The heat-setting of carpet yarns is a necessary process if you want to obtain a high quality woven or tufted carpet. Different setting processes exist, each with its respective advantages and drawbacks (hot air, overh...The heat-setting of carpet yarns is a necessary process if you want to obtain a high quality woven or tufted carpet. Different setting processes exist, each with its respective advantages and drawbacks (hot air, overheated steam, saturated steam under pressure).展开更多
This work extends to third-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a <u>p</u>oly<u>e</u>thylene-<u>r</u...This work extends to third-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a <u>p</u>oly<u>e</u>thylene-<u>r</u>eflected <u>p</u>lutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The PERP benchmark comprises 21,976 imprecisely known (uncertain) model parameters. Previous works have used the adjoint sensitivity analysis methodology to compute exactly and efficiently all of the 21,976 first-order and (21,976)<sup>2</sup> second-order sensitivities of the PERP benchmark’s leakage response to all of the benchmark’s uncertain parameters, showing that the largest and most consequential 1<sup>st</sup>- and 2<sup>nd</sup>-order response sensitivities are with respect to the total microscopic cross sections. These results have motivated extending the previous adjoint-based derivations to third-order, leading to the derivation, in this work, of the exact mathematical expressions of the (180)<sup>3</sup> third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections. The formulas derived in this work are valid not only for the PERP benchmark but can also be used for computing the 3<sup>rd</sup>-order sensitivities of the leakage response of any nuclear system involving fissionable material and internal or external neutron sources. Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of these (180)<sup>3</sup> third-order sensitivities (which turned out to be very large and consequential) and use them for a third-order uncertainty analysis of the PERP benchmark’s leakage response.展开更多
This work presents the results of the exact computation of (180)<sup>3</sup> = 5,832,000 third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental be...This work presents the results of the exact computation of (180)<sup>3</sup> = 5,832,000 third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental benchmark with respect to the benchmark’s 180 microscopic total cross sections. This computation was made possible by applying the Third-Order Adjoint Sensitivity Analysis Methodology developed by Cacuci. The numerical results obtained in this work revealed that many of the 3<sup>rd</sup>-order sensitivities are significantly larger than their corresponding 1<sup>st</sup>- and 2<sup>nd</sup>-order ones, which is contrary to the widely held belief that higher-order sensitivities are all much smaller and hence less important than the first-order ones, for reactor physics systems. In particular, the largest 3<sup>rd</sup>-order relative sensitivity is the mixed sensitivity <img src="Edit_754b8437-dfdf-487d-af68-c78c637e6d4e.png" width="180" height="24" alt="" />of the PERP leakage response with respect to the lowest energy-group (30) total cross sections of <sup>1</sup>H (“isotope 6”) and <sup>239</sup>Pu (“isotope 1”). These two isotopes are shown in this work to be the two most important parameters affecting the PERP benchmark’s leakage response. By comparison, the largest 1<sup>st</sup>-order sensitivity is that of the PERP leakage response with respect to the lowest energy-group total cross section of isotope <sup>1</sup>H, having the value <img src="Edit_a5cfcc11-6a99-41ee-b844-a5ee84b454b3.png" width="100" height="24" alt="" />, while the largest 2<sup>nd</sup>-order sensitivity is <img src="Edit_05166a2b-97f7-43f1-98ff-b21368c00228.png" width="120" height="22" alt="" />. The 3<sup>rd</sup>-order sensitivity analysis presented in this work is the first ever such analysis in the field of reactor physics. The consequences of the results presented in this work on the uncertainty analysis of the PERP benchmark’s leakage response will be presented in a subsequent work.展开更多
目的 采用HPLC法多指标成分定量测定联合正交偏最小二乘-判别分析(orthogonal partial least squares-discriminant analysis,OPLS-DA)及熵权优劣解距离法(entropy weight technique for order preference by similarity to ideal solut...目的 采用HPLC法多指标成分定量测定联合正交偏最小二乘-判别分析(orthogonal partial least squares-discriminant analysis,OPLS-DA)及熵权优劣解距离法(entropy weight technique for order preference by similarity to ideal solution,EWTOPSIS)对不同厂家降糖通脉片(Jiangtang Tongmai Tablets,JTT)质量进行综合评价,为科学评价JTT质量提供参考。方法 收集3个厂家15批JTT样品,采用HPLC法同时测定JTT中3’-羟基葛根素、葛根素、3’-甲氧基葛根素、太子参环肽B、哈巴苷、哈巴俄苷、二氢丹参酮Ⅰ、隐丹参酮、丹参酮Ⅰ和丹参酮Ⅱ_(A)的含量,运用SPSS26.0和SIMCA14.1统计软件进行层次聚类分析(hierarchical cluster analysis,HCA)、主成分分析(principal component analysis,PCA)和OPLS-DA,建立JTT HCA、PCA和OPLS-DA模型,获取得分图和载荷图及变量重要性投影(variable importance in projection,VIP)值,筛选并分析影响JTT质量差异的主要物质基础,并运用EW-TOPSIS法对不同厂家JTT进行质量优劣性评价。结果 3’-羟基葛根素、葛根素、3’-甲氧基葛根素、太子参环肽B、哈巴苷、哈巴俄苷、二氢丹参酮Ⅰ、隐丹参酮、丹参酮Ⅰ和丹参酮Ⅱ_(A)分别在5.97~298.50、14.45~722.50、4.89~244.50、0.58~29.00、6.55~327.50、2.46~123.00、1.39~69.50、3.56~178.00、4.25~212.50和7.97~398.50μg/mL(r≥0.999 1)线性关系良好,平均加样回收率(n=9)分别为99.53%、100.10%、98.95%、96.97%、100.03%、98.84%、97.06%、98.37%、99.31%、99.18%,RSD分别为0.71%、0.63%、0.98%、1.47%、0.79%、1.30%、1.26%、1.18%、1.39%、1.55%。化学计量学分析结果显示15批JTT样品聚为3类,同一厂家JTT样品聚为一类,不同生产厂家样品质量存在一定差异;葛根素、丹参酮Ⅰ、哈巴苷和丹参酮Ⅱ_(A)是影响JTT样品质量的主要潜在标志物;EW-TOPSIS法可用于不同厂家JTT质量优劣的评价。结论 建立的HPLC多指标成分定量测定方法操作便捷、结果准确,结合HCA、PCA、OPLS-DA及EW-TOPSIS法可用于JTT质量的综合评价。展开更多
The failure analysis of simply supported, isotropic, square plates is addressed. Attention focuses on minimum failure load amplitudes and failure locations, von Mises＇ equivalent stress along the plate thickness is a...The failure analysis of simply supported, isotropic, square plates is addressed. Attention focuses on minimum failure load amplitudes and failure locations, von Mises＇ equivalent stress along the plate thickness is also addressed. Several distributed and localized loading conditions are considered. Loads act on the top of the plate. Bi-sinusoidal and uniform loads are taken into account for distributed loadings, while stepwise constant centric and off-centric loadings are addressed in the case of localized loadings. Analysis is performed considering plates whose length-to-thickness ratio a/h can be as high as 100 （thin plates） and as low as 2 （very thick plates）. Results are obtained via several 2D plate models. Classical theories （CTs） and higher order models are applied. Those theories are based on polynomial approximation of the displacement field. Among the higher order theories （HOTs） HOTsa models account for the transverse shear deformations, while HOTs models account for both transverse shear and transverse normal deformations. LHOTs represent a local application of the higher order theories. A layerwise approach is thus assumed： by means of mathematical interfaces, the plate is considered to be made of several fictitious layers. The exact 3D solution is presented in order to determine the accuracy of the results obtained via the 2D models. In this way a hierarchy among the 2D theories is established. CTs provide highly accurate results for a/h greater than 10 in the case of distributed loadings and greater than 20 for localized loadings. Results obtained via HOTs are highly accurate in the case of very thick plates for bi-sinusoidal and centric loadings. In the case of uniform and off-centric loadings a high gradient is present in the neighborhood of the plate top. In those cases, LHOTs yield results that match the exact solution.展开更多
This work extends to fourth-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a <u>p</u>oly<u>e</u>thylene-<u>r</...This work extends to fourth-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a <u>p</u>oly<u>e</u>thylene-<u>r</u>eflected <u>p</u>lutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The PERP benchmark comprises 7477 imprecisely known (uncertain) model parameters which have nonzero values. These parameters are as follows: 180 microscopic total cross sections;7101 microscopic scattering sections;60 microscopic fission cross sections;60 parameters that characterize the average number of neutrons per fission;60 parameters that characterize the fission spectrum;10 parameters that characterize the fission source;and 6 parameters that characterize the isotope number densities. Previous works have used the adjoint sensitivity analysis methodology to compute exactly and efficiently all of the 7477 first-order and 27,956,503 second-order sensitivities of the PERP benchmark’s leakage response to all of the benchmark’s uncertain parameters. These works showed that largest response sensitivities involve the total microscopic cross sections, which motivated the recent computation of all of the (180)<sup>3</sup> third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections. It turned out that some of these 3<sup>rd</sup>-order cross sections were far larger than the corresponding 2<sup>nd</sup>-order ones, thereby having the largest impact on the uncertainties induced in the PERP benchmark’s response. This finding has motivated the development of the original 4<sup>th</sup>-order formulas presented in this work, which are valid not only for the PERP benchmark but can also be used for computing the 4<sup>th</sup>-order sensitivities of response of any nuclear system involving fissionable material and internal or external neutron sources. Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of the largest fourth-order sensitivities of the PERP benchmark’s response to the total microscopic cross section and use them for a pioneering fourth-order uncertainty analysis of the PERP benchmark’s response.展开更多
Let x ： Mn^n→ R^n＋1 be an n（≥2）-dimensional hypersurface immersed in Euclidean space Rn＋1. Let σi（0≤ i≤ n） be the ith mean curvature and Qn = ∑i=0^n（-1）^i＋1 （n^i）σ1^n-iσi. Recently, the author show...Let x ： Mn^n→ R^n＋1 be an n（≥2）-dimensional hypersurface immersed in Euclidean space Rn＋1. Let σi（0≤ i≤ n） be the ith mean curvature and Qn = ∑i=0^n（-1）^i＋1 （n^i）σ1^n-iσi. Recently, the author showed that Wn（x） = ∫M QndM is a conformal invariant under conformal group of R^n＋1 and called it the nth Willmore functional of x. An extremal hypersurface of conformal invariant functional Wn is called an nth order Willmore hypersurface. The purpose of this paper is to construct concrete examples of the 3rd order Willmore hypersurfaces in Ra which have good geometric behaviors. The ordinary differential equation characterizing the revolutionary 3rd Willmore hypersurfaces is established and some interesting explicit examples are found in this paper.展开更多
A compact facility for cancer therapy has been designed and is presently under construction. A slow beam extraction system using the RF-Knock Out method and 3rd-order resonance is adopted in the synchrotron of this fa...A compact facility for cancer therapy has been designed and is presently under construction. A slow beam extraction system using the RF-Knock Out method and 3rd-order resonance is adopted in the synchrotron of this facility. Eight sextupoles are used, four of them are for correcting the chromaticity and the rest for driving the 3rd-order resonance. In order to save the aperture of vacuum chamber, a 3-magnet bump is adopted during the extraction process. The extraction phase space map and the last 3 turns’ particle trajectory before extraction are given. The matching betatron functions with HEBT （high energy beam transport） are also presented.展开更多
文摘The heat-setting of carpet yarns is a necessary process if you want to obtain a high quality woven or tufted carpet. Different setting processes exist, each with its respective advantages and drawbacks (hot air, overheated steam, saturated steam under pressure).
文摘This work extends to third-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a <u>p</u>oly<u>e</u>thylene-<u>r</u>eflected <u>p</u>lutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The PERP benchmark comprises 21,976 imprecisely known (uncertain) model parameters. Previous works have used the adjoint sensitivity analysis methodology to compute exactly and efficiently all of the 21,976 first-order and (21,976)<sup>2</sup> second-order sensitivities of the PERP benchmark’s leakage response to all of the benchmark’s uncertain parameters, showing that the largest and most consequential 1<sup>st</sup>- and 2<sup>nd</sup>-order response sensitivities are with respect to the total microscopic cross sections. These results have motivated extending the previous adjoint-based derivations to third-order, leading to the derivation, in this work, of the exact mathematical expressions of the (180)<sup>3</sup> third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections. The formulas derived in this work are valid not only for the PERP benchmark but can also be used for computing the 3<sup>rd</sup>-order sensitivities of the leakage response of any nuclear system involving fissionable material and internal or external neutron sources. Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of these (180)<sup>3</sup> third-order sensitivities (which turned out to be very large and consequential) and use them for a third-order uncertainty analysis of the PERP benchmark’s leakage response.
文摘This work presents the results of the exact computation of (180)<sup>3</sup> = 5,832,000 third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental benchmark with respect to the benchmark’s 180 microscopic total cross sections. This computation was made possible by applying the Third-Order Adjoint Sensitivity Analysis Methodology developed by Cacuci. The numerical results obtained in this work revealed that many of the 3<sup>rd</sup>-order sensitivities are significantly larger than their corresponding 1<sup>st</sup>- and 2<sup>nd</sup>-order ones, which is contrary to the widely held belief that higher-order sensitivities are all much smaller and hence less important than the first-order ones, for reactor physics systems. In particular, the largest 3<sup>rd</sup>-order relative sensitivity is the mixed sensitivity <img src="Edit_754b8437-dfdf-487d-af68-c78c637e6d4e.png" width="180" height="24" alt="" />of the PERP leakage response with respect to the lowest energy-group (30) total cross sections of <sup>1</sup>H (“isotope 6”) and <sup>239</sup>Pu (“isotope 1”). These two isotopes are shown in this work to be the two most important parameters affecting the PERP benchmark’s leakage response. By comparison, the largest 1<sup>st</sup>-order sensitivity is that of the PERP leakage response with respect to the lowest energy-group total cross section of isotope <sup>1</sup>H, having the value <img src="Edit_a5cfcc11-6a99-41ee-b844-a5ee84b454b3.png" width="100" height="24" alt="" />, while the largest 2<sup>nd</sup>-order sensitivity is <img src="Edit_05166a2b-97f7-43f1-98ff-b21368c00228.png" width="120" height="22" alt="" />. The 3<sup>rd</sup>-order sensitivity analysis presented in this work is the first ever such analysis in the field of reactor physics. The consequences of the results presented in this work on the uncertainty analysis of the PERP benchmark’s leakage response will be presented in a subsequent work.
文摘目的 采用HPLC法多指标成分定量测定联合正交偏最小二乘-判别分析(orthogonal partial least squares-discriminant analysis,OPLS-DA)及熵权优劣解距离法(entropy weight technique for order preference by similarity to ideal solution,EWTOPSIS)对不同厂家降糖通脉片(Jiangtang Tongmai Tablets,JTT)质量进行综合评价,为科学评价JTT质量提供参考。方法 收集3个厂家15批JTT样品,采用HPLC法同时测定JTT中3’-羟基葛根素、葛根素、3’-甲氧基葛根素、太子参环肽B、哈巴苷、哈巴俄苷、二氢丹参酮Ⅰ、隐丹参酮、丹参酮Ⅰ和丹参酮Ⅱ_(A)的含量,运用SPSS26.0和SIMCA14.1统计软件进行层次聚类分析(hierarchical cluster analysis,HCA)、主成分分析(principal component analysis,PCA)和OPLS-DA,建立JTT HCA、PCA和OPLS-DA模型,获取得分图和载荷图及变量重要性投影(variable importance in projection,VIP)值,筛选并分析影响JTT质量差异的主要物质基础,并运用EW-TOPSIS法对不同厂家JTT进行质量优劣性评价。结果 3’-羟基葛根素、葛根素、3’-甲氧基葛根素、太子参环肽B、哈巴苷、哈巴俄苷、二氢丹参酮Ⅰ、隐丹参酮、丹参酮Ⅰ和丹参酮Ⅱ_(A)分别在5.97~298.50、14.45~722.50、4.89~244.50、0.58~29.00、6.55~327.50、2.46~123.00、1.39~69.50、3.56~178.00、4.25~212.50和7.97~398.50μg/mL(r≥0.999 1)线性关系良好,平均加样回收率(n=9)分别为99.53%、100.10%、98.95%、96.97%、100.03%、98.84%、97.06%、98.37%、99.31%、99.18%,RSD分别为0.71%、0.63%、0.98%、1.47%、0.79%、1.30%、1.26%、1.18%、1.39%、1.55%。化学计量学分析结果显示15批JTT样品聚为3类,同一厂家JTT样品聚为一类,不同生产厂家样品质量存在一定差异;葛根素、丹参酮Ⅰ、哈巴苷和丹参酮Ⅱ_(A)是影响JTT样品质量的主要潜在标志物;EW-TOPSIS法可用于不同厂家JTT质量优劣的评价。结论 建立的HPLC多指标成分定量测定方法操作便捷、结果准确,结合HCA、PCA、OPLS-DA及EW-TOPSIS法可用于JTT质量的综合评价。
文摘The failure analysis of simply supported, isotropic, square plates is addressed. Attention focuses on minimum failure load amplitudes and failure locations, von Mises＇ equivalent stress along the plate thickness is also addressed. Several distributed and localized loading conditions are considered. Loads act on the top of the plate. Bi-sinusoidal and uniform loads are taken into account for distributed loadings, while stepwise constant centric and off-centric loadings are addressed in the case of localized loadings. Analysis is performed considering plates whose length-to-thickness ratio a/h can be as high as 100 （thin plates） and as low as 2 （very thick plates）. Results are obtained via several 2D plate models. Classical theories （CTs） and higher order models are applied. Those theories are based on polynomial approximation of the displacement field. Among the higher order theories （HOTs） HOTsa models account for the transverse shear deformations, while HOTs models account for both transverse shear and transverse normal deformations. LHOTs represent a local application of the higher order theories. A layerwise approach is thus assumed： by means of mathematical interfaces, the plate is considered to be made of several fictitious layers. The exact 3D solution is presented in order to determine the accuracy of the results obtained via the 2D models. In this way a hierarchy among the 2D theories is established. CTs provide highly accurate results for a/h greater than 10 in the case of distributed loadings and greater than 20 for localized loadings. Results obtained via HOTs are highly accurate in the case of very thick plates for bi-sinusoidal and centric loadings. In the case of uniform and off-centric loadings a high gradient is present in the neighborhood of the plate top. In those cases, LHOTs yield results that match the exact solution.
文摘This work extends to fourth-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a <u>p</u>oly<u>e</u>thylene-<u>r</u>eflected <u>p</u>lutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The PERP benchmark comprises 7477 imprecisely known (uncertain) model parameters which have nonzero values. These parameters are as follows: 180 microscopic total cross sections;7101 microscopic scattering sections;60 microscopic fission cross sections;60 parameters that characterize the average number of neutrons per fission;60 parameters that characterize the fission spectrum;10 parameters that characterize the fission source;and 6 parameters that characterize the isotope number densities. Previous works have used the adjoint sensitivity analysis methodology to compute exactly and efficiently all of the 7477 first-order and 27,956,503 second-order sensitivities of the PERP benchmark’s leakage response to all of the benchmark’s uncertain parameters. These works showed that largest response sensitivities involve the total microscopic cross sections, which motivated the recent computation of all of the (180)<sup>3</sup> third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections. It turned out that some of these 3<sup>rd</sup>-order cross sections were far larger than the corresponding 2<sup>nd</sup>-order ones, thereby having the largest impact on the uncertainties induced in the PERP benchmark’s response. This finding has motivated the development of the original 4<sup>th</sup>-order formulas presented in this work, which are valid not only for the PERP benchmark but can also be used for computing the 4<sup>th</sup>-order sensitivities of response of any nuclear system involving fissionable material and internal or external neutron sources. Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of the largest fourth-order sensitivities of the PERP benchmark’s response to the total microscopic cross section and use them for a pioneering fourth-order uncertainty analysis of the PERP benchmark’s response.
文摘Let x ： Mn^n→ R^n＋1 be an n（≥2）-dimensional hypersurface immersed in Euclidean space Rn＋1. Let σi（0≤ i≤ n） be the ith mean curvature and Qn = ∑i=0^n（-1）^i＋1 （n^i）σ1^n-iσi. Recently, the author showed that Wn（x） = ∫M QndM is a conformal invariant under conformal group of R^n＋1 and called it the nth Willmore functional of x. An extremal hypersurface of conformal invariant functional Wn is called an nth order Willmore hypersurface. The purpose of this paper is to construct concrete examples of the 3rd order Willmore hypersurfaces in Ra which have good geometric behaviors. The ordinary differential equation characterizing the revolutionary 3rd Willmore hypersurfaces is established and some interesting explicit examples are found in this paper.
基金Supported by State Key Development Program of Basic Research of China (2010CB834204)
文摘A compact facility for cancer therapy has been designed and is presently under construction. A slow beam extraction system using the RF-Knock Out method and 3rd-order resonance is adopted in the synchrotron of this facility. Eight sextupoles are used, four of them are for correcting the chromaticity and the rest for driving the 3rd-order resonance. In order to save the aperture of vacuum chamber, a 3-magnet bump is adopted during the extraction process. The extraction phase space map and the last 3 turns’ particle trajectory before extraction are given. The matching betatron functions with HEBT （high energy beam transport） are also presented.
