The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Huaxin Lin - One of the best experts on this subject based on the ideXlab platform.
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minimal dynamical systems on the product of the Cantor Set and the circle
Communications in Mathematical Physics, 2005Co-Authors: Huaxin Lin, Hiroki MatuiAbstract:We prove that a crossed product algebra arising from a minimal dynamical system on the product of the Cantor Set and the circle has real rank zero if and only if the Set of invariant measures of the system come from the associated Cantor minimal system. In the case that cocycles take values in the rotation group, it is also shown that this condition implies tracial rank zero, and in particular, the crossed product algebra is isomorphic to a unital simple AT-algebra of real rank zero. Under the same assumption, we show that two systems are approximately K-conjugate if and only if there exists a sequence of isomorphisms between two associated crossed products which approximately maps Open image in new window
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minimal dynamical systems on the product of the Cantor Set and the circle
arXiv: Operator Algebras, 2004Co-Authors: Huaxin Lin, Hiroki MatuiAbstract:We prove that a crossed product algebra arising from a minimal dynamical system on the product of the Cantor Set and the circle has real rank zero if and only if that system is rigid. In the case that cocycles take values in the rotation group, it is also shown that rigidity implies tracial rank zero, and in particular, the crossed product algebra is isomorphic to a unital simple AT-algebra of real rank zero. Under the same assumption, we show that two systems are approximately $K$-conjugate if and only if there exists a sequence of isomorphisms between two associated crossed products which approximately maps $C(X\times \T)$ onto $C(X\times \T)$.
Dusan Krajcinovic - One of the best experts on this subject based on the ideXlab platform.
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random Cantor Set models for the elastic perfectly plastic contact of rough surfaces
Wear, 1996Co-Authors: Thomas L Warren, Dusan KrajcinovicAbstract:The objective of this study was to formulate discrete and continuous spatial models to describe the elastic-perfectly plastic deformation of two rough surfaces in contact. The two surfaces in contact are assumed to exhibit fractal behavior and are modeled as an effective fractal surface compressed into a smooth rigid substrate. The rough self-affine fractal structure of the effective surface is approximated by a random Cantor Set representation embedded in two dimensions. Both of the proposed models admit analytical solutions whether the plastic deformation is volume conserving or not. Presented results illustrate the effects that volume conservation and initial surface structure have on the elastic-perfectly plastic deformation process. The results from the continuous model are compared with the results obtained from the discrete model, and existing experimental load displacement data for the deformation of a bead-blasted steel surface.
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fractal models of elastic perfectly plastic contact of rough surfaces based on the Cantor Set
International Journal of Solids and Structures, 1995Co-Authors: Thomas L Warren, Dusan KrajcinovicAbstract:Abstract The objective of this study was to formulate discrete and continuous models to describe the elastic-perfectly plastic deformation of two rough surfaces in contact. The two surfaces in contact are assumed to exhibit fractal behavior and are modeled as an effective fractal surface compressed into a smooth rigid substrate. The rough self-affine fractal structure of the effective surface is approximated using a Cantor Set representation. Both of the proposed models admit analytical solutionś for the cases when the plastic deformation is volume conserving or not. Results are presented that illustrate the effects that volume conservation and initial surface structure have on the elastic-perfectly plastic deformation process. The results from the continuous model are compared with the results obtained from the discrete model, and also with existing experimental load displacement results for the deformation of a ground steel surface.
Hiroki Matui - One of the best experts on this subject based on the ideXlab platform.
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minimal dynamical systems on the product of the Cantor Set and the circle
Communications in Mathematical Physics, 2005Co-Authors: Huaxin Lin, Hiroki MatuiAbstract:We prove that a crossed product algebra arising from a minimal dynamical system on the product of the Cantor Set and the circle has real rank zero if and only if the Set of invariant measures of the system come from the associated Cantor minimal system. In the case that cocycles take values in the rotation group, it is also shown that this condition implies tracial rank zero, and in particular, the crossed product algebra is isomorphic to a unital simple AT-algebra of real rank zero. Under the same assumption, we show that two systems are approximately K-conjugate if and only if there exists a sequence of isomorphisms between two associated crossed products which approximately maps Open image in new window
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minimal dynamical systems on the product of the Cantor Set and the circle
arXiv: Operator Algebras, 2004Co-Authors: Huaxin Lin, Hiroki MatuiAbstract:We prove that a crossed product algebra arising from a minimal dynamical system on the product of the Cantor Set and the circle has real rank zero if and only if that system is rigid. In the case that cocycles take values in the rotation group, it is also shown that rigidity implies tracial rank zero, and in particular, the crossed product algebra is isomorphic to a unital simple AT-algebra of real rank zero. Under the same assumption, we show that two systems are approximately $K$-conjugate if and only if there exists a sequence of isomorphisms between two associated crossed products which approximately maps $C(X\times \T)$ onto $C(X\times \T)$.
Thomas L Warren - One of the best experts on this subject based on the ideXlab platform.
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random Cantor Set models for the elastic perfectly plastic contact of rough surfaces
Wear, 1996Co-Authors: Thomas L Warren, Dusan KrajcinovicAbstract:The objective of this study was to formulate discrete and continuous spatial models to describe the elastic-perfectly plastic deformation of two rough surfaces in contact. The two surfaces in contact are assumed to exhibit fractal behavior and are modeled as an effective fractal surface compressed into a smooth rigid substrate. The rough self-affine fractal structure of the effective surface is approximated by a random Cantor Set representation embedded in two dimensions. Both of the proposed models admit analytical solutions whether the plastic deformation is volume conserving or not. Presented results illustrate the effects that volume conservation and initial surface structure have on the elastic-perfectly plastic deformation process. The results from the continuous model are compared with the results obtained from the discrete model, and existing experimental load displacement data for the deformation of a bead-blasted steel surface.
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fractal models of elastic perfectly plastic contact of rough surfaces based on the Cantor Set
International Journal of Solids and Structures, 1995Co-Authors: Thomas L Warren, Dusan KrajcinovicAbstract:Abstract The objective of this study was to formulate discrete and continuous models to describe the elastic-perfectly plastic deformation of two rough surfaces in contact. The two surfaces in contact are assumed to exhibit fractal behavior and are modeled as an effective fractal surface compressed into a smooth rigid substrate. The rough self-affine fractal structure of the effective surface is approximated using a Cantor Set representation. Both of the proposed models admit analytical solutionś for the cases when the plastic deformation is volume conserving or not. Results are presented that illustrate the effects that volume conservation and initial surface structure have on the elastic-perfectly plastic deformation process. The results from the continuous model are compared with the results obtained from the discrete model, and also with existing experimental load displacement results for the deformation of a ground steel surface.
Sam R Dolan - One of the best experts on this subject based on the ideXlab platform.
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binary black hole shadows chaotic scattering and the Cantor Set
Classical and Quantum Gravity, 2016Co-Authors: Jake O Shipley, Sam R DolanAbstract:We investigate the qualitative features of binary black hole shadows using the model of two extremally charged black holes in static equilibrium (a Majumdar–Papapetrou solution). Our perspective is that binary spacetimes are natural exemplars of chaotic scattering, because they admit more than one fundamental null orbit, and thus an uncountably infinite Set of perpetual null orbits which generate scattering singularities in initial data. Inspired by the three-disc model, we develop an appropriate symbolic dynamics to describe planar null geodesics on the double black hole spacetime. We show that a one-dimensional (1D) black hole shadow may be constructed through an iterative procedure akin to the construction of the Cantor Set; thus the 1D shadow is self-similar. Next, we study non-planar rays, to understand how angular momentum affects the existence and properties of the fundamental null orbits. Taking slices through 2D shadows, we observe three types of 1D shadow: regular, Cantor-like, and highly chaotic. The switch from Cantor-like to regular occurs where outer fundamental orbits are forbidden by angular momentum. The highly chaotic part is associated with an unexpected feature: stable and bounded null orbits, which exist around two black holes of equal mass M separated by , where . To show how this possibility arises, we define a certain potential function and classify its stationary points. We conjecture that the highly chaotic parts of the 2D shadow possess the Wada property. Finally, we consider the possibility of following null geodesics through event horizons, and chaos in the maximally extended spacetime.
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binary black hole shadows chaotic scattering and the Cantor Set
arXiv: General Relativity and Quantum Cosmology, 2016Co-Authors: Jake O Shipley, Sam R DolanAbstract:We investigate the qualitative features of binary black hole shadows using the model of two extremally charged black holes in static equilibrium (a Majumdar--Papapetrou solution). Our perspective is that binary spacetimes are natural exemplars of chaotic scattering, because they admit more than one fundamental null orbit, and thus an uncountably-infinite Set of perpetual null orbits which generate scattering singularities in initial data. Inspired by the three-disc model, we develop an appropriate symbolic dynamics to describe planar null geodesics on the double black hole spacetime. We show that a one-dimensional (1D) black hole shadow may constructed through an iterative procedure akin to the construction of the Cantor Set; thus the 1D shadow is self-similar. Next, we study non-planar rays, to understand how angular momentum affects the existence and properties of the fundamental null orbits. Taking slices through 2D shadows, we observe three types of 1D shadow: regular, Cantor-like, and highly chaotic. The switch from Cantor-like to regular occurs where outer fundamental orbits are forbidden by angular momentum. The highly chaotic part is associated with an unexpected feature: stable and bounded null orbits, which exist around two black holes of equal mass $M$ separated by $a_1 < a < \sqrt{2} a_1$, where $a_1 = 4M/\sqrt{27}$. To show how this possibility arises, we define a certain potential function and classify its stationary points. We conjecture that the highly chaotic parts of the 2D shadow possess the Wada property. Finally, we consider the possibility of following null geodesics through event horizons, and chaos in the maximally-extended spacetime.