The Fabry–Perot(FP) resonant cavity is widely used in laser and spectroscopic measurements due to its unique interference transfer function(ITF). In the ideal case of parallel incident light, the ITF of the FP resona...The Fabry–Perot(FP) resonant cavity is widely used in laser and spectroscopic measurements due to its unique interference transfer function(ITF). In the ideal case of parallel incident light, the ITF of the FP resonant cavity can be expressed by the Airy function. However, in reality, it is difficult to achieve perfect parallelism with collimated beams. In this article, a theoretical model is established for non-parallel light incidence, which assumes that the non-parallel incident light is a cone-shaped beam, and the cone angle is used to quantify the non-parallelism of the beam. The transmittance function of the FP resonant cavity under non-parallel light incidence is derived. The accuracy of the model is experimentally verified. Based on this model, the effects of divergence angle, tilt angle and FP cavity parameters(reflectivity, cavity length)on the ITF are studied. The reasons for the decrease in peak value, broadening and asymmetry of the interference peak under non-parallel light incidence are explained. It is suggested that a fine balance between the interference peak and the collimation effect of the incident light should be considered in the design and application of FP resonant cavities, especially for tilted applications such as angle-scanned spectroscopy. The research results of this article have certain significance for the design and application of FP resonant cavities.展开更多
Failure of rock mass that is subjected to compressive loads occurs from initiation, propagation, and linkage of new cracks from preexisting fissures. Our research investigates the cracking behaviour and coalescence pr...Failure of rock mass that is subjected to compressive loads occurs from initiation, propagation, and linkage of new cracks from preexisting fissures. Our research investigates the cracking behaviour and coalescence process in a brittle material with two non-parallel overlapping flaws using a high-speed camera. The coalescence tensile crack and tensile wing cracks were the first cracks to occur from the preexisting flaws. The initiation stresses of the primary cracks at the two tips of each flaw were simultaneous and decreased with reduced flaw inclination angle. The following types of coalescence cracks were identified between the flaws: primary tensile coalescence crack, tensile crack linkage, shear crack linkage, mixed tensile-shear crack, and indirect crack coalescence. Coalescence through tensile linkage occurred mostly at pre-peak stress. In contrast, coalescence through shear or mixed tensile-shear cracks occurred at higher stress. Overall, this study indicates that the geometry of preexisting flaws affect crack initiation and coalescence behaviour.展开更多
Coalescence among fractures would have influence on the stability of rock masses. Deep understanding of mechanical behavior of fractured rock masses is an important mean to identify failure mechanism of geological dis...Coalescence among fractures would have influence on the stability of rock masses. Deep understanding of mechanical behavior of fractured rock masses is an important mean to identify failure mechanism of geological disaster. In this study, crack propagation processing was studied through loading pre-fractured specimens of concrete block, termed as rock-like material, in uniaxial compression tests. New non-parallel double-crack geometry was introduced to observe crack coalescence. The flaw combinations are different from the normally used flaw configurations. In addition, ultrasonic detection tests were performed on the test blocks. The stress and strain data of these tests and characteristic parameters of sound wave were recorded. The stress-strain curves of each test block under the uniaxial compression test were drawn, relations among deformation characteristics and crack angle of the crack specimens, and their overall strength were analyzed. It is found that strength of the specimen decreases as crack inclination increases under two crack inclinations. The highest uniaxial compressive strength is found in the specimen with the cracks at the same angle in different directions. Based on description of the crack initiation location, crack surface and the ultimate failure patterns, failure modes of eight subtype for test blocks are divided into three categories. It is expected that the study results could be beneficial for engineering application of jointed rock masses.展开更多
The e-N method is widely used in transition prediction. The amplitude growth rate used in the e-N method is usually provided by the linear stability theory （LST） based on the local parallel hypothesis. Considering t...The e-N method is widely used in transition prediction. The amplitude growth rate used in the e-N method is usually provided by the linear stability theory （LST） based on the local parallel hypothesis. Considering the non-parallelism effect, the parabolized stability equation （PSE） method lacks local characteristic of stability analysis. In this paper, a local stability analysis method considering non-parallelism is proposed, termed as EPSE since it may be considered as an expansion of the PSE method. The EPSE considers variation of the shape function in the streamwise direction. Its local characteristic is convenient for stability analysis. This paper uses the EPSE in a strong non-parallel flow and mode exchange problem. The results agree well with the PSE and the direct numerical simulation （DNS）. In addition, it is found that the growth rate is related to the normalized method in the non-parallel flow. Different results can be obtained using different normalized methods. Therefore, the normalized method must be consistent.展开更多
The research on boundary-layer receptivity is the key issue for the laminarturbulent transition prediction in fluid mechanics. Many of the previous studies for local receptivity are on the basis of the parallel flow a...The research on boundary-layer receptivity is the key issue for the laminarturbulent transition prediction in fluid mechanics. Many of the previous studies for local receptivity are on the basis of the parallel flow assumption which cannot accurately reflect the real physics. To overcome this disadvantage, local receptivity in the non-parallel boundary layer is studied in this paper by the direct numerical simulation （DNS）. The difference between the non-parallel and parallel boundary layers on local receptivity is investigated. In addition, the effects of the disturbance frequency, the roughness location, and the multiple roughness elements on receptivity are also determined. Besides, the relations of receptivity with the amplitude of free-stream turbulence （FST）, with the roughness height, and with the roughness length are ascertained as well. The Tollmien- Schlichting （T-S） wave packets are excited in the non-parallel boundary layer under the interaction of the FST and the localized wall roughness. A group of T-S waves are separated by the fast Fourier transform. The obtained results are in accordance with Dietz＇s measurements, Wu＇s theoretical calculations, and the linear stability theory （LST）.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No.U19A2044)the National Natural Science Foundation of China (Grant No.41975037)the Key Technologies Research and Development Program of Anhui Province (Grant No.202004i07020013)。
文摘The Fabry–Perot(FP) resonant cavity is widely used in laser and spectroscopic measurements due to its unique interference transfer function(ITF). In the ideal case of parallel incident light, the ITF of the FP resonant cavity can be expressed by the Airy function. However, in reality, it is difficult to achieve perfect parallelism with collimated beams. In this article, a theoretical model is established for non-parallel light incidence, which assumes that the non-parallel incident light is a cone-shaped beam, and the cone angle is used to quantify the non-parallelism of the beam. The transmittance function of the FP resonant cavity under non-parallel light incidence is derived. The accuracy of the model is experimentally verified. Based on this model, the effects of divergence angle, tilt angle and FP cavity parameters(reflectivity, cavity length)on the ITF are studied. The reasons for the decrease in peak value, broadening and asymmetry of the interference peak under non-parallel light incidence are explained. It is suggested that a fine balance between the interference peak and the collimation effect of the incident light should be considered in the design and application of FP resonant cavities, especially for tilted applications such as angle-scanned spectroscopy. The research results of this article have certain significance for the design and application of FP resonant cavities.
基金supported by the National Natural Science Foundation of China (Grants 41572310, 41272351)the Strategic Priority Research Program of the Chinese Academy of Sciences (Grants XDB10030301, XDB10030304)support provided by the CAS-TWAS Presidential Fellowship, University of Chinese Academy of Sciences, Beijing, China
文摘Failure of rock mass that is subjected to compressive loads occurs from initiation, propagation, and linkage of new cracks from preexisting fissures. Our research investigates the cracking behaviour and coalescence process in a brittle material with two non-parallel overlapping flaws using a high-speed camera. The coalescence tensile crack and tensile wing cracks were the first cracks to occur from the preexisting flaws. The initiation stresses of the primary cracks at the two tips of each flaw were simultaneous and decreased with reduced flaw inclination angle. The following types of coalescence cracks were identified between the flaws: primary tensile coalescence crack, tensile crack linkage, shear crack linkage, mixed tensile-shear crack, and indirect crack coalescence. Coalescence through tensile linkage occurred mostly at pre-peak stress. In contrast, coalescence through shear or mixed tensile-shear cracks occurred at higher stress. Overall, this study indicates that the geometry of preexisting flaws affect crack initiation and coalescence behaviour.
文摘Coalescence among fractures would have influence on the stability of rock masses. Deep understanding of mechanical behavior of fractured rock masses is an important mean to identify failure mechanism of geological disaster. In this study, crack propagation processing was studied through loading pre-fractured specimens of concrete block, termed as rock-like material, in uniaxial compression tests. New non-parallel double-crack geometry was introduced to observe crack coalescence. The flaw combinations are different from the normally used flaw configurations. In addition, ultrasonic detection tests were performed on the test blocks. The stress and strain data of these tests and characteristic parameters of sound wave were recorded. The stress-strain curves of each test block under the uniaxial compression test were drawn, relations among deformation characteristics and crack angle of the crack specimens, and their overall strength were analyzed. It is found that strength of the specimen decreases as crack inclination increases under two crack inclinations. The highest uniaxial compressive strength is found in the specimen with the cracks at the same angle in different directions. Based on description of the crack initiation location, crack surface and the ultimate failure patterns, failure modes of eight subtype for test blocks are divided into three categories. It is expected that the study results could be beneficial for engineering application of jointed rock masses.
基金Project supported by the National Natural Science Foundation of China(Nos.11332007,11172203,and 91216111)
文摘The e-N method is widely used in transition prediction. The amplitude growth rate used in the e-N method is usually provided by the linear stability theory （LST） based on the local parallel hypothesis. Considering the non-parallelism effect, the parabolized stability equation （PSE） method lacks local characteristic of stability analysis. In this paper, a local stability analysis method considering non-parallelism is proposed, termed as EPSE since it may be considered as an expansion of the PSE method. The EPSE considers variation of the shape function in the streamwise direction. Its local characteristic is convenient for stability analysis. This paper uses the EPSE in a strong non-parallel flow and mode exchange problem. The results agree well with the PSE and the direct numerical simulation （DNS）. In addition, it is found that the growth rate is related to the normalized method in the non-parallel flow. Different results can be obtained using different normalized methods. Therefore, the normalized method must be consistent.
基金supported by the National Natural Science Foundation of China(No.11172143)the Research Innovation Program for College Graduates of Jiangsu Province(No.CXZZ130518)
文摘The research on boundary-layer receptivity is the key issue for the laminarturbulent transition prediction in fluid mechanics. Many of the previous studies for local receptivity are on the basis of the parallel flow assumption which cannot accurately reflect the real physics. To overcome this disadvantage, local receptivity in the non-parallel boundary layer is studied in this paper by the direct numerical simulation （DNS）. The difference between the non-parallel and parallel boundary layers on local receptivity is investigated. In addition, the effects of the disturbance frequency, the roughness location, and the multiple roughness elements on receptivity are also determined. Besides, the relations of receptivity with the amplitude of free-stream turbulence （FST）, with the roughness height, and with the roughness length are ascertained as well. The Tollmien- Schlichting （T-S） wave packets are excited in the non-parallel boundary layer under the interaction of the FST and the localized wall roughness. A group of T-S waves are separated by the fast Fourier transform. The obtained results are in accordance with Dietz＇s measurements, Wu＇s theoretical calculations, and the linear stability theory （LST）.
文摘数据驱动的多元化发展导致数据异构性增强、维度提升和特征量规模扩大,给贸易经济分析带来更大挑战。为了提高贸易经济分析的科学性,采用非平行超平面支持向量机算法(support vector machine,SVM)对贸易经济进行预测分析。首先,根据贸易经济影响因素进行主成分分析,获取影响贸易经济的关键特征,并对特征进行量化和去噪处理。然后,采用广义特征值最接近支持向量机(proximal support vector machine via generalized eigenvalues,GEPSVM)进行贸易经济预测分类。根据预测指标要求,选择核函数GEPSVM算法(KGEPSVM算法)对分类的非平行超平面求解,通过类别划分函数获得经济预测结果。实证分析表明,对比常用的非平行超平面支持向量机算法,所提算法的贸易经济预测性能更优,而且在常用贸易经济指标的预测中,表现出较高预测精度和稳定性。
基金National Natural Science Foundation of China(Nos.51874351,52078495)Hunan Institute of Technology Introduced Talents Research Start-up Fund Project,China(No.HQ22016)。
