A path information is defined in connection with different possible paths of irregular dynamic systems moving in its phase space between two points. On the basis of the assumption that the paths are physically differentiated by their actions, we show that the maximum path information leads to a path probability distribution in exponentials of action. This means that the most probable paths are just the paths of least action. This distribution naturally leads to important laws of normal diffusion. A conclusion of this work is that, for probabilistic mechanics or irregular dynamics, the principle of maximization of path information is equivalent to the least action principle for regular dynamics.We also show that an average path information between the initial phase volume and the final phase volume can be related to the entropy change defined with natural invariant measure of dynamic system. Hence the principles of least action and maximum path information suggest the maximum entropy change. This result is used for some chaotic systems evolving in fractal phase space in order to derive their invariant measures. 相似文献
Granodiorite from the Gęsiniec Intrusion, Strzelin Crystalline Massif, SW Poland contains complexly zoned plagioclases. Five chemically and structurally distinct zones can be correlated among crystals: ‘cores’ (25–35% An), inner mantles (40–45% An), outer mantles (40–25% An), resorption zones (35–50% An) and rims (35–30% An). Good structural and chemical (major and trace elements) correlation of zones between crystals indicates that zonation was produced by changes in conditions of crystallization on a magma chamber scale. Plagioclase, being the liquidus phase, records a time span from the beginning of crystallization to emplacement and rapid cooling of granodiorite as thin dykes.
Crystallization began with the formation of inner mantles. The paucity and different sizes of inner mantles suggests slow crystallization in high temperature magma. Normally zoned inner mantles were formed under increasing undercooling. Compositional trends in mantles suggest closed system crystallization.
The major resorption zones were caused by injection of less evolved magma as indicated by the strontium increase in plagioclase. The injection triggered a rapid rise of magma and plagioclase crystals facilitating mixing but also inducing fast, kinetically controlled growth of complex multiple, oscillatory zonation within resorption zones. The ascent of magma caused decompression melting of plagioclase and produced melt inclusions within inner mantles—the ‘cores’. The decompression range is estimated at a minimum of 2 kbar. Emplacement of granodiorite as thin dykes allow rapid cooling and preservation of magmatic zonation in plagioclases. Melt inclusions crystallized completely during post-magmatic cooling.
The zonation styles of plutonic plagioclase differ markedly from volcanic ones suggesting different magma evolution. Zones in plutonic plagioclase are well correlated indicating crystallization in quiescent magma where crystals accumulation and compositional magma stratification may occur. Crystals probably did not travel between different regimes. Resorption occurred but as single albeit complex episodes. Good correlation of zones in plutonic plagioclases allows a distinction between the main processes controlling zonation and superimposed kinetic effects. 相似文献
A paleomagnetic study has been conducted on a formation dated as Autunian in the Nekheila area (31.4°N, 1.5°W) in the Mezarif basin. ChRM was thermally isolated in 117 samples from seven sites. This ChRM (D = 131.8°, I = 15.7°, k = 196, α95 = 3.8° after dip correction; corresponding pole 29.3°S, 56.4°E) is very similar to that obtained in the neighboring Abadla basin from a formation of the same age. Fold tests associated with progressive unfolding applied to the full merged data from the dated formations of these two basins clearly indicate that the magnetization acquisition predates the deformation, which is attributed to the last phase of the late-Hercynian. The magnetization in these basins is therefore primary or acquired just after deposition. For the African Apparent Polar Wander Path, the age of the paleomagnetic poles of the Autunian part is now confirmed by paleomagnetic test. 相似文献
Fifty diamond crystals of different morphological types (octahedra, dodecahedroids, cubes and single tetrahexahedroid) with differing internal structures were examined using methods of cathodoluminescence (CL), anomalous birefringence and local infrared (IR) analysis. The main objective of the study was to examine the regularities of nitrogen impurity distribution in diamond with differing internal structures. Almost all the analyzed octahedra, as well as dodecahedroids with zonal structures and the blocky dodecahedroids, are characterized either by nearly isothermic growth conditions or by a decrease in formation temperature during the crystallization process. In contrast to zoned octahedra and dodecahedroids, dodecahedroids with zonal–sectorial and sectorial internal structures show a notably different distribution of nitrogen defects, with Ntot generally decreasing from crystal cores to marginal areas, and degree of nitrogen aggregation increasing in the same direction. From this, it would follow that in these crystals, the temperature of diamond formation of the outer crystal zones is approximately 40–50 °C higher than that of the inner zones. The same result (15 to 80 °C) was obtained for diamond crystals with cubic habit, which generally show a fibrous internal structure, reflecting normal mechanisms of growth. The anomalous distribution of nitrogen centres in diamond crystals that grew through the normal mechanism, with a high rate of growth and in an oversaturated medium, might point to non-equilibrium relationships between the concentrations of different nitrogen centres. It is likely that in crystals of this type, the rate of growth is higher than the rate of structural nitrogen aggregation. Thus, it appears that in these peculiar crystals of diamond we deal with non-equilibrium concentrations of nitrogen B centres and, consequently, with anomalous, non-actual diamond formation temperatures. 相似文献
The results of a series of experiments are reported in this paper which were designed to differentiate between the forces of crystal growth and hydration in salt weathering, using a single salt-hydrate system (sodium sulphate), five contrasting rock types, and several diurnal temperature-relative humidity cycles which permitted or inhibited these processes and simulated ground surface climates in hot, arid environments. It was shown that hydration of sodium sulphate is an effective mechanism of rock disintegration but that it is significantly less destructive than crystal growth pressure. Crystallization of thenardite (Na2SO4) is, in turn, more effective in rock weathering than the crystal growth of mirabilite (Na2SO4.10H2O). In general, rates of disintegration were most rapid where the diurnal temperature range was extreme and relative humidity lowest. 相似文献