The path-integral quantization of thermal scalar, vector, and spinor fields is performed newly in the coherent-state representation. In doing this, we choose the thermal electrodynamics and psi(4) theory as,examples. ...The path-integral quantization of thermal scalar, vector, and spinor fields is performed newly in the coherent-state representation. In doing this, we choose the thermal electrodynamics and psi(4) theory as,examples. By this quantization, correct expressions of the partition functions and the generating functionals for the quantum thermal electrodynamics and psi(4) theory are obtained in the coherent-state representation. These expressions allow us to perform analytical calculations of the partition functions and generating functionals and therefore are useful in practical applications. Especially, the perturbative expansions of the generating functionals are derived specifically by virtue of the stationary-phase method. The generating functionals formulated in the position space are re-derived from the ones given in the coherent-state representation.展开更多
Under the direction of the principle of interaction between plastic volumetric and shear strains, the general expression of constitutive relation for geotechnical materials has been derived within the framework of irr...Under the direction of the principle of interaction between plastic volumetric and shear strains, the general expression of constitutive relation for geotechnical materials has been derived within the framework of irreversible thermo- dynamics. The constitutive modeling, in fact, is an inverse problem that belongs to the medium inverse problems of model identification, which is expressed as a reversion of coefficient of differential equation. Thus the constitutive modeling of geotechnical materials will become the reversion of coefficient functions of the general expression of constitutive relation, which is carried out in the stress field （p,q） by means Of numerical techniques, so that is called numerical modeling. Applying the numerical modeling, a number of plasticity-based models for clay and sand have been obtained, which are able to characterize the fundamental features of deformation for geotechnieal materials. In addition, the approach of numerical modeling also can be applied to the situation of unsaturated soils by means of the Bishop＇s effective stress formula and Khalili＇s expression of effective stress parameter.展开更多
In this paper we elaborate a general expression of the conditional expectation related to pricing problem of the American options using the Malliavin derivative （without localization）. This work is a generalization ...In this paper we elaborate a general expression of the conditional expectation related to pricing problem of the American options using the Malliavin derivative （without localization）. This work is a generalization of paper of Bally et al. （2005） [ 1 ] for the one dimensional case. Basing on the density function of the asset price, Bally and al. used the Malliavin calculus to evaluate the conditional expectation related to pricing American option problem, but in our work we use the Malliavin derivative to resolve the previous problem.展开更多
It is the aim of the present article to give a general expression of flow equations of the q-KP hierarchy.The distinct difference between the q-KP hierarchy and the KP hierarchy is due to q-binomial and the action of ...It is the aim of the present article to give a general expression of flow equations of the q-KP hierarchy.The distinct difference between the q-KP hierarchy and the KP hierarchy is due to q-binomial and the action of q-shift operator θ, which originates from the Leibnitz rule of the quantum calculus. We further show that the n-reduction leads to a recursive scheme for these flow equations. The recursion operator for the flow equations of the q-KP hierarchy under the n-reduction is also derived.展开更多
A theoretical model to explain the mechanism of the electromagnetic wave propagation in the quasi two-dimensional layer of counterions adjacent to the surface of a charged cylindrical membrane is presented. By using M...A theoretical model to explain the mechanism of the electromagnetic wave propagation in the quasi two-dimensional layer of counterions adjacent to the surface of a charged cylindrical membrane is presented. By using Maxwell and hydrodynamic equations with appropriate boundary conditions, general expression of dispersion relation is obtained for the electromagnetic wave with mixed TE and TM modes.展开更多
The emission spectrum of a two-level atom interacting with a single mode radiation field in the case of periodic oscillation coupling coefficient is investigated.A general expression for the emission spectrum is deriv...The emission spectrum of a two-level atom interacting with a single mode radiation field in the case of periodic oscillation coupling coefficient is investigated.A general expression for the emission spectrum is derived.The numerical results for the initial field in pure number stare are calculated.It is found that the effect of the coupling coefficient modulation on the spectral structure is very obvious in the case of a low modulation frequency and larger amplitude when the initial field is vacuum,which is potentially useful for exploring a modulated light source.展开更多
Corresponding to optical Fresnel diffraction, we show that the exponential quadratic operator exp is actually a generalized single-mode Fresnel operator （GFO） in compact form, where [Q,P]=ih. We also demonstrate tha...Corresponding to optical Fresnel diffraction, we show that the exponential quadratic operator exp is actually a generalized single-mode Fresnel operator （GFO） in compact form, where [Q,P]=ih. We also demonstrate that exp{iα[（Q1＋Q2）2＋（p1-P2）2]＋iβ[（Q1-Q2）2＋（p1＋p2）2]＋iy（Q1P2＋Q2P1）} is a two-mode GFO. Their disentangling formula and normal ordering form are derived with the use of technique of integration within an ordered product （IWOP） of operators and the coherent state representation. The squeezed states generated by these two GFOs are obtained.展开更多
We develop and assess a model of the turbulent burning velocity ST over a wide range of conditions.The aim is to obtain an explicit ST model for turbulent combustion modeling and flame analysis.The model consists of s...We develop and assess a model of the turbulent burning velocity ST over a wide range of conditions.The aim is to obtain an explicit ST model for turbulent combustion modeling and flame analysis.The model consists of sub models of the stretch factor and the turbulent flame area.The stretch factor characterizes the flame response of turbulence stretch and incorporates detailed chemistry and transport effects with a lookup table of laminar counterflow flames.The flame area model captures the area growth based on Lagrangian statistics of propagating surfaces and considers the effects of turbulence length scales and fuel characteristics.The present model predicts sT via an algebraic expression without free parameters.We assess the model using 490 cases of the direct numerical simulation or experiment reported from various research groups on planar and Bunsen flames over a wide range of conditions,covering fuels from hydrogen to n-dodecane,pressures from 1 to 30 atm,lean and rich mixtures,turbulence intensity ratios from 0.1 to 177.6,and turbulence length ratios from 0.5 to 66.7.Despite the scattering sT data in the literature,the comprehensive comparison shows that the proposed ST model has an overall good agreement over the wide range of conditions,with the averaged modeling error of 28.1%.展开更多
Based on the coherence theory of diffracted optical field and the model for partially coherent beams,analytical expressions for the cross-spectral density and the irradiance spectral density in the far zone are derive...Based on the coherence theory of diffracted optical field and the model for partially coherent beams,analytical expressions for the cross-spectral density and the irradiance spectral density in the far zone are derived,respectively.Utilizing the theoretical model of radiation from secondary planar sources,the physical conditions for sources generating a cosh-Gaussian(CHG) beam are investigated.Analytical results demonstrate that the parametric conditions strongly depend on the coherence property of sources.When almost coherence property is satisfied in the source plane,the conditions are the same as those for fundamental Gaussian beams;when partial coherence or almost incoherence property is satisfied in the spatial source plane,the conditions are the same as those for Gaussian-Schell model beams.The results also indicate that the variance of cosine parameters has no influence on the conditions.Our results may provide potential applications for some investigations such as the modulations of cosh-Gaussian beams and the designs of source beam parameters.展开更多
文摘The path-integral quantization of thermal scalar, vector, and spinor fields is performed newly in the coherent-state representation. In doing this, we choose the thermal electrodynamics and psi(4) theory as,examples. By this quantization, correct expressions of the partition functions and the generating functionals for the quantum thermal electrodynamics and psi(4) theory are obtained in the coherent-state representation. These expressions allow us to perform analytical calculations of the partition functions and generating functionals and therefore are useful in practical applications. Especially, the perturbative expansions of the generating functionals are derived specifically by virtue of the stationary-phase method. The generating functionals formulated in the position space are re-derived from the ones given in the coherent-state representation.
文摘Under the direction of the principle of interaction between plastic volumetric and shear strains, the general expression of constitutive relation for geotechnical materials has been derived within the framework of irreversible thermo- dynamics. The constitutive modeling, in fact, is an inverse problem that belongs to the medium inverse problems of model identification, which is expressed as a reversion of coefficient of differential equation. Thus the constitutive modeling of geotechnical materials will become the reversion of coefficient functions of the general expression of constitutive relation, which is carried out in the stress field （p,q） by means Of numerical techniques, so that is called numerical modeling. Applying the numerical modeling, a number of plasticity-based models for clay and sand have been obtained, which are able to characterize the fundamental features of deformation for geotechnieal materials. In addition, the approach of numerical modeling also can be applied to the situation of unsaturated soils by means of the Bishop＇s effective stress formula and Khalili＇s expression of effective stress parameter.
文摘In this paper we elaborate a general expression of the conditional expectation related to pricing problem of the American options using the Malliavin derivative （without localization）. This work is a generalization of paper of Bally et al. （2005） [ 1 ] for the one dimensional case. Basing on the density function of the asset price, Bally and al. used the Malliavin calculus to evaluate the conditional expectation related to pricing American option problem, but in our work we use the Malliavin derivative to resolve the previous problem.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11271210 and 11201451Anhui Province Natural Science Foundation under Grant No.1608085MA04
文摘It is the aim of the present article to give a general expression of flow equations of the q-KP hierarchy.The distinct difference between the q-KP hierarchy and the KP hierarchy is due to q-binomial and the action of q-shift operator θ, which originates from the Leibnitz rule of the quantum calculus. We further show that the n-reduction leads to a recursive scheme for these flow equations. The recursion operator for the flow equations of the q-KP hierarchy under the n-reduction is also derived.
文摘A theoretical model to explain the mechanism of the electromagnetic wave propagation in the quasi two-dimensional layer of counterions adjacent to the surface of a charged cylindrical membrane is presented. By using Maxwell and hydrodynamic equations with appropriate boundary conditions, general expression of dispersion relation is obtained for the electromagnetic wave with mixed TE and TM modes.
基金Supported by the Shandong Province Natural Science Foundation under Grant No.ZR2009AM019
文摘The emission spectrum of a two-level atom interacting with a single mode radiation field in the case of periodic oscillation coupling coefficient is investigated.A general expression for the emission spectrum is derived.The numerical results for the initial field in pure number stare are calculated.It is found that the effect of the coupling coefficient modulation on the spectral structure is very obvious in the case of a low modulation frequency and larger amplitude when the initial field is vacuum,which is potentially useful for exploring a modulated light source.
基金supported by the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A16)the Specialized Research Fund for the Doctoral Program of Higher Education China (Grant No.20103705110001)
文摘Corresponding to optical Fresnel diffraction, we show that the exponential quadratic operator exp is actually a generalized single-mode Fresnel operator （GFO） in compact form, where [Q,P]=ih. We also demonstrate that exp{iα[（Q1＋Q2）2＋（p1-P2）2]＋iβ[（Q1-Q2）2＋（p1＋p2）2]＋iy（Q1P2＋Q2P1）} is a two-mode GFO. Their disentangling formula and normal ordering form are derived with the use of technique of integration within an ordered product （IWOP） of operators and the coherent state representation. The squeezed states generated by these two GFOs are obtained.
基金supported by the National Natural Science Foundation of China(Grant Nos.91841302,11925201,and 11988102)the National Key Research and Development.Program of China(Grant No.2020YFE0204200)。
文摘We develop and assess a model of the turbulent burning velocity ST over a wide range of conditions.The aim is to obtain an explicit ST model for turbulent combustion modeling and flame analysis.The model consists of sub models of the stretch factor and the turbulent flame area.The stretch factor characterizes the flame response of turbulence stretch and incorporates detailed chemistry and transport effects with a lookup table of laminar counterflow flames.The flame area model captures the area growth based on Lagrangian statistics of propagating surfaces and considers the effects of turbulence length scales and fuel characteristics.The present model predicts sT via an algebraic expression without free parameters.We assess the model using 490 cases of the direct numerical simulation or experiment reported from various research groups on planar and Bunsen flames over a wide range of conditions,covering fuels from hydrogen to n-dodecane,pressures from 1 to 30 atm,lean and rich mixtures,turbulence intensity ratios from 0.1 to 177.6,and turbulence length ratios from 0.5 to 66.7.Despite the scattering sT data in the literature,the comprehensive comparison shows that the proposed ST model has an overall good agreement over the wide range of conditions,with the averaged modeling error of 28.1%.
文摘Based on the coherence theory of diffracted optical field and the model for partially coherent beams,analytical expressions for the cross-spectral density and the irradiance spectral density in the far zone are derived,respectively.Utilizing the theoretical model of radiation from secondary planar sources,the physical conditions for sources generating a cosh-Gaussian(CHG) beam are investigated.Analytical results demonstrate that the parametric conditions strongly depend on the coherence property of sources.When almost coherence property is satisfied in the source plane,the conditions are the same as those for fundamental Gaussian beams;when partial coherence or almost incoherence property is satisfied in the spatial source plane,the conditions are the same as those for Gaussian-Schell model beams.The results also indicate that the variance of cosine parameters has no influence on the conditions.Our results may provide potential applications for some investigations such as the modulations of cosh-Gaussian beams and the designs of source beam parameters.
