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.     

On metrics matched to the discrete memoryless channel

A sequence of metrics {D_N} is said to be additive and matched to a discrete memoryless channel (DMC) if D_N is the sum on its coordinates of N single letter metrics and if the maximum likelihood decoder for sequences of length N is a minimum D_N-distance decoder. Necessary and sufficient conditions on the transition probabilities of a DMC for the existence of a sequence of additive metrics matched to it are given. In the case of the binary channel these are shown to be equivalent to the channel being symmetric. Explicit transition probabilities are given for a large class of ternary DMCs with an associated sequence of additive matched metrics. The problem solved here may be considered a generalization of the problem of finding the DMCs matched to the Lee metric solved by Chiang and Wolf in 1971 (2).     

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.     

Ladder realizations of multivariable positive real functions

Necessary and sufficient conditions are obtained for the realization of an m-variable positive real function (PRF) as the impedence function of a resistively-terminated ladder network of m lossless two-ports connected in cascade. Each two-port is a single-variable lossless ladder with all of its transmission zeros either at the origin or at finity. Conditions are also obtained when each of the two-ports is a Fujisawa-type lowpass ladder.     

Research findings and administrative implications for off-campus higher education

While off-campus educational programs grow in number and in importance in American higher education, little systematic research has been conducted concerning their effectiveness and intellectual and developmental impact. The project described here compared students in three categories: those studying abroad; those studying off-campus in this country; and those who remained on their home campus. The implications of the findings of the research suggest that a rethinking of existing programs is appropriate, if off-campus educational programs are to realize their full potential. The authors offer concrete suggestions toward restructuring these programs.

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Zusammenfassung Obwohl Bildungsprogramme ausserhalb der Universität in der amerikanischen Hochschulbildung an Anzahl und Bedeutung zunehmen, wurde deren Fruchtbarkeit und geistige und entwicklungsmässige Auswirkung kaum systematisch untersucht. Das hier geschilderte Projekt vergleicht Studenten dreier Kategorien: im Ausland studierende, im Lande ausserhalb der Universität studierende und solche, die in ihrem heimischen Universitätsbetrieb geblieben sind. Die Ergebnisse der Untersuchung legen die Folgerung nahe, es sei angebracht, bei eingeführten Programmen zu überdenken, ob die Bildungsprogramme ausserhalb der Universität ihre Möglichkeiten voll ausschöpfen sollen. Die Verfasser machen konkrete Vorschläge für eine Neugestaltung dieser Programme.

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Résumé Tandis que l'importance et le nombre des programmes d'éducation en dehors des universités s'accroît dans l'enseignement supérieur aux Etats-Unis, peu de recherche systématique a été effetué en ce qui concerne leur efficacité et leur impact intellectuel et de développement. Le projet décrit ici a comparé des étudiants de trois catégories: ceux qui étudient à l'étranger, ceux qui étudient hors des universités à l'intérieur du pays et ceux qui sont restés dans leurs universités d'origine. Les implications des conclusions de la recherche suggèrent qu'il convient de repenser les programmes existants, si les programmes d'éducation hors des universités doivent réaliser tout leur potentiel. Les auteurs présentent des suggestions concrètes quant à la restructuration de ces programmes.