93 resultados para Structure-Mapping Theory

em Chinese Academy of Sciences Institutional Repositories Grid Portal


Relevância:

90.00% 90.00%

Publicador:

Resumo:

We investigate the decomposition of noncommutative gauge potential (A) over cap (i), and find that it has inner structure, namely, (A) over cap (i) can he decomposed in two parts, (b) over cap (i) and (a) over cap (i), where (b) over cap (i) satisfies gauge transformations while (a) over cap (i) satisfies adjoint transformations, so close the Seiberg-Witten mapping of noncommutative, U(1) gauge potential. By, means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U(1) gauge potential and its gauge field tensor can be expressed in terms of the unit vector field. When the unit vector field has no singularity point, noncommutative gauge potential and gauge field tensor will equal ordinary gauge potential and gauge field tensor

Relevância:

80.00% 80.00%

Publicador:

Resumo:

拟南芥ast (anthocyanin spotted testa) 突变体是由碳离子束诱导产生的与花青苷生物合成有关的突变体,受单隐性核基因控制。由于花青苷的异常积累,突变体未成熟种子的种皮呈现紫红色的斑点;野生型植株幼嫩的种皮没有花青苷的异常积累,呈淡绿色。初步作图分析表明,AST基因定位于拟南芥第I号染色体上,并且位于SSLP分子标记nga280和CAPS分子标记PAB5之间。 AST基因与SSLP分子标记nga280紧密连锁,遗传距离为3.2cM;与CAPS分子标记PAB5相距较远,遗传距离为21.1cM。 采用DDRT-PCR的策略,分析野生型与突变型植株未成熟角果中基因表达的差异。通过调整DDRT-PCR中总RNA、锚定引物、随机引物、cDNA和dNTP等关键试剂的用量,优化了适用于银染检测的DDRT-PCR方法。PCR扩增产物经6%变性聚丙烯酰胺凝胶垂直电泳分离后,银染能检测到多而清晰的条带。泳道中的条带数最少为40个,最多达80个,平均为60个,条带大小分布在100bp-900bp范围,银染的灵敏度为5pg/mm2。此方法操作简便快速,灵敏度高,重复性好。采用这个改良的的方法,分析了拟南芥野生型和ast突变型植株未成熟角果中16,000个cDNA扩增产物条带,从中筛选出28个差异条带。二次PCR扩增后,进一步筛选出10个差异表达的cDNA条带,其中6个是野生型特异表达的,4个是突变型特异表达的。对这10个差异片段进行测序。BLASTN分析表明,这10个差异表达的cDNA片段与数据库中花青苷生物合成途径中的结构基因和调节基因序列没有同源性,表明用DDRT-PCR的方法克隆特定的AST基因有一定的局限性。 利用图位克隆(map-based cloning)的策略,对拟南芥AST 基因进行克隆。根据拟南芥数据库中的SNPs (simple nucleotide polymophisms) 序列和插入/缺失多态性(insertion/deletion polymorphisms)序列,设计了一系列分子标记。利用这些分子标记,对600个F2代有突变表型的植株进行重组子筛选,完成了对拟南芥AST基因的精细作图,成功地将AST 基因定位到BAC克隆T13M11上。初步确定该BAC克隆中的基因T13M11.8 可能是AST基因。该基因的DNA序列长1432bp,含有6个外显子和5个内含子,编码的蛋白与花青苷生物合成途径中的二氢黄酮醇4-还原酶有较高的同源性。功能互补实验正在进行当中。

Relevância:

80.00% 80.00%

Publicador:

Resumo:

The properties of Rashba wave function in the planar one-dimensional waveguide are studied, and the following results are obtained. Due to the Rashba effect, the plane waves of electron with the energy E divide into two kinds of waves with the wave vectors k(1)=k(0)+k(delta) and k(2)=k(0)-k(delta), where k(delta) is proportional to the Rashba coefficient, and their spin orientations are +pi/2 (spin up) and -pi/2 (spin down) with respect to the circuit, respectively. If there is gate or ferromagnetic contact in the circuit, the Rashba wave function becomes standing wave form exp(+/- ik(delta)l)sin[k(0)(l-L)], where L is the position coordinate of the gate or contact. Unlike the electron without considering the spin, the phase of the Rashba plane or standing wave function depends on the direction angle theta of the circuit. The travel velocity of the Rashba waves with the wave vector k(1) or k(2) are the same hk(0)/m*. The boundary conditions of the Rashba wave functions at the intersection of circuits are given from the continuity of wave functions and the conservation of current density. Using the boundary conditions of Rashba wave functions we study the transmission and reflection probabilities of Rashba electron moving in several structures, and find the interference effects of the two Rashba waves with different wave vectors caused by ferromagnetic contact or the gate. Lastly we derive the general theory of multiple branches structure. The theory can be used to design various spin polarized devices.

Relevância:

80.00% 80.00%

Publicador:

Resumo:

现有的机器人自适应控制基本上都是在建立机器人线性化的动力学模型的基础上,采用某种显式或隐式参数辨识的方法,在线地修正控制作用.本文针对机器人运动和动力学参数变化的固有特点,提出一种完全不同的自学习自适应方法.这种方法基于智能机器人分级系统中的两级结构,并且在空间域里而不是在时间域里处理机器人参数的变化.把机器人的作业空间划分成子空间,其中包括重力载荷的作用,每个子空间对应一组控制器.规划的轨迹映射到作业空间形成子空间序列.用自学习方法选择与这个序列对应的最佳控制器序列.该方法算法简单,计算量小.避开了通常的自适应方法遇到的一系列困难问题.

Relevância:

80.00% 80.00%

Publicador:

Resumo:

In the complex structure areas, velocity field building and structure mapping are important for seismic exploration. With the development of seismic exploration, the methods of structure mapping, reservoir prediction and reservoir description all require high precious velocity field. And more accurate depth-structure maps are required for well site design. Aiming at the problems and defects in velocity analysis and structure mapping in oil seismic exploration, the paper which is based on the studies of real data in several areas combines the theories with practical application, and analyzes the precision and applicability of several methods of velocity model building. After that, the following methods are mainly studied: the coherence inversion methods based on the pre-stack CMP gathers or stacking velocity; the interval velocity inversion methods constrained by multi-well; the Random Simulation method; 3D Image Ray Map Migration method and the structure mapping in floating datum and in fixed datum, and then we conclude the method of building high precious seismic velocity field and structure mapping with variable velocity. Firstly, the paper analyses the distributing rule of the velocity variation in the areas with complex structures in the northwest of China, then points out that velocity is a crucial factor which influences the precision of structure mapping, and the velocity variations have something to do with the shapes of the structures, the variety of lithology and so on. The key point of improving the precision of seismic velocity field is to obtain a structure mapping with high precision. We also describe the range and conditions of these methods. Secondly, by comparing many popular methods of velocity model building, we propose a new method in the use of velocity model building. The new method is more effective in velocity model building under every kind of complex condition and is worthy of spreading. At last, the paper fingers out that it is a system engineering to study variable velocity mapping in every kind of complex structure areas. Every step of the work can affect the final results. So it is important to build high efficient and practical velocity model and the flows of mapping processing. The paper builds the flows and gives some examples. The method has been applied in more than ten exploring surveys. The application proves that this method could bring good effect on researching on low-amplitude trap, reservoir prediction, reservoir description and the integrated research of oil&gas geology. Keywords: structure mapping velocity model building complex structure variable velocity media

Relevância:

80.00% 80.00%

Publicador:

Resumo:

Firstly, established sequence stratigraphy of Sinian System-Middle Triassic Series framework in Sichuan basin,be divided into 21 second-level sequence stratigraphy and 105 third-level sequence stratigraphy.From many aspects,discussed sequence stratigraphy characteristic. On the foundation of structure unconformity and fission track analysis, on the ground of An county-Shuinin county regional seismic section, using the positive evolution equilibrium principle technology, comprehensivly be mapped structure evolution of Sichuan basin. It can be divided into seven stages, that is :Pre-Sinian basement stage, cratonic depression basin(Z1-S)stage, cratonic rifted basin(D-T2)stage, passive continental margin(T3x1-3)stage, foreland basin(T3x4-6)stage, depression basin (Jurassic Period-Miocene Epoch) stage, formed basin (Holocene Epoch) stage. Analysis on structure evolution history,burial history,source rocks thermal evolution history, Maoba changxing formation gas pool forming process can be classified into four stages: ancient lithological oil pool stages in Indosinian-early Yanshanian period(T-J1-2), ancient structure- lithological gas pool stages in middle Yanshanian period(J3-K1), structure- lithological gas pool setting stages in last Yanshanian period(K2), structure- lithological gas pool adjusting and transformation stages in Himalayan period(R-Q). Maoba feixianguan formation gas pool forming process can be classified into two stages: second structure gas pool stages in last Yanshanian period(K2),second structure gas pool physical adjusting and transformation stages in Himalayan period(R-Q),and summarize reservoir formation model. On the base of newest exploration achievement and petroleum geologic comprehensive research , demonstrate how structure controls hydrocarbon accumulation. Structure controlling source rocks behaves structure controlling main source rocks’sedimentary facies, medium-large pools mainly located at center or margin of hydrocarbon generation. Structure controlling palaeo-karst reservoirs ,reef and beach facies reservoirs, fault and fracture reservoirs. Structure controlling palaeo-uplift, and palaeo-uplift controlling hydrocarbon migration, active reservoirs’forming, palaeo-structure traps forming. Structure controls distribution of mudstone and gypsolith, controls preservation. Structure controls hydrocarbon conducting, structure traps forming and hydrocarbon accumulation. Whether or no, Structure controls total process of basin forming-source rocks’generation- hydrocarbon accumulation. It is direct effect results of structure movements that large traps’ conditions, conducting migration conditions, high quality preservation. source rocks’condition and reservoirs’ condition are the indirect effect results. In the last analysis, “source rock controlling theory”, “high quality reservoir mainly controlling theory”, “palaeo-uplift controlling theory” and “current structure deciding theory” are structure controlling hydrocarbon accumulation. There are high variability and complex mechanisms in Sichuan basin , but the regional hydrocarbon accumulation conditions are very well, such as abundant source rocks, matching process of hydrocarbon accumulation and many exploration areas. By means of integrated analysis, put forward hydrocarbon exploration direction and large-middle targets of China Petroleum and Chemical Corporation .Thus, more and more hydrocarbon proved reserve and output in Sichuan basin will be contributed to China energy industry in a long future time.

Relevância:

80.00% 80.00%

Publicador:

Resumo:

When used in the determining the total electron content (TEC), which may be the most important ionospheric parameter, the worldwide GPS observation brings a revolutionary change in the ionospheric science. There are three steps in the data processing to retrieve GPS TEC: (1) to estimate slant TEC from the measurements of GPS signals; (2) to map the slant TEC into vertical; and (3) to interpolate the vertical TEC into grid points. In this scientific dissertation we focus our attention on the second step, the mapping theory and method to convert slant TEC into vertical. This is conventionally done by multiplying on the slant TEC a mapping function which is usually determined by certain models of electron density profile. Study of the vertical TEC mapping function is of significance in GPS TEC measurement. This paper first reviews briefly the three steps in GPS TEC mapping process. Then we compare the vertical TEC mapping function which were respectively calculated from the electron density profiles of the ionospheric model and retrieved from the observation of worldwide GPS TEC. We also perform the statistical analysis on the observational mapping functions. The main works and results are as follows: 1. We calculated the vertical TEC mapping functions for both SLM and Chapman models, and discussed the modulation of the ionosphere height to the mapping functions. We use two simple models, single layer model (SLM) and Chapman models, of the ionospheric electron density profiles to calculate the vertical TEC mapping function. In the case of the SLM, we discuss the control of the ionospheric altitude, i.e., the layer height hipp, to the mapping function. We find that the mapping function decreases rapidly as hipp increases. For the Chapman model we study also the control mapping function by both ionospheric altitude indicated by the peak electron density height hmF2, and the scale height, H, which present the thickness of the ionosphere. It is also found that the mapping function decreases rapidly as hmF2 increases. and it also decreases as H increases. 2. Then we estimate the mapping functions from the GPS observations and compare them with those calculated from the electron density models. We first, proposed a new method to estimate the mapping functions from GPS TEC data. This method is then used to retrieve the observational mapping function from both the slant TEC (TECS) provided by International GPS Service (IGS)and vertical TEC provide by JPL Global Ionospheric Maps (GIMs). Then we compare the observational mapping function with those calculated from the electron density models, SLM and Chapman. We find that the values of the observational mapping functions are much smaller than that from the model mapping functions, when the zenith angle is large enough. We attribute this to the effect of the plasmasphere which is above about 1000 km. 3. We statistically analyze the observational mapping functions and reveal their climatological changes. Observational mapping functions during 1999-2007 are used in our statistics. The main results are as follows. (1) The observational mapping functions decrease obviously with the decrement of the solar activity which is represented by the F10.7 index; (2) In annual variations of the observational mapping functions, the semiannual component is found at low-latitudes, and the remarkable seasonal variations at mid- and high-latitudes. (3) The diurnal variation of the observational mapping functions is that they are large in daytime and small at night, they become extremely small in the early morning before sunrise. (4) The observational mapping functions change with latitudes that they are smaller at lower latitudes and larger at higher. All of the above variations of the observational mapping functions are explained by the existence of the plasmasphere, which changes more slowly with time and more rapidly with latitude than the ionosphere does . In summary, our study on the vertical TEC mapping function imply that the ionosphere height has a modulative effect on the mapping function. We first propose the concept of the 'observational mapping functions' , and provide a new method to calculate them. This is important in improving the TEC mapping. It may also possible to retrieving the plasmaspheric information from GPS observations.

Relevância:

80.00% 80.00%

Publicador:

Resumo:

The engineering geological properties of Neogene hard clays and related engineering problems are frontiers in the fields of Engineering Geology, Soil Mechanics and Rock Mechanics. Recently, it has been recognized that Neogene hard clay is the intermediate type of material between the soil and the rock. Many aspects of them, such as sampling, testing, calculating and engineering process, are special, which could not be researched by means of theories and methods of traditional Soil Mechanics of Rock Mechanics. In order to get real knowledge and instruct the engineering practice, intersect studying of multiple disciplines, including Engineering Geology, Soil Mechanics and Rock Mechanics, etc., is necessary. Neogene hard clay is one of the important study objects of regional problem rocks & soils in our country, which extensively distributed in China, especially in Eastern China. Taking the related areas along the middle line of the Project of Transferring Water from the South to the North (e.g. Nanyang basin, Fangcheng-Baofeng area and Handan-Yongnian area), South-west of Shandong, Xu-Huai area and Beijing area, etc. as main study areas, the paper divided Neogene hard clays into reduction environment dominated origin and oxidation environment dominated origin, which distributed on areas western and eastern to Mount Taihangshan respectively. Intermediate types are also existed in some areas, which mainly distribute near the edges of depositional basins; they are usually of transitions between diluvial and lacustrine deposits. As to Neogene hard clays from Eastern China, the clay particle content is high, and montmorillonite or illite/montmorillonite turbostratic mineral is the dominating clay mineral. The content of effective montmorillonite is very high in each area, which is the basis for the undesirable engineering properties of Neogene hard clays. For hard clays from the same area, the content of effective montmorillonite in gray-greenish hard clay is much higher than that in purple-brownish or brown-yellowish hard clay, which is the reason why the gray-greenish hard clay usually has outstanding expansive property. On the other hand, purple-brownish or brown-yellowish hard clay has relatively less montmorillonite, so its property is better. All of these prove that the composition (clay mineral) of Neogene hard clay is the control factor for the engineering properties. Neogene hard clays have obvious properties such as fissured, overconsolidated and expansive, which are the main reasons that many engineering problems and geological harzards usually occur in Neogene hard clays. The paper systematically elaborates the engineering properties of Neogene hard clays from Eastern China, analyses the relationships between engineering properties and basic indexes. The author introduces the ANN method into the prediction of engineering property indexes of hard clays, which provides a new way for quantitatively assessment and prediction of engineering property indexes. During investigation in the field, the author found that there exists obvious seam-sheared zone between different hard clays in Miocene Xiacaowan formation in Xu-Huai area. Similar phenomenon also exists near the borderline between Neogene hard clays and underlying coal measures in the Southwest of Shandong province, which could be observed in the cores. The discovery of seam-sheard zone has important theoretical and practical significance for engineering stability analysis and revealing the origin of fissures in Neogene hard clays. The macrostructure, medium structure and microstructure together control the engineering properties of hard clays. The author analyses and summarizes the structural effects on hard clays in detail. The complex of the strength property of hard clays is mostly related to the characteristics of fissures, which is one of the main factors that affect the choice of shear strength parameters. So structure-control theory must be inseparably combined with composition-control theory during the engineering geological and rock/soil mechanics research of hard clays. The engineering properties, such as fissured, overconsolidated and expansive, control the instability of engineering behaviors of Neogene hard clays under the condition of excavation, i.e. very sensitive to the change of existence environment. Based on test data analysis, the author elaborates the effects of engineering environment change on the engineering properties. Taking Nanyang basin as example, the author utilizes FEM to study the effects of various factors on stability of cutting canal slopes, than sets forth the characteristics, development laws and formation mechanism of the deformation and failure of hard clay canal slopes, summarizes the protection and reinforcement principles, as well as the protection and remedy steps. On the basis of comparison of engineering properties of domestic and foreign Neogene muddy deposits, in the view of whole globe and associated with the geological characteristics of China, the paper demonstrates that the intermediate type of the material between the soil and the rock, named "hard clay/soft rock", which can not be separated abruptly, really exists in China. The author has given a preliminary classification based on its geological origin and distribution law, which is very significant for promoting the mixture of Engineering Geology, Soil Mechanics and Rock Mechanics. In the course of large scales engineering construction in China, many engineering experiences and testing data are gained, summarizing these testing results and automatically managing them with computer technology are very necessary. The author develops a software named "Hard Clay-Soft Rock Engineering Geological Information Management and Analysis System (HRGIMS)", realizes the automatic and visual management of geo-engineering information, on the basis of information management, the functions of test data analysis and engineering property prediction are strengthened. This system has well merits for practice and popularization.

Relevância:

80.00% 80.00%

Publicador:

Resumo:

As a marginal subject, dynamic responses of slopes is not only an important problem of engineering geology (Geotechnical problem), but also of other subjects such as seismology, geophysics, seismic engineering and engineering seismic and so on. Owning to the gulf between different subjects, it is arduous to study dynamic responses of slopes and the study is far from ripeness. Studying on the dynamic responses of slopes is very important in theories as well as practices. Supported by hundreds of bibliographies, this paper systemically details the development process of this subject, introduces main means to analyze this subject, and then gives brief remarks to each means respectively. Engineering geology qualitative analysis is the base of slopes dynamic responses study. Because of complexity of geological conditions, engineering geology qualitative analysis is very important in slopes stability study, especially to rock slopes with complex engineering geology conditions. Based on research fruits of forerunners, this paper summarizes factors influencing slopes dynamic stability into five aspects as geology background, stratums, rock mass structure, and topography as well as hydrogeology condition. Based on rock mass structure controlling theory, engineering geology model of the slope is grouped into two typical classes, one is model with obvious controlling discontinuities, which includes horizontal bedded slope, bedding slope, anti-dip slope, slide as well as slope with base rock and weathered crust; the other is model without obvious controlling discontinuities, which includes homogeneous soil slope, joint rock mass slope. Study on slope failure mechanism under dynamic force, the paper concludes that there are two effects will appear in slope during strong earthquake, one is earthquake inertia force, the other is ultra pore pressure buildup. The two effects lead to failure of the slope. To different types of slope failure, the intensity of two effects acting on the slope is different too. To plastic flow failure, pore pressure buildup is dominant; to falling rock failure and toppling failure, earthquake inertia force is dominant in general. This paper briefly introduces the principle of Lagrangian element method. Through a lot of numerical simulations with FLAC3D, the paper comprehensively studies dynamic responses of slopes, and finds that: if the slope is low, displacement, velocity and acceleration are linear enlarging with elevation increasing in vertical direction; if the slope is high enough, displacement, velocity and acceleration are not linear with elevation any more, on the other hand, they fluctuate with certain rhythm. At the same time, the rhythm appears in the horizontal direction in the certain area near surface of the slope. The distribution form of isoline of displacement, velocity and acceleration in the section of the slope is remarkably affected by the slope angle. In the certain area near the slope surface, isoline of displacement, velocity and acceleration is parallel to the surface of the slope, in the mean time, the strike direction of the extreraum area is parallel to the surface of the slope too. Beyond this area, the isoline direction and the strike direction of the extremum area turn to horizontal with invariable distance. But the rhythm appearing or not has nothing to with the slope angle. The paper defines the high slope effect and the low slope effect of slopes dynamic responses, discusses the threshold height H^t of the dynamic high slope effect, and finds that AW is proportional to square root of the dynamic elastic moduli El P , at the same time, it is proportional to period Tof the dynamic input. Thus, the discriminant of H^t is achieved. The discriminant can tell us that to a slope, if its height is larger than one fifth of the wavelength, its response regular will be the dynamic high slope effect; on the other hand, its response regular will be the dynamic low slope effect. Based on these, the discriminant of different slopes taking on same response under the same dynamic input is put forward in this paper. At the same time, the paper studies distribution law of the rhythm extremum point of displacement, velocity and acceleration, and finds that there exists relationship of N = int among the slope height H, the number of the rhythm extremum VHlhro) point N and ffthre- Furthermore, the paper points out that if N^l, the response of the slope will be dynamic high slope effect; \fN

Relevância:

40.00% 40.00%

Publicador:

Resumo:

Photoelectron angular distributions produced in above-threshold ionization (ATI) are analysed using a nonperturbative scattering theory. The numerical results are in good qualitative agreement with recent measurements. Our study shows that the origin of the jet-like structure arises from the inherent properties of the ATI process and not from the angular momentum of either the initial or the excited states of the atom.

Relevância:

40.00% 40.00%

Publicador:

Resumo:

The Hamiltonian of the wurtzite quantum dots in the presence of an external homogeneous magnetic field is given. The electronic structure and optical properties are studied in the framework of effective-mass envelope function theory. The energy levels have new characteristics, such as parabolic property, antisymmtric splitting, and so on, different from the Zeeman splitting. With the crystal field splitting energy Delta(c)=25 meV, the dark excitons appear when the radius is smaller than 25.85 A in the absence of external magnetic field. This result is more consistent with the experimental results reported by Efros [Phys. Rev. B 54, 4843 (1996)]. It is found that dark excitons become bright under appropriate magnetic field depending on the radius of dots. The circular polarization factors of the optical transitions of randomly oriented dots are zero in the absence of external magnetic field and increase with the increase of magnetic field, in agreement with the experimental results. The circular polarization factors of single dots change from nearly 0 to about 1 as the orientation of the magnetic field changes from the x axis of the crystal structure to the z axis, which can be used to determine the orientation of the z axis of the crystal structure of individual dots. The antisymmetric Hamiltonian is very important to the effects of magnetic field on the circular polarization of the optical transition of quantum dots.

Relevância:

40.00% 40.00%

Publicador:

Resumo:

Based on the effective-mass model and the mean-field approximation, we investigate the energy levels of the electron and hole states of the Mn-doped ZnO quantum wires (x=0.0018) in the presence of the external magnetic field. It is found that either twofold degenerated electron or fourfold degenerated hole states split in the field. The splitting energy is about 100 times larger than those of undoped cases. There is a dark exciton effect when the radius R is smaller than 16.6 nm, and it is independent of the effective doped Mn concentration. The lowest state transitions split into six Zeeman components in the magnetic field, four sigma(+/-) and two pi polarized Zeeman components, their splittings depend on the Mn-doped concentration, and the order of pi and sigma(+/-) polarized Zeeman components is reversed for thin quantum wires (R < 2.3 nm) due to the quantum confinement effect.

Relevância:

40.00% 40.00%

Publicador:

Resumo:

A theoretical model for the electronic structure of porous Si is presented. Three geometries of porous Si (wire with square cross section, pore with square cross section, and pore with circular cross section) along both the [001] and [110] directions are considered. It is found that the confinement geometry affects decisively the ordering of conduction-band states. Due to the quantum confinement effect, there is a mixing between the bulk X and GAMMA states, resulting in finite optical transition matrix elements, but smaller than the usual direct transition matrix elements by a factor of 10(-3). We found that the strengths of optical transitions are sensitive to the geometry of the structure. For (001) porous Si the structure with circular pores has much stronger optical transitions compared to the other two structures and it may play an important role in the observed luminescence. For this structure the energy difference between the direct and the indirect conduction-band minima is very small. Thus it is possible to observe photoluminescence from the indirect minimum at room temperature. For (110) porous Si of similar size of cross section the energy gap is smaller than that of (001) porous Si. The optical transitions for all three structures of (110) porous Si tend to be much stronger along the axis than perpendicular to the axis.