The settling flux of biodeposition affects the environmental quality of cage culture areas and determines their environmental carrying capacity.Simple and effective simulation of the settling flux of biodeposition is ...The settling flux of biodeposition affects the environmental quality of cage culture areas and determines their environmental carrying capacity.Simple and effective simulation of the settling flux of biodeposition is extremely important for determining the spatial distribution of biodeposition.Theoretically,biodeposition in cage culture areas without specific emission rules can be simplified as point source pollution.Fluent is a fluid simulation software that can simulate the dispersion of particulate matter simply and efficiently.Based on the simplification of pollution sources and bays,the settling flux of biodeposition can be easily and effectively simulated by Fluent fluid software.In the present work,the feasibility of this method was evaluated by simulation of the settling flux of biodeposition in Maniao Bay,Hainan Province,China,and 20 sampling sites were selected for determining the settling fluxes.At sampling sites P1,P2,P3,P4,P5,Z1,Z2,Z3,Z4,A1,A2,A3,A4,B1,B2,C1,C2,C3 and C4,the measured settling fluxes of biodeposition were 26.02,15.78,10.77,58.16,6.57,72.17,12.37,12.11,106.64,150.96,22.59,11.41,18.03,7.90,19.23,7.06,11.84,5.19 and 2.57 g d^(−1)m^(−2),respectively.The simulated settling fluxes of biodeposition at the corresponding sites were 16.03,23.98,8.87,46.90,4.52,104.77,16.03,8.35,180.83,213.06,39.10,17.47,20.98,9.78,23.25,7.84,15.90,6.06 and 1.65 g d^(−1)m^(−2),respectively.There was a positive correlation between the simulated settling fluxes and measured ones(R=0.94,P=2.22×10^(−9)<0.05),which implies that the spatial differentiation of biodeposition flux was well simulated.Moreover,the posterior difference ratio of the simulation was 0.38,and the small error probability was 0.94,which means that the simulated results reached an acceptable level from the perspective of relative error.Thus,if nonpoint source pollution is simplified to point source pollution and open waters are simplified based on similarity theory,the setting flux of biodeposition in the open waters can be simply and effectively simulated by the fluid simulation software Fluent.展开更多
Beam splitting is one of the main approaches to achieving x-ray ghost imaging, and the intensity correlation between diffraction beam and transmission beam will directly affect the imaging quality. In this paper, we i...Beam splitting is one of the main approaches to achieving x-ray ghost imaging, and the intensity correlation between diffraction beam and transmission beam will directly affect the imaging quality. In this paper, we investigate the intensity correlation between the split x-ray beams by Laue diffraction of stress-free crystal. The analysis based on the dynamical theory of x-ray diffraction indicates that the spatial resolution of diffraction image and transmission image are reduced due to the position shift of the exit beam. In the experimental setup, a stress-free crystal with a thickness of hundredmicrometers-level is used for beam splitting. The crystal is in a non-dispersive configuration equipped with a double-crystal monochromator to ensure that the dimension of the diffraction beam and transmission beam are consistent. A correlation coefficient of 0.92 is achieved experimentally and the high signal-to-noise ratio of the x-ray ghost imaging is anticipated.Results of this paper demonstrate that the developed beam splitter of Laue crystal has the potential in the efficient data acquisition of x-ray ghost imaging.展开更多
Recently, Shiet al. [2008 Phys. Left. A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an e...Recently, Shiet al. [2008 Phys. Left. A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory (EFT) and a mean-field theory (MFT). The MFT results are in conflict with those of the earlier work of Tome and de Oliveira, [1990 Phys. Rev. A 41 4251]. We calculate the dynamic phase diagrams and find that our results are similar to those of the earlier work of Tome and de Oliveira; hence the dynamic phase diagrams calculated by Shiet al. are incomplete within both theories, except the low values of frequencies for the MFT calculation. We also investigate the influence of external field frequency (w) and static external field amplitude (h0) for both MFT and EFT calculations. We find that the behaviour of the system strongly depends on the values of w and h0.展开更多
Aiming at the large deformation and support problems of high-stress and broken-expansion surrounding rock, and taking 1 000 m level roadway of Mine II in Jinchuan as the research object, an investigation on the deform...Aiming at the large deformation and support problems of high-stress and broken-expansion surrounding rock, and taking 1 000 m level roadway of Mine II in Jinchuan as the research object, an investigation on the deformation and damage of roadway surrounding rock and an analysis of its mechanism were carried out. The gray correlation theory was used in support scheme optimization design. First, causes and mechanism of deformation of the 1 000 m horizontal transport channel were analyzed through field investigation, laboratory test and data processing methods. We arguued that poor engineering geological conditions and deep pressure increases were the main factors, and the deformation mechanism was mainly the ground deformation pressure. Second, the gray correlation theory was used to construct supporting optimization decision method in the deep roadway. This method more comprehensively considers various factors, including construction, costs, and supporting material functions. The combined support with pre-stressed anchor cables, shotcrete layer, bolt and metal net was put forward according to the actual roadway engineering characteristics. Finally, 4 support schemes were put forward for new roadways. The gray relational theory was applied to optimizing the supporting method, undertaking technical and economic comparison to obtain the correlation degree, and accordingly the schemes were evaluated. It was concluded as follows: the best was the flexible retaining scheme using the steel strand anchor; the second best was the one using plate anchors on the top and rigid common screw steel bolt on the two sides; the third was; the rigid common screw steel bolt in full section of roadway; and the worst is the planished steel rigid support. The optimized scheme was applied to the 1000 m level of new excavation roadway. The results show that the roadway surrounding rock can reach a stable state after 5 to 6 months monitoring, with a convergence rate less than 1 mm/d.展开更多
Conventional modal parameter identifications are usually based on frequencyresponse functions, which require measurements of both the input force and the resulting response.However, in many cases, only response data a...Conventional modal parameter identifications are usually based on frequencyresponse functions, which require measurements of both the input force and the resulting response.However, in many cases, only response data are available while the actual excitations (such aswind/wave load) are not measurable. Modal parameters estimation must base itself on response-onlydata. Over the past years, many time-domain modal parameter identification techniques fromoutput-only are proposed. A poly-reference frequency-domain modal identification scheme onresponse-only is presented. It is based on coupling the cross-correlation theory with conventionalfrequency-domain modal parameter extraction. An experiment using an airplane model is performed toverify the proposed method.展开更多
By means of the effective-field theory (EFT) with correlations, the thermodynamic and magnetic quantities (such as magnetization, susceptibility, internal energy, specific heat, free energy, hysteresis curves, and ...By means of the effective-field theory (EFT) with correlations, the thermodynamic and magnetic quantities (such as magnetization, susceptibility, internal energy, specific heat, free energy, hysteresis curves, and compensation behaviors) of the spin-l/2 hexagonal Ising nanowire (HIN) system with core/shell structure have been presented. The hysteresis curves are obtained for different values of the system parameters, in both ferromagnetic and antiferromagnetic cases. It has been shown that the system only undergoes a second-order phase transition. Moreover, from the thermal variations of the total magnetization, the five compensation types can be found under certain conditions, namely the Q-, R-, S-, P-, and N-types.展开更多
We propose and apply a new algorithm of principal component analysis which is suitable for a large sized, highly random time series data, such as a set of stock prices in a stock market. This algorithm utilizes the fa...We propose and apply a new algorithm of principal component analysis which is suitable for a large sized, highly random time series data, such as a set of stock prices in a stock market. This algorithm utilizes the fact that the major part of the time series is random, and compare the eigenvalue spectrum of cross correlation matrix of a large set of random time series, to the spectrum derived by the random matrix theory (RMT) at the limit of large dimension (the number of independent time series) and long enough length of time series. We test this algorithm on the real tick data of American stocks at different years between 1994 and 2002 and show that the extracted principal components indeed reflects the change of leading stock sectors during this period.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
We show that the quantum solitons occurring in theories describing a complex scalar field in (1 + 1)-dimensions with a Z(N) symmetry may be identified with sine-Gordon quantum solitons in the phase of this field. Then...We show that the quantum solitons occurring in theories describing a complex scalar field in (1 + 1)-dimensions with a Z(N) symmetry may be identified with sine-Gordon quantum solitons in the phase of this field. Then using both the Euclidean thermal Green function of the two-dimensional free massless scalar field in coordinate space and its dual, we obtain an explicit series expression for the corresponding solitonic correlation function at finite temperature.展开更多
When Einstein developed the special theory of relativity (STR), he assumed the principle of relativity, i.e. that all inertial frames are equivalent. Einstein thought it was impossible to differentiate inertial frames...When Einstein developed the special theory of relativity (STR), he assumed the principle of relativity, i.e. that all inertial frames are equivalent. Einstein thought it was impossible to differentiate inertial frames into classically stationary frames where light propagates isotropically, and classically moving frames where light propagates anisotropically. However, the author has previously pointed out that classically moving frames have a velocity vector attached, and presented a thought experiment for determining the size of that velocity vector. The author has already shown a violation of the STR, but this paper presents a violation of the STR using different reasoning. More specifically, this paper searches for a coordinate system where light propagates anisotropically. This is done by using the correlation of two photons pair-generated from a photon pair generator. If the existence of such a coordinate system can be ascertained, it will constitute a violation of the STR.展开更多
As pointed out in the paper preceding this one, in the case of functionals whose independent variable must obey conditions of integral normalization, conventional functional differentiation, defined in terms of an arb...As pointed out in the paper preceding this one, in the case of functionals whose independent variable must obey conditions of integral normalization, conventional functional differentiation, defined in terms of an arbitrary test function, is generally inapplicable and functional derivatives with respect to the density must be evaluated through the alternative and widely used limiting procedure based on the Dirac delta function. This leads to the determination of the rate of change of the dependent variable with respect to its independent variable at each isolated pair, , that may not be part of a functional (a set of ordered pairs). This extends the concept of functional derivative to expectation values of operators with respect to wave functions leading to a density even if the wave functions (and expectation values) do not form functionals. This new formulation of functional differentiation forms the basis for the study of the mathematical integrity of a number of concepts in density functional theory (DFT) such as the existence of a universal functional of the density, of orbital-free density functional theory, the derivative discontinuity of the exchange and correlation functional and the extension of DFT to open systems characterized by densities with fractional normalization. It is shown that no universal functional exists but, rather, a universal process based only on the density and independent of the possible existence of a potential, leads to unique functionals of the density determined through the minimization procedure of the constrained search. The mathematical integrity of two methodologies proposed for the treatment of the Coulomb interaction, the self-interaction free method and the optimized effective potential method is examined and the methodologies are compared in terms of numerical calculations. As emerges from this analysis, the optimized effective potential method is found to be numerically approximate but formally invalid, contrary to the rigorously exact results of the self-interaction-free method.展开更多
“Objective Correlative”theory was first proposed by T.S. Eliot, who holds that people’s emotion can find expression in a series of objective correlative. In his poem The Love Song of J.Alfred Prufrock, the use of o...“Objective Correlative”theory was first proposed by T.S. Eliot, who holds that people’s emotion can find expression in a series of objective correlative. In his poem The Love Song of J.Alfred Prufrock, the use of objective correlative fully reflects and reveals modern people’s loneliness, futility and alienation.展开更多
We investigate the electronic structure ofβ-uranium,which has five nonequivalent atomic sites in its unit cell,by means of the density functional theory plus Hubbard-U correction with U from linear response calculati...We investigate the electronic structure ofβ-uranium,which has five nonequivalent atomic sites in its unit cell,by means of the density functional theory plus Hubbard-U correction with U from linear response calculation.It is found that the 5f electronic correlations inβ-uranium are moderate.More interestingly,their strengths are site selective,depending on the local atomic environment of the present uranium atom.As a consequence,the occupation matrices and partial 5f density of states ofβ-uranium manifest site dependence.In addition,the complicate experimental structure ofβ-uranium could be well reproduced within this theoretical framework.展开更多
This article discusses the covariance correlation tensor (CCT) in quantum network theory for four Bell bases in detail. Furthermore, it gives the expression of the density operator in terms of CCT for a quantum networ...This article discusses the covariance correlation tensor (CCT) in quantum network theory for four Bell bases in detail. Furthermore, it gives the expression of the density operator in terms of CCT for a quantum network of three nodes, thus gives the criterion of entanglement for this case, i.e. the conditions of complete separability and partial separability for a given quantum state of three bodies. Finally it discusses the general case for the quantum network of m≥3 nodes.展开更多
In engineering,all movable expanse revolving objects manifest gyroscopic effects.These effects are created by the action of the outer load on the revolving items whose rotating mass originates eight inertial torques a...In engineering,all movable expanse revolving objects manifest gyroscopic effects.These effects are created by the action of the outer load on the revolving items whose rotating mass originates eight inertial torques about two axes.Two torques of centrifugal forces,one torque of the Coriolis force originated by the rotating distributed mass,and the torque of the change in the angular momentum of the center mass act about each axis.The inertial torques activate rotations of the gyroscope by the determined correlation.Inertial torques depend on their geometry and orientation at the spatial coordinate system.The known analytical model for the rotation of the revolving disc about axes contains a mechanical error.This error was obtained by the incorrect integration of the centrifugal inertial torque.The corrected inertial torque yields the accurate expression for the interacted rotations of the revolving disc about axes.展开更多
基金support from the National Key Research and Development Program of China(No.2018YFD0900704)the National Natural Science Foundation of China(No.31972796).
文摘The settling flux of biodeposition affects the environmental quality of cage culture areas and determines their environmental carrying capacity.Simple and effective simulation of the settling flux of biodeposition is extremely important for determining the spatial distribution of biodeposition.Theoretically,biodeposition in cage culture areas without specific emission rules can be simplified as point source pollution.Fluent is a fluid simulation software that can simulate the dispersion of particulate matter simply and efficiently.Based on the simplification of pollution sources and bays,the settling flux of biodeposition can be easily and effectively simulated by Fluent fluid software.In the present work,the feasibility of this method was evaluated by simulation of the settling flux of biodeposition in Maniao Bay,Hainan Province,China,and 20 sampling sites were selected for determining the settling fluxes.At sampling sites P1,P2,P3,P4,P5,Z1,Z2,Z3,Z4,A1,A2,A3,A4,B1,B2,C1,C2,C3 and C4,the measured settling fluxes of biodeposition were 26.02,15.78,10.77,58.16,6.57,72.17,12.37,12.11,106.64,150.96,22.59,11.41,18.03,7.90,19.23,7.06,11.84,5.19 and 2.57 g d^(−1)m^(−2),respectively.The simulated settling fluxes of biodeposition at the corresponding sites were 16.03,23.98,8.87,46.90,4.52,104.77,16.03,8.35,180.83,213.06,39.10,17.47,20.98,9.78,23.25,7.84,15.90,6.06 and 1.65 g d^(−1)m^(−2),respectively.There was a positive correlation between the simulated settling fluxes and measured ones(R=0.94,P=2.22×10^(−9)<0.05),which implies that the spatial differentiation of biodeposition flux was well simulated.Moreover,the posterior difference ratio of the simulation was 0.38,and the small error probability was 0.94,which means that the simulated results reached an acceptable level from the perspective of relative error.Thus,if nonpoint source pollution is simplified to point source pollution and open waters are simplified based on similarity theory,the setting flux of biodeposition in the open waters can be simply and effectively simulated by the fluid simulation software Fluent.
基金Project supported by the National Key Research and Development Program of China (Grant Nos.2022YFF0709103,2022YFA1603601,2021YFF0601203,and 2021YFA1600703)the National Natural Science Foundation of China (Grant No.81430087)the Shanghai Pilot Program for Basic Research-Chinese Academy of Sciences,Shanghai Branch (Grant No.JCYJ-SHFY-2021-010)。
文摘Beam splitting is one of the main approaches to achieving x-ray ghost imaging, and the intensity correlation between diffraction beam and transmission beam will directly affect the imaging quality. In this paper, we investigate the intensity correlation between the split x-ray beams by Laue diffraction of stress-free crystal. The analysis based on the dynamical theory of x-ray diffraction indicates that the spatial resolution of diffraction image and transmission image are reduced due to the position shift of the exit beam. In the experimental setup, a stress-free crystal with a thickness of hundredmicrometers-level is used for beam splitting. The crystal is in a non-dispersive configuration equipped with a double-crystal monochromator to ensure that the dimension of the diffraction beam and transmission beam are consistent. A correlation coefficient of 0.92 is achieved experimentally and the high signal-to-noise ratio of the x-ray ghost imaging is anticipated.Results of this paper demonstrate that the developed beam splitter of Laue crystal has the potential in the efficient data acquisition of x-ray ghost imaging.
基金Project supported by the Scientific and Technological Research Council of Turkey (TBTAK) (Grant No. 107T533)the Erciyes University Research Funds (Grant Nos. FBA-06-01 and FBD-08-593)
文摘Recently, Shiet al. [2008 Phys. Left. A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory (EFT) and a mean-field theory (MFT). The MFT results are in conflict with those of the earlier work of Tome and de Oliveira, [1990 Phys. Rev. A 41 4251]. We calculate the dynamic phase diagrams and find that our results are similar to those of the earlier work of Tome and de Oliveira; hence the dynamic phase diagrams calculated by Shiet al. are incomplete within both theories, except the low values of frequencies for the MFT calculation. We also investigate the influence of external field frequency (w) and static external field amplitude (h0) for both MFT and EFT calculations. We find that the behaviour of the system strongly depends on the values of w and h0.
基金Funded by Plan Projects of Hunan Provincial Science&Technology Department(2014FJ3046)Scientific Research Fund of Hunan Provincial Education Department(No.14A045)+1 种基金National Natural Science Foundation of China(Grant Nos.51434006,51374105 and 51374106)China Postdoctoral Science Foundation 2014M562135)
文摘Aiming at the large deformation and support problems of high-stress and broken-expansion surrounding rock, and taking 1 000 m level roadway of Mine II in Jinchuan as the research object, an investigation on the deformation and damage of roadway surrounding rock and an analysis of its mechanism were carried out. The gray correlation theory was used in support scheme optimization design. First, causes and mechanism of deformation of the 1 000 m horizontal transport channel were analyzed through field investigation, laboratory test and data processing methods. We arguued that poor engineering geological conditions and deep pressure increases were the main factors, and the deformation mechanism was mainly the ground deformation pressure. Second, the gray correlation theory was used to construct supporting optimization decision method in the deep roadway. This method more comprehensively considers various factors, including construction, costs, and supporting material functions. The combined support with pre-stressed anchor cables, shotcrete layer, bolt and metal net was put forward according to the actual roadway engineering characteristics. Finally, 4 support schemes were put forward for new roadways. The gray relational theory was applied to optimizing the supporting method, undertaking technical and economic comparison to obtain the correlation degree, and accordingly the schemes were evaluated. It was concluded as follows: the best was the flexible retaining scheme using the steel strand anchor; the second best was the one using plate anchors on the top and rigid common screw steel bolt on the two sides; the third was; the rigid common screw steel bolt in full section of roadway; and the worst is the planished steel rigid support. The optimized scheme was applied to the 1000 m level of new excavation roadway. The results show that the roadway surrounding rock can reach a stable state after 5 to 6 months monitoring, with a convergence rate less than 1 mm/d.
基金This project is supported by Aeronautics Foundation (No. 1152059), Civil Aviation Foundation (No.1007-272) the 9-th Five Plan of the Aeronautical Industrial Corporation (No.62.2.2.1), China.
文摘Conventional modal parameter identifications are usually based on frequencyresponse functions, which require measurements of both the input force and the resulting response.However, in many cases, only response data are available while the actual excitations (such aswind/wave load) are not measurable. Modal parameters estimation must base itself on response-onlydata. Over the past years, many time-domain modal parameter identification techniques fromoutput-only are proposed. A poly-reference frequency-domain modal identification scheme onresponse-only is presented. It is based on coupling the cross-correlation theory with conventionalfrequency-domain modal parameter extraction. An experiment using an airplane model is performed toverify the proposed method.
文摘By means of the effective-field theory (EFT) with correlations, the thermodynamic and magnetic quantities (such as magnetization, susceptibility, internal energy, specific heat, free energy, hysteresis curves, and compensation behaviors) of the spin-l/2 hexagonal Ising nanowire (HIN) system with core/shell structure have been presented. The hysteresis curves are obtained for different values of the system parameters, in both ferromagnetic and antiferromagnetic cases. It has been shown that the system only undergoes a second-order phase transition. Moreover, from the thermal variations of the total magnetization, the five compensation types can be found under certain conditions, namely the Q-, R-, S-, P-, and N-types.
文摘We propose and apply a new algorithm of principal component analysis which is suitable for a large sized, highly random time series data, such as a set of stock prices in a stock market. This algorithm utilizes the fact that the major part of the time series is random, and compare the eigenvalue spectrum of cross correlation matrix of a large set of random time series, to the spectrum derived by the random matrix theory (RMT) at the limit of large dimension (the number of independent time series) and long enough length of time series. We test this algorithm on the real tick data of American stocks at different years between 1994 and 2002 and show that the extracted principal components indeed reflects the change of leading stock sectors during this period.
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.
文摘We show that the quantum solitons occurring in theories describing a complex scalar field in (1 + 1)-dimensions with a Z(N) symmetry may be identified with sine-Gordon quantum solitons in the phase of this field. Then using both the Euclidean thermal Green function of the two-dimensional free massless scalar field in coordinate space and its dual, we obtain an explicit series expression for the corresponding solitonic correlation function at finite temperature.
文摘When Einstein developed the special theory of relativity (STR), he assumed the principle of relativity, i.e. that all inertial frames are equivalent. Einstein thought it was impossible to differentiate inertial frames into classically stationary frames where light propagates isotropically, and classically moving frames where light propagates anisotropically. However, the author has previously pointed out that classically moving frames have a velocity vector attached, and presented a thought experiment for determining the size of that velocity vector. The author has already shown a violation of the STR, but this paper presents a violation of the STR using different reasoning. More specifically, this paper searches for a coordinate system where light propagates anisotropically. This is done by using the correlation of two photons pair-generated from a photon pair generator. If the existence of such a coordinate system can be ascertained, it will constitute a violation of the STR.
文摘As pointed out in the paper preceding this one, in the case of functionals whose independent variable must obey conditions of integral normalization, conventional functional differentiation, defined in terms of an arbitrary test function, is generally inapplicable and functional derivatives with respect to the density must be evaluated through the alternative and widely used limiting procedure based on the Dirac delta function. This leads to the determination of the rate of change of the dependent variable with respect to its independent variable at each isolated pair, , that may not be part of a functional (a set of ordered pairs). This extends the concept of functional derivative to expectation values of operators with respect to wave functions leading to a density even if the wave functions (and expectation values) do not form functionals. This new formulation of functional differentiation forms the basis for the study of the mathematical integrity of a number of concepts in density functional theory (DFT) such as the existence of a universal functional of the density, of orbital-free density functional theory, the derivative discontinuity of the exchange and correlation functional and the extension of DFT to open systems characterized by densities with fractional normalization. It is shown that no universal functional exists but, rather, a universal process based only on the density and independent of the possible existence of a potential, leads to unique functionals of the density determined through the minimization procedure of the constrained search. The mathematical integrity of two methodologies proposed for the treatment of the Coulomb interaction, the self-interaction free method and the optimized effective potential method is examined and the methodologies are compared in terms of numerical calculations. As emerges from this analysis, the optimized effective potential method is found to be numerically approximate but formally invalid, contrary to the rigorously exact results of the self-interaction-free method.
文摘“Objective Correlative”theory was first proposed by T.S. Eliot, who holds that people’s emotion can find expression in a series of objective correlative. In his poem The Love Song of J.Alfred Prufrock, the use of objective correlative fully reflects and reveals modern people’s loneliness, futility and alienation.
基金supported by the National Natural Science Foundation of China (Grant Nos.22176181,11874329,11934020,and U1930121)the Foundation of the President of China Academy of Engineering Physics (Grant No.YZJJZQ2022011)the Foundation of Science and Technology on Surface Physics and Chemistry Laboratory (Grant No.WDZC202101)。
文摘We investigate the electronic structure ofβ-uranium,which has five nonequivalent atomic sites in its unit cell,by means of the density functional theory plus Hubbard-U correction with U from linear response calculation.It is found that the 5f electronic correlations inβ-uranium are moderate.More interestingly,their strengths are site selective,depending on the local atomic environment of the present uranium atom.As a consequence,the occupation matrices and partial 5f density of states ofβ-uranium manifest site dependence.In addition,the complicate experimental structure ofβ-uranium could be well reproduced within this theoretical framework.
文摘This article discusses the covariance correlation tensor (CCT) in quantum network theory for four Bell bases in detail. Furthermore, it gives the expression of the density operator in terms of CCT for a quantum network of three nodes, thus gives the criterion of entanglement for this case, i.e. the conditions of complete separability and partial separability for a given quantum state of three bodies. Finally it discusses the general case for the quantum network of m≥3 nodes.
文摘In engineering,all movable expanse revolving objects manifest gyroscopic effects.These effects are created by the action of the outer load on the revolving items whose rotating mass originates eight inertial torques about two axes.Two torques of centrifugal forces,one torque of the Coriolis force originated by the rotating distributed mass,and the torque of the change in the angular momentum of the center mass act about each axis.The inertial torques activate rotations of the gyroscope by the determined correlation.Inertial torques depend on their geometry and orientation at the spatial coordinate system.The known analytical model for the rotation of the revolving disc about axes contains a mechanical error.This error was obtained by the incorrect integration of the centrifugal inertial torque.The corrected inertial torque yields the accurate expression for the interacted rotations of the revolving disc about axes.