Ostwald ripening: an approach with dynamical systems

This approach assumes three functions independently acting on a set of microparticles. The first one, w1, concerns re-distribution of mass to decrease the surface energy. The second one, w2, concerns re-distribution of mass to increase the entropy of the microparticle set. The third one, w3, is a further re-distribution of mass that vanishes a microparticle. Once vanished, its mass is distributed among its neighbors. w1 and w3 release energy, whereas w2 absorbs energy. Part of the energy released should be available to sustain w2. The action frequency of w1, w2, and w3, the amount of mass exchanged in each iteraction, the fraction of released energy available to sustain w2, and the size of a vanishing microparticle can be varied. As the dynamical system formed by w1, w2, and w3 act on an initial microparticle set, it is observed an evolution resembling the Ostwald ripening concerning steady-state size distribution and microparticle growth

The Relative Variational Model - A Topological View Of Matter And Its Properties: Uo2±x Density

Formal definitions of convergence, connectedness and continuity were established to characterize and describe the crystalline solid and its properties as a unified notion in the topological space. The crystalline solid is a previously empty space that has been filled with atoms and phonons, i.e., the crystal is built with packages of matter and energy in a regular and orderly repetitive pattern along three orthogonal dimensions of the space. The spatial occupation of the atom in the crystal structure is determined by its mean vibrational volume. Thus, the changes of volume and the changes of internal energy are intrinsically linked. In fact, physical and material properties are the interdependent and bijective quantifications associated with variations of the internal energy. These properties are modeled by means of an intrinsic and invariable form function: the Relative Variational Model. In this paper, the lattice parameter and specific mass of UO2±x are depicted in dependence on the variations of the stoichiometry in the band of -0.016 ≤ x <0.25 and temperature from 0 K up to melting point.545124521ANS Reactor Physics Division,ANS Mathematics and Computations Division,U. S. Department of Energy - Office of Nuclear Energy,Oak Ridge National Laboratory (ORNL),TerraPowerKingery, W.D., Bowen, H.K., Uhlmann, D.R., (1976) Introduction to Ceramics, p. 1032. , 2a Ed. New York: John Wiley &ampSonsShannon, R.D., Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides (1976) Acta Cryst., A32, pp. 751-767Dias, M.S., Vasconcelos, V., Mattos, J.R.L., Jordão, E., THE RELATIVE VARIATIONAL MODEL - A topological view of matter and its properties: Thermal expansion Advances in Reactor Physics - Linking Research, Industry, and Education (PHYSOR 2012), Knoxville, Tennessee, USA, April 15-20, (2012), , Submitted toDias, M.S., Vasconcelos, V., Mattos, J.R.L., Jordão, E., THE RELATIVE VARIATIONAL MODEL - A topological view of matter and its properties: Specific heat and enthalpy Advances in Reactor Physics - Linking Research, Industry, and Education (PHYSOR 2012), Knoxville, Tennessee, USA, April 15-20, (2012), , Submitted toDias, M.S., Vasconcelos, V., Mattos, J.R.L., Jordão, E., THE RELATIVE VARIATIONAL MODEL - A topological view of matter and its properties: Space occupancy by the atoms Advances in Reactor Physics - Linking Research, Industry, and Education (PHYSOR 2012), Knoxville, Tennessee, USA, April 15-20, (2012), , Submitted toOhmichi, T., Fukushima, S., Maeda, A., Watanabe, H., On the relation between lattice parameter and O/M ratio for uranium dioxide-trivalent rare earth oxide solid solution (1981) J. Nucl. Mater., Amsterdam, 102 (1-2), pp. 40-46(2002) TABLE CURVE 3D - Version 4.0 for Windows, , SYSTAT Software Inc. Richmond, CA, USADias, M.S., Jordão, E., Vasconcelos, V., (2007) Desenvolvimento de Modelos Analíticos Paras As Propriedades Térmicas e Condução de Calor Transiente Em Varetas Combustíveis Nucleares, , DSc Thesis, Campinas State Univ., São PauloRonchi, C., Sheindlin, M., Musella, M., Hyland, G.J., Thermal conductivity of uranium dioxide up to 2900 K from simultaneous measurement of the heat capacity and thermal diffusivity (1999) J. of Applied Phys., 85 (2), pp. 776-789. , Lancaster, PennFink, J.K., Review - Thermophysical properties of uranium dioxide (2000) J. Nucl. Mater., 279 (1), pp. 1-18. , AmsterdamHagrman, D.T., MATPRO - A Library of Materials Properties for Light-Water-Reactor Accident Analysis (1994) SCDAP/RELAP5/MOD3.1 Code Manual, 4, p. 681. , Idaho Falls:, Idaho National Engineering Lab., NUREG/CR-6150, EGG-2720, Volume I