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.     

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.     

The graph-theoretic field model—I. Modelling and formulations

The Graph-Theoretical Field Model provides a unifying approach for developing numerical models of field and continuum problems. The methodology examines the field problem from the first stages of conceptualization without recourse to the governing differential equations of the field problem; this is accomplished by deriving discrete statements of the physical laws which govern the field behaviour. There are generally three laws, and these are modelled by the “cutset equations”, the “circuit equations”, and the “terminal equations”. In order to establish these three sets of equations it is expedient first to spatially discretize the field in a manner similar to the finite difference method and then to associate a linear graph (denoted as the field graph) with the spatial discretization. The concept of “through” and “across” variables, which underlies the cutset and circuit equations respectively, enables one to define the graph in an unambiguous manner such that each “edge” of the graph identifies a pair of complementary variables. From a knowledge of the constitutive properties and the boundary conditions of the field it is possible to associate terminal equations with sets of edges. Since the resulting sets of equations represent the field equations, these equations provide the basis for a complete (but approximate) solution to the field or continuum problem. In fact, this system approach uses a two part model: one for the components and another for the interconnection pattern of the components which renders the formulation procedures totally independent of the solution procedure.This paper presents the theoretical basis of the model and several graph-theoretic formulations for steady-state problems. Examples from heat conduction and small- deformation elasticity are included.