Fractional molecular field theory(FMFT)is a phenomenological theory that describes phase transitions in crystals with randomly distributed components,such as the relaxor-ferroelectrics and spin glasses.In order to ver...Fractional molecular field theory(FMFT)is a phenomenological theory that describes phase transitions in crystals with randomly distributed components,such as the relaxor-ferroelectrics and spin glasses.In order to verify the feasibility of this theory,this paper fits it to the Monte Carlo simulations of specific heat and susceptibility versus temperature of two-dimensional(2D)random-site Ising model(2D-RSIM).The results indicate that the FMFT deviates from the 2D-RSIM significantly.The main reason for the deviation is that the 2D-RSIM is a typical system of component random distribution,where the real order parameter is spatially heterogeneous and has no symmetry of space translation,but the basic assumption of FMFT means that the parameter is spatially uniform and has symmetry of space translation.展开更多
The phase diagrams in the mixed spin-3/2 and spin-2 Ising system with two alternative layers on a honeycomb lattice are investigated and discussed by the use of the effective-field theory with correlations. The intera...The phase diagrams in the mixed spin-3/2 and spin-2 Ising system with two alternative layers on a honeycomb lattice are investigated and discussed by the use of the effective-field theory with correlations. The interaction of the nearest-neighbour spins of each layer is taken to be positive （ferromagnetic interaction） and the interaction of the adjacent spins of the nearest-neighbour layers is considered to be either positive or negative （ferromagnetic or antiferromagnetic interaction）. The temperature dependence of the layer magnetizations of the system is examined to characterize the nature （continuous or discontinuous） of the phase transitions and obtain the phase transition temperatures. The system exhibits both second- and first-order phase transitions besides triple point （TP）, critical end point （E）, multicritical point （A）, isolated critical point （C） and reentrant behaviour depending on the interaction parameters. We have also studied the temperature dependence of the total magnetization to find the compensation points, as well as to determine the type of behaviour, and N-type behaviour in Neel classification nomenclature existing in the system. The phase diagrams are constructed in eight different planes and it is found that the system also presents the compensation phenomena depending on the sign of the bilinear exchange interactions.展开更多
A numerical simulation based on a regularized phase field model is developed to describe faceted dendrite growth morphology. The effects of mesh grid, anisotropy, supersaturation and fold symmetry on dendrite growth m...A numerical simulation based on a regularized phase field model is developed to describe faceted dendrite growth morphology. The effects of mesh grid, anisotropy, supersaturation and fold symmetry on dendrite growth morphology were investigated, respectively. These results indicate that the nucleus grows into a hexagonal symmetry faceted dendrite. When the mesh grid is above 640×640, the size has no much effect on the shape. With the increase in the anisotropy value, the tip velocities of faceted dendrite increase and reach a balance value, and then decrease gradually. With the increase in the supersaturation value, crystal evolves from circle to the developed faceted dendrite morphology. Based on the Wulff theory and faceted symmetry morphology diagram, the proposed model was proved to be effective, and it can be generalized to arbitrary crystal symmetries.展开更多
Lithium metal anode is one of the most important anode materials for next-generation high-specificenergy secondary batteries.Structured lithium metal anodes have received extensive attention in the development of prac...Lithium metal anode is one of the most important anode materials for next-generation high-specificenergy secondary batteries.Structured lithium metal anodes have received extensive attention in the development of practical lithium metal batteries.Methods of driving lithium metal to deposit inside the pores of structured lithium metal anodes have always been one of the most concerned issues,especially for highly conductive frameworks.An electrochemical phase field theory with galvanostatic lithium plating process is employed in this work,the mechanism that illustrates the preference of lithium metal to deposit at the top of the framework structure has been revealed,and through the simulation analysis of various regulating strategies,the strategies that can efficiently drive lithium to deposit inside structured pores are summarized.This work presents the theoretical calculation and analysis methods that can be used for the rational design of lithium metal batteries.展开更多
The phase behaviours of diblock copolymers under cylindrical confinement are studied in two-dimensional space by using the self-consistent field theory. Several phase parameters are adjusted to investigate the cylindr...The phase behaviours of diblock copolymers under cylindrical confinement are studied in two-dimensional space by using the self-consistent field theory. Several phase parameters are adjusted to investigate the cylindrical-confinement-induced phase behaviours of diblock copolymers. A series of lamella-cylinder mixture phases, such as the mixture of broken-lamellae and cylinders and the mixture of square-lamellae and cylinders, are observed by varying the phase parameters, in which the behaviours of these mixture phases are discussed in the corresponding phase diagrams. Furthermore, the free energies of these mixture phases are investigated to illustrate their evolution processes. Our results are compared with the available observations from the experiments and simulations respectively, and they are in good agreement and provide an insight into the phase behaviours under cylindrical confinement.展开更多
We investigate the effect of interaction, temperature, and anisotropic parameter on the quantum phase transitions in an anisotropic square-octagon lattice with fermions under the framework of the single band Hubbard m...We investigate the effect of interaction, temperature, and anisotropic parameter on the quantum phase transitions in an anisotropic square-octagon lattice with fermions under the framework of the single band Hubbard model through using the combination of cellular dynamical mean field theory and a continuous time Monte Carlo algorithm. The competition between interaction and temperature shows that with the increase of the anisotropic parameter, the critical on-site repulsive interaction for the metal-insulator transition increases for fixed temperature. The interaction-anisotropic parameter phase diagram reveals that with the decrease of temperature, the critical anisotropic parameter for the Mott transition will increase for fixed interaction cases.展开更多
Phase diagram and thermodynamic parameters of the random field Ising model （RFIM） on spherical lattice are studied by using mean field theory. This lattice is placed in an external magnetic field （B）. The random f...Phase diagram and thermodynamic parameters of the random field Ising model （RFIM） on spherical lattice are studied by using mean field theory. This lattice is placed in an external magnetic field （B）. The random field （hi） is assumed to be Gaussian distributed with zero mean and a variance （hi2） = HRF2. The free energy （F）, the magnetization （M） and the order parameter （q） are calculated. The ferromagnetic （FM） spin-glass （SG） phase transition is clearly observed. The critical temperature （Tc） is computed under a critical intensity of random field HRF = V/2/πJ. The phase transition from FM to paramagnetic （PM） occurs at TC = J/k in the absence of magnetic field. The critical temperature decreases as HRF increases in the phase boundary of FM-to-SG. The magnetic susceptibility （X） shows a sharp cusp at TC and the specific heat （C） has a singularity in small random field. The internal energy （U） has a similar behaviour to that obtained from the Monte Carlo simulation.展开更多
The molecular field theory (MF) of nematic to isotropic (N-I) phase transition in surface-aligned nematic film is proposed by using Lebwohl-Lasher model. The calculated results indicate that the N-I-phase transition w...The molecular field theory (MF) of nematic to isotropic (N-I) phase transition in surface-aligned nematic film is proposed by using Lebwohl-Lasher model. The calculated results indicate that the N-I-phase transition will be strongly affected by the interaction between liquid crystal molecules and substrate. The nematic film can be divided into three regions according to their phase transition behavior: the interface, the bulk and the free surface. The interface phase transition depends strongly on the strength of interaction between liquid crystal and substrate, and its phase transition temperature is higher than that of bulk phase transition. Especially, the order parameter will become a continuous function of temperature when the anchoring energy is strong enough. In the bulkregion, the N-I phase transition is still of the first order while in the free surface, the N-I phase transition belongs to the typical second order transition behaviour. When the temperature is increased, the N-I phase transition starts in the free surface region and then extends to the bulk and interface regions gradually. All these results are confirmed by Monte Carlo (MC) study and agree with the Landau-de Gennes theory.展开更多
Based on Witten’s T-duality and mirror symmetry we show, following earlier work, the fundamental complimentarity of the Casimir energy and dark energy. Such a conclusion opens new vistas in cold fusion technology in ...Based on Witten’s T-duality and mirror symmetry we show, following earlier work, the fundamental complimentarity of the Casimir energy and dark energy. Such a conclusion opens new vistas in cold fusion technology in the wider sense of the word which we tackle via fractal nano technologies leading to some design proposals for a nano Casimir-dark energy reactor.展开更多
In the mean-field theory of atom-molecule systems, where the bosonic atoms combine to form molecules, there is no usual U（1） symmetry, which presents an apparent hurdle for calculating the Berry connection in these ...In the mean-field theory of atom-molecule systems, where the bosonic atoms combine to form molecules, there is no usual U（1） symmetry, which presents an apparent hurdle for calculating the Berry connection in these systems. We develop a perturbation expansion method of Hannay＇s angle suitable for calculating the Berry curvature in the atom- molecule systems. With this Berry curvature, the Berry connection can be computed naturally. We use a three-level atom-molecule system to illustrate our results. In particular, with this method, we compute the curvature for Hannay＇s angle analytically, and compare it to the Berry curvature obtained with the second-quantized model of the same system. An excellent agreement is found, indicating the validity of our method.展开更多
Using the effective-field theory we studied the magnetic properties of a spin-1/2 Ising supedattice, which consist of three different ferromagnet materials. The magnetic behavior of this superlattice is examined. The ...Using the effective-field theory we studied the magnetic properties of a spin-1/2 Ising supedattice, which consist of three different ferromagnet materials. The magnetic behavior of this superlattice is examined. The critical temperature and the compensation temprature of the system are studied as a function of the exchange interactions between the nearest-neiboring spins across the interface and in the intraface. Temperature dependence of magenetizations is also given.展开更多
基金Project supported by the Open Project of the Key Laboratory of Xinjiang Uygur Autonomous Region,China(Grant No.2021D04015)the Yili Kazakh Autonomous Prefecture Science and Technology Program Project,China(Grant No.YZ2022B021).
文摘Fractional molecular field theory(FMFT)is a phenomenological theory that describes phase transitions in crystals with randomly distributed components,such as the relaxor-ferroelectrics and spin glasses.In order to verify the feasibility of this theory,this paper fits it to the Monte Carlo simulations of specific heat and susceptibility versus temperature of two-dimensional(2D)random-site Ising model(2D-RSIM).The results indicate that the FMFT deviates from the 2D-RSIM significantly.The main reason for the deviation is that the 2D-RSIM is a typical system of component random distribution,where the real order parameter is spatially heterogeneous and has no symmetry of space translation,but the basic assumption of FMFT means that the parameter is spatially uniform and has symmetry of space translation.
基金Project supported by the Scientific and Technological Research Council of Turkey (TBTAK) (Grant No. 107T533)Erciyes University Research Funds (Grant No. FBD-08-593)
文摘The phase diagrams in the mixed spin-3/2 and spin-2 Ising system with two alternative layers on a honeycomb lattice are investigated and discussed by the use of the effective-field theory with correlations. The interaction of the nearest-neighbour spins of each layer is taken to be positive （ferromagnetic interaction） and the interaction of the adjacent spins of the nearest-neighbour layers is considered to be either positive or negative （ferromagnetic or antiferromagnetic interaction）. The temperature dependence of the layer magnetizations of the system is examined to characterize the nature （continuous or discontinuous） of the phase transitions and obtain the phase transition temperatures. The system exhibits both second- and first-order phase transitions besides triple point （TP）, critical end point （E）, multicritical point （A）, isolated critical point （C） and reentrant behaviour depending on the interaction parameters. We have also studied the temperature dependence of the total magnetization to find the compensation points, as well as to determine the type of behaviour, and N-type behaviour in Neel classification nomenclature existing in the system. The phase diagrams are constructed in eight different planes and it is found that the system also presents the compensation phenomena depending on the sign of the bilinear exchange interactions.
基金Projects(11102164,11304243)supported by the National Natural Science Foundation of ChinaProject(2014JQ1039)supported by the Natural Science Foundation of Shannxi Province,China+1 种基金Project(3102016ZY027)supported by the Fundamental Research Funds for the Central Universities of ChinaProject(13GH014602)supported by the Program of New Staff and Research Area Project of NWPU,China
文摘A numerical simulation based on a regularized phase field model is developed to describe faceted dendrite growth morphology. The effects of mesh grid, anisotropy, supersaturation and fold symmetry on dendrite growth morphology were investigated, respectively. These results indicate that the nucleus grows into a hexagonal symmetry faceted dendrite. When the mesh grid is above 640×640, the size has no much effect on the shape. With the increase in the anisotropy value, the tip velocities of faceted dendrite increase and reach a balance value, and then decrease gradually. With the increase in the supersaturation value, crystal evolves from circle to the developed faceted dendrite morphology. Based on the Wulff theory and faceted symmetry morphology diagram, the proposed model was proved to be effective, and it can be generalized to arbitrary crystal symmetries.
基金supported by Beijing Natural Science Foundation(JQ20004)National Key Research and Development Program(2021YFB2400300)+1 种基金National Natural Scientific Foundation of China(22109011)the China Postdoctoral Science Foundation(BX20200047,2021M690380)。
文摘Lithium metal anode is one of the most important anode materials for next-generation high-specificenergy secondary batteries.Structured lithium metal anodes have received extensive attention in the development of practical lithium metal batteries.Methods of driving lithium metal to deposit inside the pores of structured lithium metal anodes have always been one of the most concerned issues,especially for highly conductive frameworks.An electrochemical phase field theory with galvanostatic lithium plating process is employed in this work,the mechanism that illustrates the preference of lithium metal to deposit at the top of the framework structure has been revealed,and through the simulation analysis of various regulating strategies,the strategies that can efficiently drive lithium to deposit inside structured pores are summarized.This work presents the theoretical calculation and analysis methods that can be used for the rational design of lithium metal batteries.
基金supported by the National Natural Science Foundation of China (Grant Nos. 20574052 and 20774066)the Program for New Century Excellent Talents in University, China (Grant No. NCET-05-0538)the Natural Science Foundation of Zhejiang Province, China (Grant Nos. R404047, Y4090174, and Y405553)
文摘The phase behaviours of diblock copolymers under cylindrical confinement are studied in two-dimensional space by using the self-consistent field theory. Several phase parameters are adjusted to investigate the cylindrical-confinement-induced phase behaviours of diblock copolymers. A series of lamella-cylinder mixture phases, such as the mixture of broken-lamellae and cylinders and the mixture of square-lamellae and cylinders, are observed by varying the phase parameters, in which the behaviours of these mixture phases are discussed in the corresponding phase diagrams. Furthermore, the free energies of these mixture phases are investigated to illustrate their evolution processes. Our results are compared with the available observations from the experiments and simulations respectively, and they are in good agreement and provide an insight into the phase behaviours under cylindrical confinement.
基金supported by the National Natural Science Foundation of China(Grant Nos.11174169,11234007,and 51471093)
文摘We investigate the effect of interaction, temperature, and anisotropic parameter on the quantum phase transitions in an anisotropic square-octagon lattice with fermions under the framework of the single band Hubbard model through using the combination of cellular dynamical mean field theory and a continuous time Monte Carlo algorithm. The competition between interaction and temperature shows that with the increase of the anisotropic parameter, the critical on-site repulsive interaction for the metal-insulator transition increases for fixed temperature. The interaction-anisotropic parameter phase diagram reveals that with the decrease of temperature, the critical anisotropic parameter for the Mott transition will increase for fixed interaction cases.
文摘Phase diagram and thermodynamic parameters of the random field Ising model （RFIM） on spherical lattice are studied by using mean field theory. This lattice is placed in an external magnetic field （B）. The random field （hi） is assumed to be Gaussian distributed with zero mean and a variance （hi2） = HRF2. The free energy （F）, the magnetization （M） and the order parameter （q） are calculated. The ferromagnetic （FM） spin-glass （SG） phase transition is clearly observed. The critical temperature （Tc） is computed under a critical intensity of random field HRF = V/2/πJ. The phase transition from FM to paramagnetic （PM） occurs at TC = J/k in the absence of magnetic field. The critical temperature decreases as HRF increases in the phase boundary of FM-to-SG. The magnetic susceptibility （X） shows a sharp cusp at TC and the specific heat （C） has a singularity in small random field. The internal energy （U） has a similar behaviour to that obtained from the Monte Carlo simulation.
基金Project supported by the National Natural Science Foundation of China, Fok Ying Tung Education Foundation and the State Education Commission of China.
文摘The molecular field theory (MF) of nematic to isotropic (N-I) phase transition in surface-aligned nematic film is proposed by using Lebwohl-Lasher model. The calculated results indicate that the N-I-phase transition will be strongly affected by the interaction between liquid crystal molecules and substrate. The nematic film can be divided into three regions according to their phase transition behavior: the interface, the bulk and the free surface. The interface phase transition depends strongly on the strength of interaction between liquid crystal and substrate, and its phase transition temperature is higher than that of bulk phase transition. Especially, the order parameter will become a continuous function of temperature when the anchoring energy is strong enough. In the bulkregion, the N-I phase transition is still of the first order while in the free surface, the N-I phase transition belongs to the typical second order transition behaviour. When the temperature is increased, the N-I phase transition starts in the free surface region and then extends to the bulk and interface regions gradually. All these results are confirmed by Monte Carlo (MC) study and agree with the Landau-de Gennes theory.
文摘Based on Witten’s T-duality and mirror symmetry we show, following earlier work, the fundamental complimentarity of the Casimir energy and dark energy. Such a conclusion opens new vistas in cold fusion technology in the wider sense of the word which we tackle via fractal nano technologies leading to some design proposals for a nano Casimir-dark energy reactor.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10825417)
文摘In the mean-field theory of atom-molecule systems, where the bosonic atoms combine to form molecules, there is no usual U（1） symmetry, which presents an apparent hurdle for calculating the Berry connection in these systems. We develop a perturbation expansion method of Hannay＇s angle suitable for calculating the Berry curvature in the atom- molecule systems. With this Berry curvature, the Berry connection can be computed naturally. We use a three-level atom-molecule system to illustrate our results. In particular, with this method, we compute the curvature for Hannay＇s angle analytically, and compare it to the Berry curvature obtained with the second-quantized model of the same system. An excellent agreement is found, indicating the validity of our method.
基金The project supported by Shanghai Leading Academic Discipline Project under Grant No. T0104
文摘Using the effective-field theory we studied the magnetic properties of a spin-1/2 Ising supedattice, which consist of three different ferromagnet materials. The magnetic behavior of this superlattice is examined. The critical temperature and the compensation temprature of the system are studied as a function of the exchange interactions between the nearest-neiboring spins across the interface and in the intraface. Temperature dependence of magenetizations is also given.
