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
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
Carbonate-based electrolytes still retain their top preference in sodium-ion battery(SIB)as in lithium-ion battery(LIBs)owing to their cost-effectiveness and accessibility.However,extensive studies have consistently d...Carbonate-based electrolytes still retain their top preference in sodium-ion battery(SIB)as in lithium-ion battery(LIBs)owing to their cost-effectiveness and accessibility.However,extensive studies have consistently demonstrated a mismatch between the hard carbon(HC)anode and carbonate-based electrolytes[1,2].Specifically,as for lowconcentration carbonate-based electrolytes(LCEs).展开更多
The development of aqueous Zn batteries is limited by parasitic water reactions,corrosion,and dendrite growth.To address these challenges,an inner Helmholtz plane(IHP)regulation method is proposed by employing low-cos...The development of aqueous Zn batteries is limited by parasitic water reactions,corrosion,and dendrite growth.To address these challenges,an inner Helmholtz plane(IHP)regulation method is proposed by employing low-cost,non-toxic maltitol as the electrolyte additive.The preferential adsorption behavior of maltitol can expel the water from the inner Helmholtz plane,and thus hinder the immediate contact between Zn metal and H_(2)O.Meanwhile,strong interaction between maltitol and H_(2)O molecules can restrain the activity of H_(2)O.Besides,the"IHP adsorption effect"along with the low LUMO energy level of maltitol-CF_(3)SO_(3)^(-)can promote the in-situ formation of an organic-inorganic complex solid electrolyte interface(SEI)layer.As a result,the hydrogen/oxygen evolution side reaction,corrosion,and dendrites issues are effectively suppressed,thereby leading to highly reversible and dendrite-free Zn plating/stripping.The Zn‖I_(2)battery with hybrid electrolytes also demonstrates high electrochemical performance and ultralong cycling stability,showing a capacity retention of 75%over 20000 charge-discharge cycles at a large current density of 5 A g^(-1).In addition,the capacity of the device has almost no obvious decay over20000 cycles even at-30℃.This work offers a successful electrolyte regulation strategy via the IHP adsorption effect to design electrolytes for high-performance rechargeable Zn-ion batteries.展开更多
Helmholtz resonators are widely used to control low frequency noise propagating in pipes.In this paper,the elastic bottom plate of Helmholtz resonator is simplified as a single degree of freedom(SDOF)vibration system ...Helmholtz resonators are widely used to control low frequency noise propagating in pipes.In this paper,the elastic bottom plate of Helmholtz resonator is simplified as a single degree of freedom(SDOF)vibration system with acoustic excitation,and a one-dimensional lumped-parameter analytical model was developed to accurately characterize the structure-acoustic coupling and sound transmission loss(STL)of a Helmholtz resonator with an elastic bottom plate.The effect of dynamical parameters of elastic bottom plate on STL is analyzed by utilizing the model.A design criterion to circumvent the effect of wall elasticity of Helmholtz resonators is proposed,i.e.,the structural natural frequency of the wall should be greater than three times the resonant frequency of the resonator to avoid the adverse effects of wall elasticity.This study can provide guidance for the rapid and effective design of Helmholtz resonators.展开更多
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 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.
基金Supported by the National Natural Science Foundation of China(U22A20438,52106090,T2325012)the Natural Science Foundation of Hubei Province(2023BAB036)Fundamental Research Funds for the Central Universities。
文摘Carbonate-based electrolytes still retain their top preference in sodium-ion battery(SIB)as in lithium-ion battery(LIBs)owing to their cost-effectiveness and accessibility.However,extensive studies have consistently demonstrated a mismatch between the hard carbon(HC)anode and carbonate-based electrolytes[1,2].Specifically,as for lowconcentration carbonate-based electrolytes(LCEs).
基金supported by the National Natural Science Foundation of China(52261160384)the Shenzhen Science and Technology Innovation Commission(RCYX20221008092934093)+1 种基金the Shenzhen Science and Technology Program(KJZD20230923114107014)the support from Testing Technology Center of Materials and Devices,Tsinghua Shenzhen International Graduate School。
文摘The development of aqueous Zn batteries is limited by parasitic water reactions,corrosion,and dendrite growth.To address these challenges,an inner Helmholtz plane(IHP)regulation method is proposed by employing low-cost,non-toxic maltitol as the electrolyte additive.The preferential adsorption behavior of maltitol can expel the water from the inner Helmholtz plane,and thus hinder the immediate contact between Zn metal and H_(2)O.Meanwhile,strong interaction between maltitol and H_(2)O molecules can restrain the activity of H_(2)O.Besides,the"IHP adsorption effect"along with the low LUMO energy level of maltitol-CF_(3)SO_(3)^(-)can promote the in-situ formation of an organic-inorganic complex solid electrolyte interface(SEI)layer.As a result,the hydrogen/oxygen evolution side reaction,corrosion,and dendrites issues are effectively suppressed,thereby leading to highly reversible and dendrite-free Zn plating/stripping.The Zn‖I_(2)battery with hybrid electrolytes also demonstrates high electrochemical performance and ultralong cycling stability,showing a capacity retention of 75%over 20000 charge-discharge cycles at a large current density of 5 A g^(-1).In addition,the capacity of the device has almost no obvious decay over20000 cycles even at-30℃.This work offers a successful electrolyte regulation strategy via the IHP adsorption effect to design electrolytes for high-performance rechargeable Zn-ion batteries.
基金funded by the Open Foundation of the State Key Laboratory of Vehicle NVH and Safety Technology(Grant No.NVHSKL-202202).
文摘Helmholtz resonators are widely used to control low frequency noise propagating in pipes.In this paper,the elastic bottom plate of Helmholtz resonator is simplified as a single degree of freedom(SDOF)vibration system with acoustic excitation,and a one-dimensional lumped-parameter analytical model was developed to accurately characterize the structure-acoustic coupling and sound transmission loss(STL)of a Helmholtz resonator with an elastic bottom plate.The effect of dynamical parameters of elastic bottom plate on STL is analyzed by utilizing the model.A design criterion to circumvent the effect of wall elasticity of Helmholtz resonators is proposed,i.e.,the structural natural frequency of the wall should be greater than three times the resonant frequency of the resonator to avoid the adverse effects of wall elasticity.This study can provide guidance for the rapid and effective design of Helmholtz resonators.
