35 resultados para Feynman-Kac formula Markov semigroups principal eigenvalue


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The principal tidal constituents M-2, S-2, K-1 and O-1 in the South China Sea, Gulf of Tonkin and Gulf of Thailand are simulated simultaneously using the numerical scheme of Kwok et al. (1995 Proceedings of the 1st Asian Computational Fluid Dynamics Conference, pp. 16-19). The average differences between the computed and observed harmonic constants are mostly within 5 cm and 10 degrees for amplitudes and phase-lags, respectively. The simulated tidal regimes in the present model are believed to be more accurate than the previous numerical results. Our studies confirm that a clockwise rotating M-2 amphidromic system lies in the southeast of the Gulf of Thailand and an S-2 amphidromic system at the near-shore area of the northeast South China Sea. The linear tidal energy equation developed by Garrett (1975 Deep-Sea Research 22, 23-35) is generalized to the nonlinear case. Based on the numerical results, the energy budgets in the South China Sea and its subareas, namely the Taiwan Strait, the Gulf of Tonkin, the Gulf of Thailand and the remaining area are investigated. The tidal motion in the Taiwan Strait is maintained mainly by the energy fluxes from the East China Sea for both semidiurnal and diurnal species and partially from the Luzon Strait for semidiurnal species. For the other parts of the South China Sea, the tidal motion is mainly maintained by the energy fluxes through the Luzon Strait. The energy inputs from the tide-generating force are negative for semidiurnal species and positive for diurnal species. (C) 1999 Elsevier Science Ltd. All rights reserved.

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Magnetic storm is a kind of severe disturbances in the whole solar-earth electromagnetic space. It has significant effects on communication, electric power, oil transport pipe and human activities in space. Therefore, magnetic storms are worth for applications systems, not only being a favorable issue for scientists. In this paper, the spatial and temporal distributions of the magnetic fields produced by the magnetosphere-ionosphere current systems during storms are studied. Four parts are included in this paper decomposion of different disturbances with different origins, topological structure of the ring current, the asymmetric characteristics of the ring current, and the statistic peculiarities of the day-to-day variability (DTD) of Sq. 1 The decomposition of magnetic disturbances at mid-low latitudes and its evolutions during storms Transient variations in the geomagnetic field recorded at mid-low latitudes mainly include the storm-time variation (Dst), solar quiet daily variation (Sq) and disturbance daily variation (SD). With the data of the geomagnetic meridian chain observatories in China, 25 storms during the period of 1997 to 1999 have been analyzed. According to the features of different variations, a method of “three-steps decomposition” is developed by using the method of Natural Orthogonal Components (NOC), Correlation Analysis and Fourier Analysis to separate those three components in turn. The results show that, the first eigenmode by the MNOC clearly describing the special distribution and temporal evolution of storm-time variation, in addition, Correlation Analysis and Fourier Analysis offer a useful method to extract the Sq and SD variations. The latitudinal shift of the Sq current focus seems to be the principal reason of the day-to-day variaitons in the daily range of Sq. The magnitude of SD reaches a maximum during the main phase, and then gradually decreases. 2 The topology structure of the ring current during storms Both the mechanism of the ring current and the geomagnetic data suggest that the central plane of the ring current is declining to the geomagnetic equator plane with a tilt angle δ. Using the H and Z component data at two stations in a meridian chain, we deduce a new parameter describing the invariable peculiarity of different storms. Then the δ angle is calculated by using the data from a meridian chain and tested with the ERC model. Finally the deduced tilt angles are used to modify Dst index. 3 The asymmetric characteristics of the ring current during storms The variations of the geomagnetic field at mid-low latitudes show a significant dawn-dusk asymmetry, resulting from the superposition of the fields from the symmetric ring current and the partial ring current. On the basis of the data from the 20°E, 30°E meridian chains and 30°N latitudinal chain, the dawn-dusk asymmetry is investigated by using three methods, namely, statistic analysis, ring current model calculation and typical event analysis. This characteristic implies the asymmetry of the spatial distribution of the ring current. In addition, during the main phase after the sudden commencement (SC), H field increases and reaches maximum around noontime, implying the effect of the Chapman-Ferraro current. 4 The statistic characteristics of the day-to-day variability and its mechanism The day-to-day variability of the geomagnetic Sq field is studied by using the magnetic data from a meridian chain of magnetometers along 120° E longitude. The method of NOC is applied to separate the Sq variation from complicated disturbances. The first eigenmode with the largest eigenvalue represents fairly well the Sq variation with a conspicuous day-to-day variability in the daily range. For the stations on the same north- or south-side of the Sq current system focus, the day-to-day variations show a positive correlation. In contrast, for the stations on the different sides of the Sq focus, they show a negative correlation, suggesting an important role of latitudinal shift of the Sq current system focus to the day-to-day variability of the Sq daily range. The Sq daily range is correlated with the magnetic indices Ap and Dst in a peculiar way: on some severe disturbed days, noticeably enhancements of the Sq are observed, implying increases of the ionospheric conductivities and/or tidal wind velocities; on other severe disturbed days, however, dramatically reduced Sq variations occur, suggesting dominant effects of the ‘disturbance dynamo’ process.

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The research on mechanical effects of water-rock and soil interaction on deformation and failure of rocks and soils involves three aspects of mechanics, physics and chemistry. It is the cross between geochemistry and rock mechanics and soil mechanics. To sum up, the mechanical effects of water-rock and soil interaction is related to many complex processes. Research in this respect has been being an important forward field and has broad prospects. In connection with the mechanism of the effects of the chemical action of water-rock on deformation and failure of rocks and soils, the research significance, the present state, the developments in this research domain are summarized. Author prospects the future of this research. The research of the subject should be possessed of important position in studying engineering geology and will lead directly to a new understand on geological hazard and control research. In order to investigation the macroscopic mechanics effects of chemical kinetics of water-rock interaction on the deformation and failure, calcic rock, red sandstone and grey granite reacting chemically with different aqueous solution at atmospheric temperature and atmospheric pressure are uniaxially compressed. The quantitative results concerning the changes of uniaxially compressive strength and elastic modulus under different conditions are obtained. It is found that the mechanical effects of water on rock is closely related to the chemical action of water-rock or the chemical damage in rock, and the intensity of chemical damage is direct ratio to the intensity of chemical action in water-rock system. It is also found that the hydrochemical action on rock is time-dependent through the test. The mechanism of permeation and hydrochemical action resulting in failure of loaded rock mass or propagation of fractures in rocks would be a key question in rock fracture mechanics. In this paper, the fracture mechanical effects of chemical action of water-rock and their time- and chemical environment-dependent behavior in grey granite, green granite, grey sandstone and red sandstone are analyzed by testing K_(IC) and COD of rock under different conditions. It is found that: ①the fracture mechanical effect of chemical action of water-rock is outstanding and time-dependent, and high differences exist in the influence of different aqueous solution, different rocks, different immersion ways and different velocity of cycle flow on the fracture mechanical effects in rock. ②the mechanical effects of water-rock interaction on propagation of fractures is consistent with the mechanical effects on the peak strength of rock. ③the intensity of the mechanical fracture effects increases as the intensity of chemical action of water-rock increases. ④iron and calcium ion bearing mineral or cement in rock are some key ion or chemical composition, and especially iron ion-bearing mineral resulting in chemical action of water-rock to be provided with both positive and negative mechanical effects on rock. Through the above two tests, we suggest that primary factors influencing chemical damage in rock consist of the chemical property of rock and aqueous solution, the structure or homogeneity of rocks, the flow velocity of aqueous solution passing through rock, and cause of formation or evolution of rock. The paper explores the mechanism on the mechanical effects of water-rock interaction on rock by using the theory of chemistry and rock fracture mechanics with chemical damage proposed by author, the modeling method and the energy point of view. In this paper, the concept of absorbed suction between soil grains caused by capillary response is given and expounded, and the relation and basic distinction among this absorbed suction, surface tension and capillary pressure of the soil are analyzed and established. The law of absorbed suction change and the primary factors affecting it are approached. We hold that the structure suction are changeable along with the change of the saturation state in unsaturated soils. In view of this, the concept of intrinsic structure suction and variable structure suction are given and expounded, and this paper points out: What we should study is variable structure suction when studying the effective stress. By IIIy κHH's theory of structure strength of soils, the computer method for variable structure suction is analyzed, the measure method for variable structure suction is discussed, and it reach the conclusions: ①Besides saturation state, variable structure suction is affected by grain composition and packing patter of grains. ②The internal relations are present between structure parameter N in computing structure suction and structure parameter D in computing absorbed suction. We think that some problems exit in available principle of effective stress and shear strength theory for unsaturated soil. Based on the variable structure suction and absorbed suction, the classification of saturation in soil and a principle of narrow sense effective stress are proposed for unsaturated soils. Based on generalized suction, the generalized effective stress formula and a principle of generalized effective stress are proposed for unsaturated soils. The experience parameter χ in Bishop's effective stress formula is defined, and the principal factors influencing effective stress or χ. The primary factor affecting the effective stress in unsaturated soils, and the principle classifying unsaturated soils and its mechanics methods analyzing unsaturated soils are discussed, and this paper points out: The theory on studying unsaturated soil mechanics should adopt the micromechanics method, then raise it to macromechanics and to applying. Researching the mechanical effects of chemical action of water-soil on soil is of great importance to geoenvironmental hazard control. The texture of soil and the fabric of soil mass are set forth. The tests on physical and mechanical property are performed to investigate the mechanism of the positive and negative mechanical effects of different chemical property of aqueous solution. The test results make clear that the plastic limit, liquid limit and plasticity index are changed, and there exists both positive and negative effects on specimens in this test. Based on analyzing the mechanism of the mechanical effects of water-soil interaction on soil, author thinks that hydrochemical actions being provided with mechanical effects on soil comprise three kinds of dissolution, sedimentation or crystallization. The significance of these tests lie in which it is recognized for us that we may improve, adjust and control the quality of soils, and may achieve the goal geological hazard control and prevention.The present and the significance of the research on environmental effects of water-rock and soil interaction. Various living example on geoenvironmental hazard in this field are enumerated. Following above thinking, we have approached such ideals that: ①changing the intensity and distribution of source and sink in groundwater flow system can be used to control the water-rock and soil interaction. ②the chemical action of water-rock and soil can be used to ameliorate the physical and mechanical property of rocks and soils. Lastly, the research thinking and the research methods on mechanical effects and environmental effects of water-rock and soil interaction are put forward and detailed.