fractal

摘要： The“tailing”effect caused by residual non-aqueous phase liquids(NAPLs)in porous aquifers is one of the frontiers in pollution hydrogeology research.Based on the current knowledge that the residual NAPLs is mainly controlled by the pore structure of soil,this study established a method for evaluating the residual saturation of NAPLs by investigating the fractal dimension of porous media.In this study,the soil column experiments of residual light NAPLs(LNAPLs)in sandy aquifer with different ratios of sands and soil were carried out,and the correlation between the fractal dimension of the medium,the residual of LNAPLs and the soil structure parameters are statistically analyzed,and its formation mechanism and main control factors are discussed.The results show that:Under our experimental condition:(1)the fractal dimension of the medium has a positive correlation with the residual saturation of NAPLs generally,and the optimal fitting function can be described by a quadratic model:S_(R)=192.02 D2-890.73 D+1040.8;(2)the dominant formation mechanism is:Smaller pores in the medium is related to larger fractal dimension,which leads to higher residual saturation of NAPLs;stronger heterogeneity of the medium is related to larger fractal dimension,which also leads to higher residual saturation of NAPLs;(3)the micro capillary pores characterized by fine sand are the main controlling factors of the formation mechanism.It is concluded that both the theory and the method of using fractal dimension of the medium to evaluate the residual saturation of NAPLs are feasible.This study provides a new perspective for the research of“tailing”effect of NAPLs in porous media aquifer.

摘要： Nano or micro-scale particles are considered as a zero-dimensional material,and their shape is difficult to control.Here the crystal-like microparticles are formed,and the existence criterion of crystal-like low dimensional materials is established.The hydrothermal method is used to fabricate copper-1,3,5-phenyltricarboxylate(Cu-BTC)microparticles,which have a regular geometric shape with regular triangle,quadrangle and hexagon.The benzene ring and carboxyls(-COOH)attached to the benzene ring form two basic molecular structures of[Cu3(BTC)2]n,which play an essential role in the construction of a three-dimensional crystal-like structure.

摘要： This paper considers the thermoelastic beam system of type Ⅲ with friction dissipations acting on the whole system. By using the methods developed by Chueshov and Lasiecka, we get the quasi-stability property of the system and obtain the existence of a global attractor with finite fractal dimension. Result on exponential attractors of the system is also proved.

摘要： Based on the Fermat’s Last Theorem and the Po, P1 projections from the 4th space coordinate to the time variable for Po and to the remaining 3D space variables for P1, the carbon 12 nucleus is shown explicitly as given by the hard-sphere dense packing model that also satisfies the Gell-Mann standard model. It is through these that C12 is a vital element in all biomaterials, and all proteins as well as the Nitrogenous bases in DNAs, are of hexagon geometric structures. Furthermore, the unique presence of a 3D × 1D space void within the C12 nucleus provides for the monopole Boson field tunneling to occur, giving rise to the enormous variety spectra in the DNA of life forms. In addition, on the surface of the bio cells, the carbon valence band p electron excitation into the empty conduction band separated by a bandgap G, can result in HTC Excitonic induced superconductivity binding gaps from the Excitonic spectra, which match part of those of the DNA and thus produce the self-grow mechanism of numerous different cells in a life form.

摘要： To determine the type of surface roughness pattern that is suitable for adaptive suppression of the drag of an obstacle, we observed flow structures introduced by such obstacles. Several roughness patterns were tested: geometric patterns, fractal patterns, reptile-skin patterns, and patterns of circular cylinders arranged in a lattice and in a zigzag manner. A suitable pattern for adaptive control of flow is one that generates longitudinal vortices with nonconstant distances. The preferred instability mode of a laminar boundary layer is expected to be selected automatically from fluctuations involving many frequencies and caused by fractal patterns. Snake- and reptile-skin patterns may have a similar ability as fractal patterns because they consist of multiscale patterns. The longitudinal vortices generated from peculiar positions and concave corners in patterns were observed. The distance between these vortices is not constant because the onset of vortices is at concave corners in fractal patterns. These vortices have differing strengths and easily cause nonlinear interactions, so they can disturb a laminar boundary layer with several higher-harmonic frequencies. The velocity profiles of the laminar boundary-layer flow over the fractal patterns were measured by using hydrogen bubbles. The results show the down-wash flow between the longitudinal vortices, which means that the vortices may effectively suppress the boundary layer separation in an adverse pressure gradient.

摘要： This paper considers the thermoelastic beam system of type Ⅲ with friction dissipations acting on the whole system. By using the methods developed by Chueshov and Lasiecka, we get the quasi-stability property of the system and obtain the existence of a global attractor with finite fractal dimension. Result on exponential attractors of the system is also proved.

摘要： Starting from the 2D Euler equations for an incompressible potential flow, a dimension-reduced model describing deep-water surface waves is derived. Similar to the Shallow-Water case, the z-dependence of the dependent variables is found explicitly from the Laplace equation and a set of two one- dimensional equations in x for the surface velocity and the surface elevation remains. The model is nonlocal and can be formulated in conservative form, describing waves over an infinitely deep layer. Finally, numerical solutions are presented for several initial conditions. The side-band instability of Stokes waves and stable envelope solitons are obtained in agreement with other work. The conservation of the total energy is checked.

摘要： A consistent physical and mathematical model of the propagation of electromagnetic waves in an inhomogeneous medium with strong discontinuities of the electromagnetic field at the interface of two media, which is a rough surface, was developed. Mathematical modeling of rough surfaces and their profiles was carried out using fractal geometry, which allows us to display the topology of the object as close as possible to reality. For real heterogeneous rough structures, we have developed a through-counting method that takes into account the continuity of the total current at the interfaces of adjacent media, the effect of induced surface charge and surface current. This approach lets one avoid the necessity to set surface impedances depending on the structure of the field being determined and on the material properties.

摘要： This paper studies the exponential attractor for a class of the Kirchhoff-type equations with strongly damped terms and source terms. The exponential attractor is also called the inertial fractal set, which is an intermediate step between global attractors and inertial manifolds. Obtaining a set that attracts all the trajectories of the dynamical system at an exponential rate by the methods of Eden A. Under appropriate assumptions, we firstly construct an invariantly compact set. Secondly, showing the solution semigroups of the Kirchhoff-type equations is squeezing and Lipschitz continuous. Finally, the finite fractal dimension of the exponential attractor is obtained.

摘要： Texture analysis is important in several image segmentation and classification problems. Different image textures manifest themselves by dissimilarity in both the property values and the spatial interrelationships of their component texture primitives. We use this fact in a texture discrimination system. This paper focuses on how to apply texture operators based on co-occurrence matrix, texture filters and fractal dimension to the problem of object recognition and image segmentation.