As a novel class of purely organic fluores-cent materials,multiple resonance thermal-ly activated delayed fluorescence(MR-TADF)compounds hold significant promise for next-generation display technologies.The efficiency...As a novel class of purely organic fluores-cent materials,multiple resonance thermal-ly activated delayed fluorescence(MR-TADF)compounds hold significant promise for next-generation display technologies.The efficiency of exciton utilization and the overall performance of organic light-emit-ting devices are closely linked to the singlet-triplet energy gap(ΔEST)of MR-TADF emitters.Identifying an economic and accu-rate theoretical approach to predictΔESTwould be beneficial for high-throughput screening and facilitate the inverse design of MR-TADF molecules.In this study,we evaluated the S1state energy(E(S1)),T1state ener-gy(E(T1)),andΔESTusing three different physical interpretations:adiabatic excitation ener-gy,vertical absorption energy,and vertical emission energy.We employed the time-depen-dent density functional theory(TDDFT)and delta self-consistent field(ΔSCF)methods to calculate E(S1),E(T1),andΔESTfor 20 MR-TADF molecules reported in the literature.We compared these calculated values with experimental data obtained from fluorescence spec-troscopy at room-temperature(or 77 K)and phosphorescence spectroscopy conducted at 77 K.Our findings indicate that the vertical absorption energy at the S0 state minimum,deter-mined by theΔSCF method,accurately predicts the S1state energy.Similarly,the vertical absorption energy at the S0 state minimum,calculated using the TDDFT method,effectively predicts the T1state energy.TheΔESTderived from the difference between these two excita-tion energies exhibited the smallest mean absolute error of only 0.039 eV compared to the ex-perimental values.This combination represents the most accurate and cost-effective method reported to date for predicting theΔESTof MR-TADF molecules,and can be integrated into AI-driven inverse design workflows for new emitters.展开更多
Infinitely many conservation laws for some (1+1)-dimension soliton hierarchy with self-consistent sources are constructed from their corresponding Lax pairs directly. Three examples are given. Besides, infinitely m...Infinitely many conservation laws for some (1+1)-dimension soliton hierarchy with self-consistent sources are constructed from their corresponding Lax pairs directly. Three examples are given. Besides, infinitely many conservation laws for Kadomtsev-Petviashvili (KP) hierarchy with self-consistent sources are obtained from the pseudo-differential operator and the Lax pair.展开更多
In this study,we investigate the ef-ficacy of a hybrid parallel algo-rithm aiming at enhancing the speed of evaluation of two-electron repulsion integrals(ERI)and Fock matrix generation on the Hygon C86/DCU(deep compu...In this study,we investigate the ef-ficacy of a hybrid parallel algo-rithm aiming at enhancing the speed of evaluation of two-electron repulsion integrals(ERI)and Fock matrix generation on the Hygon C86/DCU(deep computing unit)heterogeneous computing platform.Multiple hybrid parallel schemes are assessed using a range of model systems,including those with up to 1200 atoms and 10000 basis func-tions.The findings of our research reveal that,during Hartree-Fock(HF)calculations,a single DCU ex-hibits 33.6 speedups over 32 C86 CPU cores.Compared with the efficiency of Wuhan Electronic Structure Package on Intel X86 and NVIDIA A100 computing platform,the Hygon platform exhibits good cost-effective-ness,showing great potential in quantum chemistry calculation and other high-performance scientific computations.展开更多
N-soliton solutions of the hierarchy of non-isospectral mKdV equation with self-consistent sources andthe hierarchy of non-isospectral sine-Gordon equation with self-consistent sources are obtained via the inverse sca...N-soliton solutions of the hierarchy of non-isospectral mKdV equation with self-consistent sources andthe hierarchy of non-isospectral sine-Gordon equation with self-consistent sources are obtained via the inverse scatteringtransform.展开更多
This paper analyses a three-cavity frequency-quadrupling terahertz gyroklystron with successive frequency-doubling in each cavity with self-consistent nonlinear theory. The beam-wave interaction efficiency and the ele...This paper analyses a three-cavity frequency-quadrupling terahertz gyroklystron with successive frequency-doubling in each cavity with self-consistent nonlinear theory. The beam-wave interaction efficiency and the electron bunching process are studied. The variation of output efficiency with the length of drift tubes and output power and the variation of Ohmic loss with the length of output cavity are considered. Numerical simulations predict an optimal output efficiency of 1.8%, a power output of more than 2 kW and a gain of 33 dB after taking into account Ohmic losses when the frequency-quadrupling gyroklystron, driven by a 40-kV, 3-A electron beam and 1 Watt input power, operates at 225 CHz.展开更多
The combined self-consistent and Mori-Tanaka approach proposed for the evaluation of the effective elastic property of particulate composites is extended to evMuate the effective elastoplastic property of particulate ...The combined self-consistent and Mori-Tanaka approach proposed for the evaluation of the effective elastic property of particulate composites is extended to evMuate the effective elastoplastic property of particulate composites. Suppose there are sufficient identical particle inclusions with total volume fraction c in a representative volume element (RVE) of a particulate composite, these inclusions are separated into two groups, with volume fractions (1 -A-1)c and c/A over the RVE, respectively. We assume that the first group of inclusions has already been embedded in the original matrix to form a fictitious matrix, and the RVE of the composite consists of the fictitious matrix and the second group of particle inclusions. The property of the fictitious matrix is determined by the conventional self-consistent scheme, while the effective elastoplastic property of the composite is determined by the conventional Mori-Tanaka scheme. Analysis shows that, the conventional Mori-Tanaka scheme and self-consistent scheme can be obtained as the two limit cases of the extended approach as A = 1 and A = c~, respectively. The constitutive behavior of the inclusions in either Group I or Group II is identical, indicating the consistency in the description of the constitutive behavior in the two steps. ~klrthermore, the effective elastoplastic behavior of some typical particulate composites is analyzed, and the satisfactory agreement between the computational and experimental results demonstrates the validity of the extended approach. The introduced A can serve reasonably as a parameter, which is related to the actual property of composites and can be identified by experiments, for a more accurate evaluation of the effective elastoplastic property of particulate composites.展开更多
The coupled Korteweg-de Vries (CKdV) equation with self-consistent sources (CKdVESCS) and its Lax representation are derived. We present a generalized binary Darboux transformation (GBDT) with an arbitrary time-...The coupled Korteweg-de Vries (CKdV) equation with self-consistent sources (CKdVESCS) and its Lax representation are derived. We present a generalized binary Darboux transformation (GBDT) with an arbitrary time- dependent function for the CKdVESCS as well as the formula for the N-times repeated GBDT. This GBDT provides non-auto-Biicklund transformation between two CKdVESCSs with different degrees of sources and enables us to construct more generM solutions with N arbitrary t-dependent functions. We obtain positon, negaton, complexiton, and negaton- positon solutions of the CKdVESCS.展开更多
The parabolized stability equation (PSE) method has been proven to be a useful and convenient tool for the investigation of the stability and transition problems of boundary layers. However, in its original formulat...The parabolized stability equation (PSE) method has been proven to be a useful and convenient tool for the investigation of the stability and transition problems of boundary layers. However, in its original formulation, for nonlinear problems, the complex wave number of each Fourier mode is determined by the so-called phase-locked rule, which results in non-self-consistency in the wave numbers. In this paper, a modification is proposed to make it self-consistent. The main idea is that, instead of allowing wave numbers to be complex, all wave numbers are kept real, and the growth or decay of each mode is simply manifested in the growth or decay of the modulus of its shape function. The validity of the new formulation is illustrated by comparing the results with those from the corresponding direct numerical simulation (DNS) as applied to a problem of compressible boundary layer with Mach number 6.展开更多
The adsorption of flexible polyelectrolyte (PE) with the smeared charge distribution onto an oppositely charged sphere immersed in a PE solution is studied numerically with the continuum self-consistent field theory...The adsorption of flexible polyelectrolyte (PE) with the smeared charge distribution onto an oppositely charged sphere immersed in a PE solution is studied numerically with the continuum self-consistent field theory. The power law scaling relationships between the boundary layer thickness and the surface charge density and the charge fraction of PE chains revealed in the study are in good agreement with the existing analytical result. The curvature effect on the degree of charge compensation of the total amount of charges on the adsorbed PE chains over the surface charges is examined, and a clear understanding of it based on the dependences of the degree of charge compensation on the surface charge density and the charge fraction of PE chains is established.展开更多
Bilayer membranes self-assembled from amphiphilic molecules such as lipids, surfactants, and block copolymers are ubiquitous in biological and physiochemical systems. The shape and structure of bilayer membranes depen...Bilayer membranes self-assembled from amphiphilic molecules such as lipids, surfactants, and block copolymers are ubiquitous in biological and physiochemical systems. The shape and structure of bilayer membranes depend crucially on their mechanical properties such as surface tension, bending moduli, and line tension. Understanding how the molecular properties of the amphiphiles determine the structure and mechanics of the self-assembled bilayers requires a molecularly detailed theoretical framework. The self-consistent field theory provides such a theoretical framework, which is capable of accurately predicting the mechanical parameters of self-assembled bilayer membranes. In this mini review we summarize the formulation of the self-consistent field theory, as exemplified by a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents, and its application to the study of self-assembled bilayer membranes.展开更多
A new six-component super soliton hierarchy is obtained based on matrix Lie super algebras. Super trace identity is used to furnish the super Hamiltonian structures for the resulting nonlinear super integrable hierarc...A new six-component super soliton hierarchy is obtained based on matrix Lie super algebras. Super trace identity is used to furnish the super Hamiltonian structures for the resulting nonlinear super integrable hierarchy. After that, the self- consistent sources of the new six-component super soliton hierarchy are presented. Furthermore, we establish the infinitely many conservation laws for the integrable super soliton hierarchy.展开更多
By means of the Lie algebra B 2,a new extended Lie algebra F is constructed.Based on the Lie algebras B 2 and F,the nonlinear Schro¨dinger-modified Korteweg de Vries(NLS-mKdV) hierarchy with self-consistent sou...By means of the Lie algebra B 2,a new extended Lie algebra F is constructed.Based on the Lie algebras B 2 and F,the nonlinear Schro¨dinger-modified Korteweg de Vries(NLS-mKdV) hierarchy with self-consistent sources as well as its nonlinear integrable couplings are derived.With the help of the variational identity,their Hamiltonian structures are generated.展开更多
A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with s/(4) has been presented (Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6...A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with s/(4) has been presented (Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6613). Based on this method, we construct two integrable couplings of the soliton hierarchy with self-consistent sources by using the loop algebra sl(4). In this paper, we also point out that there are some errors in these references and we have corrected these errors and set up new formula. The method can be generalized to other soliton hierarchy with self-consistent sources.展开更多
Recently Zheng & Hwang established a series of independence theorems concerning with planar effective elastic properties. It is manifested that the estimation of the effective elastic properties of microcracked so...Recently Zheng & Hwang established a series of independence theorems concerning with planar effective elastic properties. It is manifested that the estimation of the effective elastic properties of microcracked solids through the generalized self-consistent method (GSCM) contradicts with these independence theorems. In this paper it is shown that such contradiction is actually caused by the approximate algorithm adopted, while the exact solution of GSCM is consistent with these rigorously established independence theorems. Since only an approximate algorithm in GCSM is available in dealing with problems involving non-circular inclusions or holes, an intrinsic GSCM is proposed, which can be performed based on an approximate algorithm and the corresponding estimations are consistent with the independence theorems.展开更多
Integrable Rosochatius deformations of finite-dimensional integrable systems are generalized to the solitonhierarchy with self-consistent sources.The integrable Rosochatius deformations of the Kaup-Newell hierarchy wi...Integrable Rosochatius deformations of finite-dimensional integrable systems are generalized to the solitonhierarchy with self-consistent sources.The integrable Rosochatius deformations of the Kaup-Newell hierarchy withself-consistent sources,of the TD hierarchy with self-consistent sources,and of the Jaulent Miodek hierarchy with self-consistentsources,together with their Lax representations are presented.展开更多
The non-isospectral sine-Gordon equation with self-consistent sources is derived.Its solutions are obtainedby means of Hirota method and Wronskian technique,respectively.Non-isospectral dynamics including one-solitonc...The non-isospectral sine-Gordon equation with self-consistent sources is derived.Its solutions are obtainedby means of Hirota method and Wronskian technique,respectively.Non-isospectral dynamics including one-solitoncharacteristics,two-soliton scattering,and ghost solitons,are investigated.展开更多
A hierarchy of non-isospectral Ablowitz-Kaup-Newell-Segur (AKNS) equations with self-consistent sources is derived. As a general reduction case, a hierarchy of non-isospectral nonlinear SchrSdinger equations (NLSE...A hierarchy of non-isospectral Ablowitz-Kaup-Newell-Segur (AKNS) equations with self-consistent sources is derived. As a general reduction case, a hierarchy of non-isospectral nonlinear SchrSdinger equations (NLSE) with selfconsistent sources is obtained. Moreover, a new non-isospectral integrable coupling of the AKNS soliton hierarchy with self-consistent sources is constructed by using the Kronecker product.展开更多
We propose a systematic method for generalizing the integrable couplings of soliton eqhations hierarchy with self-consistent sources associated with s/(4). The JM equations hierarchy with self-consistent sources is ...We propose a systematic method for generalizing the integrable couplings of soliton eqhations hierarchy with self-consistent sources associated with s/(4). The JM equations hierarchy with self-consistent sources is derived. Furthermore, an integrable couplings of the JM soliton hierarchy with self-consistent sources is presented by using of the loop algebra sl(4).展开更多
We have carried out a theoretical study of double-5-doped InAlAs/InGaAs/InP high electron mobility transistor (HEMT) by means of the finite differential method. The electronic states in the quantum well of the HEMT ...We have carried out a theoretical study of double-5-doped InAlAs/InGaAs/InP high electron mobility transistor (HEMT) by means of the finite differential method. The electronic states in the quantum well of the HEMT are calculated self-consistently. Instead of boundary conditions, initial conditions are used to solve the Poisson equation. The concentration of two-dimensional electron gas (2DEG) and its distribution in the HEMT have been obtained. By changing the doping density of upper and lower impurity layers we find that the 2DEG concentration confined in the channel is greatly affected by these two doping layers. But the electrons depleted by the Schottky contact are hardly affected by the lower impurity layer. It is only related to the doping density of upper impurity layer. This means that we can deal with the doping concentrations of the two impurity layers and optimize them separately. Considering the sheet concentration and the mobility of the electrons in the channel, the optimized doping densities are found to be 5 × 10^12 and 3× 10^12 cm^-2 for the upper and lower impurity layers, respectively, in the double-5-doped InAlAs/InGaAs/InP HEMTs.展开更多
Based on the matrix Lie super algebra and supertrace identity, the integrable super-Geng hierarchy with self-consistent is established. Furthermore, we establish the infinitely many conservation laws for the integrabl...Based on the matrix Lie super algebra and supertrace identity, the integrable super-Geng hierarchy with self-consistent is established. Furthermore, we establish the infinitely many conservation laws for the integrable super-Geng hierarchy. The methods derived by us can be generalized to other nonlinear equation hierarchies.展开更多
基金support provided by the National Natural Science Foundation of China(No.22273043).
摘要As a novel class of purely organic fluores-cent materials,multiple resonance thermal-ly activated delayed fluorescence(MR-TADF)compounds hold significant promise for next-generation display technologies.The efficiency of exciton utilization and the overall performance of organic light-emit-ting devices are closely linked to the singlet-triplet energy gap(ΔEST)of MR-TADF emitters.Identifying an economic and accu-rate theoretical approach to predictΔESTwould be beneficial for high-throughput screening and facilitate the inverse design of MR-TADF molecules.In this study,we evaluated the S1state energy(E(S1)),T1state ener-gy(E(T1)),andΔESTusing three different physical interpretations:adiabatic excitation ener-gy,vertical absorption energy,and vertical emission energy.We employed the time-depen-dent density functional theory(TDDFT)and delta self-consistent field(ΔSCF)methods to calculate E(S1),E(T1),andΔESTfor 20 MR-TADF molecules reported in the literature.We compared these calculated values with experimental data obtained from fluorescence spec-troscopy at room-temperature(or 77 K)and phosphorescence spectroscopy conducted at 77 K.Our findings indicate that the vertical absorption energy at the S0 state minimum,deter-mined by theΔSCF method,accurately predicts the S1state energy.Similarly,the vertical absorption energy at the S0 state minimum,calculated using the TDDFT method,effectively predicts the T1state energy.TheΔESTderived from the difference between these two excita-tion energies exhibited the smallest mean absolute error of only 0.039 eV compared to the ex-perimental values.This combination represents the most accurate and cost-effective method reported to date for predicting theΔESTof MR-TADF molecules,and can be integrated into AI-driven inverse design workflows for new emitters.
基金supported by the National Natural Science Foundation of China (Grant Nos.10371070, 10671121)the Shanghai Leading Academic Discipline Project (Grant No.J50101)the President Foundation of East China Institute of Technology (Grant No.DHXK0810)
摘要Infinitely many conservation laws for some (1+1)-dimension soliton hierarchy with self-consistent sources are constructed from their corresponding Lax pairs directly. Three examples are given. Besides, infinitely many conservation laws for Kadomtsev-Petviashvili (KP) hierarchy with self-consistent sources are obtained from the pseudo-differential operator and the Lax pair.
基金supported by the National Natural Science Foundation of China(No.22373112 to Ji Qi,No.22373111 and 21921004 to Minghui Yang)GH-fund A(No.202107011790)。
摘要In this study,we investigate the ef-ficacy of a hybrid parallel algo-rithm aiming at enhancing the speed of evaluation of two-electron repulsion integrals(ERI)and Fock matrix generation on the Hygon C86/DCU(deep computing unit)heterogeneous computing platform.Multiple hybrid parallel schemes are assessed using a range of model systems,including those with up to 1200 atoms and 10000 basis func-tions.The findings of our research reveal that,during Hartree-Fock(HF)calculations,a single DCU ex-hibits 33.6 speedups over 32 C86 CPU cores.Compared with the efficiency of Wuhan Electronic Structure Package on Intel X86 and NVIDIA A100 computing platform,the Hygon platform exhibits good cost-effective-ness,showing great potential in quantum chemistry calculation and other high-performance scientific computations.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10371070,10671121the Foundation of Shanghai Education Committee for Shanghai Prospective Excellent Young Teachers+1 种基金Shanghai Leading Academic Discipline Project under Grant No.J50101 the President Foundation of East China Institute of Technology under Grant No.DHXK0810
摘要N-soliton solutions of the hierarchy of non-isospectral mKdV equation with self-consistent sources andthe hierarchy of non-isospectral sine-Gordon equation with self-consistent sources are obtained via the inverse scatteringtransform.
基金Project supported by National Natural Science Foundation of China (Grant No 10676110)973 Program of China (Grant No2007CB310401)
摘要This paper analyses a three-cavity frequency-quadrupling terahertz gyroklystron with successive frequency-doubling in each cavity with self-consistent nonlinear theory. The beam-wave interaction efficiency and the electron bunching process are studied. The variation of output efficiency with the length of drift tubes and output power and the variation of Ohmic loss with the length of output cavity are considered. Numerical simulations predict an optimal output efficiency of 1.8%, a power output of more than 2 kW and a gain of 33 dB after taking into account Ohmic losses when the frequency-quadrupling gyroklystron, driven by a 40-kV, 3-A electron beam and 1 Watt input power, operates at 225 CHz.
基金Project supported by the National Natural Science Foundation of China-NSAF (No. 10976032)Japan Society for the Promotion of Science (No. L08538)
摘要The combined self-consistent and Mori-Tanaka approach proposed for the evaluation of the effective elastic property of particulate composites is extended to evMuate the effective elastoplastic property of particulate composites. Suppose there are sufficient identical particle inclusions with total volume fraction c in a representative volume element (RVE) of a particulate composite, these inclusions are separated into two groups, with volume fractions (1 -A-1)c and c/A over the RVE, respectively. We assume that the first group of inclusions has already been embedded in the original matrix to form a fictitious matrix, and the RVE of the composite consists of the fictitious matrix and the second group of particle inclusions. The property of the fictitious matrix is determined by the conventional self-consistent scheme, while the effective elastoplastic property of the composite is determined by the conventional Mori-Tanaka scheme. Analysis shows that, the conventional Mori-Tanaka scheme and self-consistent scheme can be obtained as the two limit cases of the extended approach as A = 1 and A = c~, respectively. The constitutive behavior of the inclusions in either Group I or Group II is identical, indicating the consistency in the description of the constitutive behavior in the two steps. ~klrthermore, the effective elastoplastic behavior of some typical particulate composites is analyzed, and the satisfactory agreement between the computational and experimental results demonstrates the validity of the extended approach. The introduced A can serve reasonably as a parameter, which is related to the actual property of composites and can be identified by experiments, for a more accurate evaluation of the effective elastoplastic property of particulate composites.
基金The project supported by the National Fundamental Research Program of China(973 Program)under Grant No.2007CB814800National Natural Science Foundation of China under Grant No.10601028
摘要The coupled Korteweg-de Vries (CKdV) equation with self-consistent sources (CKdVESCS) and its Lax representation are derived. We present a generalized binary Darboux transformation (GBDT) with an arbitrary time- dependent function for the CKdVESCS as well as the formula for the N-times repeated GBDT. This GBDT provides non-auto-Biicklund transformation between two CKdVESCSs with different degrees of sources and enables us to construct more generM solutions with N arbitrary t-dependent functions. We obtain positon, negaton, complexiton, and negaton- positon solutions of the CKdVESCS.
基金supported by the National Natural Science Foundation of China(Nos.11202147,11472188,11332007,11172203,and 91216111)the Specialized Research Fund(New Teacher Class)for the Doctoral Program of Higher Education(No.20120032120007)
摘要The parabolized stability equation (PSE) method has been proven to be a useful and convenient tool for the investigation of the stability and transition problems of boundary layers. However, in its original formulation, for nonlinear problems, the complex wave number of each Fourier mode is determined by the so-called phase-locked rule, which results in non-self-consistency in the wave numbers. In this paper, a modification is proposed to make it self-consistent. The main idea is that, instead of allowing wave numbers to be complex, all wave numbers are kept real, and the growth or decay of each mode is simply manifested in the growth or decay of the modulus of its shape function. The validity of the new formulation is illustrated by comparing the results with those from the corresponding direct numerical simulation (DNS) as applied to a problem of compressible boundary layer with Mach number 6.
基金Project supports by the National Natural Science Foundation of China(Grant Nos.21074062 and 11174163)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,Ministry of Education of Chinathe Scientific Research Fund of Zhejiang Provincial Educational Department,China(Grant No.Y200907455)
摘要The adsorption of flexible polyelectrolyte (PE) with the smeared charge distribution onto an oppositely charged sphere immersed in a PE solution is studied numerically with the continuum self-consistent field theory. The power law scaling relationships between the boundary layer thickness and the surface charge density and the charge fraction of PE chains revealed in the study are in good agreement with the existing analytical result. The curvature effect on the degree of charge compensation of the total amount of charges on the adsorbed PE chains over the surface charges is examined, and a clear understanding of it based on the dependences of the degree of charge compensation on the surface charge density and the charge fraction of PE chains is established.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11421101 and 21274005)the Natural Sciences and Engineering Research Council(NSERC)of Canada
摘要Bilayer membranes self-assembled from amphiphilic molecules such as lipids, surfactants, and block copolymers are ubiquitous in biological and physiochemical systems. The shape and structure of bilayer membranes depend crucially on their mechanical properties such as surface tension, bending moduli, and line tension. Understanding how the molecular properties of the amphiphiles determine the structure and mechanics of the self-assembled bilayers requires a molecularly detailed theoretical framework. The self-consistent field theory provides such a theoretical framework, which is capable of accurately predicting the mechanical parameters of self-assembled bilayer membranes. In this mini review we summarize the formulation of the self-consistent field theory, as exemplified by a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents, and its application to the study of self-assembled bilayer membranes.
基金supported by the National Natural Science Foundation of China(Grant Nos.11547175,11271008 and 61072147)the First-class Discipline of University in Shanghai,Chinathe Science and Technology Department of Henan Province,China(Grant No.152300410230)
摘要A new six-component super soliton hierarchy is obtained based on matrix Lie super algebras. Super trace identity is used to furnish the super Hamiltonian structures for the resulting nonlinear super integrable hierarchy. After that, the self- consistent sources of the new six-component super soliton hierarchy are presented. Furthermore, we establish the infinitely many conservation laws for the integrable super soliton hierarchy.
基金Project supported by the Innovation Group Project of the Chinese Academy of Sciences (Grant No. KZCX2-YW-Q07-01)the Key Foundation of the National Natural Science Foundation of China (Grant No. 41030855)the Special Funding of Marine Science Study,State Ocean Administration of China (Grant No. 20090513-2)
摘要By means of the Lie algebra B 2,a new extended Lie algebra F is constructed.Based on the Lie algebras B 2 and F,the nonlinear Schro¨dinger-modified Korteweg de Vries(NLS-mKdV) hierarchy with self-consistent sources as well as its nonlinear integrable couplings are derived.With the help of the variational identity,their Hamiltonian structures are generated.
基金Project supported by the Natural Science Foundation of Shanghai (Grant No. 09ZR1410800)the Science Foundation of Key Laboratory of Mathematics Mechanization (Grant No. KLMM0806)+2 种基金the Shanghai Leading Academic Discipline Project (Grant No. J50101)the Key Disciplines of Shanghai Municipality (Grant No. S30104)the National Natural Science Foundation of China (Grant Nos. 61072147 and 11071159)
摘要A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with s/(4) has been presented (Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6613). Based on this method, we construct two integrable couplings of the soliton hierarchy with self-consistent sources by using the loop algebra sl(4). In this paper, we also point out that there are some errors in these references and we have corrected these errors and set up new formula. The method can be generalized to other soliton hierarchy with self-consistent sources.
摘要Recently Zheng & Hwang established a series of independence theorems concerning with planar effective elastic properties. It is manifested that the estimation of the effective elastic properties of microcracked solids through the generalized self-consistent method (GSCM) contradicts with these independence theorems. In this paper it is shown that such contradiction is actually caused by the approximate algorithm adopted, while the exact solution of GSCM is consistent with these rigorously established independence theorems. Since only an approximate algorithm in GCSM is available in dealing with problems involving non-circular inclusions or holes, an intrinsic GSCM is proposed, which can be performed based on an approximate algorithm and the corresponding estimations are consistent with the independence theorems.
基金Supported by National Basic Research Program of China (973 Program) under Grant No.2007CB814800National Natural Science Foundation of China under Grant No.10801083
摘要Integrable Rosochatius deformations of finite-dimensional integrable systems are generalized to the solitonhierarchy with self-consistent sources.The integrable Rosochatius deformations of the Kaup-Newell hierarchy withself-consistent sources,of the TD hierarchy with self-consistent sources,and of the Jaulent Miodek hierarchy with self-consistentsources,together with their Lax representations are presented.
基金The project supported by National Natural Science Foundation of China under Grant No.10371070the Foundation of Shanghai Education Committee for Shanghai Prospective Excellent Young Teachers
摘要The non-isospectral sine-Gordon equation with self-consistent sources is derived.Its solutions are obtainedby means of Hirota method and Wronskian technique,respectively.Non-isospectral dynamics including one-solitoncharacteristics,two-soliton scattering,and ghost solitons,are investigated.
基金Project supported by the Research work of Liaoning Provincial Development of Education, China (Grant No 2008670)
摘要A hierarchy of non-isospectral Ablowitz-Kaup-Newell-Segur (AKNS) equations with self-consistent sources is derived. As a general reduction case, a hierarchy of non-isospectral nonlinear SchrSdinger equations (NLSE) with selfconsistent sources is obtained. Moreover, a new non-isospectral integrable coupling of the AKNS soliton hierarchy with self-consistent sources is constructed by using the Kronecker product.
基金Supported by the Research Work of Liaoning Provincial Development of Education under Grant No,2008670
摘要We propose a systematic method for generalizing the integrable couplings of soliton eqhations hierarchy with self-consistent sources associated with s/(4). The JM equations hierarchy with self-consistent sources is derived. Furthermore, an integrable couplings of the JM soliton hierarchy with self-consistent sources is presented by using of the loop algebra sl(4).
摘要We have carried out a theoretical study of double-5-doped InAlAs/InGaAs/InP high electron mobility transistor (HEMT) by means of the finite differential method. The electronic states in the quantum well of the HEMT are calculated self-consistently. Instead of boundary conditions, initial conditions are used to solve the Poisson equation. The concentration of two-dimensional electron gas (2DEG) and its distribution in the HEMT have been obtained. By changing the doping density of upper and lower impurity layers we find that the 2DEG concentration confined in the channel is greatly affected by these two doping layers. But the electrons depleted by the Schottky contact are hardly affected by the lower impurity layer. It is only related to the doping density of upper impurity layer. This means that we can deal with the doping concentrations of the two impurity layers and optimize them separately. Considering the sheet concentration and the mobility of the electrons in the channel, the optimized doping densities are found to be 5 × 10^12 and 3× 10^12 cm^-2 for the upper and lower impurity layers, respectively, in the double-5-doped InAlAs/InGaAs/InP HEMTs.
基金Supported by the National Natural Science Foundation of China(11271008, 61072147, 11547175) Supported by the Science and Technology Department of Henan Province(152300410230)+1 种基金 Supported by the Key Scientific Research Projects of Henan Province(16A110026) Supported by the Education Department of Henan Province(13All0101)
摘要Based on the matrix Lie super algebra and supertrace identity, the integrable super-Geng hierarchy with self-consistent is established. Furthermore, we establish the infinitely many conservation laws for the integrable super-Geng hierarchy. The methods derived by us can be generalized to other nonlinear equation hierarchies.