The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensiona...The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensional space and one-dimensional time.With broad applications spanning fluid dynamics,shallow water waves,plasma physics,and condensed matter physics,the investigation of its solutions holds significant importance.Traditional analytical methods face limitations due to their dependence on bilinear forms.To overcome this constraint,this letter proposes a novel multi-modal neurosymbolic reasoning intelligent algorithm(MMNRIA)that achieves 100%accurate solutions for nonlinear partial differential equations without requiring bilinear transformations.By synergistically integrating neural networks with symbolic computation,this approach establishes a new paradigm for universal analytical solutions of nonlinear partial differential equations.As a practical demonstration,we successfully derive several exact analytical solutions for the(3+1)-dimensional BLMP equation using MMNRIA.These solutions provide a powerful theoretical framework for studying intricate wave phenomena governed by nonlinearity and dispersion effects in three-dimensional physical space.展开更多
The quantum anomalous Hall(QAH)effect,characterized by dissipationless chiral edge states without requiring an external magnetic field,represents a cornerstone of topological physics.The first experimental observation...The quantum anomalous Hall(QAH)effect,characterized by dissipationless chiral edge states without requiring an external magnetic field,represents a cornerstone of topological physics.The first experimental observation of the QAH effect was achieved in chromium-doped(Bi,Sb)2Te 3 topological insulator(TI)thin films[1].展开更多
Optimal microstructure design of battery materials is critical to enhance the performance of batteries for tailored applications such as high power cells.Accurate simulation of the thermodynamics,transport,and electro...Optimal microstructure design of battery materials is critical to enhance the performance of batteries for tailored applications such as high power cells.Accurate simulation of the thermodynamics,transport,and electrochemical reaction kinetics in commonly used polycrystalline battery materials remains a challenge.Here,we combine state-of-the-art multiphase field modelling with the smoothed boundary method to accurately simulate complex battery microstructures and multiphase physics.The phase-field method is employed to parameterize complex open pore cathode microstructures and we present a formulation to impose galvanostatic charging conditions on the diffuse boundary representation.By extending the smoothed boundary method to the multiphase-field method,we build a simulation framework which is capable of simulating the coupled effects of intercalation,anisotropic diffusion,and phase transitions in arbitrary complex polycrystalline agglomerates.This method is directly compatible with voxel-based data,e.g.,from X-ray tomography.The simulation framework is used to study the reversible phase transitions in Li_(X)NiO_(2)in dense and nanoporous agglomerates.Based on the thermodynamic consistency of phase-field approaches with ab-initio simulations and the open circuit potential,we reconstruct the Gibbs free energies of four individual phases(H1,M,H_(2)and H_(3))from experimental cycling data.The results show remarkable agreement with previously published DFT results.From charge simulations,we discover a strong influence of particle morphology on the phase transition behaviour,in particular a shrinking core-like behaviour in dense polycrystalline structures and a particle-by-particle mosaic behavior in nanoporous samples.Overall,the proposed simulation framework enables the detailed study of phase transitions in intercalation materials to enhance microstructure design and fast charging protocols.展开更多
As we have known,the 20th century represents an era of quantum physics.Based on the quantum physics,the physics and technology of semiconductors andmicroelec-tronics,lasers and masers,superconductors and devices,etc.,...As we have known,the 20th century represents an era of quantum physics.Based on the quantum physics,the physics and technology of semiconductors andmicroelec-tronics,lasers and masers,superconductors and devices,etc.,have been developed rapidly and widely.These build the hardware for the information science and technology,which have become the main driving force behind the re-garded“third industrial revolution”.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.62303289)Tianyuan Fund for Mathematics of the National Natural Science Foundation of China(Grant No.12426105)+3 种基金the Scientific and Technological Innovation Programs(STIP)of Higher Education Institutions in Shanxi(Grant No.2024L022)Fundamental Research Program of Shanxi Province(Grant Nos.202403021222001 and 202203021222003)the“Wen Ying Young Scholars”Talent Project of Shanxi University(Grant Nos.138541088,138541090,and 138541127)Funded by Open Foundation of Hubei Key Laboratory of Applied Mathematics(Hubei University)(Grant No.HBAM202401).
文摘The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensional space and one-dimensional time.With broad applications spanning fluid dynamics,shallow water waves,plasma physics,and condensed matter physics,the investigation of its solutions holds significant importance.Traditional analytical methods face limitations due to their dependence on bilinear forms.To overcome this constraint,this letter proposes a novel multi-modal neurosymbolic reasoning intelligent algorithm(MMNRIA)that achieves 100%accurate solutions for nonlinear partial differential equations without requiring bilinear transformations.By synergistically integrating neural networks with symbolic computation,this approach establishes a new paradigm for universal analytical solutions of nonlinear partial differential equations.As a practical demonstration,we successfully derive several exact analytical solutions for the(3+1)-dimensional BLMP equation using MMNRIA.These solutions provide a powerful theoretical framework for studying intricate wave phenomena governed by nonlinearity and dispersion effects in three-dimensional physical space.
文摘The quantum anomalous Hall(QAH)effect,characterized by dissipationless chiral edge states without requiring an external magnetic field,represents a cornerstone of topological physics.The first experimental observation of the QAH effect was achieved in chromium-doped(Bi,Sb)2Te 3 topological insulator(TI)thin films[1].
基金funded by the German Research Foundation (DFG) under Project ID 390874152 (POLiS Cluster of Excellence)Support by the Helmholtz association though the MTET programme (no. 38.02.01) is gratefully acknowledged.
文摘Optimal microstructure design of battery materials is critical to enhance the performance of batteries for tailored applications such as high power cells.Accurate simulation of the thermodynamics,transport,and electrochemical reaction kinetics in commonly used polycrystalline battery materials remains a challenge.Here,we combine state-of-the-art multiphase field modelling with the smoothed boundary method to accurately simulate complex battery microstructures and multiphase physics.The phase-field method is employed to parameterize complex open pore cathode microstructures and we present a formulation to impose galvanostatic charging conditions on the diffuse boundary representation.By extending the smoothed boundary method to the multiphase-field method,we build a simulation framework which is capable of simulating the coupled effects of intercalation,anisotropic diffusion,and phase transitions in arbitrary complex polycrystalline agglomerates.This method is directly compatible with voxel-based data,e.g.,from X-ray tomography.The simulation framework is used to study the reversible phase transitions in Li_(X)NiO_(2)in dense and nanoporous agglomerates.Based on the thermodynamic consistency of phase-field approaches with ab-initio simulations and the open circuit potential,we reconstruct the Gibbs free energies of four individual phases(H1,M,H_(2)and H_(3))from experimental cycling data.The results show remarkable agreement with previously published DFT results.From charge simulations,we discover a strong influence of particle morphology on the phase transition behaviour,in particular a shrinking core-like behaviour in dense polycrystalline structures and a particle-by-particle mosaic behavior in nanoporous samples.Overall,the proposed simulation framework enables the detailed study of phase transitions in intercalation materials to enhance microstructure design and fast charging protocols.
文摘As we have known,the 20th century represents an era of quantum physics.Based on the quantum physics,the physics and technology of semiconductors andmicroelec-tronics,lasers and masers,superconductors and devices,etc.,have been developed rapidly and widely.These build the hardware for the information science and technology,which have become the main driving force behind the re-garded“third industrial revolution”.
