Two Minkowski functionals were tested in the capacity of morphological descriptors to quantitatively compare the arrays of vertically-aligned graphene flakes grown on smooth and nanoporous alumina and silica surfaces....Two Minkowski functionals were tested in the capacity of morphological descriptors to quantitatively compare the arrays of vertically-aligned graphene flakes grown on smooth and nanoporous alumina and silica surfaces. Specifically, the Euler-Poincaré characteristic and fractal dimension graphs were used to characterize the degree of connectivity and order in the systems, i.e. in the graphene flake patterns of petal-like and tree-like morphologies on solid substrates, and meshlike patterns (networks) grown on nanoporous alumina treated in low-temperature inductivelycoupled plasma. It was found that the Minkowski functionals return higher connectivity and fractal dimension numbers for the graphene flakepatterns with more complex morphologies, and indeed can be used as morphological descriptors to differentiate among various configurations of vertically-aligned graphene flakes grown on surfaces.展开更多
Strong shock may induce complex processes in porous materials. We use the newly developed materialpoint-method to simulate such processes in an HMX-like material. To pick out relevant information, morphological charac...Strong shock may induce complex processes in porous materials. We use the newly developed materialpoint-method to simulate such processes in an HMX-like material. To pick out relevant information, morphological characterization is used to treat with the temperature map. Via the Minkowski funetional analysis the dynamics and thermodynamics of the shock wave reaction on porous HMX-like material are studied. The geometrical and topological properties of the ＂hot-spots＂ are revealed. Numerical results indicate that, shocks in porous materials are not simple jump states as classically viewed, but rather are a complex sequence of compressions and rarefactions. They cover a broad spectrum of states. We can use coarse-grained description to the wave series. A threshold value of temperature presents a Turing pattern dynamical procedure. A higher porosity is generally preferred when the energetic material needs a higher temperature for initiation. The technique of data analysis can be used to other physical quantities, for example, density, particle velocity, some specific stress, etc. From a series of studies along the line, one may get a large quantity of information for desiring the fabrication of material and choosing shock strength according to what needed is scattered or connected ＂hot-spots＂. PACS numbers： 05.70.Ln, 05 Key words： porous material 70.-a, 05.40.-a, 62.50.Ef shock wave, Minkowski functionals展开更多
The goal of much research in computational materials science is to quantify necessary morphological information and then to develop stochastic models which both accurately reflect the material morphology and allow one...The goal of much research in computational materials science is to quantify necessary morphological information and then to develop stochastic models which both accurately reflect the material morphology and allow one to estimate macroscopic physical properties. A novel method of characterizing the morphology of disordered systems is presented based on the evolution of a family of integral geometric measures during erosion and dilation operations. The method is used to determine the accuracy of model reconstructions of random systems. It is shown that the use of erosion/dilation operations on the original image leads to a more accurate discrimination of morphology than previous methods.展开更多
This paper shows some properties of symmetry function induced by a convex body in a normal linear space. Some relationships between symmetry function induced by a convex body and Minkowski functional of the convex bod...This paper shows some properties of symmetry function induced by a convex body in a normal linear space. Some relationships between symmetry function induced by a convex body and Minkowski functional of the convex body are presented.展开更多
Let pj ∈ N and pj ≥-1, j = 2,...,n be a fixed positive integer. In this paper a generalized Roper-Suffridge extension operator F（z） ={f（Z1）＋f＇（z1）} on Reinhardt domain is defined. Some different conditions f...Let pj ∈ N and pj ≥-1, j = 2,...,n be a fixed positive integer. In this paper a generalized Roper-Suffridge extension operator F（z） ={f（Z1）＋f＇（z1）} on Reinhardt domain is defined. Some different conditions for Pj areestablished under which the operator preserves an almost spirallike mapping of type fl and order a and spirallike mapping of type β and order α, respectively. In particular, our results reduce to many well-known results.展开更多
In terms of Caratheodory metric and Kobayashi metric, distortion theorems for biholomorphic convex mappings on bounded circular convex domains are given.
In this paper, we consider the following Reinhardt domains. Let M = （M1, M2,..., Mn） ： [0,1] → [0,1]^n be a C2-function and Mj（0） = 0, Mj（1） = 1, Mj″ 〉 0, C1jr^pj-1 〈 Mj′（r） 〈 C2jr^pj-1, r∈ （0, 1）, ...In this paper, we consider the following Reinhardt domains. Let M = （M1, M2,..., Mn） ： [0,1] → [0,1]^n be a C2-function and Mj（0） = 0, Mj（1） = 1, Mj″ 〉 0, C1jr^pj-1 〈 Mj′（r） 〈 C2jr^pj-1, r∈ （0, 1）, pj 〉 2, 1 ≤ j ≤ n, 0 〈 C1j 〈 C2j be constants. Define DM={z=（z1,z2,…,Zn）^T∈C^n：n∑j=1 Mj（｜zj｜）〈1}Then DM C^n is a convex Reinhardt domain. We give an extension theorem for a normalized biholomorphic convex mapping f ： DM -→ C^n.展开更多
文摘Two Minkowski functionals were tested in the capacity of morphological descriptors to quantitatively compare the arrays of vertically-aligned graphene flakes grown on smooth and nanoporous alumina and silica surfaces. Specifically, the Euler-Poincaré characteristic and fractal dimension graphs were used to characterize the degree of connectivity and order in the systems, i.e. in the graphene flake patterns of petal-like and tree-like morphologies on solid substrates, and meshlike patterns (networks) grown on nanoporous alumina treated in low-temperature inductivelycoupled plasma. It was found that the Minkowski functionals return higher connectivity and fractal dimension numbers for the graphene flakepatterns with more complex morphologies, and indeed can be used as morphological descriptors to differentiate among various configurations of vertically-aligned graphene flakes grown on surfaces.
基金Supported by Science Foundations of Laboratory of Computational Physics and China Academy of Engineering Physics under Grant Nos.2009A0102005 and 2009B0101012National Science Foundation of China under Grant Nos.10702010,10775018,and 10604010
文摘Strong shock may induce complex processes in porous materials. We use the newly developed materialpoint-method to simulate such processes in an HMX-like material. To pick out relevant information, morphological characterization is used to treat with the temperature map. Via the Minkowski funetional analysis the dynamics and thermodynamics of the shock wave reaction on porous HMX-like material are studied. The geometrical and topological properties of the ＂hot-spots＂ are revealed. Numerical results indicate that, shocks in porous materials are not simple jump states as classically viewed, but rather are a complex sequence of compressions and rarefactions. They cover a broad spectrum of states. We can use coarse-grained description to the wave series. A threshold value of temperature presents a Turing pattern dynamical procedure. A higher porosity is generally preferred when the energetic material needs a higher temperature for initiation. The technique of data analysis can be used to other physical quantities, for example, density, particle velocity, some specific stress, etc. From a series of studies along the line, one may get a large quantity of information for desiring the fabrication of material and choosing shock strength according to what needed is scattered or connected ＂hot-spots＂. PACS numbers： 05.70.Ln, 05 Key words： porous material 70.-a, 05.40.-a, 62.50.Ef shock wave, Minkowski functionals
文摘The goal of much research in computational materials science is to quantify necessary morphological information and then to develop stochastic models which both accurately reflect the material morphology and allow one to estimate macroscopic physical properties. A novel method of characterizing the morphology of disordered systems is presented based on the evolution of a family of integral geometric measures during erosion and dilation operations. The method is used to determine the accuracy of model reconstructions of random systems. It is shown that the use of erosion/dilation operations on the original image leads to a more accurate discrimination of morphology than previous methods.
基金Supported by the Natural Science Foundation of China（10771086） Supported by the Natural Science Foundation of Fujian Province（S0650021）
文摘This paper shows some properties of symmetry function induced by a convex body in a normal linear space. Some relationships between symmetry function induced by a convex body and Minkowski functional of the convex body are presented.
文摘Let pj ∈ N and pj ≥-1, j = 2,...,n be a fixed positive integer. In this paper a generalized Roper-Suffridge extension operator F（z） ={f（Z1）＋f＇（z1）} on Reinhardt domain is defined. Some different conditions for Pj areestablished under which the operator preserves an almost spirallike mapping of type fl and order a and spirallike mapping of type β and order α, respectively. In particular, our results reduce to many well-known results.
文摘In terms of Caratheodory metric and Kobayashi metric, distortion theorems for biholomorphic convex mappings on bounded circular convex domains are given.
基金the Natural Science Foundation of China (Grant No.10671194 and 10731080/A01010501)
文摘In this paper, we consider the following Reinhardt domains. Let M = （M1, M2,..., Mn） ： [0,1] → [0,1]^n be a C2-function and Mj（0） = 0, Mj（1） = 1, Mj″ 〉 0, C1jr^pj-1 〈 Mj′（r） 〈 C2jr^pj-1, r∈ （0, 1）, pj 〉 2, 1 ≤ j ≤ n, 0 〈 C1j 〈 C2j be constants. Define DM={z=（z1,z2,…,Zn）^T∈C^n：n∑j=1 Mj（｜zj｜）〈1}Then DM C^n is a convex Reinhardt domain. We give an extension theorem for a normalized biholomorphic convex mapping f ： DM -→ C^n.
