Analysis and conservation of modern modeling materials found in Auguste Rodin's sculptures

Prior to the exhibition Portrait-making, Rodin and his models (2009), the Rodin museum wanted to restore two busts of Hanako and Clemenceau. Interestingly, these two sculptures contain pieces of modern modeling materials (MMMs) invented at the end of the nineteenth century as an alternative to clay or waxes. The poor state of conservation of the two portraits made any handling and exhibition impossible. Accordingly, the purpose of this article is twofold: to contribute to technical art history and conservation. Elemental and chemical analyses were done on samples from 12 sculptures (SEM–EDX, FTIR, GC–MS, GC–FID, XRD, synchrotron-based µXRF, µXANES, and µFTIR) aimed at identifying the composition of MMMs used by Rodin on plaster sculptures and establishing hypotheses about the origins of their degradation. This thorough study of their composition and degradation was necessary to implement an appropriate restoration plan. The development of conservation protocols adapted to such materials is rarely documented. Different tests were performed on mock-ups (pH, solubility, adhesion, consolidation, and cleaning). In particular, a protocol based on laser cleaning was developed and successfully applied to remove superficial dust and crusts so that the sculptures regained their original aspect.     

Dynamics of the basketball shot with application to the free throw

A completely general three-dimensional dynamic model is presented for the motion of basketball shots that may contact the rim, the backboard, the bridge between the rim and board, and possibly the board and the bridge simultaneously. Non-linear ordinary differential equations with six degrees of freedom describe the ball angular velocity and ball centre position. The model includes radial ball compliance and damping and contains five sub-models: purely gravitational flight, and ball-rim, ball-bridge, ball-board, and ball-bridge-board contact. Each contact sub-model has both slipping and non-slipping motions. Switching between the sub-models depends on the reaction force at, and velocity of, the contact point. Although the model can be used to study shots from any point on the court, we here use it to study the sets of free throw release angle, velocity, angular velocity, and lateral deviation angle that result in success (capture), as well as underhand free throws and those using an under-inflated ball. Free throw shots with larger backspin, lower inflation pressures, and underhand release conditions are shown to result in larger capture percentages.     

The distance-time relationship over a century of running Olympic performances: A limit on the critical speed concept

We analyse the evolution of the slope (critical speed) and the y-intercept (anaerobic distance capacity) of the linear distance-time relationship over a century of Olympic running performances. The distance-time relationship of each Olympic Games (1920-2004) was plotted using the performances in the 800-, 1500- and 5000-m track events. Values for critical speed and anaerobic distance capacity were determined by linear modelling. Mean performances for the 800, 1500 and 5000 m were 104.9 +/- 1.5 s (1.4%), 217.2 +/- 2.8 s (1.3%) and 808.9 +/- 18.4 s (2.3%), respectively. Critical speed improved during the first three-quarters of the twentieth century to reach a plateau in 1984. This is in accordance with the literature (Peronnet & Thibault, 1989) and suggests that "human aerobic endurance" has improved within the century (+13.4%) and tends to stabilize. Anaerobic distance capacity was highly variable over the century (coefficient of variation = 9.4%) and did not show a linear improvement over the years as has previously been suggested (Peronnet & Thibault, 1989). This could be due to an artefact in the application of the two-parameter model to only three Olympic performances. A limitation to the use of this linear mathematical model to fit physiological data may have been demonstrated.     

The graph-theoretic field model— II. application of multi-terminal representations to field problems

This paper is a sequel to a paper entitled “The Graph-Theoretic Field Model—I: Modelling and Formulations” (1). Herein, the Theory of Multi-Terminal Representations is applied to the Graph-Theoretic Field Model to provide mathematical models of finite elements. The element models are obtained solely from the algebraic building blocks of the Graph-Theoretic Field Model, without recourse to any functional mathematics. The theory of Multi-Terminal Representations is developed for both linear and non-linear problems. Examples of the application of the theory to one- and two-dimensional field problems are presented from heat conduction and electrostatics.