Ulrich Zurcher

AN INSTANTANEOUS NORMAL MODE DESCRIPTION OF RELAXATION IN SUPERCOOLED LIQUIDS

Relaxation in supercooled liquids is formulated from the instantaneous normal modes (INM) point of view. The frequency and temperature dependence of the unstable, imaginary frequency lobe of the INM density of states, 〈ρu(ω,T)〉 (for simplicity we write ω instead of iω), is investigated and characterized over a broad temperature range, 10⩾T⩾0.42, in the unit density Lennard-Jones liquid. INM theories of diffusion invoke Im-ω modes descriptive of barrier crossing, but not all imaginary frequency modes fall into this category. There exists a cutoff frequency ωc such that modes with ω ωc. Given that only modes with ω>ωc contribute to diffusion, the barrier crossing rate, ωh, and the self diffusion constant D, are shown to be proportional to the density of states evaluated at the cutoff frequency, 〈ρu(ωc,T)〉. The density of states exhibits crossover behavior in its temperature dependence such that...

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.

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.

Torque around the center of mass: dynamic stability during quadrupedal arboreal locomotion in the Siberian chipmunk (Tamias sibiricus)

When animals travel on tree branches, avoiding falls is of paramount importance. Animals swiftly running on a narrow branch must rely on movement to create stability rather than on static methods. We examined how Siberian chipmunks (Tamias sibiricus) remain stable while running on a narrow tree branch trackway. We examined the pitch, yaw, and rolling torques around the center of mass, and hypothesized that within a stride, any angular impulse (torque during step time) acting on the center of mass would be canceled out by an equal and opposite angular impulse. Three chipmunks were videotaped while running on a 2cm diameter branch trackway. We digitized the videos to estimate center of mass and center of pressure positions throughout the stride. A short region of the trackway was instrumented to measure components of the substrate reaction force. We found that positive and negative pitch angular impulse was by far the greatest in magnitude. The anterior body was pushed dorsally (upward) when the forelimbs landed simultaneously, and then the body pitched in the opposite direction as both hindlimbs simultaneously made contact. There was no considerable difference between yaw and rolling angular impulses, both of which were small and equal between fore- and hindlimbs. Net angular impulses around all three axes were usually greater than or less than zero (not balanced). We conclude that the chipmunks may balance out the torques acting on the center of mass over the course of two or more strides, rather than one stride as we hypothesized.

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.

Comment on a critique of the instantaneous normal mode (INM) approach to diffusion [J. Chem. Phys. 107, 4618 (1997)]

A critique of the instantaneous normal mode (INM) theory of diffusion by Gezelter, Rabani, and Berne (GRB) [J. Chem. Phys. 107, 4618 (1997)] is analyzed. GRB assert that imaginary-frequency INM are corrupted with modes unrelated to barrier crossing, that proposals for removing such nondiffusive (ND) modes are inadequate, and thus that INM cannot be used to predict the self-diffusion constant, D. In rebuttal it is argued that Lennard-Jones, the system studied by GRB, is anamolously rich in ND modes. INM in molecular liquids are shown to behave as excellent indicators of barrier crossing. Even in LJ ND-INM, while plentiful, do not dominate D except in supercooled liquids near Tg and in the crystal; hence the many successes of the theories already reported in LJ. Agreement of simulated Im-ω densities of states with calculations modeling the INM as excitations in the soft potential model also indicate that the INM reflect the potential energy landscape in liquids.

Stability During Arboreal Locomotion

Arboreal locomotion – traveling on the branches, twigs, and trunks of trees and woody shrubs – is very common among mammals. Most primates, many rodents, marsupials, carnivores, and even an occasional artiodactyl travel on arboreal substrates to forage, escape predators, and acquire shelter. Arboreal supports are usually far enough from the ground that a slip or fall could cause serious injury or death, or deprive the animal of a mate, food, or energy. Thus, stability is of great importance for an animal traveling on arboreal supports. The considerable variation among arboreal supports makes stability during locomotion a mechanical challenge. Supports vary in diameter, slope, compliance, texture, direction (that is, bends or curves in a branch), and number and distribution. Furthermore there may be interaction among these variables; for example, compliance varies with diameter – thinner branches are more compliant than thick branches. Also, the thin branches frequently have leaves that act like sails in the wind, causing even more movement in the substrate. Substrate texture often varies with diameter, where narrow twigs have smoother bark than large branches or trunks. Therefore one might expect a considerable number of morphological, behavioral, and biomechanical mechanisms to enhance stability on arboreal supports. Stability can be divided into two categories: static and dynamic. Static stability is the process by which objects at rest remain stable, i.e., neither move (translation) nor rotate about a point or axis. For example, a table is statically stable because the forces and moments (torques) produced by gravity (weight) are balanced by ground reaction forces and the moments generated by them. One way an animal might remain stable is by not moving and adhering to or gripping the support; this definition is the ultimate example of static stability in an animal. Although this strategy allows no movement, it is nevertheless a valid locomotor strategy for an animal attempting to travel on an arboreal support subjected to a sudden gust of wind or other disturbance (Stevens, 2003). This analysis also applies when the animal walks very slowly, but fails when it walks or runs at considerable speed. Because the distribution of the mass is changing from one instant to the next, the forces and torques necessary to maintain static stability would also change with time. That is, it requires an active control by the nervous system. Because stability is critical, it is very likely that the animal employs both active and passive control (Full et al., 2002). Passive control can be due to dynamic processes of the animal’s body, and is referred to as dynamic stability. For example, a hiker might cross a stream or river by running across a fallen log; the rotation of the limbs around the hips and shoulder

Human food consumption: a primer on nonequilibrium thermodynamics for college physics

Students often have great difficulties with applications of the energy principle, especially those from biology, although most introductory physics texts include a brief discussion of metabolism. We point out that many of these discussions are unsatisfactory, since they often fail to mention how biological systems are thermal systems in stationary nonequilibrium states. This has important implications: in particular, that energy input is in the form of work (i.e., change of potential energy) and that energy outflux is in the form of heat, which is necessary to maintain a stationary state. We focus on some key aspects of metabolism by using a mechanical analogue: energy input is the work done by the gravitational force on an object with mass m, and heat production is modelled as the energy dissipated by turbulent air flow around the object.

Geometric constructions for image formation by a converging lens

Light rays emerge from an object in all directions. In introductory texts, three ‘special’ rays are selected to draw the image produced by lenses and mirrors. This presentation may suggest to students that these three rays are necessary for the formation of an image. We discuss that the three rays attain their ‘special status’ from the geometric solution of the equation of a hyperbola x−1 + y−1 = c−1 (mirror/lens equation). The material is suitable for use in introductory courses for science majors.

Projectile motion in the ‘language’ of orbital motion

We consider the orbit of projectiles launched with arbitrary speeds from the Earths surface. This is a generalization of Newtons discussion about the transition from parabolic to circular orbits, when the launch speed approaches the value . We find the range for arbitrary launch speeds and angles, and calculate the eccentricity of the elliptical orbits.