A RESEARCH NOTE COMPRESSIVE STRESS-STRAIN RELATIONSHIPS of AGGLOMERATED INSTANT COFFEE1

Shallow beds (3–9 mm) of two commercial agglomerated spray dried instant coffees were compressed using a Universal testing machine. the stress-stress relationships had the sigmoid shape characteristic of cellular solids and could be described by a four parameter model originally developed for solid foams. the magnitude of the model parameters was less sensitive to the relative humidity level at storage in the range of 11–65% than to the bed's thickness. the jaggedness of the stress-strain relationship is a manifestation of the particles brittleness and crumbliness and it is considerably reduced when they are plasticized, as a result of moisture uptake, for example. the degree of jaggedness, determined in the normalized (dimensionless) stress-strain relationships, could be qualified and compared in terms of an apparent (“natural”) fractal dimension. It was calculated from the linear region of the corresponding Richardson plots using the “blanket” algorithm. This apparent fractal dimension, however, was only a relative measure of jaggedness, since both the scales and resolution of the mechanical signatures were arbitrarily selected. the jaggedness of the individual agglomerates signatures could not be directly inferred from those of their assemblies, primarily because the effects of averaging and the bed's cushioning could not be separated.     

STIFFNESS ASSESSMENT FROM JAGGED FORCE-DEFORMATION RELATIONSHIPS1

Brittle and crunchy foods are notorious for their irregular and irreproducible force-deformation relationships which cannot be converted to stress-strain relationships because of geometric considerations. However, a fairly consistent assessment of their stiffness can still be extracted from their jagged force-deformation curves. For example, either the averaged force at a given deformation (e.g., 20%), determined directly or calculated by fitting the curves of several specimens with a polynomial model, can be considered a legitimate stiffness measure albeit a relative one. But since the magnitude of such parameters is affected by occasional force lows and minima as well as failure and sliding events at preceding deformations, they can only provide a low estimate of the material actual stiffness. Application of an algorithm that identifies the peak forces in the force-deformation relationship produces a new relationship that has a fairly regular and much smoother shape. Derivation of stiffness parameters from such curves is not only easier because of the regular shape and reduced number of points but also provides a closer estimate of the material actual stiffness.     

Mathematical Characterization of the Compressive Stress-Strain Relationships of Spongy Baked Goods

The compressive stress-strain relationships of selected breads, English muffins and sponge cake were determined with a Universal Testing Machine and described mathematically in terms of a three-parameter empirical model. These parameters gave account of the overall mechanical resistance of the sponge, the existence of a shoulder in its stress-strain curve and the strain level at which densification of the sponge becomes the dominant deformation mechanism. They were also sensitive indicators of the changes that were observed in the stress-strain relationship as a result of successive compression and could be used to distinguish between the deformation patterns of the various products.     

INSTRUMENTAL AND SENSORY DETECTION OF SIMULTANEOUS BRITTLENESS LOSS AND MOISTURE TOUGHENING IN THREE PUFFED CEREALS1

The jaggedness of the compressive force-displacement relationship of cheese balls®, cocoa puffs® and peanut butter crunch® particles at various moisture contents was determined in terms of their apparent fractal dimension, and the mean magnitude of the power spectrum of their normalized residuals. The plots of these measures versus moisture contents had a characteristic sigmoid shape very similar to that of the corresponding sensory crispness and crunchiness vs moisture content relationships. This close similarity suggests that the jaggedness of the force-displacement relationship is a manifestation of the same failure events that produce the crispness or crunchiness sensation. (In the context of the tested products the two terms, crispness and crunchiness, were found to be synonymous.) In all three products moisture toughening could be clearly detected instrumentally but only in two there was an unambiguous corresponding increase in the sensory hardness scores. This indicates that at least in certain cereal products moisture toughening can be perceived simultaneously with brittleness loss.     

EFFECT OF SAMPLE VOLUME ON THE COMPRESSIVE FORCE-DEFORMATION CURVES OF CORN FLAKES TESTED IN BULK1

Two national brands of cornflakes were compressed in cells of various dimensions (height 38–76 mm and diameter 50–91 mm) using a Universal Testing Machine. The stress-strain (σ vs. ε) relationships could be described by a four parameter model originally developed for cellular materials, i. e., σ(ε) = k₁εⁿ¹+ k₂εⁿ² where the k's and n's are constants (n₁ < 1, n₂ > 1). The scatter around the fitted relationships was normalized and its jaggedness determined in terms of an apparent fractal dimension and the mean magnitude of the power spectrum after filtering. The magnitude of both depended on the cell diameter and height indicating that the observed degree of jaggedness is influenced simultaneously by “averaging” and “cushioning” effects.     

DO IRREGULAR STRESS-STRAIN RELATIONSHIPS OF CRUNCHY FOODS HAVE REGULAR PERIODICITIES?1

The attractors of the jagged, normalized, dimensionless, stress-strain relationships of three dry snacks, breadstick, pretzel and Zwieback, were constructed using the Packard-Taken method. No unambiguous pattern could be revealed but the shape of the attractors differed from that of a totally random sequence. Although the existence of underlying characteristic periodicities could not be proven using the method with the available data it could not be ruled out either.     

Effect of starch, sucrose and their combinations on the mechanical and acoustic properties of freeze-dried alginate gels

Alginate gels (2%) with and without incorporated starch and/or sucrose were freeze-dehydrated to produce cellular sponges. The stress–strain relationships of these dried gels were all irregular and jagged, typical of brittle cellular solids. The stiffness was assessed in terms of the fitted (‘smoothed’) apparent engineering stress at two pre-selected engineering strain levels (40 and 60%) using a polynomial model. Their brittleness was assessed in terms of the apparent fractal dimension of their stress-strain curves using the compass and box counting algorithms which yield the Richardson's and Kolmogorov's dimensions, respectively. The presence of starch in the dried gels solid matrix invariably increased their stiffness, but not in a manner that could be predicted on the basis of a stochiometric relationship or density increase. Sucrose, in contrast, could have the opposite effect suggesting that its presence in the solid matrix might interfere with its mechanical integrity. All the dried gels had a ‘rich’ acoustic signature as judged by the magnitude of their apparent fractal dimension, which was determined by the ‘blanket’ algorithm. But if there were differences between the different dried gels' acoustic signatures, they were too subtle to be detected by the apparent fractal dimension alone.     

Comparison of Four Models for the Compressibility of Breads and Plastic Foams

The sigmoid compressive stress-strain relationship of lye bread, pumpernickel bread and two polyurethane foams (0-75% deformation) were fitted by four empirical models having three or four parameters. No unique model was inherently superior for goodness of fit or for strain definition, that is whether it was presented as an engineering or Hencky's strain. Two models, however, one with three and the other with four parameters, were easier to interpret in terms of stress-strain relationship shape characteristics and are recommended.     

DETERMINATION OF THE APPARENT FRACTAL DIMENSION OF THE FORCE-DISPLACEMENT CURVES OF BRITTLE SNACKS BY FOUR DIFFERENT ALGORITHMS1

The apparent fractal dimension of digitized experimental force-displacement curves of cheese balls and Zwiebacks at various levels of water activity were determined with the Richardson, Minkowski, Kolmogorov and Korcak algorithms. All four, but especially the first three, produced a consistent dimension despite the fact that the curves themselves were not truly fractal. These calculated dimensions were effective jaggedness measures and could be used interchangeably to monitor moisture sorption effects on the shape of force-displacement relationships. The apparent dimension versus water activity plot had a sigmoid form which was characterized by a shifted Fermi equation. The center point of the jaggedness loss as well as its span was revealed from the magnitude of the equation's constants or directly from the plot.     

CHARACTERIZATION OF THE POWER SPECTRUM OF FORCE-DEFORMATION RELATIONSHIPS OF CRUNCHY FOODS1

The mean magnitude of the power spectra of the compressive force-deformation relationships of breadsticks, pretzels and zwiebacks, exposed to five levels of relative humidity, was determined at various cutoff frequencies. In all three foods the mean magnitude had a linear correlation with the Fractal dimension of the normalized original force-deformation relationship, regardless of the cutoff frequency. This implies that the jaggedness of the force-deformation curve, which is most probably a manifestation of the material crunchiness or crumbliness, can be quantified by an additional single numerical index, the mean magnitude of the power spectrum. The correlation's independence of the cutoff frequency is an indication that the loss of crunchiness, as a result of moisture sorption, can be expressed in the shape of the whole spectrum and not only in its high frequency region.     

A RESEARCH NOTE UNIAXIAL COMPRESSION OF DOUBLE LAYERS OF SOLID FOODS 1

The compressive force deformation relationships of various foods, that included breads, cheeses and sausages, were described by a two parameter power model. To predict the behavior of double layered arrays of some foods, their model parameters were incorporated into an equation that describes the relationships between the force and the total deformation of the array for a given cross-sectional area and any initial thickness of each of the two layers. Construction of the force-deformation relationships of the double layered array was done by numerical solution of this equation for various levels of deformation. The force deformation relationships predicted in this way were found to be in good agreement with experimental relationships. This was irrespective of whether the force deformation curve of the components had a concave upward or downward shape.     

Detection of mastitis in dairy cattle by use of mixture models for repeated somatic cell scores: a Bayesian approach via Gibbs sampling

The distribution of somatic cell scores could be regarded as a mixture of at least two components depending on a cow's udder health status. A heteroscedastic two-component Bayesian normal mixture model with random effects was developed and implemented via Gibbs sampling. The model was evaluated using datasets consisting of simulated somatic cell score records. Somatic cell score was simulated as a mixture representing two alternative udder health statuses ("healthy" or "diseased"). Animals were assigned randomly to the two components according to the probability of group membership (Pm). Random effects (additive genetic and permanent environment), when included, had identical distributions across mixture components. Posterior probabilities of putative mastitis were estimated for all observations, and model adequacy was evaluated using measures of sensitivity, specificity, and posterior probability of misclassification. Fitting different residual variances in the two mixture components caused some bias in estimation of parameters. When the components were difficult to disentangle, so were their residual variances, causing bias in estimation of Pm and of location parameters of the two underlying distributions. When all variance components were identical across mixture components, the mixture model analyses returned parameter estimates essentially without bias and with a high degree of precision. Including random effects in the model increased the probability of correct classification substantially. No sizable differences in probability of correct classification were found between models in which a single cow effect (ignoring relationships) was fitted and models where this effect was split into genetic and permanent environmental components, utilizing relationship information. When genetic and permanent environmental effects were fitted, the between-replicate variance of estimates of posterior means was smaller because the model accounted for random genetic drift.     

Characterization of the Jagged Stress-strain Relationships of Puffed Extrudates using the Fast Fourier Transform and Fractal Analysis

The jaggedness of the stress-strain relationship of two kinds of puffed extrudates stored under different humidity conditions was assessed by the power spectrum of the Fast Fourier Transform and the Natural Fractal dimension of normalized compression curves. Both analyses, performed with a micro-computer, provided a consistent measure of jaggedness. The apparent Fractal dimension, obtained using the Blanket algorithm, was the most convenient measure of overall ruggedness since it was expressed by a single number. The power spectrum that resulted from the Fourier transform, however, could be used to identify the length scale of structural features where fracture takes place, and its shape could be more directly related to structural features and textural properties.     

26—STRUCTURAL AND NON-STRUCTURAL EFFECTS IN THE OBSERVED STRESS-STRAIN CURVE FOR WET WOOL FIBRES

This paper describes a detailed theoretical and experimental investigation into the relationship between wool-fibre non-uniformities and stress-strain behaviour. The shape of the stress-strain curve in the yield region is closely related to the fibre cumulative cross-sectional-area distribution. The fibre-material yield slope is found to be nearly zero, and the changes from Hookean to yield region and from yield to post-yield region for the material are quite sharp. The observed relative yield slope (relative to the stress at 15% extension) and the coefficient of variation of area interact in the manner predicted except that there are quantitative differences between the experimentally and theoretically derived relationships; these deviations are interpreted as structural effects due to fluctuations in the stress at 15% extension along the fibres, a variation that is relatively independent of the changes in cross-sectional area along the fibres. The mean effective coefficient of variation of area due to this structural variation is found to be of the same magnitude as the mean coefficient of variation of area for the wool-fibre types examined.

Previous results relating crimp to the cross-sectional area and the Hookean slope are confirmed; within the fibre groups, thicker fibres have a higher crimp level and a lower relative Hookean slope (relative to the stress at 15% extension), whereas between groups the thicker fibres have a lower crimp level and a higher relative Hookean slope than thinner fibres. The stress at 15% extension is significantly different for the different wool-fibre types, which indicates real structural differences between the fibre types. As the fibre mean cross-sectional area increases, the fibres show a tendency to be structurally ‘stronger’, the magnitude of this effect agreeing with values obtained by other investigators. Thinner fibres, as well as being structurally ‘weaker’, tend to be more variable in cross-sectional area and less elliptical in cross-section.     

Using a change-point model to describe temporal bitter relationships among hop-derived compounds

The bitterness of four hop-derived compounds was measured over a range of concentrations using a time–intensity protocol to determine temporal bitterness relationships. Bitter attributes were compared among compounds by applying a three parameter, change-point model to all concentration-dependent attributes whereby α represented the bitter parameter’s magnitude at very low compound concentrations up to a change-point concentration, θ, and β represented the log-linear concentration dependency of the bitter parameter above the change-point concentration, θ. Panelist reliability was determined by evaluating how well their data fit the model parameters as determined via a t-statistic. Analysis of variance of the concentration-dependent parameters, maximum intensity, duration, area-under-curve, and, decreasing area, identified differences among compounds. In the case of panelist × compound interactions, within-panelist analysis of change-point parameters yielded panel-wise relationships not initially detected.     

On the use of the Weibull model to describe thermal inactivation of microbial vegetative cells

This paper evaluates the applicability of the Weibull model to describe thermal inactivation of microbial vegetative cells as an alternative for the classical Bigelow model of first-order kinetics; spores are excluded in this article because of the complications arising due to the activation of dormant spores. The Weibull model takes biological variation, with respect to thermal inactivation, into account and is basically a statistical model of distribution of inactivation times. The model used has two parameters, the scale parameter alpha (time) and the dimensionless shape parameter beta. The model conveniently accounts for the frequently observed nonlinearity of semilogarithmic survivor curves, and the classical first-order approach is a special case of the Weibull model. The shape parameter accounts for upward concavity of a survival curve (beta < 1), a linear survival curve (beta = 1), and downward concavity (beta > 1). Although the Weibull model is of an empirical nature, a link can be made with physiological effects. Beta < 1 indicates that the remaining cells have the ability to adapt to the applied stress, whereas beta > 1 indicates that the remaining cells become increasingly damaged. Fifty-five case studies taken from the literature were analyzed to study the temperature dependence of the two parameters. The logarithm of the scale parameter alpha depended linearly on temperature, analogous to the classical D value. However, the temperature dependence of the shape parameter beta was not so clear. In only seven cases, the shape parameter seemed to depend on temperature, in a linear way. In all other cases, no statistically significant (linear) relation with temperature could be found. In 39 cases, the shape parameter beta was larger than 1, and in 14 cases, smaller than 1. Only in two cases was the shape parameter beta = 1 over the temperature range studied, indicating that the classical first-order kinetics approach is the exception rather than the rule. The conclusion is that the Weibull model can be used to model nonlinear survival curves, and may be helpful to pinpoint relevant physiological effects caused by heating. Most importantly, process calculations show that large discrepancies can be found between the classical first-order approach and the Weibull model. This case study suggests that the Weibull model performs much better than the classical inactivation model and can be of much value in modelling thermal inactivation more realistically, and therefore, in improving food safety and quality.     

Survival curves of heated bacterial spores: effect of environmental factors on Weibull parameters

The classical D-value of first order inactivation kinetic is not suitable for quantifying bacterial heat resistance for non-log linear survival curves. One simple model derived from the Weibull cumulative function describes non-log linear kinetics of micro-organisms. The influences of environmental factors on Weibull model parameters, shape parameter "p" and scale parameter "delta", were studied. This paper points out structural correlation between these two parameters. The environmental heating and recovery conditions do not present clear and regular influence on the shape the parameter "p" and could not be described by any model tried. Conversely, the scale parameter "delta" depends on heating temperature and heating and recovery medium pH. The models established to quantify these influences on the classical "D" values could be applied to this parameter "delta". The slight influence of the shape parameter p variation on the goodness of fit of these models can be neglected and the simplified Weibull model with a constant p-value for given microbial population can be applied for canning process calculations.     

酯的定量结构与色谱保留指数相关性

采用拓扑指数（^mQ）、定位基参数（Sox）与酯类物质在两种固定相上的气相色谱保留指数值（RI）进行分析，发现RI与上述参数之间存在良好的相关性，其关系可表示为：RI=d＋a^0Q-b^1Q＋cSox，式中a，b，c，d为系数。相关系数均大于0．99。继以留一法（Leave-one-out，LOO）进行交互检验，相关系数瓯均大于0．98。表明所建定量结构一保留关系（QSRR）模型具有良好的稳定性和预测能力，较好地揭示了酯类物质在不同固定相上气相色谱保留指数的变化规律。     

Modelling thermal inactivation of Listeria monocytogenes in sucrose solutions of various water activities

The heat resistance of Listeria monocytogenes was determined in sucrose solutions with water activity (a(w)) ranging from 0.99 to 0.90. At all temperatures investigated shape of the survival curves depended on the a(w) of the treatment medium. The survival curves for a(w)=0.99 appeared to be linear, for a(w)=0.96 were slightly upwardly concaved and for a(w)=0.93 and 0.90 were markedly concave upward. A mathematical model based on the Weibull distribution provided a good fit for all the survival curves obtained in this investigation. The effect of the temperature and a(w) on the Weibull model parameters was also studied. The shape parameter (p) depended on the a(w) of the treatment medium but in each medium of different a(w) the temperature did not have a significant effect on this parameter. The p parameter followed a linear relationship with a(w). The scale parameter (delta) decreased with the temperature following an exponential relationship and increased by decreasing the a(w) in the range from 0.99 to 0.93. However the delta parameter of survival curves obtained at a(w)=0.90 were lower than those obtained at a(w)=0.93. A mathematical model based on the Weibull parameters was built to describe the joint effect of temperature and a(w) on thermal inactivation of L. monocytogenes. This model provides a more complete information on the influence of the a(w) on the L. monocytogenes than the data initially generated. The model developed indicated that the effect of the a(w) on the thermal resistance of L. monocytogenes varied depending upon the temperature of treatment.     

弹力纱弹性统计模型与品质参数

根据弹性纱线拉伸试验应力与应变曲线的特征,运用指数拟合的方法,建立弹性纱线的应力与应变关系指数的数学模型,模型的相关系数R表明所得的关系是可靠的。结合弹性纱线的物理结构,建立弹性纱线应力应变的统计物理模型,得到与数学模型相似的应力应变关系。在此基础上,定义描述弹性纱线品质的2个指标。实验表明,2个品质指标所评价弹性纱线品质与实际相符合,在实践中具有一定的应用价值。