地球磁层顶频发的开尔文–赫姆霍兹(Kelvin-Helmholtz,K-H)不稳定性在太阳风的物质和能量向地球磁层的输运过程中发挥着重要的作用.研究筛选出2015-2020年中磁尾区域(X≈–60 Re)的磁层顶穿越事件,结合51个中磁尾处的K-H不稳定性事件,...地球磁层顶频发的开尔文–赫姆霍兹(Kelvin-Helmholtz,K-H)不稳定性在太阳风的物质和能量向地球磁层的输运过程中发挥着重要的作用.研究筛选出2015-2020年中磁尾区域(X≈–60 Re)的磁层顶穿越事件,结合51个中磁尾处的K-H不稳定性事件,统计研究了K-H不稳定性在中磁尾磁层顶的晨昏不对称性分布.结果表明,在中磁尾区域,磁层顶晨侧的K-H不稳定性发生率较高.在行星际磁场(Interplanetary Magnetic Field,IMF)北向条件下,发生在磁层顶晨侧的K-H不稳定性事件数量明显超越昏侧;当帕克–螺旋(Parker-Spiral,PS)IMF主导时,昏侧K-H不稳定性事件更多.太阳风的不同参数也会显著影响中磁尾区域磁层顶晨昏两侧的KH涡旋分布.磁尾区域的K-H波动也是导致磁尾等离子体片中不同温度的等离子体分布不对称的原因之一.展开更多
本文研究了在环状区域上利用积分方程方法求解Helmholtz方程Cauchy问题。首先利用Green公式将方程解用积分方程表示,然后利用跳跃关系将区域内点趋于边界,得到两条边界上的积分方程组,采用单双层位势算子表示积分方程组,采用核裂解的方...本文研究了在环状区域上利用积分方程方法求解Helmholtz方程Cauchy问题。首先利用Green公式将方程解用积分方程表示,然后利用跳跃关系将区域内点趋于边界,得到两条边界上的积分方程组,采用单双层位势算子表示积分方程组,采用核裂解的方法离散积分方程组中的奇异积分,并使用Tikhonov正则化结合Morozov偏差原理求解病态方程。两种添加了噪声的数值算例验证了算法的有效性。In this paper, we study the problem of solving the Cauchy problem of Helmholtz’s equation on a toroidal region using the integral equation method. Firstly, the solution of the equation is expressed in terms of integral equations using Green’s formula, then the jump relation is used to converge the points in the region to the boundary to get the set of integral equations on the two boundaries, the single and double-layer potential operator is used to express the set of integral equations, the kernel cleavage method is used to discretize the singular integrals in the set of integral equations, and the pathological equation is solved by using the Tikhonov regularization combined with the Morozov’s deviation principle. Two numerical examples with added noise verify the effectiveness of the algorithm.展开更多
A broadband tunable acoustic metasurface(BTAM)is conceived with Helmholtz resonators(HRs).The tunability of HRs’neck enables precise control over the phase shift of the unit cell.Through careful arrangement of unit c...A broadband tunable acoustic metasurface(BTAM)is conceived with Helmholtz resonators(HRs).The tunability of HRs’neck enables precise control over the phase shift of the unit cell.Through careful arrangement of unit cells,the BTAMs are engineered to exhibit various phase differences,thereby inducing anomalous reflections and acoustic focusing.Numerical simulations demonstrate the BTAM’s remarkable efficacy in manipulating the angle of reflection wave and achieving wave focusing across a broadband frequency range.Experimental investigations of the phase shift and anomalous reflection further validate the design of metasurface.This work contributes to the fields of broadband and tunable acoustic wave manipulation and provides a flexible and efficient approach for acoustic control devices.展开更多
The boundary knot method(BKM)is a simple boundary-type meshless method.Due to the use of non-singular general solutions rather than singular fundamental solutions,BKM does not need to consider the artificial boundary....The boundary knot method(BKM)is a simple boundary-type meshless method.Due to the use of non-singular general solutions rather than singular fundamental solutions,BKM does not need to consider the artificial boundary.Therefore,this method has the merits of purely meshless,easy to program,high solution accuracy and so on.In this paper,we investigate the effectiveness of the BKM for solving Helmholtz-type problems under various conditions through a series of novel numerical experiments.The results demonstrate that the BKM is efficient and achieves high computational accuracy for problems with smooth or continuous boundary conditions.However,when applied to discontinuous boundary problems,the method exhibits significant numerical instability,potentially leading to substantial deviations in the computed results.Finally,three potential improvement strategies are proposed to mitigate this limitation.展开更多
基于圆周排列的Helmholtz共振腔单元,设计并实现了一种具有低频宽禁带的声人工结构,可以在结构中心处实现二维隔声效果.针对实际模型,搭建了二维声场测量平台,进行了相应的实验研究,实验结果与有限元仿真结果符合较好.该结构在较宽的频...基于圆周排列的Helmholtz共振腔单元,设计并实现了一种具有低频宽禁带的声人工结构,可以在结构中心处实现二维隔声效果.针对实际模型,搭建了二维声场测量平台,进行了相应的实验研究,实验结果与有限元仿真结果符合较好.该结构在较宽的频带内(680—1050 Hz)可以实现较好的隔声效果,最大隔声量可达41 d B.实验中还研究了单元参数及共振状态对隔声效果的影响.隔声区的大小与共振单元的分布形式有直接关系,而良好的共振状态将对提高隔声量有一定帮助.研究结果对设计新型声防护结构具有理论与应用价值.展开更多
文摘地球磁层顶频发的开尔文–赫姆霍兹(Kelvin-Helmholtz,K-H)不稳定性在太阳风的物质和能量向地球磁层的输运过程中发挥着重要的作用.研究筛选出2015-2020年中磁尾区域(X≈–60 Re)的磁层顶穿越事件,结合51个中磁尾处的K-H不稳定性事件,统计研究了K-H不稳定性在中磁尾磁层顶的晨昏不对称性分布.结果表明,在中磁尾区域,磁层顶晨侧的K-H不稳定性发生率较高.在行星际磁场(Interplanetary Magnetic Field,IMF)北向条件下,发生在磁层顶晨侧的K-H不稳定性事件数量明显超越昏侧;当帕克–螺旋(Parker-Spiral,PS)IMF主导时,昏侧K-H不稳定性事件更多.太阳风的不同参数也会显著影响中磁尾区域磁层顶晨昏两侧的KH涡旋分布.磁尾区域的K-H波动也是导致磁尾等离子体片中不同温度的等离子体分布不对称的原因之一.
文摘本文研究了在环状区域上利用积分方程方法求解Helmholtz方程Cauchy问题。首先利用Green公式将方程解用积分方程表示,然后利用跳跃关系将区域内点趋于边界,得到两条边界上的积分方程组,采用单双层位势算子表示积分方程组,采用核裂解的方法离散积分方程组中的奇异积分,并使用Tikhonov正则化结合Morozov偏差原理求解病态方程。两种添加了噪声的数值算例验证了算法的有效性。In this paper, we study the problem of solving the Cauchy problem of Helmholtz’s equation on a toroidal region using the integral equation method. Firstly, the solution of the equation is expressed in terms of integral equations using Green’s formula, then the jump relation is used to converge the points in the region to the boundary to get the set of integral equations on the two boundaries, the single and double-layer potential operator is used to express the set of integral equations, the kernel cleavage method is used to discretize the singular integrals in the set of integral equations, and the pathological equation is solved by using the Tikhonov regularization combined with the Morozov’s deviation principle. Two numerical examples with added noise verify the effectiveness of the algorithm.
基金supported by the National Natural Science Foundation of China(Grant Nos.11991030,11991031 and 12202054)Aeronautical Science Foundation(Grant No.ASFC20230042072010).
文摘A broadband tunable acoustic metasurface(BTAM)is conceived with Helmholtz resonators(HRs).The tunability of HRs’neck enables precise control over the phase shift of the unit cell.Through careful arrangement of unit cells,the BTAMs are engineered to exhibit various phase differences,thereby inducing anomalous reflections and acoustic focusing.Numerical simulations demonstrate the BTAM’s remarkable efficacy in manipulating the angle of reflection wave and achieving wave focusing across a broadband frequency range.Experimental investigations of the phase shift and anomalous reflection further validate the design of metasurface.This work contributes to the fields of broadband and tunable acoustic wave manipulation and provides a flexible and efficient approach for acoustic control devices.
基金Supported by the Key Scientific Research Plan of Colleges and Universities in Henan Province(23B140006)。
文摘The boundary knot method(BKM)is a simple boundary-type meshless method.Due to the use of non-singular general solutions rather than singular fundamental solutions,BKM does not need to consider the artificial boundary.Therefore,this method has the merits of purely meshless,easy to program,high solution accuracy and so on.In this paper,we investigate the effectiveness of the BKM for solving Helmholtz-type problems under various conditions through a series of novel numerical experiments.The results demonstrate that the BKM is efficient and achieves high computational accuracy for problems with smooth or continuous boundary conditions.However,when applied to discontinuous boundary problems,the method exhibits significant numerical instability,potentially leading to substantial deviations in the computed results.Finally,three potential improvement strategies are proposed to mitigate this limitation.
文摘基于圆周排列的Helmholtz共振腔单元,设计并实现了一种具有低频宽禁带的声人工结构,可以在结构中心处实现二维隔声效果.针对实际模型,搭建了二维声场测量平台,进行了相应的实验研究,实验结果与有限元仿真结果符合较好.该结构在较宽的频带内(680—1050 Hz)可以实现较好的隔声效果,最大隔声量可达41 d B.实验中还研究了单元参数及共振状态对隔声效果的影响.隔声区的大小与共振单元的分布形式有直接关系,而良好的共振状态将对提高隔声量有一定帮助.研究结果对设计新型声防护结构具有理论与应用价值.
