Ordering induced by chemical, thermal and mechanical constraints at solid interfaces

We know that classical thermodynamics even out of equilibrium always leads to stable situation which means degradation and consequently d sorder. Many experimental evidences in different fields show that gradation and order (symmetry breaking) during time and space evolution may appear when maintaining the system far from equilibrium. Order through fluctuations, stochastic processes which occur around critical points and dissipative structures are the fundamental background of the Prigogine-Glansdorff and Nicolis theory. The thermodynamics of macroscopic fluctuations to stochastic approach as well as the kinetic deterministic laws allow a better understanding of the peculiar fascinating behavior of organized matter. The reason for the occurence of this situation is directly related to intrinsic non linearities of the different mechanisms responsible for the evolution of the system. Moreover, when dealing with interfaces separating two immiscible phases (liquid - gas, liquid -liquid, liquid - solid, solid - solid), the situation is rather more complicated. Indeed coupling terms playing the major role in the conditions of instability arise from the peculiar singular static and dynamic properties of the surface and of its vicinity. In other words, the non linearities are not only intrinsic to classical steps involving feedbacks, but they may be imbedded with the non-autonomous character of the surface properties. In order to illustrate our goal we discuss three examples of ordering in far from equilibrium conditions: i) formation of chemical structures during the oxidation of metals and alloys; ii) formation of mechanical structures during the oxidation of metals iii) formation of patterns at a solid-liquid moving interface due to supercooling condition in a melt of alloy. © 1984, Walter de Gruyter. All rights reserved.

Localization in systems of non-identical oscillators

A singular perturbation method is applied to a non-conservative system of two weakly coupled strongly nonlinear non-identical oscillators. For certain parameters, localized solutions exist for which the amplitude of one oscillator is an order of magnitude smaller than the other. It is shown that these solutions are described by coupled equations for the phase difference and scaled amplitudes. Three types of localized solutions are obtained as solutions to these equations which correspond to phase locking, phase drift, and phase entrainment. Quantitative results for the phases and amplitudes of the oscillators and the stability of these phenomena are expressed in terms of the parameters of the model.

Characterization of autonomous thyroid adenoma: metabolism, gene expression, and pathology.

Fifty-one in vivo characterized autonomous single adenomas have been studied for functional parameters in vitro, for gene and protein expression and for pathology, and have been systematically compared to the corresponding extratumoral quiescent tissue. The adenomas were characterized by a high level of iodide trapping that corresponds to a high level of Na+ /iodide symporter gene expression, a high thyroperoxidase mRNA and protein content, and a low H2O2 generation. This explains the iodide metabolism characteristics demonstrated before, ie, the main cause of the "hot" character of the adenomas is their increased iodide transport. The adenomas spontaneously secreted higher amounts of thyroid hormone than the quiescent tissue and in agreement with previous in vivo data, this secretion could be further enhanced by thyrotropin (TSH). Inositol uptake was also increased but there was no spontaneous increase of the generation of inositol phosphates and this metabolism could be further activated by TSH. These positive responses to TSH are in agreement with the properties of TSH-stimulated thyroid cells in vitro and in vivo. They are compatible with the characteristics of mutated TSH receptors whose constitutive activation accounts for the majority of autonomous thyroid adenomas in Europe. The number of cycling cells, as evaluated by MIB-1 immunolabeling was low but increased in comparison with the corresponding quiescent tissue or normal tissue. The cycling cells are observed mainly at the periphery; there was very little apoptosis. Both findings account for the slow growth of these established adenomas. On the other hand, by thyroperoxidase immunohistochemistry, the whole lesion appeared hyperfunctional, which demonstrates a dissociation of mitogenic and functional stimulations. Thyroglobulin, TSH receptor, and E-cadherin mRNA accumulations were not modified in a consistent way, which confirms the near-constitutive expression of the corresponding genes in normal differentiated tissue. On the contrary, early immediate genes expressions (c-myc, NGF1B, egr 1, genes of the fos and jun families) were decreased. This may be explained by the proliferative heterogeneity of the lesion and the previously described short, biphasic expression of these genes when induced by mitogenic agents. All the characteristics of the autonomous adenomas can therefore be explained by the effect of the known activating mutations of genes coding for proteins of the TSH cyclic adenosine monophosphate (cAMP) cascade, all cells being functionally activated while only those at the periphery multiply. The reason of this heterogeneity is unknown.