The mass density distribution of Newtonian self-gravitating systems is studied analytically in the field theoretical method. Modeling the system as a fluid in hydrostatic equilibrium, we apply Schwinger's function...The mass density distribution of Newtonian self-gravitating systems is studied analytically in the field theoretical method. Modeling the system as a fluid in hydrostatic equilibrium, we apply Schwinger's functional derivative on the average of the field equation of mass density, and obtain the field equation of 2-point correlation function ξ(r) of the mass density fluctuation, which includes the next order of nonlinearity beyond the Gaussian approximation. The 3-point correlation occurs hierarchically in the equation,and is cut off by the Groth-Peebles ansatz, making it closed. We perform renormalization and write the equation with three nonlinear coefficients. The equation tells us that ξ depends on the point mass m and the Jeans wavelength scale λ_0, which are different for galaxies and clusters. Applying this to large scale structures, it predicts that the profile of ξcc for clusters is similar to ξgg for galaxies but with a higher amplitude, and that the correlation length increases with the mean separation between clusters, i.e., a scaling behavior r_0■0.4 d. The solution yields the galaxy correlation ξ_(gg)(r)■(r_0/r)^(1.7) valid only in a range1 < r < 10 h^(-1) Mpc. At larger scales the solution ξgg deviates below the power law and goes to zero around ~50 h^(-1) Mpc, just as the observations show. We also derive the field equation of the 3-point correlation function in the Gaussian approximation and its analytical solution, for which the Groth-Peebles ansatz with Q = 1 holds.展开更多
Based on the field theory of density fiuctuation under Newtonian gravity,we obtain analytically the nonlinear equation of 3-pt correlation functionζof galaxies in a homogeneous,isotropic,static universe.The density f...Based on the field theory of density fiuctuation under Newtonian gravity,we obtain analytically the nonlinear equation of 3-pt correlation functionζof galaxies in a homogeneous,isotropic,static universe.The density fiuctuation has been kept up to second order.By the Fry-Peebles ansatz and the Groth-Peebles ansatz,the equation ofζbecomes closed and differs from the Gaussian approximate equation.Using the boundary condition inferred from the data of SDSS,we obtain the solutionζ(r,u,θ)at fixed u=2,which exhibits a shallow U-shape along the angleθand,nevertheless,decreases monotonously along the radial r.We show its difference with the Gaussian solution.As a direct criterion of non-Gaussianity,the reduced Q(r,u,θ)deviates from the Gaussianity plane Q=1,exhibits a deeper U-shape alongθand varies weakly along r,agreeing with the observed data.展开更多
Applying functional differentiation to the density field with Newtonian gravity,we obtain the static,nonlinear equation of the three-point correlation functionζof galaxies to the third order density perturbations.We ...Applying functional differentiation to the density field with Newtonian gravity,we obtain the static,nonlinear equation of the three-point correlation functionζof galaxies to the third order density perturbations.We make the equation closed and perform renormalization of the mass and the Jeans wavenumber.Using the boundary condition inferred from observations,we obtain the third order solutionζ(r,u,θ)at fixed u=2,which is positive,exhibits a Ushape along the angleθ,and decreases monotonously along the radial r up to the range r≤30 h^(-1)Mpc in our computation.The corresponding reduced Q(r,u,θ)deviates from 1 of the Gaussian case,has a deeper U-shape alongθ,and varies non-monotonously along r.The third order solution agrees with the SDSS data of galaxies,quite close to the previous second order solution,especially at large scales.This indicates that the equations of correlation functions with increasing orders of density perturbation provide a stable description of the nonlinear galaxy system.展开更多
BACKGROUND Heart failure is generally regarded as a progressive and irreversible medical condition.The EVAHEART is an implantable left ventricular assist system.CASE SUMMARY We report the anesthesia management of a 56...BACKGROUND Heart failure is generally regarded as a progressive and irreversible medical condition.The EVAHEART is an implantable left ventricular assist system.CASE SUMMARY We report the anesthesia management of a 56-year-old male patient with dilated cardiomyopathy undergoing an EVAHEART implantation.Transesophageal echocardiography is crucial to ensure the correct positioning of the device and the proper aortic valve outflow.Because the continuous blood flow device functions best under low systemic and pulmonary vascular resistance,milrinone is the preferred drug.Our patient was accompanied by pulmonary hypertension,so during the operation,nitric oxide was used to reduce pulmonary artery pressure.CONCLUSION The cardiac output achieved by the patient with the assistance of EVAHEART can reach 4 L/min,which of course depends on the front load,rear load,and pump speed.展开更多
基金Y. Zhang is supported by the National Natural Science Foundation of China (Grant Nos. 11421303, 11675165 and 11633001)SRFDP+1 种基金CASthe Strategic Priority Research Program "The Emergence of Cosmological Structures" of the Chinese Academy of Sciences (Grant No. XDB09000000)
文摘The mass density distribution of Newtonian self-gravitating systems is studied analytically in the field theoretical method. Modeling the system as a fluid in hydrostatic equilibrium, we apply Schwinger's functional derivative on the average of the field equation of mass density, and obtain the field equation of 2-point correlation function ξ(r) of the mass density fluctuation, which includes the next order of nonlinearity beyond the Gaussian approximation. The 3-point correlation occurs hierarchically in the equation,and is cut off by the Groth-Peebles ansatz, making it closed. We perform renormalization and write the equation with three nonlinear coefficients. The equation tells us that ξ depends on the point mass m and the Jeans wavelength scale λ_0, which are different for galaxies and clusters. Applying this to large scale structures, it predicts that the profile of ξcc for clusters is similar to ξgg for galaxies but with a higher amplitude, and that the correlation length increases with the mean separation between clusters, i.e., a scaling behavior r_0■0.4 d. The solution yields the galaxy correlation ξ_(gg)(r)■(r_0/r)^(1.7) valid only in a range1 < r < 10 h^(-1) Mpc. At larger scales the solution ξgg deviates below the power law and goes to zero around ~50 h^(-1) Mpc, just as the observations show. We also derive the field equation of the 3-point correlation function in the Gaussian approximation and its analytical solution, for which the Groth-Peebles ansatz with Q = 1 holds.
基金supported by NSFC Grant Nos.11675165,11633001 and 11961131007in part by the National Key RD Program of China(2021YFC2203100)。
文摘Based on the field theory of density fiuctuation under Newtonian gravity,we obtain analytically the nonlinear equation of 3-pt correlation functionζof galaxies in a homogeneous,isotropic,static universe.The density fiuctuation has been kept up to second order.By the Fry-Peebles ansatz and the Groth-Peebles ansatz,the equation ofζbecomes closed and differs from the Gaussian approximate equation.Using the boundary condition inferred from the data of SDSS,we obtain the solutionζ(r,u,θ)at fixed u=2,which exhibits a shallow U-shape along the angleθand,nevertheless,decreases monotonously along the radial r.We show its difference with the Gaussian solution.As a direct criterion of non-Gaussianity,the reduced Q(r,u,θ)deviates from the Gaussianity plane Q=1,exhibits a deeper U-shape alongθand varies weakly along r,agreeing with the observed data.
基金supported by NSFC(Grant Nos.11675165,11633001,and 11961131007)in part by the National Key RD Program of China(2021YFC2203100)。
文摘Applying functional differentiation to the density field with Newtonian gravity,we obtain the static,nonlinear equation of the three-point correlation functionζof galaxies to the third order density perturbations.We make the equation closed and perform renormalization of the mass and the Jeans wavenumber.Using the boundary condition inferred from observations,we obtain the third order solutionζ(r,u,θ)at fixed u=2,which is positive,exhibits a Ushape along the angleθ,and decreases monotonously along the radial r up to the range r≤30 h^(-1)Mpc in our computation.The corresponding reduced Q(r,u,θ)deviates from 1 of the Gaussian case,has a deeper U-shape alongθ,and varies non-monotonously along r.The third order solution agrees with the SDSS data of galaxies,quite close to the previous second order solution,especially at large scales.This indicates that the equations of correlation functions with increasing orders of density perturbation provide a stable description of the nonlinear galaxy system.
文摘BACKGROUND Heart failure is generally regarded as a progressive and irreversible medical condition.The EVAHEART is an implantable left ventricular assist system.CASE SUMMARY We report the anesthesia management of a 56-year-old male patient with dilated cardiomyopathy undergoing an EVAHEART implantation.Transesophageal echocardiography is crucial to ensure the correct positioning of the device and the proper aortic valve outflow.Because the continuous blood flow device functions best under low systemic and pulmonary vascular resistance,milrinone is the preferred drug.Our patient was accompanied by pulmonary hypertension,so during the operation,nitric oxide was used to reduce pulmonary artery pressure.CONCLUSION The cardiac output achieved by the patient with the assistance of EVAHEART can reach 4 L/min,which of course depends on the front load,rear load,and pump speed.
