This article presents a generalization of the standard art gallery problem to the case where the sides of the gallery are continuous curves which are limits of polygonal arcs. The allowable limiting processes for such...This article presents a generalization of the standard art gallery problem to the case where the sides of the gallery are continuous curves which are limits of polygonal arcs. The allowable limiting processes for such generalized art galleries are defined. We construct an art gallery in which one side is the Koch fractal and the other sides are three sides of a rectangle. The appropriate measure of coverage by guards is not the total number of guards but, rather, the guards-to-side ratio. We compute this ratio for the cases of shallow and deep versions of the Koch fractal art gallery.展开更多
A flexible or planar eddy current probe with a differential structure can suppress the lift-off noise during the inspection of defects.However,the extent of the lift-off effect on differential probes,including differe...A flexible or planar eddy current probe with a differential structure can suppress the lift-off noise during the inspection of defects.However,the extent of the lift-off effect on differential probes,including different coil structures,varies.In this study,two planar eddy current probes with differential pickup structures and the same size,Koch and circular probes,were used to compare lift-off effects.The eddy current distributions of the probes perturbed by 0°and 90°cracks were obtained by finite element analysis.The analysis results show that the 90°crack can impede the eddy current induced by the Koch probe even further at relatively low lift-off distance.The peak-to-peak values of the signal output from the two probes were compared at different lift-off distances using finite element analysis and experimental methods.In addition,the effects of different frequencies on the lift-off were studied experimentally.The results show that the signal peak-to-peak value of the Koch probe for the inspection of cracks in 90°orientation is larger than that of the circular probe when the lift-off distance is smaller than 1.2 mm.In addition,the influence of the lift-off distance on the peak-to-peak signal value of the two probes was studied via normalization.This indicates that the influence becomes more evident with an increase in excitation frequency.This research discloses the lift-off effect of differential planar eddy current probes with different coil shapes and proves the detection merit of the Koch probe for 90°cracks at low lift-off distances.展开更多
In this study,the wave propagation properties of lattice metamaterials with Koch fractal structures are investigated in terms of band structures and directional wave propagation.The analytical models of lattice metama...In this study,the wave propagation properties of lattice metamaterials with Koch fractal structures are investigated in terms of band structures and directional wave propagation.The analytical models of lattice metamaterials are established using the finite element method,and the dispersion relation is solved using the Bloch’s theorem.The band structures of the lattice metamaterials with different numbers of iterations are studied,and the group velocities at a selected frequency are calculated to analyze the directional wave propagation characteristics.Furthermore,dynamic responses of the finite structures are calculated using commercial finite element software to verify the band gaps and directional wave propagation behaviors in the lattice metamaterials.The results show that multiple and low band gaps are present in the lattice materials with various geometric parameters of the Koch fractal,and the position of the lowest band gap decreases as the number of iterations increases.The results indicate the potential applications of lattice metamaterials with Koch fractals for vibration isolation and multi-functional design.展开更多
A novel asymmetrical Pi-shaped defected ground structure （DGS） with 3-interations Koch fractal curves is proposed to design a microstrip low-pass filter （LPF） with uhra-wide stop-band （SB）. The proposed LPFs wit...A novel asymmetrical Pi-shaped defected ground structure （DGS） with 3-interations Koch fractal curves is proposed to design a microstrip low-pass filter （LPF） with uhra-wide stop-band （SB）. The proposed LPFs with a single resonator and two cascaded resonators are both designed, simulated, manufactured and measured. Simulation and experiment results demonstrate that the designed LPF has a very sharp transition band （TB） and an ultra-wide SB performance compared with the existed similar symmetrical and asymmetrical DGS. The proposed LPF with two cascaded resonators is with a compact size of 36. 8 mm x 24.0 mm, a very low insertion loss of less than 0.7 dB under 1.9 GHz, and a wide SB from 2.2 GHz to 8 GHz with rejection of larger than 30 dB.展开更多
In this paper, we introduce a K Hölder p-adic derivative that can be applied to fractal curves with different Hölder exponent K. We will show that the Koch curve satisfies the Hölder conditi...In this paper, we introduce a K Hölder p-adic derivative that can be applied to fractal curves with different Hölder exponent K. We will show that the Koch curve satisfies the Hölder condition with exponent and has a 4-adic arithmetic-analytic representation. We will prove that the Koch curve has exact -Hölder 4-adic derivative.展开更多
文摘This article presents a generalization of the standard art gallery problem to the case where the sides of the gallery are continuous curves which are limits of polygonal arcs. The allowable limiting processes for such generalized art galleries are defined. We construct an art gallery in which one side is the Koch fractal and the other sides are three sides of a rectangle. The appropriate measure of coverage by guards is not the total number of guards but, rather, the guards-to-side ratio. We compute this ratio for the cases of shallow and deep versions of the Koch fractal art gallery.
基金Supported by Gansu Provincial Natural Science Foundation of China(Grant No.22JR5RA229)National Natural Science Foundation of China(Grant Nos.51807086,12162021)Hongliu Youth Found of Lanzhou University of Technology and Gansu Provincial Outstanding Graduate Student Innovation Star of China(Grant No.2021CXZX-453).
文摘A flexible or planar eddy current probe with a differential structure can suppress the lift-off noise during the inspection of defects.However,the extent of the lift-off effect on differential probes,including different coil structures,varies.In this study,two planar eddy current probes with differential pickup structures and the same size,Koch and circular probes,were used to compare lift-off effects.The eddy current distributions of the probes perturbed by 0°and 90°cracks were obtained by finite element analysis.The analysis results show that the 90°crack can impede the eddy current induced by the Koch probe even further at relatively low lift-off distance.The peak-to-peak values of the signal output from the two probes were compared at different lift-off distances using finite element analysis and experimental methods.In addition,the effects of different frequencies on the lift-off were studied experimentally.The results show that the signal peak-to-peak value of the Koch probe for the inspection of cracks in 90°orientation is larger than that of the circular probe when the lift-off distance is smaller than 1.2 mm.In addition,the influence of the lift-off distance on the peak-to-peak signal value of the two probes was studied via normalization.This indicates that the influence becomes more evident with an increase in excitation frequency.This research discloses the lift-off effect of differential planar eddy current probes with different coil shapes and proves the detection merit of the Koch probe for 90°cracks at low lift-off distances.
基金Funding for this work has been provided by the National Natural Science Foundation of China(Nos.11872313 and 11502202)National Key R&D Program of China(2017YFB1102801)Fundamental Research Funds for the Central Universities and Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University(CX2020107).
文摘In this study,the wave propagation properties of lattice metamaterials with Koch fractal structures are investigated in terms of band structures and directional wave propagation.The analytical models of lattice metamaterials are established using the finite element method,and the dispersion relation is solved using the Bloch’s theorem.The band structures of the lattice metamaterials with different numbers of iterations are studied,and the group velocities at a selected frequency are calculated to analyze the directional wave propagation characteristics.Furthermore,dynamic responses of the finite structures are calculated using commercial finite element software to verify the band gaps and directional wave propagation behaviors in the lattice metamaterials.The results show that multiple and low band gaps are present in the lattice materials with various geometric parameters of the Koch fractal,and the position of the lowest band gap decreases as the number of iterations increases.The results indicate the potential applications of lattice metamaterials with Koch fractals for vibration isolation and multi-functional design.
基金supported by the National Natural Science Foundation of China (21656001)
文摘A novel asymmetrical Pi-shaped defected ground structure （DGS） with 3-interations Koch fractal curves is proposed to design a microstrip low-pass filter （LPF） with uhra-wide stop-band （SB）. The proposed LPFs with a single resonator and two cascaded resonators are both designed, simulated, manufactured and measured. Simulation and experiment results demonstrate that the designed LPF has a very sharp transition band （TB） and an ultra-wide SB performance compared with the existed similar symmetrical and asymmetrical DGS. The proposed LPF with two cascaded resonators is with a compact size of 36. 8 mm x 24.0 mm, a very low insertion loss of less than 0.7 dB under 1.9 GHz, and a wide SB from 2.2 GHz to 8 GHz with rejection of larger than 30 dB.
文摘In this paper, we introduce a K Hölder p-adic derivative that can be applied to fractal curves with different Hölder exponent K. We will show that the Koch curve satisfies the Hölder condition with exponent and has a 4-adic arithmetic-analytic representation. We will prove that the Koch curve has exact -Hölder 4-adic derivative.
