In this paper,we compute sub-Riemannian limits of Gaussian curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for a Euclidean C2-smooth surface in the Heisenberg gro...In this paper,we compute sub-Riemannian limits of Gaussian curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for a Euclidean C2-smooth surface in the Heisenberg group away from characteristic points and signed geodesic curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for Euclidean C2-smooth curves on surfaces.We get Gauss-Bonnet theorems associated to two kinds of Schouten-Van Kampen affine connections in the Heisenberg group.展开更多
考虑理想弹塑性弯扭-Mohr-Coulomb-最大拉应力破坏准则,以及拉伸失效、压剪失效、转动屈服和扭转屈服4种失效模式,提出一种新的离散元弹塑性本构模型。该模型植入二次开发的三维颗粒流程序,通过数值试验研究宏细观参数关系,模拟Lac du B...考虑理想弹塑性弯扭-Mohr-Coulomb-最大拉应力破坏准则,以及拉伸失效、压剪失效、转动屈服和扭转屈服4种失效模式,提出一种新的离散元弹塑性本构模型。该模型植入二次开发的三维颗粒流程序,通过数值试验研究宏细观参数关系,模拟Lac du Bonnet(LDB)花岗岩试样压剪和拉伸强度试验。研究表明:颗粒转动弹塑性弯扭矩对宏观内摩擦角和黏聚力具有显著影响;宏观黏聚力随细观黏聚力和屈服弯扭矩增加而趋于恒定;宏观内摩擦角随屈服弯扭矩和细观摩擦系数增加而增加;岩石宏观单轴抗拉强度随细观极限拉应力的增加而趋于恒定;宏观弹性模量和泊松比主要受细观弹性模量和刚度比影响。弹塑性颗粒流本构模型模拟的LDB花岗岩的强度参数和变形参数,以及压拉强度比和裂缝分布与室内试验结果吻合较好。LDB花岗岩单轴压剪模拟试验在达到峰值应力前,试样内部裂缝以细观拉伸裂缝为主,从试样端部向中部发展成近似X状;在接近或超过峰值应力后,试样内部开始出现压剪裂缝、转动屈服裂缝和扭转屈服裂缝,从试样一端向另一端发展成单斜状,其倾角与宏观破坏倾角接近,发展成宏观压剪破坏面,从而揭示了宏观裂缝形成的细观机理。展开更多
Charles Bonnet综合征(CBS)的主要特征为发生于非精神异常患者的复杂性幻视,患病率约为0.4%～40%。其病因学尚不明确,临床特征亦复杂多样,目前尚无有效药物治疗。及时诊断、合理解释将有助于缓解患者情绪。治疗方案仍有待进一步研究。...Charles Bonnet综合征(CBS)的主要特征为发生于非精神异常患者的复杂性幻视,患病率约为0.4%～40%。其病因学尚不明确,临床特征亦复杂多样,目前尚无有效药物治疗。及时诊断、合理解释将有助于缓解患者情绪。治疗方案仍有待进一步研究。本文将近年来有关CBS的研究进行综述。展开更多
The bonnet tool polishing is a novel, advanced and ultra-precise polishing process, by which the freeform surface can be polished. However, during the past few years, not only the key technology of calculating the dwe...The bonnet tool polishing is a novel, advanced and ultra-precise polishing process, by which the freeform surface can be polished. However, during the past few years, not only the key technology of calculating the dwell time and controlling the surface form in the bonnet polishing has been little reported so far, but also little attention has been paid to research the material removal function of the convex surface based on the geometry model considering the influence of the curvature radius. Firstly in this paper, for realizing the control of the freeform surface automatically by the bonnet polishing, on the basis of the simplified geometric model of convex surface, the calculation expression of the polishing contact spot on the convex surface considering the influence of the curvature radius is deduced, and the calculation model of the pressure distribution considering the influence of the curvature radius on the convex surface is derived by the coordinate transformation. Then the velocity distribution model is built in the bonnet polishing the convex surface. On the basis of the above research and the semi-experimental modified Preston equation obtained from the combination method of experimental and theoretical derivation, the material removal model of the convex surface considering the influence of the curvature radius in the bonnet polishing is established. Finally, the validity of the model through the simulation method has been validated. This research presents an effective prediction model and the calculation method of material removal for convex surface in bonnet polishing and prepares for the bonnet polishing the free surface numerically and automatically.展开更多
The paper firstly analyzes the influence factor on material removal rate of curved optical work-pieces in the bonnet polishing. Then the experiments are conducted to reveal the effects of several polishing parameters ...The paper firstly analyzes the influence factor on material removal rate of curved optical work-pieces in the bonnet polishing. Then the experiments are conducted to reveal the effects of several polishing parameters on the material removal rate when the spherical optical glasses are polished with different curvature radius, such as the decrement of the bonnet, the rotational speed of the bonnet and the curvature radius of the work-piece＇s surface using a bonnet trial-manufacturing machine developed by our assignment groups. In the end, the curvilinear relationships between these parameters and the material removal rate are acquired and the laws of the effects on material removal rate in bonnet polishing by several parameters are given. When the spherical-pieces are polished with smaller curvature radius, it is not proportional to either bonnet decrement or bonnet rotational speed as described by the Preston equation although the removal rate increases as the relative velocity or the applied pressure increases. Therefore, for the purpose of calculating more accurately the material removal of the spherical work-pieces, the Preston equation should be modified and studied further.展开更多
With the increasing demand for high-precision optical components,bonnet polishing technology is increasingly being used in the polishing process of optical components owing to its high removal efficiency and high surf...With the increasing demand for high-precision optical components,bonnet polishing technology is increasingly being used in the polishing process of optical components owing to its high removal efficiency and high surface accuracy.However,it is expensive and difficult to implement dedicated bonnet polishing machine tools,and their processing range is limited.This research combines bonnet polishing technology with industrial robot-assisted processing technology to propose a robotic bonnet polishing control model for large-diameter axisymmetric aspherical optical components.Using the transformation relations of the spatial coordinate system,the transformation relations of the workpiece coordinate system,local coordinate system of the polishing point,and tool coordinate system of the bonnet sphere center are established to obtain the bonnet precession polishing motion model.The polishing trajectory of large-diameter axisymmetric aspherical components and the variation in the linkage angle difference were simulated by adding an efficiency-optimal control strategy to the motion model.The robot motion was simulated in Robostudio to verify the correctness of the precession motion model and control algorithm.Lastly,the robotic bonnet polishing system was successfully applied to the polishing process of the optical components.展开更多
Motivated by recent work,nonmonotonic behaviors of photon sphere radius can be used to reflect black hole phase transition for Reissner–Nordstr?m–AdS(RN–AdS)black holes,we study the case of five-dimensional charged...Motivated by recent work,nonmonotonic behaviors of photon sphere radius can be used to reflect black hole phase transition for Reissner–Nordstr?m–AdS(RN–AdS)black holes,we study the case of five-dimensional charged Gauss–Bonnet–AdS black holes in the reduced parameter space.We find that the nonmonotonic behaviors of photon sphere radius still exist.Using the coexistence line calculated from P–V plane,we capture the photon sphere radius of saturated small and large black holes(the boundary of the coexistence phase),then illustrate the reduced coexistence region.The results show that,reduced coexistence region decreases with charge Q but increases with Gauss–Bonnet coefficientα.When the charge vanishes,reduced coexistence region does not vary with Gauss–Bonnet coefficientαany more.In this case,the Gauss–Bonnet coefficientαplays the same role as the charge of five-dimensional RN–AdS black holes.Also,the situation of higher dimension is studied in the end.展开更多
Recently, a novel 4 D Einstein–Gauss–Bonnet gravity has been proposed by Glavan and Lin(2020 Phys. Rev. Lett. 124 081301) by rescaling the coupling α→α(D-4) and taking the limit D→ 4 at the level of equations of...Recently, a novel 4 D Einstein–Gauss–Bonnet gravity has been proposed by Glavan and Lin(2020 Phys. Rev. Lett. 124 081301) by rescaling the coupling α→α(D-4) and taking the limit D→ 4 at the level of equations of motion. This prescription, though was shown to bring non-trivial effects for some spacetimes with particular symmetries, remains mysterious and calls for scrutiny. Indeed, there is no continuous way to take the limit D→4 in the higher Ddimensional equations of motion because the tensor indices depend on the spacetime dimension and behave discretely. On the other hand, if one works with 4 D spacetime indices the contribution corresponding to the Gauss–Bonnet term vanishes identically in the equations of motion. A necessary condition(but may not be sufficient) for this procedure to work is that there is an embedding of the 4 D spacetime into the higher D-dimensional spacetime so that the equations in the latter can be properly interpreted after taking the limit. In this note, working with2 D Einstein gravity, we show several subtleties when applying the method used in(2020 Phys.Rev. Lett. 124 081301).展开更多
文摘In this paper,we compute sub-Riemannian limits of Gaussian curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for a Euclidean C2-smooth surface in the Heisenberg group away from characteristic points and signed geodesic curvature associated to two kinds of Schouten-Van Kampen affine connections and the adapted connection for Euclidean C2-smooth curves on surfaces.We get Gauss-Bonnet theorems associated to two kinds of Schouten-Van Kampen affine connections in the Heisenberg group.
文摘考虑理想弹塑性弯扭-Mohr-Coulomb-最大拉应力破坏准则,以及拉伸失效、压剪失效、转动屈服和扭转屈服4种失效模式,提出一种新的离散元弹塑性本构模型。该模型植入二次开发的三维颗粒流程序,通过数值试验研究宏细观参数关系,模拟Lac du Bonnet(LDB)花岗岩试样压剪和拉伸强度试验。研究表明:颗粒转动弹塑性弯扭矩对宏观内摩擦角和黏聚力具有显著影响;宏观黏聚力随细观黏聚力和屈服弯扭矩增加而趋于恒定;宏观内摩擦角随屈服弯扭矩和细观摩擦系数增加而增加;岩石宏观单轴抗拉强度随细观极限拉应力的增加而趋于恒定;宏观弹性模量和泊松比主要受细观弹性模量和刚度比影响。弹塑性颗粒流本构模型模拟的LDB花岗岩的强度参数和变形参数,以及压拉强度比和裂缝分布与室内试验结果吻合较好。LDB花岗岩单轴压剪模拟试验在达到峰值应力前,试样内部裂缝以细观拉伸裂缝为主,从试样端部向中部发展成近似X状;在接近或超过峰值应力后,试样内部开始出现压剪裂缝、转动屈服裂缝和扭转屈服裂缝,从试样一端向另一端发展成单斜状,其倾角与宏观破坏倾角接近,发展成宏观压剪破坏面,从而揭示了宏观裂缝形成的细观机理。
基金Supported by Young Teacher Independent Research Subject of Yanshan University of China(Grant No.15LGA002)
文摘The bonnet tool polishing is a novel, advanced and ultra-precise polishing process, by which the freeform surface can be polished. However, during the past few years, not only the key technology of calculating the dwell time and controlling the surface form in the bonnet polishing has been little reported so far, but also little attention has been paid to research the material removal function of the convex surface based on the geometry model considering the influence of the curvature radius. Firstly in this paper, for realizing the control of the freeform surface automatically by the bonnet polishing, on the basis of the simplified geometric model of convex surface, the calculation expression of the polishing contact spot on the convex surface considering the influence of the curvature radius is deduced, and the calculation model of the pressure distribution considering the influence of the curvature radius on the convex surface is derived by the coordinate transformation. Then the velocity distribution model is built in the bonnet polishing the convex surface. On the basis of the above research and the semi-experimental modified Preston equation obtained from the combination method of experimental and theoretical derivation, the material removal model of the convex surface considering the influence of the curvature radius in the bonnet polishing is established. Finally, the validity of the model through the simulation method has been validated. This research presents an effective prediction model and the calculation method of material removal for convex surface in bonnet polishing and prepares for the bonnet polishing the free surface numerically and automatically.
基金Foundation of Harbin Institute of Technology,China(No.HIT.2001.10)Harbin Municipal Youth Foundation of China(No.2002AFQXJ040).
文摘The paper firstly analyzes the influence factor on material removal rate of curved optical work-pieces in the bonnet polishing. Then the experiments are conducted to reveal the effects of several polishing parameters on the material removal rate when the spherical optical glasses are polished with different curvature radius, such as the decrement of the bonnet, the rotational speed of the bonnet and the curvature radius of the work-piece＇s surface using a bonnet trial-manufacturing machine developed by our assignment groups. In the end, the curvilinear relationships between these parameters and the material removal rate are acquired and the laws of the effects on material removal rate in bonnet polishing by several parameters are given. When the spherical-pieces are polished with smaller curvature radius, it is not proportional to either bonnet decrement or bonnet rotational speed as described by the Preston equation although the removal rate increases as the relative velocity or the applied pressure increases. Therefore, for the purpose of calculating more accurately the material removal of the spherical work-pieces, the Preston equation should be modified and studied further.
基金Science and Technology Projects of Shenzhen(Grant No.JCYJ20180306172924636).
文摘With the increasing demand for high-precision optical components,bonnet polishing technology is increasingly being used in the polishing process of optical components owing to its high removal efficiency and high surface accuracy.However,it is expensive and difficult to implement dedicated bonnet polishing machine tools,and their processing range is limited.This research combines bonnet polishing technology with industrial robot-assisted processing technology to propose a robotic bonnet polishing control model for large-diameter axisymmetric aspherical optical components.Using the transformation relations of the spatial coordinate system,the transformation relations of the workpiece coordinate system,local coordinate system of the polishing point,and tool coordinate system of the bonnet sphere center are established to obtain the bonnet precession polishing motion model.The polishing trajectory of large-diameter axisymmetric aspherical components and the variation in the linkage angle difference were simulated by adding an efficiency-optimal control strategy to the motion model.The robot motion was simulated in Robostudio to verify the correctness of the precession motion model and control algorithm.Lastly,the robotic bonnet polishing system was successfully applied to the polishing process of the optical components.
基金supported by the National Natural Science Foundation of China(Grant No.11235003)Overseas Study Fellowship Project from Physics Department of Beijing Normal University+1 种基金supported in part by the Government of Canada through the Department of Innovation,Science and Economic Developmentby the Province of Ontario through the Ministry of Research,Innovation and Science。
文摘Motivated by recent work,nonmonotonic behaviors of photon sphere radius can be used to reflect black hole phase transition for Reissner–Nordstr?m–AdS(RN–AdS)black holes,we study the case of five-dimensional charged Gauss–Bonnet–AdS black holes in the reduced parameter space.We find that the nonmonotonic behaviors of photon sphere radius still exist.Using the coexistence line calculated from P–V plane,we capture the photon sphere radius of saturated small and large black holes(the boundary of the coexistence phase),then illustrate the reduced coexistence region.The results show that,reduced coexistence region decreases with charge Q but increases with Gauss–Bonnet coefficientα.When the charge vanishes,reduced coexistence region does not vary with Gauss–Bonnet coefficientαany more.In this case,the Gauss–Bonnet coefficientαplays the same role as the charge of five-dimensional RN–AdS black holes.Also,the situation of higher dimension is studied in the end.
文摘Recently, a novel 4 D Einstein–Gauss–Bonnet gravity has been proposed by Glavan and Lin(2020 Phys. Rev. Lett. 124 081301) by rescaling the coupling α→α(D-4) and taking the limit D→ 4 at the level of equations of motion. This prescription, though was shown to bring non-trivial effects for some spacetimes with particular symmetries, remains mysterious and calls for scrutiny. Indeed, there is no continuous way to take the limit D→4 in the higher Ddimensional equations of motion because the tensor indices depend on the spacetime dimension and behave discretely. On the other hand, if one works with 4 D spacetime indices the contribution corresponding to the Gauss–Bonnet term vanishes identically in the equations of motion. A necessary condition(but may not be sufficient) for this procedure to work is that there is an embedding of the 4 D spacetime into the higher D-dimensional spacetime so that the equations in the latter can be properly interpreted after taking the limit. In this note, working with2 D Einstein gravity, we show several subtleties when applying the method used in(2020 Phys.Rev. Lett. 124 081301).
