LetΓbe a Jordan curve in the complex plane and let Γ_(λ) be the constant distance boundary ofΓ.Vellis and Wu[10]introduced the notion of a(ζ,r_(0))-chordal property which guarantees that,whenλis not too large, ...LetΓbe a Jordan curve in the complex plane and let Γ_(λ) be the constant distance boundary ofΓ.Vellis and Wu[10]introduced the notion of a(ζ,r_(0))-chordal property which guarantees that,whenλis not too large, Γ_(λ) is a Jordan curve whenζ=1/2 and Γ_(λ) is a quasicircle when 0<ζ<1/2.We introduce the(ζ,r_(0),t)-chordal property,which generalizes the(ζ,r_(0))-chordal property,and we show that under the condition thatΓis(ζ,r_(0),√t)-chordal with 0<ζ<r_(0)^(1−√t)/2,there existsε>0 such that Γ_(λ) is a t-quasicircle once Γ_(λ) is a Jordan curve when 0<λ<ε.In the last part of this paper,we provide an example:Γis a kind of Koch snowflake curve which does not have the(ζ,r_(0))-chordal property for any 0<ζ<1/2,however Γ_(λ) is a Jordan curve whenλis small enough.Meanwhile,Γhas the(ζ,r_(0),√t)-chordal property with 0<ζ<r_(0)^(1−√t)/2 for any t∈(0,1/4).As a corollary of our main theorem, Γ_(λ) is a t-quasicircle for all 0<t<1/4 whenλis small enough.This means that our(ζ,r_(0),t)-chordal property is more general and applicable to more complicated curves.展开更多
Based on the kinematic viewpoint, the concept of proportional movement is abstracted to explain the strange behaviors of fractal snowflakes. A transformation group for proportional movement is defined. Under the propo...Based on the kinematic viewpoint, the concept of proportional movement is abstracted to explain the strange behaviors of fractal snowflakes. A transformation group for proportional movement is defined. Under the proportional movement transformation groups, necessary and sufficient conditions for self-similarity of multilevel structures are presented. The characteristic topology of snowflake-like fractal patterns, identical to the topology of ternary-segment fractal line, is proved. Moreover, the topological evolution of N-segment line is explored. The concepts of limit growth and infinite growth are clarified,and the corresponding growth conditions are derived. The topological invariant properties of N-segment line are exposed. In addition, the proposition that the topological evolution of the N-segment line is mainly controlled by the topological invariant N is verified.展开更多
The Chinese Fusion Engineering Test Reactor（CFETR） represents the next generation of full superconducting fusion reactors in China. Recently, CFETR was redesigned with a larger size and will be operated in two phase...The Chinese Fusion Engineering Test Reactor（CFETR） represents the next generation of full superconducting fusion reactors in China. Recently, CFETR was redesigned with a larger size and will be operated in two phases. To reduce the heat flux on the target plate, a snowflake（SF）divertor configuration is proposed. In this paper we show that by adding two dedicated poloidal field（PF） coils, the SF configuration can be achieved in both phases. The equilibria were calculated by TEQ code for a range of self-inductances l_i3. The coil currents were calculated at some fiducial points in the flattop phase. The results indicate that the PF coil system has the ability to maintain a long flattop phase in 7.5 and 10 MA inductive scenarios for the single null divertor（SND） and SF divertor configurations. The properties of the SF configuration were also analyzed. The connection length and flux expansion of the SF divertor were both increased significantly over the SND.展开更多
Fall velocity–diameter relationships for four different snowflake types（dendrite,plate,needle,and graupel） were investigated in northeastern South Korea,and a new algorithm for classifying hydrometeors is proposed ...Fall velocity–diameter relationships for four different snowflake types（dendrite,plate,needle,and graupel） were investigated in northeastern South Korea,and a new algorithm for classifying hydrometeors is proposed for distrometric measurements based on the new relationships.Falling ice crystals（approximately 40 000 particles） were measured with a two-dimensional video disdrometer（2DVD） during a winter experiment from 15 January to 9 April 2010.The fall velocity–diameter relationships were derived for the four types of snowflakes based on manual classification by experts using snow photos and 2DVD measurements：the coefficients（exponents） for different snowflake types were 0.82（0.24） for dendrite,0.74（0.35） for plate,1.03（0.71） for needle,and 1.30（0.94） for graupel,respectively.These new relationships established in the present study（PS） were compared with those from two previous studies.Hydrometeor types were classified with the derived fall velocity–diameter relationships,and the classification algorithm was evaluated using 3 × 3 contingency tables for one rain–snow transition event and three snowfall events.The algorithm showed good performance for the transition event：the critical success indices（CSIs） were 0.89,0.61 and 0.71 for snow,wet-snow and rain,respectively.For snow events,the algorithm performance for dendrite and plate（CSIs = 1.0 and 1.0,respectively） was better than for needle and graupel（CSIs = 0.67 and 0.50,respectively）.展开更多
ArbiTER(Arbitrary Topology Equation Reader)is a new code for solving linear eigenvalue problems arising from a broad range of physics and geometry models.The primary application area envisioned is boundary plasma phys...ArbiTER(Arbitrary Topology Equation Reader)is a new code for solving linear eigenvalue problems arising from a broad range of physics and geometry models.The primary application area envisioned is boundary plasma physics in magnetic confinement devices;however ArbiTER should be applicable to other science and engineering fields as well.The code permits a variable numbers of dimensions,making possible application to both fluid and kinetic models.The use of specialized equation and topology parsers permits a high degree of flexibility in specifying the physics and geometry.展开更多
文摘LetΓbe a Jordan curve in the complex plane and let Γ_(λ) be the constant distance boundary ofΓ.Vellis and Wu[10]introduced the notion of a(ζ,r_(0))-chordal property which guarantees that,whenλis not too large, Γ_(λ) is a Jordan curve whenζ=1/2 and Γ_(λ) is a quasicircle when 0<ζ<1/2.We introduce the(ζ,r_(0),t)-chordal property,which generalizes the(ζ,r_(0))-chordal property,and we show that under the condition thatΓis(ζ,r_(0),√t)-chordal with 0<ζ<r_(0)^(1−√t)/2,there existsε>0 such that Γ_(λ) is a t-quasicircle once Γ_(λ) is a Jordan curve when 0<λ<ε.In the last part of this paper,we provide an example:Γis a kind of Koch snowflake curve which does not have the(ζ,r_(0))-chordal property for any 0<ζ<1/2,however Γ_(λ) is a Jordan curve whenλis small enough.Meanwhile,Γhas the(ζ,r_(0),√t)-chordal property with 0<ζ<r_(0)^(1−√t)/2 for any t∈(0,1/4).As a corollary of our main theorem, Γ_(λ) is a t-quasicircle for all 0<t<1/4 whenλis small enough.This means that our(ζ,r_(0),t)-chordal property is more general and applicable to more complicated curves.
基金Project supported by the National Natural Science Foundation of China(Nos.10872114,11072125,and 11272175)the National Natural Science Foundation of Jiangsu Province(No.SBK201140044)the Fundation of Tutor for Doctor Degree of Higher Education of China(No.20130002110044)
文摘Based on the kinematic viewpoint, the concept of proportional movement is abstracted to explain the strange behaviors of fractal snowflakes. A transformation group for proportional movement is defined. Under the proportional movement transformation groups, necessary and sufficient conditions for self-similarity of multilevel structures are presented. The characteristic topology of snowflake-like fractal patterns, identical to the topology of ternary-segment fractal line, is proved. Moreover, the topological evolution of N-segment line is explored. The concepts of limit growth and infinite growth are clarified,and the corresponding growth conditions are derived. The topological invariant properties of N-segment line are exposed. In addition, the proposition that the topological evolution of the N-segment line is mainly controlled by the topological invariant N is verified.
基金supported by the National Magnetic Confinement Fusion Program under grant nos 2014GB106001,2014GB110003 and 2013GB111000National Natural Science Foundation of China under grant no.11675221
文摘The Chinese Fusion Engineering Test Reactor（CFETR） represents the next generation of full superconducting fusion reactors in China. Recently, CFETR was redesigned with a larger size and will be operated in two phases. To reduce the heat flux on the target plate, a snowflake（SF）divertor configuration is proposed. In this paper we show that by adding two dedicated poloidal field（PF） coils, the SF configuration can be achieved in both phases. The equilibria were calculated by TEQ code for a range of self-inductances l_i3. The coil currents were calculated at some fiducial points in the flattop phase. The results indicate that the PF coil system has the ability to maintain a long flattop phase in 7.5 and 10 MA inductive scenarios for the single null divertor（SND） and SF divertor configurations. The properties of the SF configuration were also analyzed. The connection length and flux expansion of the SF divertor were both increased significantly over the SND.
基金funded by the Korea Meteorological Administration Research and Development Program under Grant KMIPA2015-1010
文摘Fall velocity–diameter relationships for four different snowflake types（dendrite,plate,needle,and graupel） were investigated in northeastern South Korea,and a new algorithm for classifying hydrometeors is proposed for distrometric measurements based on the new relationships.Falling ice crystals（approximately 40 000 particles） were measured with a two-dimensional video disdrometer（2DVD） during a winter experiment from 15 January to 9 April 2010.The fall velocity–diameter relationships were derived for the four types of snowflakes based on manual classification by experts using snow photos and 2DVD measurements：the coefficients（exponents） for different snowflake types were 0.82（0.24） for dendrite,0.74（0.35） for plate,1.03（0.71） for needle,and 1.30（0.94） for graupel,respectively.These new relationships established in the present study（PS） were compared with those from two previous studies.Hydrometeor types were classified with the derived fall velocity–diameter relationships,and the classification algorithm was evaluated using 3 × 3 contingency tables for one rain–snow transition event and three snowfall events.The algorithm showed good performance for the transition event：the critical success indices（CSIs） were 0.89,0.61 and 0.71 for snow,wet-snow and rain,respectively.For snow events,the algorithm performance for dendrite and plate（CSIs = 1.0 and 1.0,respectively） was better than for needle and graupel（CSIs = 0.67 and 0.50,respectively）.
文摘ArbiTER(Arbitrary Topology Equation Reader)is a new code for solving linear eigenvalue problems arising from a broad range of physics and geometry models.The primary application area envisioned is boundary plasma physics in magnetic confinement devices;however ArbiTER should be applicable to other science and engineering fields as well.The code permits a variable numbers of dimensions,making possible application to both fluid and kinetic models.The use of specialized equation and topology parsers permits a high degree of flexibility in specifying the physics and geometry.
