Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridyna...Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.展开更多
In this work,we develop energy stable numerical methods to simulate electromagnetic waves propagating in optical media where the media responses include the linear Lorentz dispersion,the instantaneous nonlinear cubic ...In this work,we develop energy stable numerical methods to simulate electromagnetic waves propagating in optical media where the media responses include the linear Lorentz dispersion,the instantaneous nonlinear cubic Kerr response,and the nonlinear delayed Raman molecular vibrational response.Unlike the first-order PDE-ODE governing equations considered previously in Bokil et al.(J Comput Phys 350:420–452,2017)and Lyu et al.(J Sci Comput 89:1–42,2021),a model of mixed-order form is adopted here that consists of the first-order PDE part for Maxwell’s equations coupled with the second-order ODE part(i.e.,the auxiliary differential equations)modeling the linear and nonlinear dispersion in the material.The main contribution is a new numerical strategy to treat the Kerr and Raman nonlinearities to achieve provable energy stability property within a second-order temporal discretization.A nodal discontinuous Galerkin(DG)method is further applied in space for efficiently handling nonlinear terms at the algebraic level,while preserving the energy stability and achieving high-order accuracy.Indeed with d_(E)as the number of the components of the electric field,only a d_(E)×d_(E)nonlinear algebraic system needs to be solved at each interpolation node,and more importantly,all these small nonlinear systems are completely decoupled over one time step,rendering very high parallel efficiency.We evaluate the proposed schemes by comparing them with the methods in Bokil et al.(2017)and Lyu et al.(2021)(implemented in nodal form)regarding the accuracy,computational efficiency,and energy stability,by a parallel scalability study,and also through the simulations of the soliton-like wave propagation in one dimension,as well as the spatial-soliton propagation and two-beam interactions modeled by the two-dimensional transverse electric(TE)mode of the equations.展开更多
The solution of Poisson’s Equation plays an important role in many areas, including modeling high-intensity and high-brightness beams in particle accelerators. For the computational domain with a large aspect ratio, ...The solution of Poisson’s Equation plays an important role in many areas, including modeling high-intensity and high-brightness beams in particle accelerators. For the computational domain with a large aspect ratio, the integrated Green’s function method has been adopted to solve the 3D Poisson equation subject to open boundary conditions. In this paper, we report on the efficient implementation of this method, which can save more than a factor of 50 computing time compared with the direct brute force implementation and its improvement under certain extreme conditions.展开更多
Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision mod...Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision model of the momentum exchange between the differential propellant mass element (dm) and the rocket final mass (m1), in which dm initially travels forward to collide with m1 and rebounds to exit through the exhaust nozzle with a velocity that is known as the effective exhaust velocity ve. We observe that such a model does not explain how dm was able to acquire its initial forward velocity without the support of a reactive mass traveling in the opposite direction. We show instead that the initial kinetic energy of dm is generated from dm itself by a process of self-combustion and expansion. In our ideal rocket with a single particle dm confined inside a hollow tube with one closed end, we show that the process of self-combustion and expansion of dm will result in a pair of differential particles each with a mass dm/2, and each traveling away from one another along the tube axis, from the center of combustion. These two identical particles represent the active and reactive sub-components of dm, co-generated in compliance with Newton’s third law of equal action and reaction. Building on this model, we derive a linear momentum ODE of the system, the solution of which yields what we call the Revised Tsiolkovsky Rocket Equation (RTRE). We show that RTRE has a mathematical form that is similar to TRE, with the exception of the effective exhaust velocity (ve) term. The ve term in TRE is replaced in RTRE by the average of two distinct exhaust velocities that we refer to as fast-jet, vx<sub>1</sub>, and slow-jet, vx<sub>2</sub>. These two velocities correspond, respectively, to the velocities of the detonation pressure wave that is vectored directly towards the exhaust nozzle, and the retonation wave that is initially vectored in the direction of rocket propagation, but subsequently becomes reflected from the thrust surface of the combustion chamber to exit through the exhaust nozzle with a time lag behind the detonation wave. The detonation-retonation phenomenon is supported by experimental evidence in the published literature. Finally, we use a convolution model to simulate the composite exhaust pressure wave, highlighting the frequency spectrum of the pressure perturbations that are generated by the mutual interference between the fast-jet and slow-jet components. Our analysis offers insights into the origin of combustion oscillations in rocket engines, with possible extensions beyond rocket engineering into other fields of combustion engineering.展开更多
We applied a spatial high-order finite-difference-time-domain (HO-FDTD) scheme to solve 2D Maxwell’s equations in order to develop a fluid model employed to study the production of terahertz radiation by the filament...We applied a spatial high-order finite-difference-time-domain (HO-FDTD) scheme to solve 2D Maxwell’s equations in order to develop a fluid model employed to study the production of terahertz radiation by the filamentation of two femtosecond lasers in air plasma. We examined the performance of the applied scheme, in this context, we implemented the developed model to study selected phenomena in terahertz radiation production, such as the excitation energy and conversion efficiency of the produced THz radiation, in addition to the influence of the pulse chirping on properties of the produced radiation. The obtained numerical results have clarified that the applied HO-FDTD scheme is precisely accurate to solve Maxwell’s equations and sufficiently valid to study the production of terahertz radiation by the filamentation of two femtosecond lasers in air plasma.展开更多
In this paper, some exact solutions of the (3 + 1)-dimensional variable-coefficient Yu-Toda-Sasa-Fukuyama equation are investigated. By using Hirota’s direct method and symbolic computation, we obtained N-soliton sol...In this paper, some exact solutions of the (3 + 1)-dimensional variable-coefficient Yu-Toda-Sasa-Fukuyama equation are investigated. By using Hirota’s direct method and symbolic computation, we obtained N-soliton solution. By using the long wave limit method, the N-order rational solution can be obtained from N-order soliton solution. Then, through the paired complexification of parameters, the lump solution is obtained from N-order rational solution. Meanwhile, we obtained a hybrid solution between 1-lump solution and N-soliton (N=1,2) by using the long wave limit method and parameter complex. Furthermore, four different sets of three-dimensional graphs of solitons, lump solutions and hybrid solutions are drawn by selecting four different sets of coefficient functions which include one set of constant coefficient function and three sets of variable coefficient functions.展开更多
硬炭因资源丰富、结构稳定及安全性高等优势,已成为钠离子电池常用阳极材料。其中,煤基衍生硬炭受到了广泛的关注。本工作以长焰煤为碳源,硫脲为氮硫源,NaCl为模板,通过两步炭化工艺和杂原子掺杂相结合的方法合成了N和S共掺杂的煤基硬炭...硬炭因资源丰富、结构稳定及安全性高等优势,已成为钠离子电池常用阳极材料。其中,煤基衍生硬炭受到了广泛的关注。本工作以长焰煤为碳源,硫脲为氮硫源,NaCl为模板,通过两步炭化工艺和杂原子掺杂相结合的方法合成了N和S共掺杂的煤基硬炭(NSPC1200)。两步炭化过程在调节碳微晶结构和扩大层间距方面发挥了重要的作用。N和S的共掺杂调节了炭材料的电子结构,赋予其更多的活性位点;此外,引入NaCl作为模板有助于孔结构的构建,有利于电极和电解质之间的接触,从而实现Na+和电子的有效传输。在协同作用下,样品NSPC1200表现出优异的储钠能力,在20 mA g^(−1)电流密度下呈现314.2 mAh g^(−1)的可逆容量。即使在100 mA g^(−1)下循环200次,仍保持224.4 mAh g^(−1)的比容量。这项工作成功实现了策略性调整煤基炭材料微观结构的目标,最终获得了具有优异的电化学性能的硬炭阳极。展开更多
The interface mechanism between catalyst and carbon substrate has been the focus of research.In this paper,the FeCo alloy embedded N,S co-doped carbon substrate bifunctional catalyst(FeCo/S-NC)is obtained by a simple ...The interface mechanism between catalyst and carbon substrate has been the focus of research.In this paper,the FeCo alloy embedded N,S co-doped carbon substrate bifunctional catalyst(FeCo/S-NC)is obtained by a simple one-step pyrolysis strategy.The experimental results and density functional theory(DFT)calculation show that the formation of FeCo alloy is conducive to promoting electron transfer,and the introduction of S atom can enhance the interaction between FeCo alloy and carbon substrate,thus inhibiting the migration and agglomeration of particles on the surface of carbon material.The FeCo/SNC catalysts show outstanding performance for oxygen reduction reaction(ORR)and oxygen evolution reaction(OER).FeCo/S-NC shows a high half-wave potential(E_(1/2)=0.8823 V)for ORR and a low overpotential at 10 mA cm^(-2)(E_(j=10)=299 mV)for OER.In addition,compared with Pt/C+RuO_(2) assembled Zn-air battery(ZAB),the FeCo/S-NC assembled ZAB exhibits a larger power density(198.8 mW cm^(-2)),a higher specific capacity(786.1 mA h g_(zn)~(-1)),and ultra-stable cycle performance.These results confirm that the optimized composition and the interfacial interaction between catalyst and carbon substrate synergistically enhance the electrochemical performance.展开更多
文摘Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.
基金supported by China Postdoctoral Science Foundation grant 2020TQ0344the NSFC grants 11871139 and 12101597the NSF grants DMS-1720116,DMS-2012882,DMS-2011838,DMS-1719942,DMS-1913072.
文摘In this work,we develop energy stable numerical methods to simulate electromagnetic waves propagating in optical media where the media responses include the linear Lorentz dispersion,the instantaneous nonlinear cubic Kerr response,and the nonlinear delayed Raman molecular vibrational response.Unlike the first-order PDE-ODE governing equations considered previously in Bokil et al.(J Comput Phys 350:420–452,2017)and Lyu et al.(J Sci Comput 89:1–42,2021),a model of mixed-order form is adopted here that consists of the first-order PDE part for Maxwell’s equations coupled with the second-order ODE part(i.e.,the auxiliary differential equations)modeling the linear and nonlinear dispersion in the material.The main contribution is a new numerical strategy to treat the Kerr and Raman nonlinearities to achieve provable energy stability property within a second-order temporal discretization.A nodal discontinuous Galerkin(DG)method is further applied in space for efficiently handling nonlinear terms at the algebraic level,while preserving the energy stability and achieving high-order accuracy.Indeed with d_(E)as the number of the components of the electric field,only a d_(E)×d_(E)nonlinear algebraic system needs to be solved at each interpolation node,and more importantly,all these small nonlinear systems are completely decoupled over one time step,rendering very high parallel efficiency.We evaluate the proposed schemes by comparing them with the methods in Bokil et al.(2017)and Lyu et al.(2021)(implemented in nodal form)regarding the accuracy,computational efficiency,and energy stability,by a parallel scalability study,and also through the simulations of the soliton-like wave propagation in one dimension,as well as the spatial-soliton propagation and two-beam interactions modeled by the two-dimensional transverse electric(TE)mode of the equations.
文摘The solution of Poisson’s Equation plays an important role in many areas, including modeling high-intensity and high-brightness beams in particle accelerators. For the computational domain with a large aspect ratio, the integrated Green’s function method has been adopted to solve the 3D Poisson equation subject to open boundary conditions. In this paper, we report on the efficient implementation of this method, which can save more than a factor of 50 computing time compared with the direct brute force implementation and its improvement under certain extreme conditions.
文摘Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision model of the momentum exchange between the differential propellant mass element (dm) and the rocket final mass (m1), in which dm initially travels forward to collide with m1 and rebounds to exit through the exhaust nozzle with a velocity that is known as the effective exhaust velocity ve. We observe that such a model does not explain how dm was able to acquire its initial forward velocity without the support of a reactive mass traveling in the opposite direction. We show instead that the initial kinetic energy of dm is generated from dm itself by a process of self-combustion and expansion. In our ideal rocket with a single particle dm confined inside a hollow tube with one closed end, we show that the process of self-combustion and expansion of dm will result in a pair of differential particles each with a mass dm/2, and each traveling away from one another along the tube axis, from the center of combustion. These two identical particles represent the active and reactive sub-components of dm, co-generated in compliance with Newton’s third law of equal action and reaction. Building on this model, we derive a linear momentum ODE of the system, the solution of which yields what we call the Revised Tsiolkovsky Rocket Equation (RTRE). We show that RTRE has a mathematical form that is similar to TRE, with the exception of the effective exhaust velocity (ve) term. The ve term in TRE is replaced in RTRE by the average of two distinct exhaust velocities that we refer to as fast-jet, vx<sub>1</sub>, and slow-jet, vx<sub>2</sub>. These two velocities correspond, respectively, to the velocities of the detonation pressure wave that is vectored directly towards the exhaust nozzle, and the retonation wave that is initially vectored in the direction of rocket propagation, but subsequently becomes reflected from the thrust surface of the combustion chamber to exit through the exhaust nozzle with a time lag behind the detonation wave. The detonation-retonation phenomenon is supported by experimental evidence in the published literature. Finally, we use a convolution model to simulate the composite exhaust pressure wave, highlighting the frequency spectrum of the pressure perturbations that are generated by the mutual interference between the fast-jet and slow-jet components. Our analysis offers insights into the origin of combustion oscillations in rocket engines, with possible extensions beyond rocket engineering into other fields of combustion engineering.
文摘We applied a spatial high-order finite-difference-time-domain (HO-FDTD) scheme to solve 2D Maxwell’s equations in order to develop a fluid model employed to study the production of terahertz radiation by the filamentation of two femtosecond lasers in air plasma. We examined the performance of the applied scheme, in this context, we implemented the developed model to study selected phenomena in terahertz radiation production, such as the excitation energy and conversion efficiency of the produced THz radiation, in addition to the influence of the pulse chirping on properties of the produced radiation. The obtained numerical results have clarified that the applied HO-FDTD scheme is precisely accurate to solve Maxwell’s equations and sufficiently valid to study the production of terahertz radiation by the filamentation of two femtosecond lasers in air plasma.
文摘In this paper, some exact solutions of the (3 + 1)-dimensional variable-coefficient Yu-Toda-Sasa-Fukuyama equation are investigated. By using Hirota’s direct method and symbolic computation, we obtained N-soliton solution. By using the long wave limit method, the N-order rational solution can be obtained from N-order soliton solution. Then, through the paired complexification of parameters, the lump solution is obtained from N-order rational solution. Meanwhile, we obtained a hybrid solution between 1-lump solution and N-soliton (N=1,2) by using the long wave limit method and parameter complex. Furthermore, four different sets of three-dimensional graphs of solitons, lump solutions and hybrid solutions are drawn by selecting four different sets of coefficient functions which include one set of constant coefficient function and three sets of variable coefficient functions.
文摘硬炭因资源丰富、结构稳定及安全性高等优势,已成为钠离子电池常用阳极材料。其中,煤基衍生硬炭受到了广泛的关注。本工作以长焰煤为碳源,硫脲为氮硫源,NaCl为模板,通过两步炭化工艺和杂原子掺杂相结合的方法合成了N和S共掺杂的煤基硬炭(NSPC1200)。两步炭化过程在调节碳微晶结构和扩大层间距方面发挥了重要的作用。N和S的共掺杂调节了炭材料的电子结构,赋予其更多的活性位点;此外,引入NaCl作为模板有助于孔结构的构建,有利于电极和电解质之间的接触,从而实现Na+和电子的有效传输。在协同作用下,样品NSPC1200表现出优异的储钠能力,在20 mA g^(−1)电流密度下呈现314.2 mAh g^(−1)的可逆容量。即使在100 mA g^(−1)下循环200次,仍保持224.4 mAh g^(−1)的比容量。这项工作成功实现了策略性调整煤基炭材料微观结构的目标,最终获得了具有优异的电化学性能的硬炭阳极。
基金supported by the National Natural Science Foundation of China(52374301 and 22279030)the Fundamental Research Funds for the Central Universities(N2223037)+1 种基金Hebei Key Laboratory of Dielectric and Electrolyte Functional Material,Northeastern University at Qinhuangdao(HKDEFM2021201)the Performance subsidy fund for the Key Laboratory of Dielectric and Electrolyte Functional Material Hebei Province(22567627H)。
文摘The interface mechanism between catalyst and carbon substrate has been the focus of research.In this paper,the FeCo alloy embedded N,S co-doped carbon substrate bifunctional catalyst(FeCo/S-NC)is obtained by a simple one-step pyrolysis strategy.The experimental results and density functional theory(DFT)calculation show that the formation of FeCo alloy is conducive to promoting electron transfer,and the introduction of S atom can enhance the interaction between FeCo alloy and carbon substrate,thus inhibiting the migration and agglomeration of particles on the surface of carbon material.The FeCo/SNC catalysts show outstanding performance for oxygen reduction reaction(ORR)and oxygen evolution reaction(OER).FeCo/S-NC shows a high half-wave potential(E_(1/2)=0.8823 V)for ORR and a low overpotential at 10 mA cm^(-2)(E_(j=10)=299 mV)for OER.In addition,compared with Pt/C+RuO_(2) assembled Zn-air battery(ZAB),the FeCo/S-NC assembled ZAB exhibits a larger power density(198.8 mW cm^(-2)),a higher specific capacity(786.1 mA h g_(zn)~(-1)),and ultra-stable cycle performance.These results confirm that the optimized composition and the interfacial interaction between catalyst and carbon substrate synergistically enhance the electrochemical performance.
