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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Fractal solutions of multi-component systems of dispersive evolution equations
色散演化方程 多分量系统 分形解
2023/4/27
In this talk, we investigate the fractalization phenomena for the multi-component systems of the dispersive evolution equations on a bounded interval subject to the periodic boundary conditions. The e...
Performance-based fractal fracture model for complex fracture network simulation
Fractal geometry Fractal fracture model Complex fracture network characterization Contributing reservoir volume Refracturing
2018/4/2
The paper presents a novel hydraulic fracturing model for the characterization and simulation of the complex fracture network in shale gas reservoirs. We go beyond the existing method that uses planar...
The Grundy number of an impartial game G is the size of the unique Nim heap equal to G. We introduce a new variant of Nim,Restricted Nim, which restricts the number of stones a player may remove from ...
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...
Anisotropic covering of fractal sets
Anisotropic covering of fractal sets Pattern Formation and Solitons
2012/4/26
We consider the optimal covering of fractal sets in a two-dimensional space using ellipses which become increasingly anisotropic as their size is reduced. If the semi-minor axis is \epsilon and the se...
Fractal bodies invisible in 2 and 3 directions
Billiards invisible bodies shape optimization geometrical optics problems of minimal resistance
2011/9/22
Abstract: We study the problem of invisibility for bodies with a mirror surface in the framework of geometrical optics. We show that for any two given directions it is possible to construct a two-dime...
A generalized Young inequality and some new results on fractal space
Dfractal real line number system fractional set generalized Young inequality
2011/9/21
Abstract: Starting with real line number system based on the theory of the Yang's fractional set, the generalized Young inequality is established. By using it some results on the generalized inequalit...
Transport equations with fractal noise - existence, uniqueness and regularity of the solution
Stochastic partial differential equations Transport equation Nonsmooth coefficients Fractional Brownian noise
2011/9/15
Abstract: The main result of the present paper is a statement on existence, uniqueness and regularity for mild solutions to a parabolic transport diffusion type equation that involves a non-smooth coe...
Fractal curvature measures and Minkowski content for one-dimensional self-conformal sets
Fractal curvature measures Minkowski one-dimensional self-conformal sets
2011/2/28
We investigate intrinsic geometric properties of invariant sets of one-dimensional conformal iterated function systems. We show that for such a set F the fractal cur-vature measures exist, if and only...
A nonconventional strong law of large numbers and fractal dimensions of some multiple recurrence sets
strong law of large numbers nonconventional ergodic averages
2011/1/21
We provide conditions which yield a strong law of large num-bers for expressions of the form 1/N PN n=1 FX(q1(n)), · · · ,X(qℓ(n)) where X(n), n 0’s is a sufficiently fast mixing ve...
A Fractal Example of a Continuous Monotone Function with Vanishing Derivatives on a Dense Set and Infinite Derivatives on Another Dense Set
Sierpinki Gasket harmonic function
2011/6/2
Inspired by the theory of analysis on fractals, we construct an example of a continuous, monotone function on an interval, which has vanishing derivatives on a dense set and infinite derivatives on an...
Time-Evolution of a Fractal Distribution: Particle Concentrations in Free-Surface Turbulence
Fluid Dynamics (physics.flu-dyn) Chaotic Dynamics (nlin.CD)
2010/11/11
Steady-state turbulence is generated in a tank of water and the trajectories of particles forming a compressible system on the surface are tracked in time. The initial uniformly distributed floating p...
Universal fractal scaling of self-organized networks
Universal fractal scaling self-organized networks
2010/11/10
There is an abundance of literature on complex networks describing a variety of relationships among units in social, biological, and technological systems. Such networks, consisting of interconnected ...
Furstenberg sets for a fractal set of directions
Furstenberg sets Hausdorff dimension dimension function
2010/11/29
In this note we study the behavior of the size of Fursten-berg sets with respect to the size of the set of directions defining it. For any pair α, β 2 (0, 1], we will say that a set E R2 is an F -s...
We study some properties of a class of random connected planar fractal sets induced by a
Poissonian scale-invariant and translation-invariant point process. Using the second-moment
method, we show t...