首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 78 毫秒
1.
The morphology and internal structure of individual olivine grains from ultramafic rocks in the Guli and Gal’moenan dunite massifs differing in origin are considered. To restore the ontogeny of mineral aggregates, traces of elastic deformation retained in mineral grains have been used. Comparison of anatomy of olivine grains from these two massifs showed that the mechanism of accommodation of rocks to changing geological settings is expressed as the response of the mineral aggregate structure and variation in the anatomy of individual mineral grains. At the level of individual grains, this is annihilation of older defects and origination of younger dislocations; refinement of the crystal lattice; exsolution; formation and transformation of new mineral phases; and creep and migration of subboundaries within grains. At the aggregate level, this is rotation and migration creep of the internal boundaries of rock; formation of new boundaries of mineral intergrowths; reorientation of boundaries; and variation in their extent, density, and grain dimensions. The prehistory of massifs controls the manifestation and abundance of various elastic deformations and related types of recrystallization of olivine grain boundaries and subboundaries in aggregates. New conditions and accommodation of mineral aggregates to these conditions have instigated specific schemes of recrystallization, which bear information on the history of rocks and their massifs.  相似文献   

2.
Rheological properties of polyphase rocks play an important role in the dynamics of the lithosphere and asthenosphere. However, flow laws for large portions of the polyphase rocks in the Earth's crust and mantle have not been well determined. An analysis based on the theory of mixtures has been made to calculate the general flow laws of coarse (≥5 μm), nearly equant-grained (aspect-ratio ≤3), and massive polyphase rocks and materials for which only the flow laws and volume fractions of the constituents are taken into consideration in the modeling of the bulk rheology and effects of microstructure could be ignored. The theoretical analysis is based on three assumptions: (1) the polyphase composite and the monophase aggregates of its constituents obey the same kind of flow laws (linear, power or exponential), (2) there is no change in the operative deformation mechanism of each phase when it is in the composite as compared to when it is in a monophase aggregate, and (3) neither chemical (metamorphic) reactions take place among the constituent phases nor eutectic melting occurs due to the phase mixing. The proposed iterative process allows to predict, to the first approximation, the flow laws for a large number of polyphase rocks in terms of the experimentally determined flow laws of a relatively small number of monomineralic aggregates. Applications of this approach to typical polyphase rocks such as granite, diorite, diabase, aplite and websterite as well as to synthetic two-phase materials such as forsterite–enstatite mixtures and water ice–ammonia dehydrate aggregates yield quite accurate approximations to the experimental values.  相似文献   

3.
Basaltic rocks have been widely used as aggregate for various purposes. They show a variety of textural and mineralogical characteristics that may affect their physico-mechanical properties as well as their use as construction material. The study presented in this paper was carried out on basalts that are widespread in the Middle Anatolian Region of Turkey and that comprise the major source of local crushed rock aggregates. To determine the suitability of the basalts as alternative aggregate resource, Early Quaternary Melendiz Volcanites, Quaternary Karataş volcanites andİğredağ basalts were selected around the Niğde Region. The experimental studies were conducted on these rocks. The samples were collected as being representative of 11 different types of basalt. The physico-mechanical properties of the basalts of different compositions and textures, and the properties of their aggregates were determined. The results were then compared with the typical acceptance limits in international usage. Although olivine basalts have better aggregate quality compared to other basalts, most of the basalts were found to be suitable for production of crushed rock aggregates for concrete production.  相似文献   

4.
Realistic texture‐based modelling methods, that is microstructural modelling and micromechanical modelling, are developed to simulate the rock aggregate breakage properties on the basis of the rock actual microstructure obtained using microscopic observations and image analysis. The breakage properties of three types of rocks, that is Avja, LEP and Vandle taken from three quarries in Sweden, in single aggregate breakage tests and in inter‐aggregate breakage tests are then modelled using the proposed methods. The microstructural modelling directly integrates the microscopic observation, image analysis and numerical simulation together and provides a valuable tool to investigate the mechanical properties of rock aggregates on the basis of their microstructure properties. The micromechanical modelling takes the most important microstructure properties of rock aggregates into consideration and can model the major mechanical properties. Throughout this study, it is concluded that in general, the microstructure properties of rock aggregate work together to affect their mechanical properties, and it is difficult to correlate a single microstructure property with the mechanical properties of rock aggregates. In particular, for the three types of rock Avja, LEP and Vandle in this study, crack size distribution, grain size and grain perimeter (i.e. grain shape and spatial arrangement) show good correlations with the mechanical properties. The crack length and the grain size negatively affect the mechanical properties of Avja, LEP and Vandle, but the perimeter positively influences the mechanical properties. Besides, the modelled rock aggregate breakage properties in both single aggregate and inter‐aggregate tests reveal that the aggregate microstructure, aggregate shape and loading conditions influence the breakage process of rock aggregate in service. For the rock aggregate with the same microstructure, the quadratic shape and good packing dramatically improve its mechanical properties. During services, the aggregate is easiest to be fragmented under point‐to‐point loading condition, and then in the sequence of multiple‐point, point‐to‐plane and plane‐to‐plane loading conditions. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

5.
岩石颗粒破碎是影响粒状材料剪切强度和变形的最主要因素, 岩石颗粒破碎并不是想象的那么难, 像花岗岩颗粒有时在很小的压应力作用下就可以破碎。岩石单颗粒破碎的物理试验结果常常很离散, 完成大量单颗粒破碎的物理试验费时费力不现实, 采用离散单元法(Discrete element method, DEM)PFC软件模拟单颗粒压缩破碎试验, 既能克服单颗粒破碎物理试验的缺陷, 又能解决单颗粒破碎物理试验工作量大的难题, 是研究单颗粒破碎的理想选择。基于DEM的软件PFC2D, 将粒径为0.075～0.1245mm的基本粒子捆绑成不同粒径的单颗粒, 模拟岩石单颗粒压缩破碎试验, 观察颗粒破碎演化过程, 统计单颗粒破碎强度。计算单颗粒压缩破碎后颗粒分布的分维, 验证单颗粒破碎强度的分形模型和单颗粒破碎强度的尺寸效应。文中引用玄武岩单颗粒破碎试验结果, 与单颗粒破碎的离散单元模拟结果进行比较, 验证单颗粒破碎强度的尺寸效应和修正的Weibull理论的离散单元模拟结果。  相似文献   

6.
GENERALIZED FLOW LAWS OF POLYPHASE ROCKS: AN OVERVIEW   总被引：1，自引：0，他引：1  
Rheological properties of polyphase rocks play an important role in the dynamics of the lithosphere and asthenosphere. However, such fundamental issues have not been well resolved. A theoretical analysis has been made to develop expressions for the flow laws of polyphase rocks in terms of the volume fractions and flow laws of their constituent phases. The flow strengths predicted by the proposed model for common crustal and upper mantle rocks such as granite, diorite, diabase and lherzolite, and for synthetic two-phase composites such as forsterite-enstatite and water ice-ammonia dehydrate aggregates are in good agreement with previously determined experimental values. The proposed theoretical model allows one to calculate, to the first approximation, the flow laws of a large number of polyphase rocks at geologic conditions based on the experimentally determined flow laws of a relatively small number of monomineralic aggregates.  相似文献   

7.
Rheological properties of polyphase rocks play an important role in the dynamics of the lithosphere and asthenosphere. However, such fundamental issues have not been well resolved. A theoretical analysis has been made to develop expressions for the flow laws of polyphase rocks in terms of the volume fractions and flow laws of their constituent phases. The flow strengths predicted by the proposed model for common crustal and upper mantle rocks such as granite, diorite, diabase and lherzolite, and for synthetic two-phase composites such as forsterite-enstatite and water ice-ammonia dehydrate aggregates are in good agreement with previously determined experimental values. The proposed theoretical model allows one to calculate, to the first approximation, the flow laws of a large number of polyphase rocks at geologic conditions based on the experimentally determined flow laws of a relatively small number of monomineralic aggregates.  相似文献   

8.
The relationships between petrographical and mechanical properties of rock aggregate raw materials from the hybridised, subvolcanic Jaala–Iitti complex, southeastern Finland, were investigated. Petrography was quantified from polished thin sections with a polarising microscope to determine the modal composition and grain size distribution, and resistance to fragmentation and abrasion were determined. Abundance of fine-grained minerals (especially of hornblende), fine grain size-dominated grain size distribution, uniform spatial dispersion of hornblende crystals, and intense micrographic intergrowth texture with interlocking grain boundaries were found to have the greatest positive influence on the mechanical properties. The results showed the potentiality of hybridised rocks as raw materials for high quality aggregates that can resist fragmentation and abrasion.  相似文献   

9.
Knowledge on the stresses in shotcrete tunnel shells is of great importance, as to assess their safety against severe cracking or failure. Estimation of these stresses from 3D optical displacement measurements requires shotcrete material models, which may preferentially consider variations in the water–cement and aggregate–cement ratios. Therefore, we employ two representative volume elements within a continuum micromechanics framework: the first one relates to cement paste (with a spherical material phase representing cement clinker grains, needle-shaped hydrate phases with isotropically distributed spatial orientations, a spherical water phase, and a spherical air phase; all being in mutual contact), and the second one relates to shotcrete (with phases representing cement paste and aggregates, whereby aggregate inclusions are embedded into a matrix made up by cement paste). Elasticity homogenization follows self-consistent schemes (at the cement paste level) and Mori–Tanaka estimates (at the shotcrete level), and stress peaks in the hydrates related to quasi-brittle material failure are estimated by second-order phase averages derived from the RVE-related elastic energy. The latter permits upscaling from the hydrate strength to the shotcrete strength. Experimental data from resonant frequency tests, ultrasonics tests, adiabatic tests, uniaxial compression tests, and nanoindentation tests suggest that shotcrete elasticity and strength can be reasonably predicted from mixture- and hydration-independent elastic properties of aggregates, clinker, hydrates, water, and air, and from strength properties of hydrates. At the structural level, the micromechanics model, when combined with 3D displacement measurements, predicts that a decrease of the water–cement ratio increases the safety of the shotcrete tunnel shell.  相似文献   

10.
This paper focuses on using urea hydrolysis as a bio-grouting process to increase the strength of crushed aggregates commonly used in stone columns. Various reagent phases (2, 4, 6 and 12 phases) consisted of alternately percolating solutions containing bacterial suspension and cementation solution through the soil column. In addition, a multi-soil lift strategy with options of up to four soil lifts was undertaken to test the applicability of bio-grout to cement crushed aggregate columns. While the average amount of calcium carbonate precipitation was roughly unchanged in both techniques, the distribution within the crushed aggregate columns was heterogeneous. However, the distribution of the precipitated calcium carbonate is almost uniform in crushed aggregates treated by a two-soil lift strategy and a four-phase treatment strategy. It is also deducted that both techniques can be combined to gain a uniform calcium carbonate and strength along a long sand/stone column. Furthermore, a one-soil lift resulted in higher strength than using multi-soil lifts, and a maximum strength of approximately 2.3 MPa was achieved using 4-reagent phase treatment strategy. Scanning electron microscopy and electron dispersive spectroscopy analysis validate that calcium carbonate was deposited as white crystals on the surface of the crushed aggregate particles.  相似文献   

11.
Argillaceous rocks cover about one thirds of the earth's surface. The major engineering problems encountered with weak- to medium-strength argillaceous rocks could be slaking, erosion, slope stability, settlement, and reduction in strength. One of the key properties for classifying and determining the behavior of such rocks is the slake durability. The concept of slake durability index (SDI) has been the subject of numerous researches in which a number of factors affecting the numerical value of SDI were investigated. In this regard, this paper approaches the matter by evaluating the effects of overall shape and surface roughness of the testing material on the outcome of slake durability indices.

For the purpose, different types of rocks (marl, clayey limestone, tuff, sandstone, weathered granite) were broken into chunks and were intentionally shaped as angular, subangular, and rounded and tested for slake durability. Before testing the aggregate pieces of each rock type, their surface roughness was determined by using the fractal dimension. Despite the variation of final values of SDI test results (values of Id), the rounded aggregate groups plot relatively in a narrow range, but a greater scatter was obtained for the angular and subangular aggregate groups. The best results can be obtained when using the well rounded samples having the lowest fractal values. An attempt was made to analytically link the surface roughness with the Id parameter and an empirical relationship was proposed. A chart for various fractal values of surface roughness to use as a guide for slake durability tests is also proposed. The method proposed herein becomes efficient when well rounded aggregates are not available. In such condition, the approximate fractal value for the surface roughness profile of the testing aggregates could be obtained from the proposed chart and be plugged into the empirical relation to obtain the corrected Id value. The results presented herein represent the particular rock types used in this study and care should be taken when applying these methods to different type of rocks.  相似文献   


12.
Filtration-capacity properties of terrigenous reservoir rocks significantly depend on catagenetic transformations of clay minerals. Results of our research revealed the authigenic nature and formation stages of kaolinite and chlorite. The volume and shape of pore space define the morphology of clay particles. Depending on the pore volume, kaolinite crystallizes either as thick tabular aggregates or as fan-shaped intergrowths. The formation of authigenic clays in pores of terrigenous reservoirs decreases filtration-capacity properties of rocks with low permeability and, conversely, increases filtration-capacity properties of rocks with high primary permeability and large pore volume.  相似文献   

13.
Chondrodite, a member of the humite group of minerals, forms by hydration of olivine and is stable over a range of temperatures and pressures that includes a portion of the uppermost mantle. We have measured the single crystal elastic properties of a natural chondrodite specimen at ambient conditions using Brillouin spectroscopy. The isotropic aggregate bulk (K) and shear (μ) moduli calculated from the single-crystal elastic moduli, Cij, are: KS=118.4(16) GPa and μ=75.6(7) GPa. A comparison of the structures and elasticity of olivine and chondrodite indicate that the replacement of O with (OH,F) in M2+O6 octahedra has a small effect on the elasticity of humite-group minerals. The slightly diminished elastic moduli of humite-group minerals (as compared to olivine) are likely caused by a smaller ratio of strong structural elements (SiO4 tetrahedra) to weaker octahedra, and perhaps a more flexible geometry of edge-sharing MO4(O,OH,F)2 octahedra. In contrast to the humite-olivine group minerals, the incorporation of water into garnets and spineloids leads to a more substantial decrease in the elastic properties of these minerals. This contrasting behavior is due to formation of O4H4 tetrahedra and vacant hydroxyl-bearing octahedra in the garnets and spineloids, respectively. Therefore, the mechanism of incorporation of H/OH into mineral phases, not only degree of hydration, should be taken into account when estimating the effect of water on the elastic properties of minerals. The bulk elastic wave velocities of chondrodite and olivine are very similar. If humite-like incorporation of OH is predominant in the upper mantle, then the reaction of OH with olivine will have a minor or possibly no detectable effect on seismic velocities. Thus, it may be difficult to distinguish chondrodite-bearing rocks from “anhydrous” mantle on the basis of seismically determined velocities for the Earth. Received: 25 February 1998 / Revised, accepted: 18 August 1998  相似文献   

14.
Water fluids in the Earth's crust may initiate a number of mineral reactions resulting in different microstructure changes, which may appear in the form of intergranular melt films and interstitial phases. Therefore, they have an essential influence on elastic wave velocities of rocks (for example, sandstone, amphibolite, basalt). The aim of the experiment was to determine the conditions of the silicate liquid and others interstitial phases distribution in the rock intergranular space.The results obtained using the ultrasonic method at temperature up to 950 °C and under fluid pressure of 300 MPa revealed that the formation of intergranular melt films and interstitial phases network depend on chemical composition of fluids. The experiments with use of a high-temperature centrifuge at temperature 1400 °C showed that the amount of melt films, higher than 6 %, is sufficient to form a system of interconnected intergranular channels. These studies can be contributed to the petrophysical and geochemical interpretation of geophysical measurements.  相似文献   

15.
Iron (hydr)oxides are ubiquitous in soils and sediments and play a dominant role in the geochemistry of surface and subsurface environments. Their fate depends on local environmental conditions, which in structured soils may vary significantly over short distances due to mass-transfer limitations on solute delivery and metabolite removal. In the present study, artificial soil aggregates were used to investigate the coupling of physical and biogeochemical processes affecting the spatial distribution of iron (Fe) phases resulting from reductive transformation of ferrihydrite. Spherical aggregates made of ferrihydrite-coated sand were inoculated with the dissimilatory Fe-reducing bacterium Shewanella putrefaciens strain CN-32, and placed into a flow reactor, the reaction cell simulates a diffusion-dominated soil aggregate surrounded by an advective flow domain. The spatial and temporal evolution of secondary mineralization products resulting from dissimilatory Fe reduction of ferrihydrite were followed within the aggregates in response to a range of flow rates and lactate concentrations. Strong radial variations in the distribution of secondary phases were observed owing to diffusively controlled delivery of lactate and efflux of Fe(II) and bicarbonate. In the aggregate cortex, only limited formation of secondary Fe phases were observed over 30 d of reaction, despite high rates of ferrihydrite reduction. Under all flow conditions tested, ferrihydrite transformation was limited in the cortex (70-85 mol.% Fe remained as ferrihydrite) because metabolites such as Fe(II) and bicarbonate were efficiently removed in outflow solutes. In contrast, within the inner fractions of the aggregate, limited mass-transfer results in metabolite (Fe(II) and bicarbonate) build-up and the consummate transformation of ferrihydrite - only 15-40 mol.% Fe remained as ferrihydrite after 30 d of reaction. Goethite/lepidocrocite, and minor amounts of magnetite, formed in the aggregate mid-section and interior at low lactate concentration (0.3 mM) after 30 d of reaction. Under high lactate (3 mM) concentration, magnetite was observed only as a transitory phase, and rather goethite/lepidocrocite and siderite were the dominant secondary mineralization products. Our results illustrate the importance of slow diffusive transport of both electron donor and metabolites concentrations and concomitant biogeochemical reactions within soils and sediments, giving rise to heterogeneous products over small spatial (μm) scale.  相似文献   

16.
In this research, the possibility of replacing different portions of the normally used aggregate by acidic rocks was investigated. These rock types outcrop at the northern part of Eastern Desert, southwest Ras Gharib area where large quantities of good quality acidic rocks are available their. Portland cement concrete is a composite material made up of the hydrated cement matrix, fine aggregate and coarse aggregate. The scanning electron microscope equipped with an energy dispersive X-ray analysis system (EDX) has been applied to investigate several aspects of Portland cement concrete microstructure. The topics investigated so far include the influence of aggregate composition on the development of the cement paste-aggregate interface and the formation of calcium silicate hydrate CSH/calcium silicate aluminate CSA formation. The silicate gel coated the aggregates in the concrete paste and crystallized into well defined needle like shape, cotton shape as well as euhedral to subhedral crystals of silicate/alumiante and ettringite minerals with free lime librated from the hydrolysis process. The free lime can react again with the aggregates leading to the formation of cementing materials which increase strength and durability of the concrete paste by increasing the interfacial bonds between the used aggregates.  相似文献   

17.
Most of the rocks in Precambrian shield areas have experienced a complex structural and metamorphic evolution, processes which have a strong influence on bedrock quality. The properties vary on both a local and a regional scale. It is highly beneficial to know the variations in detail when exploiting the rocks for industrial purposes. The main objective of the investigation was to study the variation of rock mechanical properties in an originally more or less isotropic rock at various stages of ductile deformation. The rocks investigated were Paleoproterozoic and with ages of ca. 1.80-1.88 Ga, and the areas chosen for sampling were situated north-east of Lake Vänern (Kristinehamn; 10 samples), south of the city of Eskilstuna, South Central Sweden (5 samples) and south of Ödeshög, near Lake Vättern in southern Sweden (7 samples). The 12 samples from the latter two areas are described in this investigation, while the 10 samples from Kristinehamn have been published earlier (Göransson et al., 2004). A comprehensive study of various parameters of importance for bedrock quality has been performed on all samples, e.g. studded tyre test (STT) and Los Angeles test (LA), uniaxial compressive strength (UCS), ultrasonic velocity, perimeter measurements of mineral phases, and petrographic and chemical analyses. The weakly deformed and massive (more or less isotropic) rocks show a tendency towards better properties of abrasion (STT) than the strongly deformed rocks and this can also be said for UCS, reflecting the greater ability of rocks to split along foliation planes. This is not entirely unambiguous, as the more deformed rocks, such as the mylonites, may have varying properties. This depends on the combined effects of, e.g. grain size, recrystallisation and foliation. However, the brittleness (LA) shows somewhat better values with increased deformation. This may depend on higher amounts of dark minerals, as their existence does not affect this test as much as in the case of abrasion tests. The perimeter values of the mineral phases display generally higher values, i.e. grain boundaries for the more strongly deformed rocks are more complicated. However, the values for the investigated mylonites may vary between low and high. The lower value may be due to dynamic recrystallisation and the creation of triple points (static recrystallisation) making the rock weaker. Besides, the development of a strong foliation may decrease rock strength despite the usually finer grain size. The results show that it is extremely important to consider all possible variations of bedrock before classification and exploitation, as the bedrock material in fact is highly heterogeneous.  相似文献   

18.
A fundamental understanding of the relation between stress concentrations at grain contacts and microfractures in granular aggregates is obtained through two-dimensional photomechanical model studies and is tested through observational studies of experimentally deformed sandstone discs, glass beads, and quartz sand.In uncemented aggregates, the state of stress in each grain is controlled by the manner in which the applied load is transmitted across grain contacts. The angles between lines connecting pairs of contacts and the axis of the principal load acting at the boundaries of the aggregate determine which of all contacts will be most highly stressed or “critical”. Microfractures follow that maximum principal stress trajectory which connects critical contacts, and they propagate through those points where the magnitude of the local maximum stress difference is the greatest. Microfractures, therefore, are extension fractures. It then follows that both the locations and orientations of fractures can be predicted if the state of stress in the grains is known.Positioning of critical contacts depends primarily on sorting, packing, grain shapes, and the boundary load conditions applied to the aggregate. Some critical contacts and, therefore, microfractures tend to join together in a series or “chain”. Orientations of chains are most strongly influenced by the direction of the maximum compressive load at the boundary of the aggregate. A hydrostatic load applied on the boundaries of an aggregate can cause microfracturing within grains. Orientations for microfractures and contact lines are random in poorly sorted aggregates, but they are influenced by packing in well sorted aggregates.Grains of cemented aggregates are more highly stressed at their centers than at contacts. By analogy, microfracture orientations depend strongly on the position of the greatest load axis and only slightly on the low-magnitude stress concentrations at contacts. These microfractures parallel the greatest principal stress trajectory in regions where the magnitude of the maximum stress difference is greatest. These observations lead to the conclusion that fractures in grains of cemented aggregates are also extension fractures and should exhibit a higher degree of preferred orientation than in uncemented counterparts.These conclusions hold when cementing materials have about the same elastic moduli as the grains. Cements may be so weak that the aggregate behaves as if it were uncemented in terms of microfracture fabric, or so stiff that the major part of the load is transmitted by the cement, and the composite is no longer an aggregate in the mechanical sense.  相似文献   

19.
In situ impedance spectroscopy in laboratory experiments at high pressure and temperature can provide crucial quantitative information on properties of rock materials at depth as well as on physical and chemical processes occurring in the deep Earth. We developed an experimental setup for in situ electrical impedance measurements in a piston-cylinder apparatus and applied it to study the kinetics of charge carriers and phase transformations in pyrophyllite and CaCO3 aggregates. From comparison with previous studies, we found that absolute values of electrical conductivity and pressure–temperature conditions for dehydration reactions in pyrophyllite and phase transformations in CaCO3 can be accurately determined using our setup. Dehydration of pyrophyllite significantly enhances the transport kinetics and the effect is more pronounced under undrained conditions than under drained conditions. When dehydroxylation and decomposition temperatures for pyrophyllite under undrained and drained conditions are combined, they appear independent of pressure rather than increasing with pressure as previously suggested. Electrical conductivity of CaCO3 varies with impurity content and grain size, and is most likely controlled by diffusion of oxygen along wet grain boundaries. When applied to the Earth, the results on pyrophyllite suggest that the increase in electrical conductivity in rocks that undergo dehydration should be taken into account in interpreting magnetotelluric surveys of regions with anomalously high conductivity found above subducting plates. The results on CaCO3 indicate that grain boundary transport controls the electrical conductivity in fine-grained calcite rocks; hence calcite mylonites may be detected using magnetotelluric methods. Order–disorder transformations, such as occurring in calcite, possibly affect the physical properties of rocks (e.g., rheology) by changing the kinetics of atomistic transport processes.  相似文献   

20.
Zones of increased concentration formed by a solvent flowing from a source are considered. A matehmatical model for forming such zones is proposed. It takes into account that such a zone is composed of a set of independent particles. Hence the distribution of a substance around the source can be explained by movement of an individual particle. In the model this movement is a continuous semi-Markov process with terminal stopping at some random point in space. Parameters of the process depend on the velocity field of the flow. Forward and backward partial differential equations for the distribution density of a random stopping point of the process are derived. The forward equation is investigated for the centrally symmetric case. Solutions of the equation demonstrate either a maximum or a local minimum at the source location. In the latter case a concentric ring around the source is formed. If different substances vary in their absorption rates, they can form separable concentration zones as a family of concentric rings.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号