PRELIMINARIES. Motivation: Sensitivity and Large-Scale Systems. Nonlinear Solid Mechanics: Continuous and Semi-Discretized Formulation. Concepts of Sensitivity Analysis for Linear Systems.THE SENSITIVITY OF NONLINEAR SYSTEMS. The Basic Concepts of Nonlinear Quasi-Static Problems at Regular States. Inelastic Systems. Shape Sensitivity. Buckling and Post-Buckling. Nonlinear Dynamics. Metal Forming Using the Flow Approach. Nonlinear Thermal Systems. Appendices. References. Index. Glossary of Symbols.

Parameter Sensitivity in Nonlinear Mechanics: Theory and Finite Element Computations

We present a bibliography on moving and free boundary problems for the heatdiffusion equation, particularly regarding the Stefan and related problems. It contains 5869 titles referring to 588 scientific Journals, 122 books, 88 symposia (having at least 3 contributions on the subject), 30 collections, 59 thesis and 247 technical reports. It tries to give a comprehensive account of the western existing mathematicalphysical-engineering literature on this research field. RESUMEN Se presenta una bibliografía sobre problemas de frontera móvil y libre para la ecuación del calor-difusión, en particular sobre el problema de Stefan y problemas relacionados. Contiene 5869 títulos distribuidos en 588 revistas científicas, 122 libros, 88 simposios (teniendo al menos 3 contribuciones en el tema), 30 colecciones, 59 tesis y 247 informes técnicos o prepublicaciones. Se da un informe amplio de la bibliografía matemática, física y de las ingenierías existente en occidente sobre este tema de investigación. Primary Mathematics Subject Classification Number (*): 35R35, 80A22 Secondary Mathematics Subject Classification Number (*): 35B40, 35C05, 35C15, 35Kxx, 35R30, 46N20, 49J20, 65Mxx, 65Nxx, 76R50, 76S05, 76T05, 93C20. (*) Following the 1991 Mathematics Subject Classification compiled by Mathematical Reviews and Zentralblatt fur Mathematik. Primary key words: Enthalpy formulation or method, Filtration, Free boundary problems, Freezing, Melting, Moving boundary problems, Mushy region, Phase-change problem, Solidification, Stefan problem. Secondary key words: Continuous mechanics, Diffusion process, Functional analysis, Heat conduction, Mathematical methods, Numerical methods, Partial differential equations, Variational inequalities, Weak solutions. Palabras claves primarias: Método o formulación en entalpía, Filtración, Problemas de frontera libre, Congelación, Derretimiento, Problemas de frontera móvil, Región pastosa, Problema de cambio de fase, Solidificación, Problema de Stefan. Palabras claves secundarias: Mecánica del continuo, Procesos difusivos, Análisis funcional, Conducción del calor, Métodos matemáticos, Métodos numéricos, Ecuaciones diferenciales a derivadas parciales, Inecuaciones variacionales, Soluciones débiles. El manuscrito fue recibido y aceptado en octubre de 1999. D.A. Tarzia, A bibliography on FBP. The Stefan problem, MAT Serie A, # 2 (2000). 3

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A bibliography on moving-free boundary problems for the heat-diffusion equation. The stefan and related problems

Abstract A new approach to the modeling of the equiaxed solidification of dendritic alloys is proposed. It is assumed that, in metallic alloys, microstructure formation is primarily controlled by solute diffusion (i.e. there is complete “thermal mixing” at the scale of one grain), and that the dendrite interface is an iso-concentrate at all times. The evolution of one dendritic grain is therefore modelled as follows: (i) complete mixing of solute within the interdendritic liquid; (ii) no back-diffusion in the solid; (iii) spherical solute diffusion in the liquid around the grain envelope; (iv) overall solute balance; (v) overall thermal balance; (vi) growth velocity, υg, of dendrite tips governed by the kinetic equation derived for the isolated dendrite case. By using an explicit finite difference scheme to solve these coupled equations, the concentration profiles, cooling curve, fraction of solid and evolution of dendritic grain envelope can be calculated. The intitial conditions used to start the calculation are provided by two parameters related to nucleation: the initial undercooling and the density of gains. The effect of nucleation and thermal conditions on equiaxed growth are studied. The theoretical predictions of recalescence and of the distribution of an interdendritic eutectic phase are in good agreement with experimental observations.

Solute diffusion model for equiaxed dendritic growth

This is the second section of the review-tutorial paper describing fundamentals of tissue optics and photonics. As the first section of the paper was mostly devoted to description of biological tissue structures and their specificity related to interactions with light [1], this section 3 describes light-tissue interactions themselves that caused by tissue dispersion, scattering, and absorption properties, including light reflection and refraction, absorption, elastic, and quasi-elastic scattering. The major tissue absorbers and modes of elastic scattering, including Rayleigh and Mie scattering, will be presented.

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Tissue Optics and Photonics: Light-Tissue Interaction

https://par.nsf.gov/servlets/purl/10025814

Infrared imaging technology for breast cancer detection – Current status, protocols and new directions

Identification of tumor region parameters using evolutionary algorithm and multiple reciprocity boundary element method

A typical task from the range of thermal theory of foundry consists in the computation of solidification and cooling processes in the system casting-mould environment. From the technological point of view one can consider the following processes: • solidification of casting in moulding sand • solidification of casting in permanent mould • solidification of ingot in ingot mould • continuous casting process The physical features characterizing each of the above-mentioned technologies as well as a sort of casting material (pure metals, alloys, etc.) determine the adequate mathematical description of thermal processes, the admissible simplifications, the significance of certain technological parameters, etc. In this paper the applications of the BEM for numerical simulation of different foundry processes will be presented, in particular, the algorithms as a composition of the BEM for parabolic equations with certain procedures taking into account the course of solidification process will be discussed.

Application of the BEM in the thermal theory of foundry

Heat transfer processes proceeding in the 3D domain of heating tissue are discussed. The problem is described by dual-phase lag equation supplemented by adequate boundary and initial conditions. To solve the problem the general boundary element method is proposed. The examples of computations are presented in the final part of the paper. The efficiency and exactness of the algorithm proposed are discussed and the conclusions are also formulated.

Ewa Majchrzak

Papers

Identification of tumor region parameters using evolutionary algorithm and multiple reciprocity boundary element method

Application of the BEM in the thermal theory of foundry

The general boundary element method for 3D dual-phase lag model of bioheat transfer

Numerical analysis of the interactions between laser and soft tissues using generalized dual-phase lag equation

Numerical model of thermal interactions between cylindrical cryoprobe and biological tissue using the dual-phase lag equation