In this paper, a simplified model of the bistable piezoelectric cantilever beam with magnets is established, and the potential energy of the bistable system is analyzed. We have proposed the bistable L-shaped beam str...In this paper, a simplified model of the bistable piezoelectric cantilever beam with magnets is established, and the potential energy of the bistable system is analyzed. We have proposed the bistable L-shaped beam structure, which has the same geometry dimensions of the bistable straight beam in the first time. The comparative study on power generations and dynamic responses of the bistable straight beam and the bistable L-shaped beam plays an important role in exploring excellent piezoelectric generator.The experiment structure includes the base layer and the piezoelectric layer. The harmonic excitation is given to the system.Theoretical analysis results show that the potential energy function of the system has two obvious steady potential wells. In addition, the depth of the upper potential well is different from that of the lower potential well when the gravity potential energy is considered. Experimental results demonstrate that the power generation for the straight beam is better than that of the horizontally placed L-shaped beam when the excitation amplitude is 450 m V. There is the existence that the energy harvesting capacity of the bistable L-shaped beam is better than that of the bistable straight beam when the excitation amplitude is 400 m V.Furthermore, the power generation of the bistable L-shaped beam with the upper potential well is obviously better than that of the bistable L-shaped beam with the lower potential well. In addition, comparing with the straight beam, the dynamic response of the bistable L-shaped beam is more complex when the external excitation frequency is changed. It is also observed that the distance between the magnets has the obvious influence on the dynamic response of the bistable system. It is very effective to select the appropriate distance between the magnets to improve the power generation of the bistable energy harvester under the fixed excitation conditions.展开更多
This paper presents an experimental study of the broadband energy harvesting and dynamic responses of an L-shaped piezoelectric cantilever beam.Experimental results show that the L-shaped piezoelectric beam generates ...This paper presents an experimental study of the broadband energy harvesting and dynamic responses of an L-shaped piezoelectric cantilever beam.Experimental results show that the L-shaped piezoelectric beam generates two optimal voltage peaks when the horizontal beam size is similar to the vertical beam size.Several optimized L-shaped piezoelectric cantilever beam structures are proposed.Power generation using the inverted bistable L-shaped beam is better.It is observed experimentally that the inverted bistable L-shaped beam structure shows obvious bistable characteristics and hard spring characteristics.Furthermore,the corresponding relationship between the bistable phase portrait and the potential energy curve is found in the experiment.This is the first time that a phase portrait for stiffness hardening of an L-shaped beam has been found experimentally.These results can be applied to analysis of new piezoelectric power generation structures.展开更多
In this paper, the disturbance propagation and active vibration control of a finite L-shaped beam axe studied. The dynamic response of the structure is obtained by the travelling wave approach. The active vibration su...In this paper, the disturbance propagation and active vibration control of a finite L-shaped beam axe studied. The dynamic response of the structure is obtained by the travelling wave approach. The active vibration suppression of the finite L-shaped beam is performed based on the structural vibration power flow. In the numerical calculation, the influences of the near field effect of the error sensor and the small error of the control forces on the control results are all considered. The simulation results indicate that the structural vibration response in the medium and high frequency regions can be effectively computed by the travelling wave method. The effect of the active control by controlling the power flow is much better than that by controlling the acceleration in some cases. And the control results by the power flow method are slightly affected by the locations of the error sensor and the small error of the control forces.展开更多
In this paper,wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges are investigated using the wave approach.The dynamic responses,active and reactive power ...In this paper,wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges are investigated using the wave approach.The dynamic responses,active and reactive power flow in the finite plate are calculated by the Mindlin plate theory （MPT） and classic plate theory （CPT）.To satisfy the boundary conditions and continuous conditions at the coupled junction of the finite L-shaped plate,the near-field and far-field waves are entirely contained in the wave approach.The in-plane longitudinal and shear waves are also considered.The results indicate that the vibratory power flow based on the MPT is different from that based on the CPT not only at high frequencies but also at low and medium frequencies.The influence of the plate thickness on the vibrational power flow is investigated.From the results it is seen that the shear and rotary inertia correction of the MPT can influence the active and reactive power at the junction of the L-shaped plate not only at high frequencies but also at low and medium frequencies.Furthermore,the effects of structural damping on the active and reactive power flow at the junction are also analyzed.展开更多
The nonuniform L-shaped spatially spread loop and dipole（SSLD） array whose inter-element spacing is greater than half a wavelength is studied. A joint parameter estimation algorithm of direction of arrival（DOA）, f...The nonuniform L-shaped spatially spread loop and dipole（SSLD） array whose inter-element spacing is greater than half a wavelength is studied. A joint parameter estimation algorithm of direction of arrival（DOA）, frequency and polarization is presented for plane-wave signals. The direct sampling and the corresponding delayed sampling data are used to construct the data correlation matrix. On the basis of the subspace theory and the least square method, the frequency and the steering vector of the whole array are obtained. According to the relationship of the array manifold vector between electric dipoles and magnetic loops,the polarization parameters are given. The unambiguous phase estimates are acquired by applying virtual baseline array transformation to the spatial steering vectors, and they are used as coarse references to disambiguate the cyclic phase ambiguities in phase differences between two adjacent array elements on the array,then the high accuracy DOA estimates are obtained. Closed-form solutions for each parameter are obtained. This method has advantages of lower calculation complexity and no parameter matching. The experiment results verify the effectiveness and feasibility of the presented algorithm.展开更多
A joint two-dimensional(2D)direction-of-arrival(DOA)and radial Doppler frequency estimation method for the L-shaped array is proposed in this paper based on the compressive sensing(CS)framework.Revised from the conven...A joint two-dimensional(2D)direction-of-arrival(DOA)and radial Doppler frequency estimation method for the L-shaped array is proposed in this paper based on the compressive sensing(CS)framework.Revised from the conventional CS-based methods where the joint spatial-temporal parameters are characterized in one large scale matrix,three smaller scale matrices with independent azimuth,elevation and Doppler frequency are introduced adopting a separable observation model.Afterwards,the estimation is achieved by L1-norm minimization and the Bayesian CS algorithm.In addition,under the L-shaped array topology,the azimuth and elevation are separated yet coupled to the same radial Doppler frequency.Hence,the pair matching problem is solved with the aid of the radial Doppler frequency.Finally,numerical simulations corroborate the feasibility and validity of the proposed algorithm.展开更多
The problem of tiling rectangles by polyominoes generated large interest. A related one is the problem of tiling parallelograms by twisted polyominoes. Both problems are related with tilings of (skewed) quadrants by p...The problem of tiling rectangles by polyominoes generated large interest. A related one is the problem of tiling parallelograms by twisted polyominoes. Both problems are related with tilings of (skewed) quadrants by polyominoes. Indeed, if all tilings of a (skewed) quadrant by a tile set can be reduced to a tiling by congruent rectangles (parallelograms), this provides information about tilings of rectangles (parallelograms). We consider a class of tile sets in a square lattice appearing from arbitrary dissections of rectangles in two L-shaped polyominoes and from symmetries of these tiles about the first bisector. Only translations of the tiles are allowed in a tiling. If the sides of the dissected rectangle are coprime, we show the existence of tilings of all (skewed) quadrants that do not follow the rectangular (parallelogram) pattern. If one of the sides of the dissected rectangle is 2 and the other is odd, we also show tilings of rectangles by the tile set that do not follow the rectangular pattern. If one of the sides of the dissected rectangle is 2 and the other side is even, we show a new infinite family of tile sets that follows the rectangular pattern when tiling one of the quadrants. For this type of dis-section, we also show a new infinite family that does not follow the rectangular pattern when tiling rectangles. Finally, we investigate more general dissections of rectangles, with. Here we show infinite families of tile sets that follow the rectangular pattern for a quadrant and infinite families that do not follow the rectangular pattern for any quadrant. We also show, for infinite families of tile sets of this type, tilings of rectangles that do not follow the rectangular pattern.展开更多
Based on the characteristics of an L-shaped column composed of concrete-filled square steel tubes, the axial compression experiment and nonlinear finite element analysis were carried out to study the mechanical proper...Based on the characteristics of an L-shaped column composed of concrete-filled square steel tubes, the axial compression experiment and nonlinear finite element analysis were carried out to study the mechanical property of the L-shaped column. The load-displacement curve for the L-shaped column, the deflection and load-strain curves for the mono columns were obtained by the axial compression experiment. The results show that the L-shaped column exhibits a flexural-torsional buckling failure mode. The numerical simulation by the finite element analysis shows that the bearing capacity and failure mode are in accordance with those of the axial compression experiment and the feasi- bility of the finite element analysis is proved. For the calculation of the bearing capacity of the L-shaped column com- posed of concrete-filled square steel tubes, an analytical method is proposed based on the theory of the elastic stability and spatial truss model. The results of the analytical method are in good agreement with those of the axial compression experiment and the finite element analysis.展开更多
Let T<sub>n </sub>be the set of ribbon L-shaped n-ominoes for some n≥4 even, and let T<sup>+</sup><sub>n</sub> be T<sub>n</sub> with an extra 2 x 2 square. We investiga...Let T<sub>n </sub>be the set of ribbon L-shaped n-ominoes for some n≥4 even, and let T<sup>+</sup><sub>n</sub> be T<sub>n</sub> with an extra 2 x 2 square. We investigate signed tilings of rectangles by T<sub>n</sub> and T<sup>+</sup><sub>n</sub> . We show that a rectangle has a signed tiling by T<sub>n</sub> if and only if both sides of the rectangle are even and one of them is divisible by n, or if one of the sides is odd and the other side is divisible by . We also show that a rectangle has a signed tiling by T<sup>+</sup><sub>n, </sub> n≥6 even, if and only if both sides of the rectangle are even, or if one of the sides is odd and the other side is divisible by . Our proofs are based on the exhibition of explicit GrÖbner bases for the ideals generated by polynomials associated to the tiling sets. In particular, we show that some of the regular tiling results in Nitica, V. (2015) Every tiling of the first quadrant by ribbon L n-ominoes follows the rectangular pattern. Open Journal of Discrete Mathematics, 5, 11-25, cannot be obtained from coloring invariants.展开更多
We show that a rectangle can be signed tiled by ribbon L n-ominoes, n odd, if and only if it has a side divisible by n. A consequence of our technique, based on the exhibition of an explicit Gröbner basis, is...We show that a rectangle can be signed tiled by ribbon L n-ominoes, n odd, if and only if it has a side divisible by n. A consequence of our technique, based on the exhibition of an explicit Gröbner basis, is that any k-inflated copy of the skewed L n-omino has a signed tiling by skewed L n-ominoes. We also discuss regular tilings by ribbon L n-ominoes, n odd, for rectangles and more general regions. We show that in this case obstructions appear that are not detected by signed tilings.展开更多
With the completion of the Qinghai-Tibetan Railway,economic development of related areas has been greatly accelerated.This,in return,calls for building or upgrading more roadways,especially high-grade roadways.In cold...With the completion of the Qinghai-Tibetan Railway,economic development of related areas has been greatly accelerated.This,in return,calls for building or upgrading more roadways,especially high-grade roadways.In cold regions,the thawing of permafrost can induce settlement damage of and even failure to railway (or roadway) embankments.Thermosyphons (self-powered refrigera-tion devices that are used to help keep the permafrost cool) have proved effective in mitigating thaw settlement by maintaining the thermal stability of the embankments.However,for high-grade roadway embankments of great width,stabilizing or cooling ef-fects of traditional geotechnological measures may be limited.To enhance the cooling effect of thermosyphons,an L-shaped thermosyphon was designed.A laboratory test was carried out to study the combined cooling effect of the L-shaped thermosyphon and thermal insulation applying to roadbed construction.The angle between the evaporator and condenser sections of the L-shaped thermosyphon is 134 degrees,and the L-shaped thermosyphon was inserted into the soil at an angle of 5 degrees with the road surface.The tested results show that the L-shaped thermosyphon is effective in removing heat from a roadway in winter.When the ambient air temperature is lower than the soil temperature,the thermosyphon is active and extracts the heat in the soil around it.When the ambient air temperature is higher than the soil temperature,the thermosyphon is inactive,and no heat is in-jected into the soil through the L-shaped thermosyphon.Compared to embankments with straight thermosyphons,the inner parts of the embankments with L-shaped thermosyphons were significantly cooled.It is hoped that the present study would be useful to the application of L-shaped thermosyphons in the construction of high-grade roadways in cold regions.展开更多
Let and let be the set of four ribbon L-shaped n-ominoes. We study tiling problems for regions in a square lattice by . Our main result shows a remarkable property of this set of tiles: any tiling of the first quadran...Let and let be the set of four ribbon L-shaped n-ominoes. We study tiling problems for regions in a square lattice by . Our main result shows a remarkable property of this set of tiles: any tiling of the first quadrant by , n even, reduces to a tiling by and rectangles, each rectangle being covered by two ribbon L-shaped n-ominoes. An application of our result is the characterization of all rectangles that can be tiled by , n even: a rectangle can be tiled by , n even, if and only if both of its sides are even and at least one side is divisible by n. Another application is the existence of the local move property for an infinite family of sets of tiles: , n even, has the local move property for the class of rectangular regions with respect to the local moves that interchange a tiling of an square by n/2 vertical rectangles, with a tiling by n/2 horizontal rectangles, each vertical/horizontal rectangle being covered by two ribbon L-shaped n-ominoes. We show that none of these results are valid for any odd n. The rectangular pattern of a tiling of the first quadrant persists if we add an extra tile to , n even. A rectangle can be tiled by the larger set of tiles if and only if it has both sides even. We also show that our main result implies that a skewed L-shaped n-omino, n even, is not a replicating tile of order k2 for any odd k.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11772008,11172009,11372015,11232009,10872010,11290152&10732020)
文摘In this paper, a simplified model of the bistable piezoelectric cantilever beam with magnets is established, and the potential energy of the bistable system is analyzed. We have proposed the bistable L-shaped beam structure, which has the same geometry dimensions of the bistable straight beam in the first time. The comparative study on power generations and dynamic responses of the bistable straight beam and the bistable L-shaped beam plays an important role in exploring excellent piezoelectric generator.The experiment structure includes the base layer and the piezoelectric layer. The harmonic excitation is given to the system.Theoretical analysis results show that the potential energy function of the system has two obvious steady potential wells. In addition, the depth of the upper potential well is different from that of the lower potential well when the gravity potential energy is considered. Experimental results demonstrate that the power generation for the straight beam is better than that of the horizontally placed L-shaped beam when the excitation amplitude is 450 m V. There is the existence that the energy harvesting capacity of the bistable L-shaped beam is better than that of the bistable straight beam when the excitation amplitude is 400 m V.Furthermore, the power generation of the bistable L-shaped beam with the upper potential well is obviously better than that of the bistable L-shaped beam with the lower potential well. In addition, comparing with the straight beam, the dynamic response of the bistable L-shaped beam is more complex when the external excitation frequency is changed. It is also observed that the distance between the magnets has the obvious influence on the dynamic response of the bistable system. It is very effective to select the appropriate distance between the magnets to improve the power generation of the bistable energy harvester under the fixed excitation conditions.
基金supported by the National Natural Science Foundation of China(Grants 11772008,11172009,11372015,11232009,10872010,11290152,10732020)the Tianjin Natural Science Foundation(Grant 19JCZDJC32300).
文摘This paper presents an experimental study of the broadband energy harvesting and dynamic responses of an L-shaped piezoelectric cantilever beam.Experimental results show that the L-shaped piezoelectric beam generates two optimal voltage peaks when the horizontal beam size is similar to the vertical beam size.Several optimized L-shaped piezoelectric cantilever beam structures are proposed.Power generation using the inverted bistable L-shaped beam is better.It is observed experimentally that the inverted bistable L-shaped beam structure shows obvious bistable characteristics and hard spring characteristics.Furthermore,the corresponding relationship between the bistable phase portrait and the potential energy curve is found in the experiment.This is the first time that a phase portrait for stiffness hardening of an L-shaped beam has been found experimentally.These results can be applied to analysis of new piezoelectric power generation structures.
基金Project supported by the National Natural Science Foundation of China (Nos. 10672017 and 10632020)
文摘In this paper, the disturbance propagation and active vibration control of a finite L-shaped beam axe studied. The dynamic response of the structure is obtained by the travelling wave approach. The active vibration suppression of the finite L-shaped beam is performed based on the structural vibration power flow. In the numerical calculation, the influences of the near field effect of the error sensor and the small error of the control forces on the control results are all considered. The simulation results indicate that the structural vibration response in the medium and high frequency regions can be effectively computed by the travelling wave method. The effect of the active control by controlling the power flow is much better than that by controlling the acceleration in some cases. And the control results by the power flow method are slightly affected by the locations of the error sensor and the small error of the control forces.
基金supported by the National Basic Research Programof China (2011CB711102)the National Natural Science Foundation of China (10672017,11002045)
文摘In this paper,wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges are investigated using the wave approach.The dynamic responses,active and reactive power flow in the finite plate are calculated by the Mindlin plate theory （MPT） and classic plate theory （CPT）.To satisfy the boundary conditions and continuous conditions at the coupled junction of the finite L-shaped plate,the near-field and far-field waves are entirely contained in the wave approach.The in-plane longitudinal and shear waves are also considered.The results indicate that the vibratory power flow based on the MPT is different from that based on the CPT not only at high frequencies but also at low and medium frequencies.The influence of the plate thickness on the vibrational power flow is investigated.From the results it is seen that the shear and rotary inertia correction of the MPT can influence the active and reactive power at the junction of the L-shaped plate not only at high frequencies but also at low and medium frequencies.Furthermore,the effects of structural damping on the active and reactive power flow at the junction are also analyzed.
基金supported by the National Natural Science Foundation of China(6120129561231017)the Fundamental Research Funds for the Central Universities(K5051307017)
文摘The nonuniform L-shaped spatially spread loop and dipole（SSLD） array whose inter-element spacing is greater than half a wavelength is studied. A joint parameter estimation algorithm of direction of arrival（DOA）, frequency and polarization is presented for plane-wave signals. The direct sampling and the corresponding delayed sampling data are used to construct the data correlation matrix. On the basis of the subspace theory and the least square method, the frequency and the steering vector of the whole array are obtained. According to the relationship of the array manifold vector between electric dipoles and magnetic loops,the polarization parameters are given. The unambiguous phase estimates are acquired by applying virtual baseline array transformation to the spatial steering vectors, and they are used as coarse references to disambiguate the cyclic phase ambiguities in phase differences between two adjacent array elements on the array,then the high accuracy DOA estimates are obtained. Closed-form solutions for each parameter are obtained. This method has advantages of lower calculation complexity and no parameter matching. The experiment results verify the effectiveness and feasibility of the presented algorithm.
文摘A joint two-dimensional(2D)direction-of-arrival(DOA)and radial Doppler frequency estimation method for the L-shaped array is proposed in this paper based on the compressive sensing(CS)framework.Revised from the conventional CS-based methods where the joint spatial-temporal parameters are characterized in one large scale matrix,three smaller scale matrices with independent azimuth,elevation and Doppler frequency are introduced adopting a separable observation model.Afterwards,the estimation is achieved by L1-norm minimization and the Bayesian CS algorithm.In addition,under the L-shaped array topology,the azimuth and elevation are separated yet coupled to the same radial Doppler frequency.Hence,the pair matching problem is solved with the aid of the radial Doppler frequency.Finally,numerical simulations corroborate the feasibility and validity of the proposed algorithm.
文摘The problem of tiling rectangles by polyominoes generated large interest. A related one is the problem of tiling parallelograms by twisted polyominoes. Both problems are related with tilings of (skewed) quadrants by polyominoes. Indeed, if all tilings of a (skewed) quadrant by a tile set can be reduced to a tiling by congruent rectangles (parallelograms), this provides information about tilings of rectangles (parallelograms). We consider a class of tile sets in a square lattice appearing from arbitrary dissections of rectangles in two L-shaped polyominoes and from symmetries of these tiles about the first bisector. Only translations of the tiles are allowed in a tiling. If the sides of the dissected rectangle are coprime, we show the existence of tilings of all (skewed) quadrants that do not follow the rectangular (parallelogram) pattern. If one of the sides of the dissected rectangle is 2 and the other is odd, we also show tilings of rectangles by the tile set that do not follow the rectangular pattern. If one of the sides of the dissected rectangle is 2 and the other side is even, we show a new infinite family of tile sets that follows the rectangular pattern when tiling one of the quadrants. For this type of dis-section, we also show a new infinite family that does not follow the rectangular pattern when tiling rectangles. Finally, we investigate more general dissections of rectangles, with. Here we show infinite families of tile sets that follow the rectangular pattern for a quadrant and infinite families that do not follow the rectangular pattern for any quadrant. We also show, for infinite families of tile sets of this type, tilings of rectangles that do not follow the rectangular pattern.
基金Foundation of Key Laboratory of Coast Civil Structure Safety (Tianjin University),Ministry of EducationChinese Program for New Century Excellent Talents in University+1 种基金Seed Foundation of Tianjin UniversitySeed Foundation of Xinjiang University
文摘Based on the characteristics of an L-shaped column composed of concrete-filled square steel tubes, the axial compression experiment and nonlinear finite element analysis were carried out to study the mechanical property of the L-shaped column. The load-displacement curve for the L-shaped column, the deflection and load-strain curves for the mono columns were obtained by the axial compression experiment. The results show that the L-shaped column exhibits a flexural-torsional buckling failure mode. The numerical simulation by the finite element analysis shows that the bearing capacity and failure mode are in accordance with those of the axial compression experiment and the feasi- bility of the finite element analysis is proved. For the calculation of the bearing capacity of the L-shaped column com- posed of concrete-filled square steel tubes, an analytical method is proposed based on the theory of the elastic stability and spatial truss model. The results of the analytical method are in good agreement with those of the axial compression experiment and the finite element analysis.
文摘Let T<sub>n </sub>be the set of ribbon L-shaped n-ominoes for some n≥4 even, and let T<sup>+</sup><sub>n</sub> be T<sub>n</sub> with an extra 2 x 2 square. We investigate signed tilings of rectangles by T<sub>n</sub> and T<sup>+</sup><sub>n</sub> . We show that a rectangle has a signed tiling by T<sub>n</sub> if and only if both sides of the rectangle are even and one of them is divisible by n, or if one of the sides is odd and the other side is divisible by . We also show that a rectangle has a signed tiling by T<sup>+</sup><sub>n, </sub> n≥6 even, if and only if both sides of the rectangle are even, or if one of the sides is odd and the other side is divisible by . Our proofs are based on the exhibition of explicit GrÖbner bases for the ideals generated by polynomials associated to the tiling sets. In particular, we show that some of the regular tiling results in Nitica, V. (2015) Every tiling of the first quadrant by ribbon L n-ominoes follows the rectangular pattern. Open Journal of Discrete Mathematics, 5, 11-25, cannot be obtained from coloring invariants.
文摘We show that a rectangle can be signed tiled by ribbon L n-ominoes, n odd, if and only if it has a side divisible by n. A consequence of our technique, based on the exhibition of an explicit Gröbner basis, is that any k-inflated copy of the skewed L n-omino has a signed tiling by skewed L n-ominoes. We also discuss regular tilings by ribbon L n-ominoes, n odd, for rectangles and more general regions. We show that in this case obstructions appear that are not detected by signed tilings.
基金supported by National Natural Science Foundation of China (Grant No.40730736 and No.40601023)the National Hi-Tech Research and Development Plan (2008AA11Z103)the Western Project Program of the Chinese Academy of Sciences (No.KZCX2-XB2-10)
文摘With the completion of the Qinghai-Tibetan Railway,economic development of related areas has been greatly accelerated.This,in return,calls for building or upgrading more roadways,especially high-grade roadways.In cold regions,the thawing of permafrost can induce settlement damage of and even failure to railway (or roadway) embankments.Thermosyphons (self-powered refrigera-tion devices that are used to help keep the permafrost cool) have proved effective in mitigating thaw settlement by maintaining the thermal stability of the embankments.However,for high-grade roadway embankments of great width,stabilizing or cooling ef-fects of traditional geotechnological measures may be limited.To enhance the cooling effect of thermosyphons,an L-shaped thermosyphon was designed.A laboratory test was carried out to study the combined cooling effect of the L-shaped thermosyphon and thermal insulation applying to roadbed construction.The angle between the evaporator and condenser sections of the L-shaped thermosyphon is 134 degrees,and the L-shaped thermosyphon was inserted into the soil at an angle of 5 degrees with the road surface.The tested results show that the L-shaped thermosyphon is effective in removing heat from a roadway in winter.When the ambient air temperature is lower than the soil temperature,the thermosyphon is active and extracts the heat in the soil around it.When the ambient air temperature is higher than the soil temperature,the thermosyphon is inactive,and no heat is in-jected into the soil through the L-shaped thermosyphon.Compared to embankments with straight thermosyphons,the inner parts of the embankments with L-shaped thermosyphons were significantly cooled.It is hoped that the present study would be useful to the application of L-shaped thermosyphons in the construction of high-grade roadways in cold regions.
文摘Let and let be the set of four ribbon L-shaped n-ominoes. We study tiling problems for regions in a square lattice by . Our main result shows a remarkable property of this set of tiles: any tiling of the first quadrant by , n even, reduces to a tiling by and rectangles, each rectangle being covered by two ribbon L-shaped n-ominoes. An application of our result is the characterization of all rectangles that can be tiled by , n even: a rectangle can be tiled by , n even, if and only if both of its sides are even and at least one side is divisible by n. Another application is the existence of the local move property for an infinite family of sets of tiles: , n even, has the local move property for the class of rectangular regions with respect to the local moves that interchange a tiling of an square by n/2 vertical rectangles, with a tiling by n/2 horizontal rectangles, each vertical/horizontal rectangle being covered by two ribbon L-shaped n-ominoes. We show that none of these results are valid for any odd n. The rectangular pattern of a tiling of the first quadrant persists if we add an extra tile to , n even. A rectangle can be tiled by the larger set of tiles if and only if it has both sides even. We also show that our main result implies that a skewed L-shaped n-omino, n even, is not a replicating tile of order k2 for any odd k.
