Using Computational Essays to Scaffold Professional Physics Practice

This article describes a curricular innovation designed to help students experience authentic physics inquiry with an emphasis on computational modeling and scientific communication. The educational design centers on a new type of assignment called a computational essay, which was developed and implemented over the course of two semesters of an intermediate electricity and magnetism course at the University of Oslo, Norway. We describe the motivation, learning goals, and scaffolds used in the computational essay project, with the intention that other educators will be able to replicate and adapt our design. We also report on initial findings from this implementation, including key features of student-written computational essays, student reflections on the inquiry process, and self-reported conceptual and attitudinal development. Based on these findings, we argue that computational essays can serve a key role in introducing students to open-ended, inquiry-based work and setting the foundation for future computational research and studies.Comment: Submitted to the European Journal of Physic

Statistics of the separation between sliding rigid rough surfaces: Simulations and extreme value theory approach

When a rigid rough solid slides on a rigid rough surface, it experiences a random motion in the direction normal to the average contact plane. Here, through simulations of the separation at single-point contact between self-affine topographies, we characterize the statistical and spectral properties of this normal motion. In particular, its rms amplitude is much smaller than that of the equivalent roughness of the two topographies, and depends on the ratio of the slider's lateral size over a characteristic wavelength of the topography. In addition, due to the non-linearity of the sliding contact process, the normal motion's spectrum contains wavelengths smaller than the smallest wavelength present in the underlying topographies. We show that the statistical properties of the normal motion's amplitude are well captured by a simple analytic model based on the extreme value theory framework, extending its applicability to sliding-contact-related topics

History-dependent friction and slow slip from time-dependent microscopic junction laws studied in a statistical framework

To study the microscopic origins of friction, we build a framework to describe the collective behaviour of a large number of individual micro-junctions forming a macroscopic frictional interface. Each micro-junction can switch in time between two states: A pinned state characterized by a displacement-dependent force, and a slipping state characterized by a time-dependent force. Instead of tracking each micro-junction individually, the state of the interface is described by two coupled distributions for (i) the stretching of pinned junctions and (ii) the time spent in the slipping state. We show how this framework represents an overarching structure for important models existing in the friction literature. We then use it to study systematically the effect of the time-scale that controls the duration of the slipping state. We first find the steady-state friction force as a function of the sliding velocity. As the framework allows for a whole family of micro-junction behaviour laws, we show how these laws can be chosen to obtain monotonic (strengthening or weakening) or non-monotonic velocity dependence at the macroscale. By then considering transient situations, we predict that the macroscopic static friction coefficient is strongly influenced by the way the interface was prepared, in particular by the slip dynamics of the previous sliding event. We also show that slow slip spontaneously occurs in the framework for a wide range of behaviour laws.Comment: 20 pages, 10 figure

On the speed of fast and slow rupture fronts along frictional interfaces

The transition from stick to slip at a dry frictional interface occurs through the breaking of the junctions between the two contacting surfaces. Typically, interactions between the junctions through the bulk lead to rupture fronts propagating from weak and/or highly stressed regions, whose junctions break first. Experiments find rupture fronts ranging from quasi-static fronts with speeds proportional to external loading rates, via fronts much slower than the Rayleigh wave speed, and fronts that propagate near the Rayleigh wave speed, to fronts that travel faster than the shear wave speed. The mechanisms behind and selection between these fronts are still imperfectly understood. Here we perform simulations in an elastic 2D spring--block model where the frictional interaction between each interfacial block and the substrate arises from a set of junctions modeled explicitly. We find that a proportionality between material slip speed and rupture front speed, previously reported for slow fronts, actually holds across the full range of front speeds we observe. We revisit a mechanism for slow slip in the model and demonstrate that fast slip and fast fronts have a different, inertial origin. We highlight the long transients in front speed even in homogeneous interfaces, and we study how both the local shear to normal stress ratio and the local strength are involved in the selection of front type and front speed. Lastly, we introduce an experimentally accessible integrated measure of block slip history, the Gini coefficient, and demonstrate that in the model it is a good predictor of the history-dependent local static friction coefficient of the interface. These results will contribute both to building a physically-based classification of the various types of fronts and to identifying the important mechanisms involved in the selection of their propagation speed.Comment: 29 pages, 21 figure

Diffusion-driven frictional aging in silicon carbide

Friction is the force resisting relative motion of objects. The force depends on material properties, loading conditions and external factors such as temperature and humidity, but also contact aging has been identified as a primary factor. Several aging mechanisms have been proposed, including increased "contact quantity" due to plastic or elastic creep and enhanced "contact quality" due to formation of strong interfacial bonds. While proposed mechanisms for frictional aging have been dependent upon the presence of a normal force, this factor is not a fundamental prerequisite for the occurrence of aging. In light of this, we present a novel demonstration of a substantial frictional aging effect within a cubic silicon carbide system, even when a normal force is entirely absent. Our observations indicate that the time-evolution of the frictional aging effect follows a logarithmic behavior, which is a pattern that has been previously observed in numerous other materials. To explain this behavior, we provide a derivation that is rooted in basic statistical mechanics, demonstrating that surface diffusion, a phenomenon that serves to minimize surface energy in the interface region, can account for the observed behavior. Upon application of a normal force, the friction force is enhanced owing to the presence of plastic creep. Although aging resulting from plastic and elastic creep is widely recognized and incorporated into most friction laws, diffusion-driven aging has received comparatively less attention. The ultimate objective is to develop or redesign friction laws by incorporating the microscopic behavior, with the potential to enhance their effectiveness

Propulsive Power in Cross-Country Skiing: Application and Limitations of a Novel Wearable Sensor-Based Method During Roller Skiing

Cross-country skiing is an endurance sport that requires extremely high maximal aerobic power. Due to downhill sections where the athletes can recover, skiers must also have the ability to perform repeated efforts where metabolic power substantially exceeds maximal aerobic power. Since the duration of these supra-aerobic efforts is often in the order of seconds, heart rate, and pulmonary VO2 do not adequately reflect instantaneous metabolic power. Propulsive power (Pprop) is an alternative parameter that can be used to estimate metabolic power, but the validity of such calculations during cross-country skiing has rarely been addressed. The aim of this study was therefore twofold: to develop a procedure using small non-intrusive sensors attached to the athlete for estimating Pprop during roller-skiing and to evaluate its limits; and (2) to utilize this procedure to determine the Pprop generated by high-level skiers during a simulated distance race. Eight elite male cross-country skiers simulated a 15 km individual distance race on roller skis using ski skating techniques on a course (13.5 km) similar to World Cup skiing courses. Pprop was calculated using a combination of standalone and differential GNSS measurements and inertial measurement units. The method's measurement error was assessed using a Monte Carlo simulation, sampling from the most relevant sources of error. Pprop decreased approximately linearly with skiing speed and acceleration, and was approximated by the equation Pprop(v,v˙) = −0.54·v −0.71·v˙ + 7.26 W·kg−1. Pprop was typically zero for skiing speeds >9 m·s−1, because the athletes transitioned to the tuck position. Peak Pprop was 8.35 ± 0.63 W·kg−1 and was typically attained during the final lap in the last major ascent, while average Pprop throughout the race was 3.35 ± 0.23 W·kg−1. The measurement error of Pprop increased with skiing speed, from 0.09 W·kg−1 at 2.0 m·s−1 to 0.58 W·kg−1 at 9.0 m·s−1. In summary, this study is the first to provide continuous measurements of Pprop for distance skiing, as well as the first to quantify the measurement error during roller skiing using the power balance principle. Therefore, these results provide novel insight into the pacing strategies employed by high-level skiers

Slow slip and the transition from fast to slow fronts in the rupture of frictional interfaces

The failure of the population of micro-junctions forming the frictional interface between two solids is central to fields ranging from biomechanics to seismology. This failure is mediated by the propagation along the interface of various types of rupture fronts, covering a wide range of velocities. Among them are so-called slow fronts, which are recently discovered fronts much slower than the materials' sound speeds. Despite intense modelling activity, the mechanisms underlying slow fronts remain elusive. Here, we introduce a multi-scale model capable of reproducing both the transition from fast to slow fronts in a single rupture event and the short-time slip dynamics observed in recent experiments. We identify slow slip immediately following the arrest of a fast front as a phenomenon sufficient for the front to propagate further at a much slower pace. Whether slow fronts are actually observed is controlled both by the interfacial stresses and by the width of the local distribution of forces among micro-junctions. Our results show that slow fronts are qualitatively different from faster fronts. Since the transition from fast to slow fronts is potentially as generic as slow slip, we anticipate that it might occur in the wide range of systems in which slow slip has been reported, including seismic faults.Comment: 35 pages, 5 primary figures, 6 supporting figures. Post-print version with improvements from review process include

Volume changes in solids induced by chemical alteration

It is a fundamental issue in material science to understand the mechanical effects of chemical alterations. Often the replacement of one chemical component by another in a solid induces local volume changes. Experiments on chemical alteration in “model” materials reveal an intricate dynamics of elastic stress build-up, fracturing and creation of porosity. In that way permeability is increased and provides a positive feedback on the process rate. Important examples from geology are presented

Minimal model for slow, sub-Rayleigh, supershear, and unsteady rupture propagation along homogeneously loaded frictional interfaces

International audienceIn nature and experiments, a large variety of rupture speeds and front modes along frictional interfaces are observed. Here, we introduce a minimal model for the rupture of homogeneously loaded interfaces with velocity strengthening dynamic friction, containing only two dimensionless parameters; τ, which governs the prestress, and ᾱ which is set by the dynamic viscosity. This model contains a large variety of front types, including slow fronts, sub-Rayleigh fronts, super-shear fronts, slip pulses, cracks, arresting fronts and fronts that alternate between arresting and propagating phases. Our results indicate that this wide range of front types is an inherent property of frictional systems with velocity strengthening branches

Precursors to sliding and static friction threshold of heterogeneous frictional interfaces

Nous utilisons un modèle multi-échelles de la transition entre frottement statique et frottement dynamique, pour étudier la vitesse des fronts de rupture le long d'interfaces multi-contact étendues. Nous montrons que la vitesse des fronts est directement contrôlée par la vitesse de glissement associée, pour toute la gamme de vitesses explorée. Nous proposons ensuite un classement, basé sur les mécanismes en jeu, pour les différents types de fronts observés. Nous montrons finalement comment le coefficient de frottement statique local est contrôlé par l'histoire du glissement, au même endroit, mais lors de la rupture précédente de l'interface