Pattern formation in directional solidification under shear flow. I: Linear stability analysis and basic patterns

An asymptotic interface equation for directional solidification near the absolute stabiliy limit is extended by a nonlocal term describing a shear flow parallel to the interface. In the long-wave limit considered, the flow acts destabilizing on a planar interface. Moreover, linear stability analysis suggests that the morphology diagram is modified by the flow near the onset of the Mullins-Sekerka instability. Via numerical analysis, the bifurcation structure of the system is shown to change. Besides the known hexagonal cells, structures consisting of stripes arise. Due to its symmetry-breaking properties, the flow term induces a lateral drift of the whole pattern, once the instability has become active. The drift velocity is measured numerically and described analytically in the framework of a linear analysis. At large flow strength, the linear description breaks down, which is accompanied by a transition to flow-dominated morphologies, described in a companion paper. Small and intermediate flows lead to increased order in the lattice structure of the pattern, facilitating the elimination of defects. Locally oscillating structures appear closer to the instability threshold with flow than without.Comment: 20 pages, Latex, accepted for Physical Review

Macrosegregation Caused by Thermosolutal Convection During Directional Solidification of Pb-Sb Alloys

Pb-2.2 and 5.8 wt pet Sb alloys were directionally solidified with a positive thermal gradient of 140 K cm(-1) at growth speeds ranging from 0.8 to 30 mu m s(-1), and then quenched to retain the mushy-zone morphology. Chemical analysis along the length of the directionally solidified portion and in the quenched melt ahead of the dendritic array showed extensive longitudinal macrosegregation, Cellular morphologies growing at smaller growth speeds are associated with larger amounts of macrosegregation as compared with the dendrites growing at higher growth speeds. Convection is caused, mainly, by the density inversion in the overlying melt ahead of the cellular/dendritic array because of the antimony enrichment at the array tip. Mixing of the interdendritic and bulk melt during directional solidification is responsible for the observed longitudinal macrosegregation

Effect of Magnetic-Field on the Microstructure and Macrosegregation in Directionally Solidified Pb-Sn Alloys

An investigation into the influence of a transverse magnetic field (0.45 T) on the mushy zone morphology and macrosegregation in directionally solidified hypoeutectic Pb-Sn alloy shows that the field has no influence on the morphology of dendritic arrays. The field does, however, cause severe distortion in the cellular array morphology. Cellular arrayed growth with the magnetic field results in an extensive channel formation in the mushy zone, as opposed to the well-aligned and uniformly distributed cells formed in the absence of the field. The channels are produced due to the anisotropy in the thermosolutal convection caused by the magnetic field. Macrosegregation, however, along the length of the directionally solidified samples is not influenced by this magnetic field for either the cellular or dendritic arrays

Time Dependence of Tip Morphology during Cellular/Dendritic Arrayed Growth

Succinonitrile-1.9 wt pct acetone has been directionally solidified in 0.7 X 0.7-cm-square cross section pyrex ampoules in order to observe the cell/dendrite tip morphologies, not influenced by the 'wall effects', which are present during growth in the generally used thin (about 200 gm) crucibles. The tips do not maintain a steady-state shape, as is generally assumed. Instead, they fluctuate within a shape envelope. The extent of fluctuation increases with decreasing growth speed, as the micro structure changes from the dendritic to cellular. The influence of natural convection has been examined by comparing these morphologies with those grown, without convection, in the thin ampoules

Mushy Zone Morphology During Directional Solidification of Pb-5.8 Wt Pct Sb Alloy

The Pb-5.8 wt pet Sb alloy was directionally solidified with a positive thermal gradient of 140 K cm(-1) at a growth speed ranging from 0.8 to 30 mu m s(-1), and then it was quenched to retain the mushy zone morphology. The morphology of the mushy zone along its entire length has been characterized by using a serial sectioning and three-dimensional image reconstruction technique. Variation in the cellular/dendritic shape factor, hydraulic radius of the interdendritic region, and fraction solid along the mushy zone length has been studied. A comparison with predictions from theoretical models indicates that convection remarkably reduces the primary dendrite spacing while its influence on the dendrite tip radius is not as significant

The Effect of Convection on Disorder in Primary Cellular and Dendritic Arrays

Directional solidification studies have been carried out to characterize the spatial disorder in the arrays of cells and dendrites. Different factors that cause array disorder are investigated experimentally and analyzed numerically. In addition to the disorder resulting from the fundamental selection of a range of primary spacings under given experimental conditions, a significant variation in primary spacings is shown to occur in bulk samples due to convection effects, especially at low growth velocities. The effect of convection on array disorder is examined through directional solidification studies in two different alloy systems, Pb-Sn and Al-Cu. A detailed analysis of the spacing distribution is carried out, which shows that the disorder in the spacing distribution is greater in the Al-Cu system than in Pb-Sn system. Numerical models are developed which show that fluid motion can occur in both these systems due to the negative axial density gradient or due the radial temperature gradient which is always present in Bridgman growth. The modes of convection have been found to be significantly different in these systems, due to the solute being heavier than the solvent in the Al-Cu system and lighter than it in the Pb-Sn system. The results of the model have been shown to explain experimental observations of higher disorder and greater solute segregation in a weakly convective Al-Cu system than those in a highly convective Pb-Sn system

Mapping geographical inequalities in childhood diarrhoeal morbidity and mortality in low-income and middle-income countries, 2000–17 : analysis for the Global Burden of Disease Study 2017

Background Across low-income and middle-income countries (LMICs), one in ten deaths in children younger than 5 years is attributable to diarrhoea. The substantial between-country variation in both diarrhoea incidence and mortality is attributable to interventions that protect children, prevent infection, and treat disease. Identifying subnational regions with the highest burden and mapping associated risk factors can aid in reducing preventable childhood diarrhoea. Methods We used Bayesian model-based geostatistics and a geolocated dataset comprising 15 072 746 children younger than 5 years from 466 surveys in 94 LMICs, in combination with findings of the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2017, to estimate posterior distributions of diarrhoea prevalence, incidence, and mortality from 2000 to 2017. From these data, we estimated the burden of diarrhoea at varying subnational levels (termed units) by spatially aggregating draws, and we investigated the drivers of subnational patterns by creating aggregated risk factor estimates. Findings The greatest declines in diarrhoeal mortality were seen in south and southeast Asia and South America, where 54·0% (95% uncertainty interval [UI] 38·1–65·8), 17·4% (7·7–28·4), and 59·5% (34·2–86·9) of units, respectively, recorded decreases in deaths from diarrhoea greater than 10%. Although children in much of Africa remain at high risk of death due to diarrhoea, regions with the most deaths were outside Africa, with the highest mortality units located in Pakistan. Indonesia showed the greatest within-country geographical inequality; some regions had mortality rates nearly four times the average country rate. Reductions in mortality were correlated to improvements in water, sanitation, and hygiene (WASH) or reductions in child growth failure (CGF). Similarly, most high-risk areas had poor WASH, high CGF, or low oral rehydration therapy coverage. Interpretation By co-analysing geospatial trends in diarrhoeal burden and its key risk factors, we could assess candidate drivers of subnational death reduction. Further, by doing a counterfactual analysis of the remaining disease burden using key risk factors, we identified potential intervention strategies for vulnerable populations. In view of the demands for limited resources in LMICs, accurately quantifying the burden of diarrhoea and its drivers is important for precision public health

Global, regional, and national cancer incidence, mortality, years of life lost, years lived with disability, and disability-adjusted life-years for 32 cancer groups, 1990 to 2015: A Systematic Analysis for the Global Burden of Disease Study Global Burden of Disease Cancer Collaboration

IMPORTANCE: Cancer is the second leading cause of death worldwide. Current estimates on the burden of cancer are needed for cancer control planning. OBJECTIVE: To estimate mortality, incidence, years lived with disability (YLDs), years of life lost (YLLs), and disability-adjusted life-years (DALYs) for 32 cancers in 195 countries and territories from 1990 to 2015. EVIDENCE REVIEW: Cancer mortality was estimated using vital registration system data, cancer registry incidence data (transformed to mortality estimates using separately estimated mortality to incidence [MI] ratios), and verbal autopsy data. Cancer incidence was calculated by dividing mortality estimates through the modeled MI ratios. To calculate cancer prevalence, MI ratios were used to model survival. To calculate YLDs, prevalence estimates were multiplied by disability weights. The YLLs were estimated by multiplying age-specific cancer deaths by the reference life expectancy. DALYs were estimated as the sum of YLDs and YLLs. A sociodemographic index (SDI) was created for each location based on income per capita, educational attainment, and fertility. Countries were categorized by SDI quintiles to summarize results. FINDINGS: In 2015, there were 17.5 million cancer cases worldwide and 8.7 million deaths. Between 2005 and 2015, cancer cases increased by 33%, with population aging contributing 16%, population growth 13%, and changes in age-specific rates contributing 4%. For men, the most common cancer globally was prostate cancer (1.6 million cases). Tracheal, bronchus, and lung cancer was the leading cause of cancer deaths and DALYs in men (1.2 million deaths and 25.9 million DALYs). For women, the most common cancer was breast cancer (2.4 million cases). Breast cancer was also the leading cause of cancer deaths and DALYs for women (523 000 deaths and 15.1 million DALYs). Overall, cancer caused 208.3 million DALYs worldwide in 2015 for both sexes combined. Between 2005 and 2015, age-standardized incidence rates for all cancers combined increased in 174 of 195 countries or territories. Age-standardized death rates (ASDRs) for all cancers combined decreased within that timeframe in 140 of 195 countries or territories. Countries with an increase in the ASDR due to all cancers were largely located on the African continent. Of all cancers, deaths between 2005 and 2015 decreased significantly for Hodgkin lymphoma (-6.1% [95% uncertainty interval (UI), -10.6% to -1.3%]). The number of deaths also decreased for esophageal cancer, stomach cancer, and chronic myeloid leukemia, although these results were not statistically significant. CONCLUSION AND RELEVANCE: As part of the epidemiological transition, cancer incidence is expected to increase in the future, further straining limited health care resources. Appropriate allocation of resources for cancer prevention, early diagnosis, and curative and palliative care requires detailed knowledge of the local burden of cancer. The GBD 2015 study results demonstrate that progress is possible in the war against cancer. However, the major findings also highlight an unmet need for cancer prevention efforts, including tobacco control, vaccination, and the promotion of physical activity and a healthy diet

Mapping local patterns of childhood overweight and wasting in low- and middle-income countries between 2000 and 2017

A double burden of malnutrition occurs when individuals, household members or communities experience both undernutrition and overweight. Here, we show geospatial estimates of overweight and wasting prevalence among children under 5 years of age in 105 low- and middle-income countries (LMICs) from 2000 to 2017 and aggregate these to policy-relevant administrative units. Wasting decreased overall across LMICs between 2000 and 2017, from 8.4 (62.3 (55.1�70.8) million) to 6.4 (58.3 (47.6�70.7) million), but is predicted to remain above the World Health Organization�s Global Nutrition Target of <5 in over half of LMICs by 2025. Prevalence of overweight increased from 5.2 (30 (22.8�38.5) million) in 2000 to 6.0 (55.5 (44.8�67.9) million) children aged under 5 years in 2017. Areas most affected by double burden of malnutrition were located in Indonesia, Thailand, southeastern China, Botswana, Cameroon and central Nigeria. Our estimates provide a new perspective to researchers, policy makers and public health agencies in their efforts to address this global childhood syndemic. © 2020, The Author(s)