Fatigue and collapse of cyclically bent strip of amorphous solid

Fatigue caused by cyclic bending of a piece of material, resulting in its mechanical failure, is a phenomenon that had been studied for ages by engineers and physicists alike. In this Letter we study such fatigue in a strip of athermal amorphous solid. On the basis of atomistic simulations we conclude that the crucial quantity to focus on is the accumulated damage. Al- though this quantity exhibits large sample-to-sample fluctuations, its dependence on the loading determines the statistics of the number of cycles to failure. Thus we can provide a scaling theory for the Wo ̈hler plots of mean number of cycles for failure as a function of the loading amplitude.

Marangoni instabilities of drops of different viscosities in stratified liquids

For an immiscible oil drop immersed in a stably stratified ethanol–water mixture, a downwards solutal Marangoni flow is generated on the surface of the drop, owing to the concentration gradient, and the resulting propulsion competes against the downwards gravitational acceleration of the heavy drop. In prior work of Li et al. (Phys. Rev. Lett., vol. 126, issue 12, 2021, 124502), we found that for drops of low viscosity, an oscillatory instability of the Marangoni flow is triggered once the Marangoni advection is too strong for diffusion to restore the stratified concentration field around the drop. Here we experimentally explore the parameter space of the concentration gradient and drop radius for high oil viscosities and find a different and new mechanism for triggering the oscillatory instability in which diffusion is no longer the limiting factor. For such drops of higher viscosities, the instability is triggered when the gravitational effect is too strong so that the viscous stress cannot maintain a stable Marangoni flow. This leads to a critical drop radius above which the equilibrium is always unstable. Subsequently, a unifying scaling theory that includes both the mechanisms for low and for high viscosities of the oil drops is developed. The transition between the two mechanisms is found to be controlled by two length scales: the drop radius $R$ and the boundary layer thickness $\delta$ of the Marangoni flow around the drop. The instability is dominated by diffusion for $\delta < R$ and by viscosity for $R<\delta$ . The experimental results for various drops of different viscosities can well be described with this unifying scaling theory. Our theoretical description thus provides a unifying view of physicochemical hydrodynamic problems in which the Marangoni stress is competing with a stable stratification.

Systematic shifts in scaling behavior based on organizational strategy in universities

To build better theories of cities, companies, and other social institutions such as universities, requires that we understand the tradeoffs and complementarities that exist between their core functions, and that we understand bounds to their growth. Scaling theory has been a powerful tool for addressing such questions in diverse physical, biological and urban systems, revealing systematic quantitative regularities between size and function. Here we apply scaling theory to the social sciences, taking a synoptic view of an entire class of institutions. The United States higher education system serves as an ideal case study, since it includes over 5,800 institutions with shared broad objectives, but ranges in strategy from vocational training to the production of novel research, contains public, nonprofit and for-profit models, and spans sizes from 10 to roughly 100,000 enrolled students. We show that, like organisms, ecosystems and cities, universities and colleges scale in a surprisingly systematic fashion following simple power-law behavior. Comparing seven commonly accepted sectors of higher education organizations, we find distinct regimes of scaling between a school’s total enrollment and its expenditures, revenues, graduation rates and economic added value. Our results quantify how each sector leverages specific economies of scale to address distinct priorities. Taken together, the scaling of features within a sector along with the shifts in scaling across sectors implies that there are generic mechanisms and constraints shared by all sectors, which lead to tradeoffs between their different societal functions and roles. We highlight the strong complementarity between public and private research universities, and community and state colleges, that all display superlinear returns to scale. In contrast to the scaling of biological systems, our results highlight that much of the observed scaling behavior is modulated by the particular strategies of organizations rather than an immutable set of constraints.

Cancer as a Model System for Testing Metabolic Scaling Theory

Biological allometries, such as the scaling of metabolism to mass, are hypothesized to result from natural selection to maximize how vascular networks fill space yet minimize internal transport distances and resistance to blood flow. Metabolic scaling theory argues two guiding principles—conservation of fluid flow and space-filling fractal distributions—describe a diversity of biological networks and predict how the geometry of these networks influences organismal metabolism. Yet, mostly absent from past efforts are studies that directly, and independently, measure metabolic rate from respiration and vascular architecture for the same organ, organism, or tissue. Lack of these measures may lead to inconsistent results and conclusions about metabolism, growth, and allometric scaling. We present simultaneous and consistent measurements of metabolic scaling exponents from clinical images of lung cancer, serving as a first-of-its-kind test of metabolic scaling theory, and identifying potential quantitative imaging biomarkers indicative of tumor growth. We analyze data for 535 clinical PET-CT scans of patients with non-small cell lung carcinoma to establish the presence of metabolic scaling between tumor metabolism and tumor volume. Furthermore, we use computer vision and mathematical modeling to examine predictions of metabolic scaling based on the branching geometry of the tumor-supplying blood vessel networks in a subset of 56 patients diagnosed with stage II-IV lung cancer. Examination of the scaling of maximum standard uptake value with metabolic tumor volume, and metabolic tumor volume with gross tumor volume, yield metabolic scaling exponents of 0.64 (0.20) and 0.70 (0.17), respectively. We compare these to the value of 0.85 (0.06) derived from the geometric scaling of the tumor-supplying vasculature. These results: (1) inform energetic models of growth and development for tumor forecasting; (2) identify imaging biomarkers in vascular geometry related to blood volume and flow; and (3) highlight unique opportunities to develop and test the metabolic scaling theory of ecology in tumors transitioning from avascular to vascular geometries.

Development and validation of vehicle wheel load scaling method for formation of durability testing loading cycle

For a vehicle durability study, performed with simulation or laboratory testing, impact on the object should be described as set of time-domain load signals, which reflects accelerated service modes of a vehicle operation. For a newly developed vehicle these load signals can be based on previously prepared loading cycle of a similar vehicle with use of the load scaling theory. Importance and certainty of the load scaling theory is approved by active use among foreign car makers and engineering centers. However, mathematical description of the theory and scaling procedure are strictly classified, despite of being based on fundamentals of vehicle dynamics. In this paper the method of scaling of time-domain wheel and driveline loads is suggested; the method is based on proportions of size and mass properties of the original and the new vehicles. Assumed that previously recorded loading cycle corresponds to the service life of a vehicle. It is worth noting that level of loading and damage accumulation, shown with scaled loading cycle and after first prototypes testing on a proving ground, will be different because of impact of chassis stiffness and damping properties. Suggested scaling theory is being studied in FSUE “NAMI” and is on the validation and verification stage. First completed experiments showed that a multiaxial test rig could perform the vehicle suspension loading cycle, obtained with the theory, with a satisfactory accuracy. This makes utilization of the theory limited to early stages of vehicle development.