Single Straight Line Research Articles

Creep behavior of eutectic Sn-Cu lead-free solder alloy

Due to a typographical error incorporated during the editing process, the following is a correction of that error.Tensile creep behavior of precipitation-strengthened tin-based eutectic Sn-0.7Cu alloy was investigated at three temperatures ranging from 303 to 393 K. The steady-state creep rates cover six orders of magnitude (10−3 s−1 to 10−8 s−1) under the stress range of σ/E=10−4 to 10−3. The initial microstructure reveals that intermetallic compound Cu6Sn5 is finely dispersed in the matrix of β-Sn. By incorporating a threshold stress, σth, into the analysis, the creep data of eutectic Sn-Cu at all temperatures can be fitted by a single straight line with a slope of 7 after normalizing the steady-state creep rate and the effective stress, indicating that the creep rates are controlled by the dislocation pipe diffusion in tin matrix. So the steady-state creep rate, \(\dot \varepsilon \), can be expressed as \(\varepsilon = A\frac{{Gb}}{{RT}}\left( {\frac{{\sigma - \sigma _{th} }}{G}} \right)\exp \left( {\frac{{ - Q_C }}{{RT}}} \right)\), where QC is the active energy for creep, G is the temperature-dependent shear modulus, b is the Burgers vector, R is the universal gas constant, T is the temperature, σ is the applied stress, A is a material-dependent constant, and σth=σOB√1−k 2R , in which σoB is the Orowan bowing stress and kR is the relaxation factor.

Creep behavior of eutectic Sn-Cu lead-free solder alloy

Tensile creep behavior of precipitation-strengthened, tin-based eutectic Sn-0.7Cu alloy was investigated at three temperatures ranging from 303-393 K. The steady-state creep rates cover six orders of magnitude (10-3 - 10-8 s-1) under the stress range of σ/E = 10-4 - 10-3. The initial microstructure reveals that the intermetallic compound Cu6Sn5 is finely dispersed in the matrix of β-Sn. By incorporating a threshold stress, σth, into the analysis, the creep data of eutectic Sn-Cu at all temperatures can be fitted by a single straight line with a slope of 7 after normalizing the steady-state creep rate and the effective stress, indicating that the creep rates are controlled by the dislocation-pipe diffusion in the tin matrix. So the steady-state creep rate, e, can be expressed as e = A Gb/RT(σth/G) exp (-Qc/RT), where Qc is the activation energy for creep, G is the temperature-dependent shear modulus, b is the Burgers vector, R is the universal gas constant, T is the temperature, σ is the applied stress, A is a material-dependent constant, and σth = (σOB√1-kR2, in which σOB is the Orowan bowing stress, and kR is the relaxation factor.

Autoxidation kinetic analysis of docosahexaenoic acid ethyl ester and docosahexaenoic triglyceride with oxygen sensor.

The application of omega-3 polyunsaturated fatty acids (PUFAs) as food additives is restricted by their chemically quite reactive properties. However, quantitative analyses of the oxidative kinetics of PUFAs are very few compared to other studies on food chemistry. In this study, the autoxidation kinetics of ethyl docosahexaenoate (DHAEE), docosahexaenoic triglyceride (DHA oil), and emulsified DHA oil were investigated with an oxygen sensor. The autocatalytic reaction rate constants for DHAEE, DHA oil, and the emulsified DHA oil with 20% (w/v) GA, 20% SSPS, or 20% SSPS containing 5% soy protein were obtained at 35, 50, and 70 degrees C. A plot of the natural logarithm of the frequency factor, In ka0, vs. the activation energy, Ea, demonstrated that In ka0 against Ea fitted well with a single straight line both for the data from this study and for other reported results. This implies that the chemical compensation relationship holds between ka0 and Ea for PUFA and emulsified DHA oil.

Bravais-Pearson and Spearman correlation coefficients: meaning, test of hypothesis and confidence interval

many other biomedical journals dealing with cancer research, often publishes papers whose principal aim it is to test the association between quantative measurements of biological variables. When these are expressed on continuous scales, the statistics most frequently adopted to test their association are the Bravais-Pearson (parametric) and the Spearman (non-parametric) correlation coefficients. In this note the correlation coefficient estimate (statistic) will be denoted by the Latin letter r, while the “true” correlation coefficient (parameter) of the underlying population will be denoted by the Greek letter ρ. The Bravais-Pearson correlation coefficient (ρBP) is a suitable measure of association when n couples of continuous data ((yi, xi) with i=1,2,...n), collected on the same experimental unit, follow a bivariate normal distribution. In this case the only relationship that can be postulated is the linear one. Two different regression lines (see Fig. 1) can be defined: the first (l1) corresponding to the linear regression of y on x and the second (l2) corresponding to the linear regression of x on y. The two straight lines intersect at a point whose coordinates are the means of the observed yi and xi, respectively; this point is the vertex of an angle θ, defined by l1 and l2, which is an expression of the strength of the linear association between y and x. The Bravais-Pearson correlation coefficient (ρBP) is the geometrical mean of the slopes of the two regression lines and corresponds to the cosine of θ. In absence of association the two straight lines are perpendicular (θ = 90°), so that ρBP = cos 90° = 0. When there is a complete association the two straight lines overlap: if the resulting single straight line has a positive slope (i.e. y increases with increasing values of x), θ = 0° and ρBP = cos 0° = 1; if it has a negative slope (i.e. y decreases with increasing values of x), θ = 180° and ρBP = cos 180° = -1. The Spearman correlation coefficient (ρS) is usually adopted when the assumption of the bivariate normal distribution is not tenable. It is known that ρS is computed as ρBP, changing the integer 1,2,...n to y1,y2,...yn according to their relative magnitude; the same procedure is performed for x1,x2,...xn. This transformation makes it possible to move from the scales in which the original data are collected towards the same scale, i.e. that of ranks. The ranks do not follow the normal bivariate distribution and therefore the correlation coefficient cannot The International Journal of Biological Markers, Vol. 17 no. 2, pp. 148-151 © 2002 Wichtig Editore

Increments and decrements in color constancy.

The present study examines whether increment-decrement asymmetries reported in a number of recent center-surround situations occur in more complex images as well. Subjects saw the CRT simulation of a whole uniformly illuminated array of foreground surfaces presented against a large background surface and, for a number of different viewing contexts, made achromatic settings over a wide range of luminance values. Three results emerged. First, subjects' achromatic loci did not fall on a single straight line in color space but rather fell on two separate lines intersecting at some point in this space. Second, the intersection points were not identical to but dependent largely on background color and showed only small effects of foreground colors. Third, cone signals that were decremental relative to the intersection point were more responsive to illuminant changes than cone signals that were incremental, the latter additionally showing some variation with foreground colors. The results are interpreted in terms of increment-decrement asymmetries. They suggest that these asymmetries occur in more complex images as well.

Chain Aggregation and Chain Collapse of Poly(methyl methacrylate) in a Mixed Solvent

Chain aggregation processes were studied for dilute solutions of PMMA with the molecular weight m = 1.57 x 10 6 g/mol in the mixed solvent tert-butyl alcohol + water (2.5 vol %) at 25.0 and 30.0 °C in the concentration range from 1.4 x 10 -4 to 5.7 x 10 -4 g/cm 3 . The weight-average molecular weight w and z-average squared radius 2 of clusters of polymer chains were determined as a function of time by static light-scattering measurements. The phase separation temperature increased from 35.7 to 36.7 °C in the concentration range. The aggregation process near the concentration c = 1.46 x 10 -4 g/cm 3 was observed for a time period of about 10 000 min at 25.0 °C and 2000 min at 30.0 °C. At each temperature both the plots of In w and In 2 vs t (min) were represented by curved lines. The initial slopes of the lines were proportional to the concentration c. Accordingly, the scaled relations of w /M(0) = exp(gct) and z /R 2 (0) = exp(hct) were obtained at small ct with g = 5.01 cm 3 /(g min) and h = 3.97 cm 3 /(g min) at 25.0 °C and with g = 16.9 and h = 13.2 at 30.0 °C, where M(0) and R 2 (0) are the values extrapolated to t = 0. The reciprocals of gc and hc give the characteristic times of the chain aggregation. The longer characteristic times at 25.0 °C than at 30.0 were attributed to the effect of the chain collapse. The exponential growth indicated a reaction-limited cluster aggregation of polymer chains. The double-logarithmic plot of w vs z 1/2 at each temperature was independent of concentration and represented by a single straight line with the slope D = 2.53 ± 0.02 at 25.0 °C and 2.66 ± 0.01 at 30.0 °C.

Defining linear segments in protein structure

The analysis of protein structure using secondary structure line segments has been widely used in many structure analysis and prediction methods over the past 20 years. Its use in methods that compare protein structures at this level of representation is becoming more important as an increasing number of protein structures become determined through structural genomic programmes. The standard method used to define line segments is to fit an axis through each secondary structure element. This approach has difficulties, however, both with inconsistent definitions of secondary structure and the problem of fitting a single straight line to a bent structure. The procedure described here avoids these problems by finding a set of line segments independently of any external secondary structure definition. This allows the segments to be used as a novel basis for secondary structure definition by taking the average rise/residue along each axis to characterise the segment. This practice has the advantage that secondary structures are described by a single (continuous) value that is not restricted to the conventional classes of α-helix, 310 and β-strand. This latter property allows structures without “classic” secondary structures to be encoded as line segments that can be used in comparison algorithms. When compared over a large number of pairs of homologous proteins, the current method was found to be slightly more consistent than a widely used method based on hydrogen bonds.

Feasibility of a Reactive Distillation Column with Ternary Mixtures

We develop feasibility criteria for reactive distillation systems in terms of phase and reaction equilibria. A reactive distillation column with the liquid-phase reaction R1 + R2 ↔ P1 can be feasible if the feed composition, the pseudo-feed composition, and the reaction difference point lie on a single straight line. In addition to this material balance constraint, the liquid composition vectors starting from the given top product composition should lie within or move toward the forward reaction region as well as lie within or move toward the reachable region from the bottom product of the nonreactive stripping section. We also perform feasibility studies on reactive distillation with the reaction 2R1 ↔ P1 + P2 in terms of the normalized product and reactant coefficient vectors. For these ternary reaction systems, the larger the reflux, the greater the reaction conversion. We finally propose several feasible flowsheets for the methyl tert-butyl ether production system.

Distortion product otoacoustic emissions in human hypercholesterolemia

Epidemiological and experimental studies suggest that hypercholesterolemia promotes the development of sensorineural hearing loss; however, the underlying cellular pathomechanism remains obscure. In the present study, 20 healthy subjects and 20 patients with familial hypercholesterolemia were compared with respect to their hearing function. None of the 40 persons reported any history of hearing disorder. In accordance with this subjective impression, mean hearing thresholds were within the normal, age-dependent ranges in both groups. In contrast, the single-generator distortion product otoacoustic emissions (sgDPOAE) were reduced at and above 4 kHz. Input–output functions of DPOAE could be subdivided into three groups: (i) normal, with unity slope at low intensities and slope less than unity (0.24±0.07 dB/dB at higher intensities; (ii) pathologic, described by a single straight line; (iii) ill-defined, with data usually indistinguishable from the background noise level. The ill-defined DPOAE behavior was only found in patients with hypercholesterolemia; namely, for 25% of patients at f 2=1.5 kHz and for 50% at f 2=4 kHz. Patients belonging to the pathologic and ill-defined DPOAE groups had significantly ( P<0.05) higher total serum cholesterol and LDL-cholesterol levels compared with subjects from the normal DPOAE group. While hearing thresholds of patients with ill-defined growth functions were not statistically different from those of normal subjects, speech scores were significantly reduced in these cases. The data imply that nonlinear mechanical processes in the cochlea are compromised in hypercholesterolemic patients.

Solubility of Solids in Supercritical Fluids: Consistency of Data and a New Model for Cosolvent Systems

The ability to correlate and predict the solubility of solids in supercritical fluids is important in the design and evaluation of supercritical extraction processes. However, a review of the literature reveals that solid solubility data obtained by different investigators often do not agree within the reported uncertainties of the measurements. We have shown previously that a simple theory of dilute solutions can be used to check the consistency of supercritical CO2−solid solubility data and also that such data can be reduced to a single straight line over a significant range of solvent density and temperature. In the present work, we first show that our binary solution model is applicable to systems in which the solvent is not CO2. We then extend the approach to ternary cosolvent systems and show that data over a range of temperatures, pressures, and cosolvent concentrations can be correlated within experimental error using a single equation. The new model has three parameters that are independent of te...

Excitation functions and mass asymmetric fission barriers for compound nuclei [formula omitted]Se

Excitation functions were measured for complex fragments with atomic number Z=5−20 emitted from the compound nuclei 70,76 Se produced in the reactions 58,64 Ni + 12 C. Mass asymmetric fission barriers were extracted by fitting the excitation functions with a transition state formalism. The extracted barriers were compared with those calculated from macroscopic nuclear models. The measured barriers for symmetric fission seem to support the hypothesis of a shape-dependent congruence energy, which doubles for fission of strongly indented saddle-point shapes. All of the measured excitation functions can be scaled onto a single straight line according to the transition state prediction.

Gauge symmetry, chirality and parity effects in four-particle systems: Coulomb's law as a universal function for diatomic molecules

Following recent work in search for a universal function (Van Hooydonk, Eur. J. Inorg. Chem., (1999), 1617), we test four symmetric ± a n R n potentials for reproducing molecular potential energy curves (PECs). Classical gauge symmetry for 1/ R-potentials results in generic left–right asymmetric PECs. A pair of symmetric perturbed Coulomb potentials is quantitatively in accordance with observed PECs. For a bond, a four-particle system, charge inversion (a parity effect, atom chirality) is the key to explain this shape generically. A parity adapted Hamiltonian reduces from ten to two terms and to a soluble Bohr-like formula, a Kratzer (1− R e/ R) 2 potential. The result is similar to the combined action of spin and wave function symmetry upon the Hamiltonian in Heitler–London theory. Analytical perturbed Coulomb functions varying with (1− R e/ R) scale attractive and repulsive branches of PECs for 13 bonds H 2, HF, LiH, KH, AuH, Li 2, LiF, KLi, NaCs, Rb 2, RbCs, Cs 2 and I 2 in a single straight line. The 400 turning points for 13 bonds are reproduced with a deviation of 0.007 Å at both branches. For 230 points at the repulsive side, the deviation is 0.003 Å. The perturbed electrostatic Coulomb law is a universal molecular function. Ab initio zero molecular parameter functions give PECs of acceptable quality, just using atomic ionisation energies. The function can be used as a model potential for inverting levels and gives a first principle's comparison of short- and long-range interactions, important for the study of cold atoms. Wave-packet dynamics, femto-chemistry applied to the crossing of covalent and ionic curves, can provide evidence for this theory. We anticipate this scale/shape invariant scheme applies to smaller scales in nuclear and high-energy particle physics. For larger gravitational scales (Newton 1/ R potentials), problems with super-unification are discussed. Reactions between hydrogen and antihydrogen, feasible in the near future, will probably produce normal H 2.

New FIB/TEM evidence for a REDR mechanism in sudden failures of 980 nm SL SQW InGaAs/AlGaAs pump laser diodes

FIB/TEM images of failed laser diodes showed features compatible with local fusion and recrystallization around extended defect of the strained active layer. The shape of the melted area calls for excess temperature along single straight lines, compatible with misfit dislocations. This uniquely defines the sequence of defect propagation and interaction, pointing to the validation of the REDR theory for intrinsic origin of sudden failures.

Relative electron density calibration of CT scanners for radiotherapy treatment planning.

Several authors have reported data on the variation of Hounsfield numbers with electron density in CT scanners. The data can be fitted with a double straight line approach. For non-bone tissues (or phantom materials with similar atomic numbers) the data from all authors can be fitted to a single straight line. For bone-like materials the line varies between authors. The method used to measure electron density has a greater effect than the differences between scanners, or the kilovoltage used on a given scanner. The effect of variation of these slopes on the accuracy of radiotherapy treatment planning is analysed. For typical radiotherapy beams, to produce a 1% error in dosimetry would require errors of over 8% in bone electron density. Using a single pair of calibration lines for all the scanners reported would give dosimetric errors of under 0.8%. A formula is recommended as a default for use in planning systems in circumstances where no data are available for a particular scanner.

A Molecular Dynamics Study of Liquid Cesium Along Vapour Pressure Curve

Molecular dynamic simulation of liquid cesium along its vapour pressure curve has been done using Ichimaru-Utsumi potential. This potential have been compared with PST and DRT potential near the triple point. We have studied static pair correlation function, time evolution of velocity auto-correlation function, and self diffusion coefficients for four thermodynamic states. It is found that the position of first peak in pair correlation function almost remains same whereas its peak height decreases as temperature is increased. the calculated values of the self-diffusion coefficient have been compared with experimental result wherever available. Using the MD values of reduced diffusion coefficients for expanded Rb and present results for expanded Cs, it is predicted that both data can be represented by a single straight line as a function of reduced density and temperature.

Two-Component Model for Crude Oil Evaporation and its Application to Weathering Prediction

ABSTRACT The model approximates a crude oil as a mixture of an evaporating and non-evaporating component of which the physico-chemical properties are calculated by their composing fractions. The ordinary differential equation with separated variables derived from the model yields a concept of the evaporation time constant TQ that is defined by the initial oil properties and thickness, and the ambient temperature and wind speed. The evaporation ratios Q measured in flume tests on six types of Middle East crude oils are analyzed for the elapsed time non-dimensionalized by TQ. The measured values collapse well to a single straight line Q-log(t/TQ) for each type of oil, independently of emulsification and wave disturbance. A single line common to all the six types of oils is enough for rough estimation. A method using the common line or, more accurately, a line derived from the distillation test of each type of oil is proposed for evaporation prediction. Further analyses of the test results reveal the one-to-one correspondence between evaporation and properties (viscosity and density) of evaporated residual water-free oil. Formulae using the correspondence are suggested for estimating the properties of residual oil. The influences of substrates and thickness of an oil slick on evaporation and oil properties were examined in a small-scale laboratory. The laboratory tests are discussed as a useful procedure for obtaining basic prediction data.

Enzyme kinetics: partial and complete non-competitive inhibition

A novel graphical method for analysing the rates of enzyme reactions to obtain kinetic parameters K i, K i′ and β (degree of partiality) and to identify the types of inhibition and the enzyme mechanisms is described. The method consists of plotting experimental data as v (V o −v) versus 1 (I) at different substrate concentrations. I is the inhibitor concentration, V o and v are the rates of enzyme reaction attained by the system in the presence of a fixed amount of substrate and in the absence and presence of inhibitor respectively. Complete inhibition gives a single straight line that passes through the origin while partial inhibition gives a straight line that intercepts the 1 (I) axis at a point away from the origin.

Transition state rates and mass asymmetric fission barriers of compound nuclei 90,94,98Mo

Excitation functions were measured for complex fragments with atomic number Z = 5–25 emitted from the compound nuclei 90,94,98Mo produced in the reactions 78,82,86Kr + 12C . Mass-asymmetric fission barriers were extracted by fitting the excitation functions with a transition state formalism. The extracted barriers are several MeV higher on average than the calculations of the Rotating Finite-Range Model and substantially lower than predicted by the Rotating Liquid Drop Model. The symmetric fission barriers measured support the hypothesis of a congruence term that doubles for the fission of strongly indented saddle-point shapes. The excitation functions were analyzed to search for atomic number Z- and energy E-dependent deviations from transition-state-method predictions. All of the measured excitation functions can be scaled onto a single universal straight line according to the transition-state predictions. No Z- and/or E-dependent effects that could be attributed to transient effects are visible.

Excited-State Equilibration and the Fluorescence-Absorption Ratio

In any complex system at temperature T the absorption cross-section and fluorescent power at a given photon energy are connected by a simple relation if the system is in thermal equilibrium while occupying one particular electronic excited state. Although this situation is impossible in principle because of finite excited-state lifetimes, it is often approximated to the extent that the simple relation, which is expressed as a linear function of energy with slope —1/kBT, holds in a variety of cases. (The usual symbols for Boltzmann's constant and absolute temperature are used.) Observed deviations are of two principal kinds: a slope characteristic of some temperature T* other than ambient, and departures from a single pure straight line. The latter may include seemingly random variations and in some cases multiple regions of straight-line behavior. We have recently introduced an effective temperature T* (E), derived from the actual local slope of the putative straight line at energy E, which turns out to be a very sensitive detector of deviations from the ideal and, we believe, from equilibrium in the excited state. Plots of T* (E) display a variety of features. An anomaly in the T* (E) spectrum of chlorophyll a can be analyzed on this model, indicating a second weakly fluorescent state about 70 meV below the well-known Qy band. The cases of chlorophyll and many others are included in a selective review of applications of the universal relation to fluorescent systems.

Perception of acute angles

Experiments are reported which examine the judgement of the mean orientation of a single straight line (lest line) in presence of nearby lines of somewhat different orientations (induction line). It is shown, that perceived orientation of a segment of the test line is biased towards orientation of the induction line when the distance between the test and the induction line less than 0.1 deg. When this distance between 0.1--0.8 deg. a segment of the test line is biased from orientation of induction line and when this distance more 0.8 deg. the orientation of a segment of the test line remains unchanged.