier-Stokes and heat equations to be simplified considerably so that the liquid pressure may be determined using an igenfunction expansion and finally the problem is reduced to solving three first order ordinary differential equations. Results are presented showing the evolution of the melting process. Further reductions to the system are made to provide simple guidelines concerning the process. Comparison of the solutions with experimental data on the melting of n-octadecane shows excellent agreement.