Miron Kaufman

Entropic characterization of mixing in microchannels

A methodology for rigorous mixing assessment in microchannels is presented. The analysis is based on numerical simulations of flow in different geometries coupled with mixing assessment using entropic measures. The results show enhanced mixing efficiency for the staggered herringbone micromixer by comparison with a mixer with straight diagonal ridges and a lack of mixing in a non-patterned channel. These results are in agreement with published experimental data.

A molar entropy model of age differences in spatial memory.

Two very-short-term-memory, spatial scanning aging experiments were conducted involving a graphics character as a target stimulus. On the probe portion of a trial, the stimulus was presented in the same position as it was on the target portion of the trial (i.e., a same trial) 50% of the time. However, on the remaining 50% of the trials, the probe stimulus was shifted (or transposed) 1, 2, or 3 positions to the right or left of the original presentation (target) position. In Experiment 1, exposure duration was manipulated. In Experiment 2, the number of potential target display positions was manipulated. For both experiments, older adults showed larger transposition distance effects than younger adults for errors. In the past (e.g., P.A. Allen, 1990, 1991), this effect has been attributed to higher levels of internal noise (entropy) in older than younger adults. This research provides converging operations to this contention by using statistical physics methods to rigorously compute the entropy in a molar neural network across age groups. After successfully fitting the statistical mechanics model to the data, the model is proved to have external validity by fitting a simplified version of it to an earlier spatial memory aging experiment reported by P. R. Bruce and J. F. Herman (1986). The results of both traditional reaction time and error rate analyses, as well as the entropy modeling analyses, indicated that older adults exhibited higher levels of entropy than did the younger adults and that this effect appeared to be generalized across processing stage.

Staggered passive micromixers with fractal surface patterning

We present a procedure for inducing chaotic mixing based on a non-periodic patterning of the walls making use of the Weierstrass fractal function to generate the locations for the grooves. We show the numerical analysis of flow in three different geometries generated with the Weierstrass function and compare the results with a fourth geometry, quite similar to the staggered herringbone mixer (SHM) of Stroock et al (2002 Science 295 647), for which the patterning is periodic. We evaluate the Lyapunov exponents for massless and non-interacting particles advected by the flow and traced along the channels. We also compute the entropy of mixing for binary mixtures. Finally, we compute generalized (fractal) dimensions associated with the interface of the two fluids. The results show consistently substantial enhancement in mixing efficiency for two of the Weierstrass channels compared to the SHM.

Comparison of spectral and entropic measures for surface electromyography time series: A pilot study

In a previous study, we reported that the mean square displacement calculated from the surface electromyography (sEMG) signal of low back muscles exhibits a plateaulike behavior for intermediate times 20 ms < t < 400 ms. This property indicates the existence of correlations in the signal for times much longer than the inverse of the median frequency (MF), which is calculated from the power spectrum 1/ = 1/(100 Hz) = 10 ms, where is the MF. This result suggests the use of methods from nonlinear analysis to characterize sEMG time series. In this study, we applied these techniques to sEMG signals and calculated the time-dependent entropy. The results showed that the entropy of physiological time series from nondisabled control subjects is higher than the entropy from subjects with low back pain (LBP). The entropy reveals properties of the sEMG signal that are not captured by the power spectrum. In turn, this suggests a possible benefit of entropy as a tool for the clinical assessment of LBP. Because the two groups of subjects were not matched by age, the physiological origin of the observed differences between groups could be attributed to either LBP, age, or both. Additional studies with larger sample sizes and age-matched subjects are needed to investigate the relationship between LBP and entropy.

Thermodynamic model for tricritical mixtures with application to ammonium sulfate + water + ethanol + benzene

Procedures are developed for using composition data in the three‐phase region and variations of meniscus heights to determine the parameters needed to relate a classical thermodynamic model for fluid mixtures near tricritical points to actual experiments. In the case of the mixture ammonium sulfate + water + ethanol + benzene, the result is a reasonably good fit to a variety of data, including light scattering measurements of intensity and correlation length. There is some evidence for deviations from the classical theory, but it is not unambiguous.

Reliability difference between spectral and entropic measures of erector spinae muscle fatigability

This study investigated back muscle fatigability of the erector spinae (ES) muscles during submaximal contractions with the use of surface electromyography (sEMG). It was important to confirm the reliability of measurements for characterizing neuromuscular alterations by establishing the difference between the Shannon (information) entropy and the power spectrum analysis in subjects with low back pain (LBP). The data was collected on two different days, one week apart, and the between-days reliability of these measures was examined. Thirty-two gender-matched subjects completed the modified Sorenson test; 16 of the subjects were female while 16 were male. The entropy of the sEMG signal was more reliable than either the median frequency (MF) or the slope of the MF. The intraclass correlation coefficient (ICC) was higher for the entropy than for the MF slope. The ICC values of entropy for between-day measurements were higher (0.82-0.85) than MF (0.54-0.64) and MF slope (0.26-0.30). The standard errors of measurement (SEM) values for entropy were lower (0.04-0.05) than MF (3.10-3.60) and MF slope (0.03-0.04). The Pearson correlation coefficients of the entropy were significantly higher (0.75-0.77) than those of the MF (0.38-0.47) and the MF slope (0.15-0.18). Therefore, the results of this study indicated that the entropy analysis could provide a reliable measure of muscle fatigability.

Characterization of Distributive Mixing in Polymer Processing Equipment using Renyi Entropies

Abstract A new method for characterization of distributive mixing in processing equipment, based on Renyi entropies, was developed. This method was applied to a twin-flight single screw extruder, in which tracer positions were determined through computer simulations of the flow field. The various entropies were calculated using particle concentrations in equal area domains of the mixer. Renyi entropies, which are function of a parameter β were calculated for extruders of different lengths. We discuss the merit of using Renyi entropies for different values of β by pointing to the different mixing characteristics they probe. The relative Renyi entropy varies between 0 and 1 and represents a measure of distributive mixing quality, with 1 corresponding to perfect mixing and 0 corresponding to poorest mixing. We compare this new method of distributive mixing characterization to traditional ones based on the concepts of Scale and Intensity of Segregation, and the calculations based on Pairwise Correlations and Correlation Sums. The results show good agreement between the relative Renyi entropy and the traditional methods. Other advantages of the Renyi entropy such as reduced calculation time and geometric independence are discussed. For the case of a twin-flight single screw extruder, it is shown that a longer extruder is not necessarily more beneficial to distributive mixing.

Gender differences in spectral and entropic measures of erector spinae muscle fatigue.

Electromyographic power spectral analysis is a valuable measurement; however, conflicting results have been reported for amplitude and frequency changes during a fatiguing submaximal muscle contraction. This study compared gender differences for two analyses in subjects with low back pain (LBP). Distinct gender differences are found in musculoskeletal illness/dysfunction, and we examined the effect of gender on entropy and median frequency (MF) slope in a cohort of subjects with LBP. A total of 44 subjects (24 female and 20 male) completed the modified Sorenson test. These subjects ranged in age from 26 to 64 years old, with an average age of 49.9 +/- 9.4 years. Overall, a significant fatigability difference was found based on MF slope (F = 21.33, p = 0.001) and entropy measures (F = 68.26, p = 0.001) of the back muscles. While the MF slope was not different (F = 0.44, p = 0.51) between genders, the entropy values were higher for the male subjects than for the female subjects (F = 6.70, p = 0.01). These results indicate that the Shannon entropy measure differentiates between genders. Further studies are needed to evaluate the effectiveness of using nonlinear analysis as a measurement tool.

A thermodynamic model for pressurized solids

A thermodynamic model for solids under pressure is developed by assuming the universal equation of state and that under zero pressure the free energy is equal to the harmonic crystal (Debye) free energy. The model is applied to gold. In the case of nanocrystals this model reproduces the observed enhancement of the isobaric heat capacity and of the thermal expansion. Our model calculations are free of the ambiguities and inconsistencies connected with the Gruneisen equation, which was used in previous theoretical work.

Dynamics of Filler Size and Spatial Distribution in a Plasticating Single Screw Extruder – Modeling and Experimental Observations

Abstract A model of agglomerate break-up, incorporating both rupture and erosion, is employed to predict the dynamics of filler size distribution in a plasticating single screw extruder. Filler spatial distribution along the extruder length was also ascertained and direct comparison of experimental and computational data proved to be satisfactory. The method was also used to investigate the effect of material properties, operating conditions and extruder geometry on the dynamics of agglomerate dispersion along a single screw extruder. Generally, dispersion levels were primarily governed by the magnitude of the hydrodynamic stresses developed in the extruder and the residence time in the melt.