On Numerical Solution of Shape Inverse Problems

The new method is proposed for the numerical solution of a class of shape inverse problems. The size and the location of a small opening in the domain of integration of an elliptic equation is identified on the basis of an observation. The observation includes the finite number of shape functionals. The approximation of the shape functionals by using the so-called topological derivatives is used to perform the learning process of an artificial neural network. The results of computations for 2D examples show, that the method allows to determine an approximation of the global solution to the inverse problem, sufficiently closed to the exact solution. The proposed method can be extended to the problems with an opening of general shape and to the identification problems of small inclusions. However, the mathematical theory of the proposed approach still requires futher research. In particular, the proof of global convergence of the method is an open problem.     

A kinetic Monte Carlo method on super-lattices for the study of the defect formation in the growth of close packed structures

A modified Kinetic Lattice Monte Carlo model has been developed to predict growth rate regimes and defect formation in the case of the homo-epitaxial growth of close packed crystalline structures. The model is an improvement over standard Monte Carlo algorithms, which usually retain fixed atom positions and bond partners indicative of perfect crystal lattices. Indeed, we extend the concepts of Monte Carlo growth simulations on super-lattices containing additional sites (defect sites) with respect to those of the reference material. This extension implies a reconsideration of the energetic mapping, which is extensively presented, and allows to describe a complex phenomenology that is out of accessibility of standard stochastic approaches. Results obtained using the Kawasaki and the Bond-Counting rules for the transition probability of the Monte Carlo event are discussed in details. These results demonstrate how the defect types (local or extended), the formation mechanisms and the defect generation regimes can be characterized using our approach.     

Form of the Spectra of Nucleus Dimensions in First-Order Phase Transitions

We study a generalization of the analytic theory of first-order phase transitions to the cases of arbitrary droplet growth, of nonisothermal processes, and of heterogeneous centers in the system. We show that in all these cases, the spectra of droplet dimensions are similar. The same forms of the spectra are also obtained for the stationary condensation process in a spatially inhomogeneous system.     

Memory effects in isothermal crystallization II. Isotactic polypropylene

The effects of temperature and duration of melting on the rate of isothermal crystallization of isotactic polypropylene were investigated by differential scanning calorimetry (DSC). Crystallization rates were found to decrease with increasing melt temperature and melting time. The results were discussed in the framework of the theoretical model of transient isothermal crystallization developed by the present authors [1]. The results suggest gradual destruction of predetermined nuclei with activation energyE _a=89±7 kJ/mole as a main mechanism of the observed effects.This work and Part I of this research [1] have been supported in part by Research Grant Number PB 1291/52/93/04 from State Committee for Scientific Research (KBN), Poland, and by 40% MURST founds, Italy.     

Densification and crystallisation of celsian glass derived from alkoxide gel

High density (98% of theoretical) was achieved at 900°C for an all-alkoxide derived bulk celsian gel prior to crystallisation. TEM indicated that crystallisation was dominated by volume nucleation and growth of hexagonal disc shaped hexacelsian. Kinetic studies using SEM indicate a maximum nucleation rate at 980°C and an activation energy for crystal growth of 566 KJ/mol. The high rates of densification and of nucleation are attributed to the high OH content in the gel-derived glass.     

The thermal properties of complex, nanophase-separated macromolecules as revealed by temperature-modulated calorimetry

Linear, flexible macromolecules are long recognized as phase structures limited to micrometer and nanometer dimensions with covalent bonds crossing the interfaces. This special, usually non-equilibrium structure leads to unique properties and a multitude of changes for different thermal and mechanical histories. Analyses that enable the study of these properties are temperature-modulated calorimetry and related techniques which allow the separation of equilibrium and non-equilibrium responses. Research on these topics is reviewed and combined to a model for the nanophases. The new approach to the complex nanophase systems yields a better understanding of the relationship between structure and thermodynamic properties. Special emphasis is placed on the size and surface effects on the glass and melting transitions, the development of rigid-amorphous phases, and the reversible melting within the globally metastable structure.     

Mechanistic Aspects of Carbon Nanotube Nucleation and Growth

The discovery, synthesis, characterization, and applicability of carbon nanotubes have produced tremendous excitement and interest among scientists and engineers. In particular, the use of these unique tubular nanostructures for new strong lightweight materials, nanoelectronics, fuel storage and cells, electron emitters and bio, scanning probe microscopy, and chemical sensing devices has created an intense effort to advance the synthesis so as to mass produce carbon nanotubes with control over diameter and helicity. The massive and controlled synthesis of this heralded nanostructure has been a great challenge. Although significant progress has advanced the preparation, more synthetic development is required. The syntheses have so far involved three main approaches: arc discharge vaporization, laser vaporization, and catalytic chemical vapor deposition. The synthetic trend has progressed to a point where further advancement with these techniques will require a better understanding of the mechanism of nucleation and growth. The mechanics of carbon nanotube nucleation and growth involve very complex and diverse phenomena occurring under extreme conditions and on the mesoscopic scale. As yet the detail mechanism is unknown. Difficulties with experimental probing and computational simulation have increased the mystery of this mechanism. This review presents an account of research on the synthesis of carbon nanotubes and the mechanism of formation. This overview includes all three mentioned synthetic approaches and hybrids thereof. On the basis of this broad account a comprehensive mechanism for carbon nanotube nucleation and growth naturally arises. This mechanism is qualitative and it hopes to inspire more quantitative exploration and synthetic advancement.     

Preparation and Characterization of N-4-Nitrophenyl-L-prolinol Nanocrystals in Sol-Gel Matrices

Organic nanocrystals of N-4-nitrophenyl-l-prolinol (NPP) have been grown in sol-gel matrices prepared from silicon alkoxide precursors. Our process is based on the control of the nucleation and growth kinetics of the dye in the pores of dense gels. Nanocomposites gel-glasses are obtained with a high optical quality due to the small size of the nanocrystals (10-20 nm). Differential scanning calorimetry experiments evidenced clearly the melting point of NPP nanocrystals, which is registered 51°C above that of NPP powder. Micro-Raman and solid state NMR spectroscopies allowed us to demonstrate that our nanocrystallization process does not chemically modify NPP molecules. We specified also the nature of interactions existing between the NPP nanocrystals and the xerogels. These strong interactions, which explain the important increase of the melting point of the nanocrystals in comparison to the NPP powder, are hydrogen bonds between nitro groups of NPP and uncondensed silanol functions of the silicate network.     

Texture of zirconia obtained by forced hydrolysis of ZrOCl2 solutions

The structure and surface properties of ZrO₂ strongly depend on its preparation. In the present work the impact of prolonged aging at basic conditions (pH = 9, T = 100°C, t = 48 h), on the phase composition and textural properties, obtained by calcination of the precipitate, was investigated using several techniques conjointly (DTA/TG, DSC, XRD, porosimetry). The thermal effects accompanying the ZrO₂·xH₂O gel formation, the coalescence of the particles and crystallization were evaluated and discussed in terms of the structural differences between the aged and non-aged samples. This revised version was published online in July 2006 with corrections to the Cover Date.     

Metastable fluid flow described via a discrete-velocity coagulation-fragmentation model

A discrete-velocity Boltzmann model is introduced. It is based on two principles: (i) clusters of particles move in ³ with seven fixed momenta; (ii) clusters may gain or lose particles according to the rules of Becker-Döring cluster equations. The model provides a kinetic representation of evaporation and condensation. The model is used to obtain macroscopic fluid equations which are valid into the metastable fluid regime, , where is any positive number, is the inelastic Knudsen number, and _s is the saturation density.