Solving two-phase freezing Stefan problems: Stability and monotonicity

[EN] The two-phase Stefan problems with phase formation and depletion are special cases ofmoving boundary problemswith interest in science and industry. In this work, we study a solidification problem, introducing a front-fixing transformation. The resulting non-linear partial differential system involves singularities, both at the beginning of the freezing process and when the depletion is complete, that are treated with special attention in the numerical modelling. The problem is decomposed in three stages, in which implicit and explicit finite difference schemes are used. Numerical analysis reveals qualitative properties of the numerical solution spatial monotonicity of both solid and liquid temperatures and the evolution of the solidification front. Numerical experiments illustrate the behaviour of the temperatures profiles with time, as well as the dynamics of the solidification front.Ministerio de Ciencia, Innovacion y Universidades, Grant/Award Number: MTM2017-89664-P.Piqueras, MA.; Company Rossi, R.; Jódar Sánchez, LA. (2020). Solving two-phase freezing Stefan problems: Stability and monotonicity. Mathematical Methods in the Applied Sciences. 43(14):7948-7960. https://doi.org/10.1002/mma.5787S794879604314Schmidt, A. (1996). Computation of Three Dimensional Dendrites with Finite Elements. Journal of Computational Physics, 125(2), 293-312. doi:10.1006/jcph.1996.0095Singh, S., & Bhargava, R. (2014). Simulation of Phase Transition During Cryosurgical Treatment of a Tumor Tissue Loaded With Nanoparticles Using Meshfree Approach. Journal of Heat Transfer, 136(12). doi:10.1115/1.4028730Company, R., Egorova, V. N., & Jódar, L. (2014). Solving American Option Pricing Models by the Front Fixing Method: Numerical Analysis and Computing. 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Dynamic Analysis of Unidirectional Pressure Infiltration of Porous Preforms by Pure Metals

Unidirectional pressure infiltration of porous preforms by molten metals is investigated numerically. A phenomenological model to describe fluid flow and transport phenomena during infiltration of fibrous preforms by a metal is formulated. The model describes the dynamics of the infiltration process, the temperature distribution, and solid fraction distribution. The numerical results are compared against classical asymptotic analyses and experimental results. This comparison shows that end effects may become important and render asymptotic results unreliable for realistic samples. Fiber volume fraction and initial temperature appear as the factors most strongly influencing infiltration. Metal superheating affects not only the length of the two-phase zone but also the solid fraction distribution in the two-phase zone. The effect of constant applied pressure, although significant on the infiltration velocity, is almost negligible on the two-phase zone length and on solid fraction distribution. When the initial preform temperature is below the metal melting point, and constant pressure is applied under adiabatic conditions, the flow ceases when sufficient solidification occurs to obstruct it. A comparison with literature experiments proves the model to be an efficient predictive tool in the analysis of infiltration processes for different preform/melt systems

Estimating malaria transmission intensity from Plasmodium falciparum serological data using antibody density models.

BACKGROUND: Serological data are increasingly being used to monitor malaria transmission intensity and have been demonstrated to be particularly useful in areas of low transmission where traditional measures such as EIR and parasite prevalence are limited. The seroconversion rate (SCR) is usually estimated using catalytic models in which the measured antibody levels are used to categorize individuals as seropositive or seronegative. One limitation of this approach is the requirement to impose a fixed cut-off to distinguish seropositive and negative individuals. Furthermore, the continuous variation in antibody levels is ignored thereby potentially reducing the precision of the estimate. METHODS: An age-specific density model which mimics antibody acquisition and loss was developed to make full use of the information provided by serological measures of antibody levels. This was fitted to blood-stage antibody density data from 12 villages at varying transmission intensity in Northern Tanzania to estimate the exposure rate as an alternative measure of transmission intensity. RESULTS: The results show a high correlation between the exposure rate estimates obtained and the estimated SCR obtained from a catalytic model (r = 0.95) and with two derived measures of EIR (r = 0.74 and r = 0.81). Estimates of exposure rate obtained with the density model were also more precise than those derived from catalytic models. CONCLUSION: This approach, if validated across different epidemiological settings, could be a useful alternative framework for quantifying transmission intensity, which makes more complete use of serological data

Simulation of Channel Segregation During Directional Solidification of In—75 wt pct Ga. Qualitative Comparison with In Situ Observations

International audienceFreckles are common defects in industrial casting. They result from thermosolutal convection due to buoyancy forces generated from density variations in the liquid. The present paper proposes a numerical analysis for the formation of channel segregation using the three-dimensional (3D) cellular automaton (CA)—finite element (FE) model. The model integrates kinetics laws for the nucleation and growth of a microstructure with the solution of the conservation equations for the casting, while introducing an intermediate modeling scale for a direct representation of the envelope of the dendritic grains. Directional solidification of a cuboid cell is studied. Its geometry, the alloy chosen as well as the process parameters are inspired from experimental observations recently reported in the literature. Snapshots of the convective pattern, the solute distribution, and the morphology of the growth front are qualitatively compared. Similitudes are found when considering the coupled 3D CAFE simulations. Limitations of the model to reach direct simulation of the experiments are discussed

A simplified study of trans-mitral Doppler patterns

<p>Abstract</p> <p>Background</p> <p>Trans-mitral Doppler produces complex patterns with a great deal of variability. There are several confusing numerical measures and indices to study these patterns. However trans-mitral Doppler produces readymade data visualization by pattern generation which could be interpreted by pattern analysis. By following a systematic approach we could create an order and use this tool to study cardiac function.</p> <p>Presentation of the hypothesis</p> <p>In this new approach we eliminate the variables and apply pattern recognition as the main criterion of study. Proper terminologies are also devised to avoid confusion. In this way we can get some meaningful information.</p> <p>Testing the hypothesis</p> <p>Trans-mitral Doppler should be seen as patterns rather than the amplitude. The hypothesis can be proven by logical deduction, extrapolation and elimination of variables. Trans-mitral flow is also analyzed <it>vis-à-vis </it>the Starling's Law applied to the left atrium.</p> <p>Implications of the hypothesis</p> <p>Trans-mitral Doppler patterns are not just useful for evaluating diastolic function. They are also useful to evaluate systolic function. By following this schema we could get useful diagnostic information and therapeutic options using simple pattern recognition with minimal measurements. This simplified but practical approach will be useful in day to day clinical practice and help in understanding cardiac function better. This will also standardize research and improve communication.</p

Interhemispheric Interactions between the Human Primary Somatosensory Cortices

In the somatosensory domain it is still unclear at which processing stage information reaches the opposite hemispheres. Due to dense transcallosal connections, the secondary somatosensory cortex (S2) has been proposed to be the key candidate for interhemispheric information transfer. However, recent animal studies showed that the primary somatosensory cortex (S1) might as well account for interhemispheric information transfer. Using paired median nerve somatosensory evoked potential recordings in humans we tested the hypothesis that interhemispheric inhibitory interactions in the somatosensory system occur already in an early cortical processing stage such as S1. Conditioning right S1 by electrical median nerve (MN) stimulation of the left MN (CS) resulted in a significant reduction of the N20 response in the target (left) S1 relative to a test stimulus (TS) to the right MN alone when the interstimulus interval between CS and TS was between 20 and 25 ms. No such changes were observed for later cortical components such as the N20/P25, N30, P40 and N60 amplitude. Additionally, the subcortically generated P14 response in left S1 was also not affected. These results document the existence of interhemispheric inhibitory interactions between S1 in human subjects in the critical time interval of 20–25 ms after median nerve stimulation

Using serological measures to monitor changes in malaria transmission in Vanuatu

BACKGROUND: With renewed interest in malaria elimination, island environments present unique opportunities to achieve this goal. However, as transmission decreases, monitoring and evaluation programmes need increasingly sensitive tools to assess Plasmodium falciparum and Plasmodium vivax exposure. In 2009, to assess the role of serological markers in evaluating malaria transmission, a cross-sectional seroprevalence study was carried out in Tanna and Aneityum, two of the southernmost islands of the Vanuatu archipelago, areas where malaria transmission has been variably reduced over the past few decades. METHODS: Malaria transmission was assessed using serological markers for exposure to P. falciparum and P. vivax. Filter blood spot papers were collected from 1,249 people from Tanna, and 517 people from Aneityum to assess the prevalence of antibodies to two P. falciparum antigens (MSP-119 and AMA-1) and two P. vivax antigens (MSP-119 and AMA-1). Age-specific prevalence was modelled using a simple catalytic conversion model based on maximum likelihood to generate a community seroconversion rate (SCR). RESULTS: Overall seropositivity in Tanna was 9.4%, 12.4% and 16.6% to P. falciparum MSP-119, AMA-1 and Schizont Extract respectively and 12.6% and 15.0% to P. vivax MSP-119 and AMA-1 respectively. Serological results distinguished between areas of differential dominance of either P. vivax or P. falciparum and analysis of age-stratified results showed a step in seroprevalence occurring approximately 30 years ago on both islands, indicative of a change in transmission intensity at this time. Results from Aneityum suggest that several children may have been exposed to malaria since the 2002 P. vivax epidemic. CONCLUSION: Seroepidemiology can provide key information on malaria transmission for control programmes, when parasite rates are low. As Vanuatu moves closer to malaria elimination, monitoring changes in transmission intensity and identification of residual malaria foci is paramount in order to concentrate intervention efforts