There are various sand tipples in the natural world. The viewpoint of Yalin is that local disturbances result in laminar instability and in sand-tipple formation, namely, local disturbance^the instability of the lamin...There are various sand tipples in the natural world. The viewpoint of Yalin is that local disturbances result in laminar instability and in sand-tipple formation, namely, local disturbance^the instability of the laminar flow→the formation of sand ripples. Based on this viewpoint, a theoretical model of the resonant triad interaction and its nonlinear interaction with the sediment is established. The purpose of this model is to explain the formation and evolution of the sand-tipple and allow for analysis of the instability of open-channel flow caused by it and sand-tipple hydro-dynamic process. This model will not only pave a road to explore the mechanism of interaction between bed-form and turbulence, but also provide a good base for the study of aeolian sand-tipple formation.展开更多
Using the Lie symmetry approach,the author has examined traveling wave solutions of coupled Benjamin-Bona-Mahony-KdV equation.The coupled Benjamin-Bona-Mahony-KdV equation is reduced to nonlinear ordinary differential...Using the Lie symmetry approach,the author has examined traveling wave solutions of coupled Benjamin-Bona-Mahony-KdV equation.The coupled Benjamin-Bona-Mahony-KdV equation is reduced to nonlinear ordinary differential equations for all optimal subalgebras by using Lie classical symmetries and various solutions are obtained by the modified(G'/G)-expansion method.Further,with the aid of solutions of the nonlinear ordinary differential equations,more explicit traveling wave solutions of the coupled Benjamin-Bona-Mahony-KdV equation are found out.The traveling wave solutions are expressed by rational function.展开更多
This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis techniq...This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.展开更多
Portable and furnished electronics appliances demand power efficient energy storage devices where electrochemical supercapacitors gain much more attention.In this concern,a simple,low-cost and industry scalable succes...Portable and furnished electronics appliances demand power efficient energy storage devices where electrochemical supercapacitors gain much more attention.In this concern,a simple,low-cost and industry scalable successive ionic layer adsorption and reaction(SILAR)approach has been adopted to deposit nanostructured VS_2onto flexible and light-weight stainless steel(SS)substrate towards supercapacitor application.The nanocrystalline nature with hexagonal crystal structure has been confirmed for VS_2through structural analysis.The VS_2electrode exhibits a maximum specific capacitance of 349 F g^(-1)with a super stable behavior in three-electrode liquid-state configuration.Fabricated flexible symmetric solid-state supercapacitor(FSSC)device using gel electrolyte yields specific power of 1.5 k W kg^(-1)(specific energy of 25.9 Wh kg^(-1))with a widen voltage window of 1.6 V.A red LED has been glown for30 s using the system consisted of two devices in series combination.Furthermore,the system glows a combination of 21 red LEDs network with acronym‘VNIT’,demonstrating commercial exposure.The attribution of device demonstration even under mechanical stress holds great promise towards advanced flexible electronics application.展开更多
Conical origami structures are characterized by their substantial out-of-plane stiffness and energy-absorptioncapacity.Previous investigations have commonly focused on the static characteristics of these lightweight s...Conical origami structures are characterized by their substantial out-of-plane stiffness and energy-absorptioncapacity.Previous investigations have commonly focused on the static characteristics of these lightweight struc-tures.However,the efficient analysis of the natural vibrations of these structures is pivotal for designing conicalorigami structures with programmable stiffness and mass.In this paper,we propose a novel method to analyzethe natural vibrations of such structures by combining a symmetric substructuring method(SSM)and a gener-alized eigenvalue analysis.SSM exploits the inherent symmetry of the structure to decompose it into a finiteset of repetitive substructures.In doing so,we reduce the dimensions of matrices and improve computationalefficiency by adopting the stiffness and mass matrices of the substructures in the generalized eigenvalue analysis.Finite element simulations of pin-jointed models are used to validate the computational results of the proposedapproach.Moreover,the parametric analysis of the structures demonstrates the influences of the number of seg-ments along the circumference and the radius of the cone on the structural mass and natural frequencies of thestructures.Furthermore,we present a comparison between six-fold and four-fold conical origami structures anddiscuss the influence of various geometric parameters on their natural frequencies.This study provides a strategyfor efficiently analyzing the natural vibration of symmetric origami structures and has the potential to contributeto the efficient design and customization of origami metastructures with programmable stiffness.展开更多
Symmetric alternating directionmethod of multipliers(ADMM)is an efficient method for solving a class of separable convex optimization problems.This method updates the Lagrange multiplier twice with appropriate step si...Symmetric alternating directionmethod of multipliers(ADMM)is an efficient method for solving a class of separable convex optimization problems.This method updates the Lagrange multiplier twice with appropriate step sizes at each iteration.However,such step sizes were conservatively shrunk to guarantee the convergence in recent studies.In this paper,we are devoted to seeking larger step sizes whenever possible.The logarithmic-quadratic proximal(LQP)terms are applied to regularize the symmetric ADMM subproblems,allowing the constrained subproblems to then be converted to easier unconstrained ones.Theoretically,we prove the global convergence of such LQP-based symmetric ADMM by specifying a larger step size domain.Moreover,the numerical results on a traffic equilibrium problem are reported to demonstrate the advantage of the method with larger step sizes.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 50979066)the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant No. 51021004)
文摘There are various sand tipples in the natural world. The viewpoint of Yalin is that local disturbances result in laminar instability and in sand-tipple formation, namely, local disturbance^the instability of the laminar flow→the formation of sand ripples. Based on this viewpoint, a theoretical model of the resonant triad interaction and its nonlinear interaction with the sediment is established. The purpose of this model is to explain the formation and evolution of the sand-tipple and allow for analysis of the instability of open-channel flow caused by it and sand-tipple hydro-dynamic process. This model will not only pave a road to explore the mechanism of interaction between bed-form and turbulence, but also provide a good base for the study of aeolian sand-tipple formation.
文摘Using the Lie symmetry approach,the author has examined traveling wave solutions of coupled Benjamin-Bona-Mahony-KdV equation.The coupled Benjamin-Bona-Mahony-KdV equation is reduced to nonlinear ordinary differential equations for all optimal subalgebras by using Lie classical symmetries and various solutions are obtained by the modified(G'/G)-expansion method.Further,with the aid of solutions of the nonlinear ordinary differential equations,more explicit traveling wave solutions of the coupled Benjamin-Bona-Mahony-KdV equation are found out.The traveling wave solutions are expressed by rational function.
基金supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12071214)the Natural Science Foundation for Colleges and Universities of Jiangsu Province of China(Grant No.20KJB110011)+1 种基金supported by the National Science Foundation(Grant No.DMS-1620335)and the Simons Foundation(Grant No.637716)supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12272347).
文摘This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.
文摘Portable and furnished electronics appliances demand power efficient energy storage devices where electrochemical supercapacitors gain much more attention.In this concern,a simple,low-cost and industry scalable successive ionic layer adsorption and reaction(SILAR)approach has been adopted to deposit nanostructured VS_2onto flexible and light-weight stainless steel(SS)substrate towards supercapacitor application.The nanocrystalline nature with hexagonal crystal structure has been confirmed for VS_2through structural analysis.The VS_2electrode exhibits a maximum specific capacitance of 349 F g^(-1)with a super stable behavior in three-electrode liquid-state configuration.Fabricated flexible symmetric solid-state supercapacitor(FSSC)device using gel electrolyte yields specific power of 1.5 k W kg^(-1)(specific energy of 25.9 Wh kg^(-1))with a widen voltage window of 1.6 V.A red LED has been glown for30 s using the system consisted of two devices in series combination.Furthermore,the system glows a combination of 21 red LEDs network with acronym‘VNIT’,demonstrating commercial exposure.The attribution of device demonstration even under mechanical stress holds great promise towards advanced flexible electronics application.
基金supported by the National Natural Science Foundation of China(Grants Nos.51978150 and 52050410334)the Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grants No.SJCX23_0069)the Fundamental Research Funds for the Central Universities.
文摘Conical origami structures are characterized by their substantial out-of-plane stiffness and energy-absorptioncapacity.Previous investigations have commonly focused on the static characteristics of these lightweight struc-tures.However,the efficient analysis of the natural vibrations of these structures is pivotal for designing conicalorigami structures with programmable stiffness and mass.In this paper,we propose a novel method to analyzethe natural vibrations of such structures by combining a symmetric substructuring method(SSM)and a gener-alized eigenvalue analysis.SSM exploits the inherent symmetry of the structure to decompose it into a finiteset of repetitive substructures.In doing so,we reduce the dimensions of matrices and improve computationalefficiency by adopting the stiffness and mass matrices of the substructures in the generalized eigenvalue analysis.Finite element simulations of pin-jointed models are used to validate the computational results of the proposedapproach.Moreover,the parametric analysis of the structures demonstrates the influences of the number of seg-ments along the circumference and the radius of the cone on the structural mass and natural frequencies of thestructures.Furthermore,we present a comparison between six-fold and four-fold conical origami structures anddiscuss the influence of various geometric parameters on their natural frequencies.This study provides a strategyfor efficiently analyzing the natural vibration of symmetric origami structures and has the potential to contributeto the efficient design and customization of origami metastructures with programmable stiffness.
基金This research was supported by National Natural Science Foundation of China Grant 11771078Natural Science Foundation of Jiangsu Province Grant BK20181258+1 种基金Project of 333 of Jiangsu Province Grant BRA2018351Postgraduate Research&Practice Innovation Program of Jiangsu Province Grant KYCX18_0200.
文摘Symmetric alternating directionmethod of multipliers(ADMM)is an efficient method for solving a class of separable convex optimization problems.This method updates the Lagrange multiplier twice with appropriate step sizes at each iteration.However,such step sizes were conservatively shrunk to guarantee the convergence in recent studies.In this paper,we are devoted to seeking larger step sizes whenever possible.The logarithmic-quadratic proximal(LQP)terms are applied to regularize the symmetric ADMM subproblems,allowing the constrained subproblems to then be converted to easier unconstrained ones.Theoretically,we prove the global convergence of such LQP-based symmetric ADMM by specifying a larger step size domain.Moreover,the numerical results on a traffic equilibrium problem are reported to demonstrate the advantage of the method with larger step sizes.
