Three-dimensional elastic analysis of cracked thick plates under bending fields

A three-dimensional analysis is presented for the bending problem of finite thick plates with through-the-thickness cracks. A general solution is obtained for Navier's equations of the theory of elasticity. It is found that the in-plane stresses and the transverse normal stress at the crack front are singular with an inverse square root singularity, while the transverse shear stresses are of the order of unity. Results from a numerical study indicate that the stress intensity factor, which varies across the thickness, is influenced by the thickness ratio in a significant manner. Results from a parametric study and those from a comparative study with existing finite element values are presented.

Coffee and risk of type 2 diabetes

Type 2 diabetes is one of the diseases that largely determined by lifestyle factors. Coffee is one of the most consumed beverages in the world and recently released data suggest the effects of coffee consumption on type 2 diabetes. The objective of the present study was to evaluate the effects of habitual coffee consumption on various aspects of type 2 diabetes and its most common complications. This study is part of the national FINRISK studies. Baseline surveys were carried out between 1972 and 1997. The surveys covered two eastern regions in 1972 and 1977, but were expanded to include a third region in southwestern Finland in 1982, 1987, 1992, and 1997. The Helsinki capital area was included in the survey in 1992 and 1997 and the Oulu province, in northern Finland, in 1997. Each survey was drawn from an independent random sample of the national register of subjects aged 25-64. In 1997, an additional sample of subjects aged 65-74 was conducted. The blood pressure, weight, and height of subjects were measured. By using self-administered questionnaires data were collected on medical history, socioeconomic factors, physical activity, smoking habits, and alcohol, coffee, and tea consumption. Higher coffee consumption was associated with higher body mass index, occupational physical activity and cigarette smoking, and lower blood pressure, education level, leisure time physical activity, tea consumption and alcohol use. Age, body mass index, systolic blood pressure and current smoking were positively associated with the risk of type 2 diabetes, however, education, and occupational, commuting and leisure time physical activity were inversely associated. The significant inverse association between coffee consumption and the risk of type 2 diabetes was found in both sexes but the association was stronger in women. Coffee consumption was significantly and inversely associated with fasting glucose, 2-hour plasma glucose, fasting insulin, impaired fasting glucose, impaired glucose regulation, and hyperinsulinemia among both men and women and with isolated impaired glucose tolerance among women. Serum gamma-glutamyltransferase modified the association between coffee consumption and incident diabetes. Among subjects with high serum -glutamyltransferase (>75th percentile), coffee consumption showed an inverse association for women, as well as men and women combined. An inverse association also occurred between coffee consumption and the risk of total, cardiovascular disease, and coronary heart disease mortality among patients with type 2 diabetes. The results of this study showed that habitual coffee consumption may be associated with a reduced risk of type 2 diabetes. Coffee consumption may have some effects on several markers of glycemia, and may lower the incident of type 2 diabetes in high normal serum -glutamyltransferase levels. Total, cardiovascular disease, and coronary heart disease mortality rate among subjects with type 2 diabetes may also be reduced by coffee consumption.

Early growth and adult health: focus on blood pressure, glucose tolerance status and body composition

Theory of developmental origins of adult health and disease proposes that experiences during critical periods of early development may have consequences on health throughout a lifespan. Thesis studies aimed to characterize associations between early growth and some components of the metabolic syndrome cluster. Participants belong to two epidemiological cohorts with data on birth measurements and, for the younger cohort, on serial recordings of weight and height during childhood. They were born as singletons between 1924-33 and 1934-44 in the Helsinki University Central Hospital, and 500 and 2003 of them, respectively, attended clinical studies at the age of 65-75 and 56-70 years, respectively. In the 65-75 year old men and women, the well-known inverse relationship between birth weight and systolic blood pressure (SBP) was confined to people who had established hypertension. Among them a 1-kg increase in birth weight was associated with a 6.4-mmHg (95% CI: 1.0 to 11.9) decrease in SBP. This relationship was further confined to people with the prevailing Pro12Pro polymorphism of the peroxisome proliferator-activated receptor-γ2 (PPARγ2) gene. People with low birth weight were more likely to receive angiotensin-converting enzyme inhibitors/angiotensin-receptor blockers (ACEI/ARB, p=0.03), and, again, this relationship was confined to the carriers of the Pro12Pro (p=0.01 for interaction). These results suggest that the inverse association between birth weight and systolic BP becomes focused in hypertensive people because pathological features of BP regulation, associated with slow fetal growth, become self-perpetuating in adult life. Insulin resistance of the Pro12Pro carriers with low birth weight may interact with the renin-angiotensin system leading to raised BP levels. Habitual physical activity protected men and women who were small at birth, and thus at increased risk for the development of type 2 diabetes, against glucose intolerance more strongly. Among subjects with birth weight ≤3000 g, the odds ratio (OR) for glucose intolerance was 5.2 (95% CI: 2.1 to 13) in those who exercised less than 3 times per week compared to regular exercisers; in those who scored their exercise light compared with moderate exercisers (defined as comparable to brisk walking) the OR was 3.5 (1.5 to 8.2). In the 56-70 year old men a 1 kg increase in birth weight corresponded to a 4.1 kg (95% CI: 3.1 to 5.1) and in women to a 2.9 kg (2.1 to 3.6) increase in adult lean mass. Rapid gain in body mass index (BMI), i.e. crossing from an original BMI percentile to a higher one, before the age of 2 years increased adult lean mass index (LMI, lean mass/height squared) without excess fat accumulation whereas rapid gain in BMI during later childhood, despite the concurrent rise in LMI, resulted in a relatively higher increase in adult body fat mass. These findings illustrate how genes, the environment and their interactions, early growth patterns, and adult lifestyle modify adult health risks which originate from early life.

Serum uric acid and metabolic risk factors in three ethnic groups: Asian Indians and Creoles in Mauritius and Chinese in Qingdao, China

In humans with a loss of uricase the final oxidation product of purine catabolism is uric acid (UA). The prevalence of hyperuricemia has been increasing around the world accompanied by a rapid increase in obesity and diabetes. Since hyperuricemia was first described as being associated with hyperglycemia and hypertension by Kylin in 1923, there has been a growing interest in the association between elevated UA and other metabolic abnormalities of hyperglycemia, abdominal obesity, dyslipidemia, and hypertension. The direction of causality between hyperuricemia and metabolic disorders, however, is unceartain. The association of UA with metabolic abnormalities still needs to be delineated in population samples. Our overall aims were to study the prevalence of hyperuricemia and the metabolic factors clustering with hyperuricemia, to explore the dynamical changes in blood UA levels with the deterioration in glucose metabolism and to estimate the predictive capability of UA in the development of diabetes. Four population-based surveys for diabetes and other non-communicable diseases were conducted in 1987, 1992, and 1998 in Mauritius, and in 2001-2002 in Qingdao, China. The Qingdao study comprised 1 288 Chinese men and 2 344 women between 20-74, and the Mauritius study consisted of 3 784 Mauritian Indian and Mauritian Creole men and 4 442 women between 25-74. In Mauritius, re-exams were made in 1992 and/or 1998 for 1 941 men (1 409 Indians and 532 Creoles) and 2 318 non pregnant women (1 645 Indians and 673 Creoles), free of diabetes, cardiovascular diseases, and gout at baseline examinations in 1987 or 1992, using the same study protocol. The questionnaire was designed to collect demographic details, physical examinations and standard 75g oral glucose tolerance tests were performed in all cohorts. Fasting blood UA and lipid profiles were also determined. The age-standardized prevalence in Chinese living in Qingdao was 25.3% for hyperuricemia (defined as fasting serum UA > 420 μmol/l in men and > 360 μmol/l in women) and 0.36% for gout in adults between 20-74. Hyperuricemia was more prevalent in men than in women. One standard deviation increase in UA concentration was associated with the clustering of metabolic risk factors for both men and women in three ethnic groups. Waist circumference, body mass index, and serum triglycerides appeared to be independently associated with hyperuricemia in both sexes and in all ethnic groups except in Chinese women, in whom triglycerides, high-density lipoprotein cholesterol, and total cholesterol were associated with hyperuricemia. Serum UA increased with increasing fasting plasma glucose levels up to a value of 7.0 mmol/l, but significantly decreased thereafter in mainland Chinese. An inverse relationship occurred between 2-h plasma glucose and serum UA when 2-h plasma glucose higher than 8.0 mmol/l. In the prospective study in Mauritius, 337 (17.4%) men and 379 (16.4%) women developed diabetes during the follow-up. Elevated UA levels at baseline increased 1.14-fold in risk of incident diabetes in Indian men and 1.37-fold in Creole men, but no significant risk was observed in women. In conclusion, the prevalence of hyperuricemia was high in Chinese in Qingdao, blood UA was associated with the clustering of metabolic risk factors in Mauritian Indian, Mauritian Creole, and Chinese living in Qingdao, and a high baseline UA level independently predicted the development of diabetes in Mauritian men. The clinical use of UA as a marker of hyperglycemia and other metabolic disorders needs to be further studied. Keywords: Uric acid, Hyperuricemia, Risk factors, Type 2 Diabetes, Incidence, Mauritius, Chinese

Turnover intentions of employees with informal eldercare responsibilities: The role of core self-evaluations and supervisor support

As longevity increases, so does the need for care of older relatives by working family members. This research examined the interactive effect of core self-evaluations and supervisor support on turnover intentions in two samples of employees with informal caregiving responsibilities. Data were obtained from 57 employees from Australia (Study 1) and 66 employees from the United States and India (Study 2). Results of Study 1 revealed a resource compensation effect, that is, an inverse relationship between core self-evaluations and turnover intentions when supervisor care support was low. Results of Study 2 extended these findings by demonstrating resource boosting effects. Specifically, there was an inverse relationship between core self-evaluations and subsequent turnover intentions for those with high supervisor work and care support. In addition, employees' satisfaction and emotional exhaustion from their work mediated the inverse relationship between core self-evaluations and subsequent turnover intentions when supervisor work support and care support were high. Overall, these findings highlight the importance of employee- and supervisor-focused intervention strategies in organizations to support informal caregivers.

Stochastic kinetics of ribosomes: Single motor properties and collective behavior

Syntheses of protein molecules in a cell are carried out by ribosomes.A ribosome can be regarded as a molecular motor which utilizes the input chemical energy to move on a messenger RNA (mRNA) track that also serves as a template for the polymerization of the corresponding protein. The forward movement, however, is characterized by an alternating sequence of translocation and pause. Using a quantitative model, which captures the mechanochemical cycle of an individual ribosome, we derive an exact analytical expression for the distribution of its dwell times at the successive positions on the mRNA track. Inverse of the average dwell time satisfies a Michaelis-Menten-type'' equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechanochemical cycle. Extending this formula appropriately, we also derive the exact force-velocity relation for a ribosome. Often many ribosomes each synthesizes a copy of the same protein. We extend the model of a single ribosome by incorporating steric exclusion of different individuals on the same track. We draw the phase diagram of this model of ribosome traffic in three-dimensional spaces spanned by experimentally controllable parameters. We suggest new experimental tests of our theoretical predictions.

Estimation of local forest attributes, utilizing two-phase sampling and auxiliary data

This thesis examines the feasibility of a forest inventory method based on two-phase sampling in estimating forest attributes at the stand or substand levels for forest management purposes. The method is based on multi-source forest inventory combining auxiliary data consisting of remote sensing imagery or other geographic information and field measurements. Auxiliary data are utilized as first-phase data for covering all inventory units. Various methods were examined for improving the accuracy of the forest estimates. Pre-processing of auxiliary data in the form of correcting the spectral properties of aerial imagery was examined (I), as was the selection of aerial image features for estimating forest attributes (II). Various spatial units were compared for extracting image features in a remote sensing aided forest inventory utilizing very high resolution imagery (III). A number of data sources were combined and different weighting procedures were tested in estimating forest attributes (IV, V). Correction of the spectral properties of aerial images proved to be a straightforward and advantageous method for improving the correlation between the image features and the measured forest attributes. Testing different image features that can be extracted from aerial photographs (and other very high resolution images) showed that the images contain a wealth of relevant information that can be extracted only by utilizing the spatial organization of the image pixel values. Furthermore, careful selection of image features for the inventory task generally gives better results than inputting all extractable features to the estimation procedure. When the spatial units for extracting very high resolution image features were examined, an approach based on image segmentation generally showed advantages compared with a traditional sample plot-based approach. Combining several data sources resulted in more accurate estimates than any of the individual data sources alone. The best combined estimate can be derived by weighting the estimates produced by the individual data sources by the inverse values of their mean square errors. Despite the fact that the plot-level estimation accuracy in two-phase sampling inventory can be improved in many ways, the accuracy of forest estimates based mainly on single-view satellite and aerial imagery is a relatively poor basis for making stand-level management decisions.

Modelling temperature, photoperiod and vernalization responses of Brunonia australis (Goodeniaceae) and Calandrinia sp (Portulacaceae) to predict flowering time

Crop models for herbaceous ornamental species typically include functions for temperature and photoperiod responses, but very few incorporate vernalization, which is a requirement of many traditional crops. This study investigated the development of floriculture crop models, which describe temperature responses, plus photoperiod or vernalization requirements, using Australian native ephemerals Brunonia australis and Calandrinia sp. A novel approach involved the use of a field crop modelling tool, DEVEL2. This optimization program estimates the parameters of selected functions within the development rate models using an iterative process that minimizes sum of squares residual between estimated and observed days for the phenological event. Parameter profiling and jack-knifing are included in DEVEL2 to remove bias from parameter estimates and introduce rigour into the parameter selection process. Development rate of B. australis from planting to first visible floral bud (VFB) was predicted using a multiplicative approach with a curvilinear function to describe temperature responses and a broken linear function to explain photoperiod responses. A similar model was used to describe the development rate of Calandrinia sp., except the photoperiod function was replaced with an exponential vernalization function, which explained a facultative cold requirement and included a coefficient for determining the vernalization ceiling temperature. Temperature was the main environmental factor influencing development rate for VFB to anthesis of both species and was predicted using a linear model. The phenology models for B. australis and Calandrinia sp. described development rate from planting to VFB and from VFB to anthesis in response to temperature and photoperiod or vernalization and may assist modelling efforts of other herbaceous ornamental plants. In addition to crop management, the vernalization function could be used to identify plant communities most at risk from predicted increases in temperature due to global warming.

Finite element analysis of moving contact in mechanically fastened joints

The Finite Element Method (FEM) has made a number of otherwise intractable problems solvable. An important aspect for achieving an economical and accurate solution through FEM is matching the formulation and the computational organisation to the problem. This was realised forcefully in the present case of the solution of a class of moving contact boundary value problems of fastener joints. This paper deals with the problem of changing contact at the pin-hole interface of a fastener joint. Due to moving contact, the stresses and displacements are nonlinear with load. This would, in general, need an interactive-incremental approach for solution. However, by posing the problem in an inverse way, a solution is sought for obtaining loads to suit given contact configuration. Numerical results are given for typical isotropic and composite plates with rigid pins. Two cases of loading are considered: (i) load applied only at the edges of the plate and (ii) load applied at the pin and reacted at a part of the edge of the plate. Load-contact relationships, compliance and stress-patterns are investigated. This paper clearly demonstrates the simplification achieved by a suitable formulation of the problem. The results are of significance to the design and analysis of fastener joints.

Dynamics of dense sheared granular flows. Part 1. Structure and diffusion

Shear flows of inelastic spheres in three dimensions in the Volume fraction range 0.4-0.64 are analysed using event-driven simulations.Particle interactions are considered to be due to instantaneous binary collisions, and the collision model has a normal coefficient of restitution e(n) (negative of the ratio of the post- and pre-collisional relative velocities of the particles along the line joining the centres) and a tangential coefficient of restitution e(t) (negative of the ratio of post- and pre-collisional velocities perpendicular to the line Joining the centres). Here, we have considered both e(t) = +1 and e(t) = e(n) (rough particles) and e(t) =-1 (smooth particles), and the normal coefficient of restitution e(n) was varied in the range 0.6-0.98. Care was taken to avoid inelastic collapse and ensure there are no particle overlaps during the simulation. First, we studied the ordering in the system by examining the icosahedral order parameter Q(6) in three dimensions and the planar order parameter q(6) in the plane perpendicular to the gradient direction. It was found that for shear flows of sufficiently large size, the system Continues to be in the random state, with Q(6) and q(6) close to 0, even for volume fractions between phi = 0.5 and phi = 0.6; in contrast, for a system of elastic particles in the absence of shear, the system orders (crystallizes) at phi = 0.49. This indicates that the shear flow prevents ordering in a system of sufficiently large size. In a shear flow of inelastic particles, the strain rate and the temperature are related through the energy balance equation, and all time scales can be non-dimensionalized by the inverse of the strain rate. Therefore, the dynamics of the system are determined only by the volume fraction and the coefficients of restitution. The variation of the collision frequency with volume fraction and coefficient of estitution was examined. It was found, by plotting the inverse of the collision frequency as a function of volume fraction, that the collision frequency at constant strain rate diverges at a volume fraction phi(ad) (volume fraction for arrested dynamics) which is lower than the random close-packing Volume fraction 0.64 in the absence of shear. The volume fraction phi(ad) decreases as the coefficient of restitution is decreased from e(n) = 1; phi(ad) has a minimum of about 0.585 for coefficient of restitution e(n) in the range 0.6-0.8 for rough particles and is slightly larger for smooth particles. It is found that the dissipation rate and all components of the stress diverge proportional to the collision frequency in the close-packing limit. The qualitative behaviour of the increase in the stress and dissipation rate are well Captured by results derived from kinetic theory, but the quantitative agreement is lacking even if the collision frequency obtained from simulations is used to calculate the pair correlation function used In the theory.

Fatty acids, fibre, carotenoids and tocopherols in relation to glucose metabolism in subjects at high risk for type 2 diabetes : a cross-sectional analysis

Fatty acids, fibre, carotenoids and tocopherols in relation to glucose metabolism in subjects at high risk for type 2 diabetes a cross-sectional analysis Type 2 diabetes (T2D) is a heterogeneous disorder of carbohydrate, lipid and protein metabolism, resulting from genetics, environmental influences and interactions between these. The disease is characterized by insulin resistance, β-cell dysfunction, hepatic glucose overproduction and disordered fat mobilization and storage. The literature on associations between dietary factors and glucose metabolism is inconsistent. One factor behind the discrepant results may be genetic heterogeneity of study populations. Data on nutrient-gene interactions in relation to glucose metabolism are scarce. Thus, investigating high-risk populations and exploring nutrient-gene interactions are essential for improving the understanding of T2D aetiology. Ideally, this information could help to develop prevention programmes that take into account the genetic predisposition to the disease. In this study, associations between measures of glucose metabolism predicting T2D and fatty acids, antioxidative nutrients and fibre were examined in a high-risk population, i.e., in non-diabetic relatives of affected patients. Interactions between the PPARG Pro12Ala polymorphism and fatty acids on glucose metabolism were taken into consideration. This common polymorphism plays an important role in the regulation of glucose metabolism. The inverse associations observed between dietary fibre and insulin resistance are consistent with the prevailing recommendations urging increased intake of fibre to prevent T2D. Beneficial associations observed between the intake of carotenoids and glucose levels stress that a high consumption of vegetables, fruits and berries rich in carotenoids might also play a role in the prevention of T2D. Whether tocopherols have an independent association with glucose metabolism remains questionable. Observed interactions between fatty acids and glucose metabolism suggest that a high intake of palmitic acid is associated with high fasting glucose levels mainly in female Ala allele carriers. Furthermore, the PPARG Pro12Ala polymorphism may modify the metabolic response to dietary marine fat. The beneficial associations of high intake of marine n 3 fatty acids with insulin resistance and glucose levels may be restricted to carriers of the Ala allele. The findings pertain to subjects with a family history of T2D, and the cross-sectional nature of the study precludes inferences about causality. Results nevertheless show that associations of dietary factors with glucose metabolism may be modulated by the genetic makeup of an individual. Additional research is warranted to elucidate the role of probably numerous nutrient-gene interactions, some of which may be sex-specific, in the aetiology of T2D.

Finite element analysis of moving contact in mechanically fastened joints

The Finite Element Method (FEM) has made a number of otherwise intractable problems solvable. An important aspect for achieving an economical and accurate solution through FEM is matching the formulation and the computational organisation to the problem. This was realised forcefully in the present case of the solution of a class of moving contact boundary value problems of fastener joints. This paper deals with the problem of changing contact at the pin-hole interface of a fastener joint. Due to moving contact, the stresses and displacements are nonlinear with load. This would, in general, need an interactive-incremental approach for solution. However, by posing the problem in an inverse way, a solution is sought for obtaining loads to suit given contact configuration. Numerical results are given for typical isotropic and composite plates with rigid pins. Two cases of loading are considered: (i) load applied only at the edges of the plate and (ii) load applied at the pin and reacted at a part of the edge of the plate. Load-contact relationships, compliance and stress-patterns are investigated. This paper clearly demonstrates the simplification achieved by a suitable formulation of the problem. The results are of significance to the design and analysis of fastener joints.

Relaminarization in highly accelerated turbulent boundary layers

The mean flow development in an initially turbulent boundary layer subjected to a large favourable pressure gradient beginning at a point x0 is examined through analyses expected a priori to be valid on either side of relaminarization. The ‘quasi-laminar’ flow in the later stages of reversion, where the Reynolds stresses have by definition no significant effect on the mean flow, is described by an asymptotic theory constructed for large values of a pressure-gradient parameter Λ, scaled on a characteristic Reynolds stress gradient. The limiting flow consists of an inner laminar boundary layer and a matching inviscid (but rotational) outer layer. There is consequently no entrainment to lowest order in Λ−1, and the boundary layer thins down to conserve outer vorticity. In fact, the predictions of the theory for the common measures of boundary-layer thickness are in excellent agreement with experimental results, almost all the way from x0. On the other hand the development of wall parameters like the skin friction suggests the presence of a short bubble-shaped reverse-transitional region on the wall, where neither turbulent nor quasi-laminar calculations are valid. The random velocity fluctuations inherited from the original turbulence decay with distance, in the inner layer, according to inverse-power laws characteristic of quasi-steady perturbations on a laminar flow. In the outer layer, there is evidence that the dominant physical mechanism is a rapid distortion of the turbulence, with viscous and inertia forces playing a secondary role. All the observations available suggest that final retransition to turbulence quickly follows the onset of instability in the inner layer.It is concluded that reversion in highly accelerated flows is essentially due to domination of pressure forces over the slowly responding Reynolds stresses in an originally turbulent flow, accompanied by the generation of a new laminar boundary layer stabilized by the favourable pressure gradient.

Realization of first order optical systems using thin lensest

A first order optical system is investigated in full generality within the context of wave optics. The problem is reduced to a study of the ray transfer matrices. The simplest such systems correspond to axially symmetric propagation. Realization of such systems by centrally located lenses separated by finite distances is studied. It is shown that, contrary to the commonly held view, the set of first order systems that can be realized using axially symmetric thin lenses exhausts the entire SL(2, R) group; at most three lenses are needed to realize any element of this group. In particular, the inverse of free propagation can be so realized. Among anisotropic systems it is again shown that every element of the lens group Sp(4, R) can be realized using a finite number of thin lenses.

Dendritic structures produced on solidification of multicomponent aqueous solutions

Dendrite structures of ice produced on undirectional solidification of ternary and quaternary aqueous solutions have been studied. Upon freezing, solutions containing more than one solute produce plate-shaped dendrites of ice. The spacing between dendrites increase linearly with the distance from the chill surface and the square root of local solidification time (or square root of inverse freezing rate) for any fixed composition. For fixed freezing conditions, the dendrite spacings from multicomponent aqueous solutions were a function of the concentrations and diffusion coefficients of the individual solutes. The dendrite spacing produced by freezing of a solution was changed by the addition of a solute different from those already present. If the main diffusion coefficient of the added solute is higher than that of solutes already present, the dendrite spacing is increased and vice versa. The dendrite spacing in multi-component systems increases with the total solute concentration if the constituent solutes are present in equal amounts. The dendrite spacing obtained on freezing of these dilute multicomponent solutions can be expressed by regression equations of the type Image Full-size image (2K) where L is the dendrite spacing in microns, C1, C2 and C3 are concentrations of individual solutes, Θf is the total freezing time and A1 −A8 are constants. A Yates analysis of the dendrite spacings in a factorial design of quaternary solutions indicates that there are strong interactions between individual solutes in regard to their effect on the dendrite spacings. A mass transport analysis has been used to calculate the interdendritic supersaturation ΔC of the individual solutes, the supercooling in the interdendritic liquid ΔT, and the transverse growth velocity of the dendrites, VT. In ternary solutions if two solutes are present in equal amount the supersaturation of the solute with higher main diffusion coefficient is lower, and vice versa. If a solute with higher main diffusion coefficient is added to a binary solution, the interface growth velocity, the interdendritic supersaturation of the base solute and the interdendritic supercooling increase with the quantity of solute added.