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中国地质大学科学技术发展院夏宇轩（博士生）,蔡建超等地空学院 2018, FRACTALS-COMPLEX GEOMETR（图）Y PATTERNS AND SCALING IN NATURE AND SOCIETY, A NEW METHOD FOR CALCULATING FRACTAL DIMENSIONS OF POROUS MEDIA BASED ON PORE SIZE DISTRIBUTION
分形；毛细管；假设的；计算；多孔介质；孔隙空间；迂曲度；分形维数
2021/10/21
日前，2018级博士研究生夏宇轩在国际学术期刊《分形》发表题为《一种基于多孔介质孔径分布的分形维数新计算方法》的论文，入选Mathematics学科领域高被引论文。在该论文中，夏宇轩提出了一种基于分形毛细管假设的计算多孔介质孔隙空间和迂曲度分形维数的新方法。
We identify and characterize a new class of fingering instabilities in liquid metals; these instabilities are unexpected due to the large interfacial tension of metals. Electrochemical oxidation lower...
When Harry Potter first went to Hogwarts, he caught his train from Kings Cross, platform 9¾.The idea of a platform between two whole numbers might seem impossible to imagine. However, for someone...
WEAK UNCERTAINTY PRINCIPLE FOR FRACTALS,GRAPHS AND METRIC MEASURE SPACES
Uncertainty principle p.c.f. fractal Heisenberg’s inequality measure metric spaces Poincar′ e inequality self-similar graphs Sierpinski ′ gasket uniform finitely ramified graphs
2015/12/10
We develop a new approach to formulate and prove the weak uncertainty inequality which was recently introduced by Okoudjou and Strichartz.We assume either an appropriate measure growth condition with ...
Fractals, coherent states and self-similarity induced noncommutative geometry
self-similarity fractals squeezed coherent states noncommutative geometry dissipation
2012/6/30
The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the $q$-deformed algebra of coherent states. Self-similar structures are relate...
Mean value properties of harmonic functions on Sierpinski gasket type fractals
Sierpinski gasket Laplacian harmonic function mean value property analysis on fractals
2012/6/27
In this paper, we establish an analogue of the classical mean value property for both the harmonic functions and some general functions in the domain of the Laplacian on the Sierpinski gasket. Further...
Hodge-de Rham Theory on Fractal Graphs and Fractals
Analysis on fractals Sierpinski gasket Hodge-deRham theory k-forms harmonic 1-forms fractal graphs
2012/6/25
We present a new approach to the theory of k-forms on self-similar fractals. We work out the details for two examples, the standard Sierpinski gasket and the 3-dimensional Sierpinski gasket, but the m...
Codes as fractals and noncommutative spaces
noncommutative spaces Codes Information Theory
2011/9/22
Abstract: We consider the CSS algorithm relating self-orthogonal classical linear codes to q-ary quantum stabilizer codes and we show that to such a pair of a classical and a quantum code one can asso...
Fractals and log-periodic corrections applied to masses and energy levels of several nuclei
Fractals log-periodic corrections masses energy levels of several nuclei
2011/8/3
Abstract: A contribution is presented to the application of fractal properties and log-periodic corrections to the masses of several nuclei (isotopes or isotones), and to the energy levels of some nuc...
The Art of Space Filling in Penrose Tilings and Fractals
Art Space Penrose Tilings and Fractals
2011/9/14
Incorporating designs into the tiles that form tessellations presents an interesting challenge for artists. Creating a viable MC Escher like image that works esthetically as well as functionally requi...
Electromagnetism on Anisotropic Fractals
Electromagnetism Anisotropic Fractals Mathematical Physics
2011/7/26
Abstract: We derive basic equations of electromagnetic fields in fractal media which are specified by three indepedent fractal dimensions {\alpha}_{i} in the respective directions x_{i} (i=1,2,3) of t...
Derivations and Dirichlet forms on fractals
Fredholm module derivation metric space Dirichlet form finitely ramified fractal
2011/7/27
Abstract: We study derivations and Fredholm modules on metric spaces with a local regular conservative Dirichlet form. In particular, on finitely ramified fractals, we show that there is a non-trivial...
Generalized Hyperspaces and Non-Metrizable Fractals
Generalized Hyperspaces Non-Metrizable Fractals
2010/11/23
Much of the structure in metric spaces that allows for the creation of fractals exists in more generalized non-metrizable spaces. In particular the same theorems regarding the behavior of compact set...
Estimates for the resolvent kernel of the Laplacian on p.c.f. self similar fractals and blowups
resolvent kernel Laplacian on p.c.f. self similar fractals blowups
2010/12/14
One of the main features of analysis on post-critically finite self-similar (pcfss) sets is
that it is possible to understand the behavior of the Laplacian and its inverse, the Green
operator, in te...
Lipschitz-Killing curvatures of self-similar random fractals
self-similar random fractals curvatures Minkowski content
2010/12/15
For a large class of self-similar random sets F in Rd geometric parameters Ck(F), k = 0, . . . , d, are introduced. They arise as a.s. (average or essential) limits of the volume Cd(F(")), the surface...