The Mapping Closure Approximation(MCA)approach is developed to describe the statistics of both conserved and reactive scalars in random flows.The statistics include Probability Density Function(PDF),Conditional Dissip...The Mapping Closure Approximation(MCA)approach is developed to describe the statistics of both conserved and reactive scalars in random flows.The statistics include Probability Density Function(PDF),Conditional Dissipation Rate(CDR)and Conditional Laplacian(CL).The statistical quantities are calculated using the MCA and compared with the results of the Direct Nu- merical Simulation(DNS).The results obtained from the MCA are in agreement with those from the DNS.It is shown that the MCA approach can predict the statistics of reactive scalars in random flows.展开更多
This paper investigates static axially symmetric models in self-interacting Brans-Dicke gravity. We discuss physically feasible sources of models, derive field equations as well as evolution equations from Bianchi ide...This paper investigates static axially symmetric models in self-interacting Brans-Dicke gravity. We discuss physically feasible sources of models, derive field equations as well as evolution equations from Bianchi identities and construct structure scalars. Using these scalars and evolution equations, the inhomogeneity factors of the system are evaluated. It is found that structure scalars related to double dual of Riemann tensor control the density inhomogeneity. Finally, we obtain exact solutions of homogenous isotropic and inhomogeneous anisotropic spheroid models. It turns out that homogenous solutions reduce to Schwarzschild type interior solutions for a spherical case. We conclude that homogenous models involve homogenous distribution of scalar field whereas inhomogeneous correspond to inhomogeneous sca/ar field.展开更多
The littlest Higgs （LH） model is the most economical one among various little Higgs models, which predicts the existence of the charged scalars Φ^±. In this paper, we study the production of the charged Higgs ...The littlest Higgs （LH） model is the most economical one among various little Higgs models, which predicts the existence of the charged scalars Φ^±. In this paper, we study the production of the charged Higgs boson Φ^- with single top quark via the process gb →tΦ^- at the CERN Large Hadron Collider （LHC）. The numerical results show that the production cross section is sma/ler than 0.2 pb in most of the parameters space, it is very difficult to observe the signatures of the charged scalars via the process pp → gb ＋ X → tΦ^- ＋ X at the LHC experiments. However, it can open a window to distinguish the top-pions in the TC2 model or charged Higgs in the MSSM from Φ^±.展开更多
In this paper, we have introduced a shell-model of Kraichnan＇s passive scalar problem. Different from the original problem, the prescribed random velocity field is non-Gaussian and σ correlated in time, and its intr...In this paper, we have introduced a shell-model of Kraichnan＇s passive scalar problem. Different from the original problem, the prescribed random velocity field is non-Gaussian and σ correlated in time, and its introduction is inspired by She and Levveque （Phys. Rev. Lett. 72, 336 （1994））. For comparison, we also give the passive scalar advected by the Gaussian random velocity field. The anomalous scaling exponents H（p） of passive scalar advected by these two kinds of random velocities above are determined for structure function with values of p up to 15 by Monte Carlo simulations of the random shell model, with Gear methods used to solve the stochastic differential equations. We find that the H（p） advected by the non-Gaussian random velocity is not more anomalous than that advected by the Gaussian random velocity. Whether the advecting velocity is non-Gaussian or Gaussian, similar scaling exponents of passive scalar are obtained with the same molecular diffusivity.展开更多
A shell-model version of passive scalar problem is introduced, which is inspired by the model of K. Ohkitani and M. Yakhot [K. Ohkitani and M. Yakhot, Phys. Rev. Lett. 60 （1988） 983; K. Ohkitani and M. Yakhot, Prog....A shell-model version of passive scalar problem is introduced, which is inspired by the model of K. Ohkitani and M. Yakhot [K. Ohkitani and M. Yakhot, Phys. Rev. Lett. 60 （1988） 983; K. Ohkitani and M. Yakhot, Prog. Theor. Phys. 81 （1988） 329]. As in the original problem, the prescribed random velocity field is Gaussian and 5 correlated in time. Deterministic differential equations are regarded as nonlinear Langevin equation. Then, the Fokker-Planck equations of PDF for passive scalars are obtained and solved numerically. In energy input range （n 〈 5, n is the shell number.）, the probability distribution function （PDF） of passive scalars is near the Gaussian distribution. In inertial range （5≤ n ≤ 16） and dissipation range （n ≥ 17）, the probability distribution function （PDF） of passive scalars has obvious intermittence. And the scaling power of passive scalar is anomalous. The results of numerical simulations are compared with experimental measurements.展开更多
We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of passive scalars of turbulence. Different to the original problem, the distribution function of the prescribed random vel...We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of passive scalars of turbulence. Different to the original problem, the distribution function of the prescribed random velocity field is multi-dimensional normal and delta-correlated in time. Here, our random velocity field is spatially correlative. For comparison, we also give the result obtained by the Gaussian random velocity field without spatial correlation. The anomalous scaling exponents H（p） of passive scalar advected by two kinds of random velocity above are determined for structure function up to p= 15 by numerical simulations of the random shell model with Runge-Kutta methods to solve the stochastic differential equations. We observed that the H（p） ＇s obtained by the multi-dimeasional normal distribution random velocity are more anomalous than those obtained by the independent Gaussian random velocity.展开更多
In this paper, we consider spatial-temporal correlation functions of the turbulent velocities. With numerical simulations on the Gledzer-Ohkitani-Yamada （GOY） shell model, we show that the correlation function decay...In this paper, we consider spatial-temporal correlation functions of the turbulent velocities. With numerical simulations on the Gledzer-Ohkitani-Yamada （GOY） shell model, we show that the correlation function decays exponentially. The advecting velocity field is regarded as a colored noise field, which is spatially and temporally correlative. For comparison, we are also given the scaling exponents of passive scalars obtained by the Gaussian random velocity field, the multi-dimensional normal velocity field and the She-Leveque velocity field, introduced by She, et al. We observe that extended self-similarity sealing exponents H（p）/H（2） of passive scalar obtained by the colored noise field are more anomalous than those obtained by the other three velocity fields.展开更多
The focal point of this paper is to present the theoretical aspects of the building blocks of the upper bounds of ISD （integer sub-decomposition） method defined by kP = k11P ＋ k12ψ1 （P） ＋ k21P ＋ k22ψ2 （P） w...The focal point of this paper is to present the theoretical aspects of the building blocks of the upper bounds of ISD （integer sub-decomposition） method defined by kP = k11P ＋ k12ψ1 （P） ＋ k21P ＋ k22ψ2 （P） with max {｜k11｜, ｜k12｜} 〈 Ca√n and max{｜k21｜, ｜k22｜}≤C√, where C=I that uses efficiently computable endomorphisms ψj for j=1,2 to compute any multiple kP of a point P of order n lying on an elliptic curve E. The upper bounds of sub-scalars in ISD method are presented and utilized to enhance the rate of successful computation of scalar multiplication kP. Important theorems that establish the upper bounds of the kernel vectors of the ISD reduction map are generalized and proved in this work. The values of C in the upper bounds, that are greater than 1, have been proven in two cases of characteristic polynomials （with degree 1 or 2） of the endomorphisms. The upper bound of ISD method with the case of the endomorphism rings over an integer ring Z results in a higher rate of successful computations kP. Compared to the case of endomorphism rings, which is embedded over an imaginary quadratic field Q = [4-D]. The determination of the upper bounds is considered as a key point in developing the ISD elliptic scalar multiplication technique.展开更多
It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics.When the domain of...It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics.When the domain of S is restricted to the space of constant scalar curvature metrics,there has been a conjecture that a critical point is also Einstein or isometric to a standard sphere.In the Riemannian case,it’s tangent space satisfies a decomposition.In this paper,we prove that if we only consider the Hermitian metrics,it also have a decomposition.Then we obtain the equation of the critical points among the Hermitian metrics.展开更多
In this paper,we derive the sub-Riemannian version of the Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for the twisted BCV spaces.We also compute the Connes conformal invariants for t...In this paper,we derive the sub-Riemannian version of the Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for the twisted BCV spaces.We also compute the Connes conformal invariants for the twisted product,as well as the sub-Riemannian limits of the Connes conformal invariants for the twisted BCV spaces.展开更多
The surprising thing is that arising almost 50 years ago from the linear sigma model （LSM） with spontaneously broken chiral symmetry, the light scalar meson problem has become central in the nonperturbative quantum ...The surprising thing is that arising almost 50 years ago from the linear sigma model （LSM） with spontaneously broken chiral symmetry, the light scalar meson problem has become central in the nonperturbative quantum chromodynamics （QCD） for it has been made clear that LSM could be the low energy realization of QCD. First we review briefly signs of four-quark nature of light scalars. Then we show that the light scalars are produced in the two photon collisions via four-quark transitions in contrast to the classic P wave tensor qq mesons that are produced via two-quark transitions γγ→qq. Thus we get new evidence of the four-quark nature of these states.展开更多
Employing a 4-form ansatz of 11-dimensional supergravity over a non-dynamical AdS_(4)×S^(7)/Z_(k)background and setting the internal space as an S1 Hopf fibration on CP3,we obtain a consistent truncation.The(pseu...Employing a 4-form ansatz of 11-dimensional supergravity over a non-dynamical AdS_(4)×S^(7)/Z_(k)background and setting the internal space as an S1 Hopf fibration on CP3,we obtain a consistent truncation.The(pseudo)scalars,in the resulting scalar equations in Euclidean AdS_(4)space,may be considered to arise from(anti)M-branes wrapping around the internal directions in the(Wick-rotated)skew-whiffed M2-brane background(as the resulting theory is for anti-M2-branes),thus realizing the modes after swapping the three fundamental representations 8_(s),8_(c),and 8_(v) of SO(8).Taking the backreaction on the external and internal spaces,we obtain the massless and massive modes,corresponding to exactly marginal and marginally irrelevant deformations on the boundary CFT3,respectively.Subsequently,we obtain a closed solution for the bulk equation and compute its correction with respect to the background action.Next,considering the Higgs-like(breathing)mode m^(2)=18,having all supersymmetries as well as parity and scale-invariance broken,solving the associated bulk equation with mathematical methods,specifically the Adomian decomposition method,and analyzing the behavior near the boundary of the solutions,we realize the boundary duals in the SU(4)×U(1)-singlet sectors of the ABJM model.Then,introducing the new dual deformationΔ_(+)=3,6 operators made of bi-fundamental scalars,fermions,and U(1)gauge fields,we obtain the SO(4)-invariant solutions as small instantons on a three-sphere with the radius at infinity,which correspond to collapsing bulk bubbles leading to big-crunch singularities.展开更多
In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,t...In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.展开更多
In this work,we construct two efficient fully decoupled,linear,unconditionally stable numerical algorithms for the thermally coupled incompressible magnetohydrodynamic equations.Firstly,in order to obtain the desired ...In this work,we construct two efficient fully decoupled,linear,unconditionally stable numerical algorithms for the thermally coupled incompressible magnetohydrodynamic equations.Firstly,in order to obtain the desired algorithm,we introduce a scalar auxiliary variable(SAV)to get a new equivalent system.Secondly,by combining the pressure-correction method and the explicit-implicit method,we perform semi-discrete numerical algorithms of first and second order,respectively.Then,we prove that the obtained algorithms follow an unconditionally stable law in energy,and we provide a detailed implementation process,which we only need to solve a series of linear differential equations with constant coefficients at each time step.More importantly,with some powerful analysis,we give the order of convergence of the errors.Finally,to illustrate theoretical results,some numerical experiments are given.展开更多
In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary varia...In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary variable approaches.By using a new pressure correction method,the accuracy of the pressure has been greatly improved.Furthermore,one only needs to solve a series of fully decoupled linear equations with constant coefficients at each time step.In addition,we prove the unconditional energy stability of the schemes,rigorously.Finally,plenty of numerical simulations are carried out to verify the convergence rates,stability,and effectiveness of the proposed schemes numerically.展开更多
From[J.Differential Geom.,1990,31(1):285-299],one can obtain that compact self-shrinking hypersufaces in R^(n+1) with constant scalar curvature must be the standard sphere S^(n)(√n)(cf.[Front.Math.,2023,18(2):417-430...From[J.Differential Geom.,1990,31(1):285-299],one can obtain that compact self-shrinking hypersufaces in R^(n+1) with constant scalar curvature must be the standard sphere S^(n)(√n)(cf.[Front.Math.,2023,18(2):417-430]).This result was generalized by Guo[J.Math.Soc.Japan,2018,70(3):1103-1110]with assumption of a lower or upper scalar curvature bound.In this paper,we will generalize the scalar curvature rigidity theorem of Guo to the case of λ-hypersurfaces.We will also give an alternative proof of the theorem(cf.[2014,arXiv:1410.5302]and[Proc.Amer.Math.Soc.,2018,146(10):4459-4471])that λ-hypersurfaces which are entire graphs must be hyperplanes.展开更多
QED(quantum electrodynamics)is the QFT(quantum field theory)describing the interaction between light and matter.While conventional QED is based on TEM(transverse electromagnetic)waves,there has been increasing interes...QED(quantum electrodynamics)is the QFT(quantum field theory)describing the interaction between light and matter.While conventional QED is based on TEM(transverse electromagnetic)waves,there has been increasing interest in the theoretical and experimental exploration of LSW(longitudinal scalar waves)solutions that are often omitted in CED(classical electrodynamics)but may have physical significance in nontrivial vacuum conditions.This paper delves into the theoretical foundation of LSW,their role in QED,and the associated mathematical equations governing their dynamics.展开更多
Several aspects of the internal structure of pseudoscalar mesons,accessible through generalized parton distri-butions in their zero-skewness limit,are examined.These include electromagnetic and gravitational form fact...Several aspects of the internal structure of pseudoscalar mesons,accessible through generalized parton distri-butions in their zero-skewness limit,are examined.These include electromagnetic and gravitational form factors related to charge and mass densities;and distributions in the impact parameter space.To this end,we employ an algebraically viable framework that is based upon the valence-quark generalized parton distribution expressed explicitly in terms of the associated distribution function and a profile function that governs the off-forward dynamics.The predominantly analytical nature of this scheme yields several algebraic results and relations while also facilitating the exploration of insightful limiting cases.With a suitable input distribution function,guided either by experiment or theory,and with an appropriate choice of the profile function,it is possible to provide testable predictions for spatial distributions of valence quarks inside pseudoscalar mesons.When comparison is possible,these predictions align well with existing experimental data as well as the findings of reliable theoretical approaches and lattice QCD.展开更多
In this paper,we prove that for certain fiber bundles there is a k-Futaki-Ono conformally Kahler metric related to a metric in any given Kahler class for any k≥2.
Solving the Dirac equation has played an important role in many areas of fundamental physics.In this work,we present the Dirac equation solver DiracSVT,which solves the Dirac equation with scalar,vector,and tensor nuc...Solving the Dirac equation has played an important role in many areas of fundamental physics.In this work,we present the Dirac equation solver DiracSVT,which solves the Dirac equation with scalar,vector,and tensor nuclear potentials in spherical coordinate space.The shooting method was used with a Runge–Kutta 4 integration scheme.The potentials are parameterized in a Woods–Saxon form,which reproduce well the known single-particle states around all doubly magic nuclei and can be applied to study the shell evolution of exotic nuclei.The code can be easily extended to the study of other systems,including atomic,hadron,and molecular physics.展开更多
基金The project supported by the National Committee of Science and Technology,China,under the Special Funds for Major Basic Research Project (G2000077305 and G1999032801),and the National Natural Science Foundation of China (10325211)
文摘The Mapping Closure Approximation(MCA)approach is developed to describe the statistics of both conserved and reactive scalars in random flows.The statistics include Probability Density Function(PDF),Conditional Dissipation Rate(CDR)and Conditional Laplacian(CL).The statistical quantities are calculated using the MCA and compared with the results of the Direct Nu- merical Simulation(DNS).The results obtained from the MCA are in agreement with those from the DNS.It is shown that the MCA approach can predict the statistics of reactive scalars in random flows.
文摘This paper investigates static axially symmetric models in self-interacting Brans-Dicke gravity. We discuss physically feasible sources of models, derive field equations as well as evolution equations from Bianchi identities and construct structure scalars. Using these scalars and evolution equations, the inhomogeneity factors of the system are evaluated. It is found that structure scalars related to double dual of Riemann tensor control the density inhomogeneity. Finally, we obtain exact solutions of homogenous isotropic and inhomogeneous anisotropic spheroid models. It turns out that homogenous solutions reduce to Schwarzschild type interior solutions for a spherical case. We conclude that homogenous models involve homogenous distribution of scalar field whereas inhomogeneous correspond to inhomogeneous sca/ar field.
文摘The littlest Higgs （LH） model is the most economical one among various little Higgs models, which predicts the existence of the charged scalars Φ^±. In this paper, we study the production of the charged Higgs boson Φ^- with single top quark via the process gb →tΦ^- at the CERN Large Hadron Collider （LHC）. The numerical results show that the production cross section is sma/ler than 0.2 pb in most of the parameters space, it is very difficult to observe the signatures of the charged scalars via the process pp → gb ＋ X → tΦ^- ＋ X at the LHC experiments. However, it can open a window to distinguish the top-pions in the TC2 model or charged Higgs in the MSSM from Φ^±.
基金Project supported by the Major Program of the National Natural Science Foundation （Grant No 10335010） and the National Natural Science Foundation-the Science Foundation of China Academy of Engineering Physics NSAF （Grant No 10576005）.Acknowledgement We are grateful to Professor She Zhen-Su for useful suggestions and Dr Sun Peng and Dr Zhang Xiao- Qiang for extensive discussion.
文摘In this paper, we have introduced a shell-model of Kraichnan＇s passive scalar problem. Different from the original problem, the prescribed random velocity field is non-Gaussian and σ correlated in time, and its introduction is inspired by She and Levveque （Phys. Rev. Lett. 72, 336 （1994））. For comparison, we also give the passive scalar advected by the Gaussian random velocity field. The anomalous scaling exponents H（p） of passive scalar advected by these two kinds of random velocities above are determined for structure function with values of p up to 15 by Monte Carlo simulations of the random shell model, with Gear methods used to solve the stochastic differential equations. We find that the H（p） advected by the non-Gaussian random velocity is not more anomalous than that advected by the Gaussian random velocity. Whether the advecting velocity is non-Gaussian or Gaussian, similar scaling exponents of passive scalar are obtained with the same molecular diffusivity.
基金The project supported by National Natural Science Foundation for Major Projects under Grant Nos.10336010 and 10576005
文摘A shell-model version of passive scalar problem is introduced, which is inspired by the model of K. Ohkitani and M. Yakhot [K. Ohkitani and M. Yakhot, Phys. Rev. Lett. 60 （1988） 983; K. Ohkitani and M. Yakhot, Prog. Theor. Phys. 81 （1988） 329]. As in the original problem, the prescribed random velocity field is Gaussian and 5 correlated in time. Deterministic differential equations are regarded as nonlinear Langevin equation. Then, the Fokker-Planck equations of PDF for passive scalars are obtained and solved numerically. In energy input range （n 〈 5, n is the shell number.）, the probability distribution function （PDF） of passive scalars is near the Gaussian distribution. In inertial range （5≤ n ≤ 16） and dissipation range （n ≥ 17）, the probability distribution function （PDF） of passive scalars has obvious intermittence. And the scaling power of passive scalar is anomalous. The results of numerical simulations are compared with experimental measurements.
基金National Natural Science Foundation of China for Major Projects under Grant No.10576005
文摘We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of passive scalars of turbulence. Different to the original problem, the distribution function of the prescribed random velocity field is multi-dimensional normal and delta-correlated in time. Here, our random velocity field is spatially correlative. For comparison, we also give the result obtained by the Gaussian random velocity field without spatial correlation. The anomalous scaling exponents H（p） of passive scalar advected by two kinds of random velocity above are determined for structure function up to p= 15 by numerical simulations of the random shell model with Runge-Kutta methods to solve the stochastic differential equations. We observed that the H（p） ＇s obtained by the multi-dimeasional normal distribution random velocity are more anomalous than those obtained by the independent Gaussian random velocity.
基金Project supported by the Major Program of the National Natural Science Foundation (Grant No 10335010)the National Natural Science Foundation-the Science Foundation of China Academy of Engineering Physics NSAF(Grant No 10576005)
文摘In this paper, we consider spatial-temporal correlation functions of the turbulent velocities. With numerical simulations on the Gledzer-Ohkitani-Yamada （GOY） shell model, we show that the correlation function decays exponentially. The advecting velocity field is regarded as a colored noise field, which is spatially and temporally correlative. For comparison, we are also given the scaling exponents of passive scalars obtained by the Gaussian random velocity field, the multi-dimensional normal velocity field and the She-Leveque velocity field, introduced by She, et al. We observe that extended self-similarity sealing exponents H（p）/H（2） of passive scalar obtained by the colored noise field are more anomalous than those obtained by the other three velocity fields.
文摘The focal point of this paper is to present the theoretical aspects of the building blocks of the upper bounds of ISD （integer sub-decomposition） method defined by kP = k11P ＋ k12ψ1 （P） ＋ k21P ＋ k22ψ2 （P） with max {｜k11｜, ｜k12｜} 〈 Ca√n and max{｜k21｜, ｜k22｜}≤C√, where C=I that uses efficiently computable endomorphisms ψj for j=1,2 to compute any multiple kP of a point P of order n lying on an elliptic curve E. The upper bounds of sub-scalars in ISD method are presented and utilized to enhance the rate of successful computation of scalar multiplication kP. Important theorems that establish the upper bounds of the kernel vectors of the ISD reduction map are generalized and proved in this work. The values of C in the upper bounds, that are greater than 1, have been proven in two cases of characteristic polynomials （with degree 1 or 2） of the endomorphisms. The upper bound of ISD method with the case of the endomorphism rings over an integer ring Z results in a higher rate of successful computations kP. Compared to the case of endomorphism rings, which is embedded over an imaginary quadratic field Q = [4-D]. The determination of the upper bounds is considered as a key point in developing the ISD elliptic scalar multiplication technique.
基金Supported by National Natural Science Foundation of China(Grant No.12171140).
文摘It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics.When the domain of S is restricted to the space of constant scalar curvature metrics,there has been a conjecture that a critical point is also Einstein or isometric to a standard sphere.In the Riemannian case,it’s tangent space satisfies a decomposition.In this paper,we prove that if we only consider the Hermitian metrics,it also have a decomposition.Then we obtain the equation of the critical points among the Hermitian metrics.
基金Supported by Science and Technology Development Plan Project of Jilin Province China(Grant No.20260102245JC)Supported by National Natural Science Foundation of China(Grant No.11771070).
文摘In this paper,we derive the sub-Riemannian version of the Kastler-Kalau-Walze type theorem and the Dabrowski-Sitarz-Zalecki type theorem for the twisted BCV spaces.We also compute the Connes conformal invariants for the twisted product,as well as the sub-Riemannian limits of the Connes conformal invariants for the twisted BCV spaces.
基金Supported by RFFI Grant No.07-02-00093 from the Russian Foundation for Basic ResearchPresidential Grant No.NSh-1027.2008.2 for Leading Scientific Schools
文摘The surprising thing is that arising almost 50 years ago from the linear sigma model （LSM） with spontaneously broken chiral symmetry, the light scalar meson problem has become central in the nonperturbative quantum chromodynamics （QCD） for it has been made clear that LSM could be the low energy realization of QCD. First we review briefly signs of four-quark nature of light scalars. Then we show that the light scalars are produced in the two photon collisions via four-quark transitions in contrast to the classic P wave tensor qq mesons that are produced via two-quark transitions γγ→qq. Thus we get new evidence of the four-quark nature of these states.
文摘Employing a 4-form ansatz of 11-dimensional supergravity over a non-dynamical AdS_(4)×S^(7)/Z_(k)background and setting the internal space as an S1 Hopf fibration on CP3,we obtain a consistent truncation.The(pseudo)scalars,in the resulting scalar equations in Euclidean AdS_(4)space,may be considered to arise from(anti)M-branes wrapping around the internal directions in the(Wick-rotated)skew-whiffed M2-brane background(as the resulting theory is for anti-M2-branes),thus realizing the modes after swapping the three fundamental representations 8_(s),8_(c),and 8_(v) of SO(8).Taking the backreaction on the external and internal spaces,we obtain the massless and massive modes,corresponding to exactly marginal and marginally irrelevant deformations on the boundary CFT3,respectively.Subsequently,we obtain a closed solution for the bulk equation and compute its correction with respect to the background action.Next,considering the Higgs-like(breathing)mode m^(2)=18,having all supersymmetries as well as parity and scale-invariance broken,solving the associated bulk equation with mathematical methods,specifically the Adomian decomposition method,and analyzing the behavior near the boundary of the solutions,we realize the boundary duals in the SU(4)×U(1)-singlet sectors of the ABJM model.Then,introducing the new dual deformationΔ_(+)=3,6 operators made of bi-fundamental scalars,fermions,and U(1)gauge fields,we obtain the SO(4)-invariant solutions as small instantons on a three-sphere with the radius at infinity,which correspond to collapsing bulk bubbles leading to big-crunch singularities.
基金Supported by Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)+2 种基金Basic Research Plan of Shanxi Province(202203021211129)Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)。
文摘In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.
基金Supported by Research Project Supported by Shanxi Scholarship Council of China(2021-029)Shanxi Provincial International Cooperation Base and Platform Project(202104041101019)Shanxi Province Natural Science Foundation(202203021211129)。
文摘In this work,we construct two efficient fully decoupled,linear,unconditionally stable numerical algorithms for the thermally coupled incompressible magnetohydrodynamic equations.Firstly,in order to obtain the desired algorithm,we introduce a scalar auxiliary variable(SAV)to get a new equivalent system.Secondly,by combining the pressure-correction method and the explicit-implicit method,we perform semi-discrete numerical algorithms of first and second order,respectively.Then,we prove that the obtained algorithms follow an unconditionally stable law in energy,and we provide a detailed implementation process,which we only need to solve a series of linear differential equations with constant coefficients at each time step.More importantly,with some powerful analysis,we give the order of convergence of the errors.Finally,to illustrate theoretical results,some numerical experiments are given.
基金Supported by the Research Project Supported of Shanxi Scholarship Council of China(No.2021-029)Shanxi Provincial International Cooperation Base and Platform Project(202104041101019)Shanxi Province Natural Science Research(202203021211129)。
文摘In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary variable approaches.By using a new pressure correction method,the accuracy of the pressure has been greatly improved.Furthermore,one only needs to solve a series of fully decoupled linear equations with constant coefficients at each time step.In addition,we prove the unconditional energy stability of the schemes,rigorously.Finally,plenty of numerical simulations are carried out to verify the convergence rates,stability,and effectiveness of the proposed schemes numerically.
文摘From[J.Differential Geom.,1990,31(1):285-299],one can obtain that compact self-shrinking hypersufaces in R^(n+1) with constant scalar curvature must be the standard sphere S^(n)(√n)(cf.[Front.Math.,2023,18(2):417-430]).This result was generalized by Guo[J.Math.Soc.Japan,2018,70(3):1103-1110]with assumption of a lower or upper scalar curvature bound.In this paper,we will generalize the scalar curvature rigidity theorem of Guo to the case of λ-hypersurfaces.We will also give an alternative proof of the theorem(cf.[2014,arXiv:1410.5302]and[Proc.Amer.Math.Soc.,2018,146(10):4459-4471])that λ-hypersurfaces which are entire graphs must be hyperplanes.
文摘QED(quantum electrodynamics)is the QFT(quantum field theory)describing the interaction between light and matter.While conventional QED is based on TEM(transverse electromagnetic)waves,there has been increasing interest in the theoretical and experimental exploration of LSW(longitudinal scalar waves)solutions that are often omitted in CED(classical electrodynamics)but may have physical significance in nontrivial vacuum conditions.This paper delves into the theoretical foundation of LSW,their role in QED,and the associated mathematical equations governing their dynamics.
基金supported by the Spanish MICINN grant PID2022-140440NB-C22the regional Andalusian project P18-FR-5057+3 种基金the Coordinación de la Investigación Científica of the Universidad Michoacana de San Nicolás de Hidalgo,Morelia,Mexico,Grant No.4.10the Consejo Nacional de Humanidades,Ciencias y Tecnologías,Mexico,project CBF2023-2024-3544the Beatriz-Galindo support during his current scientific stay at the University of Huelva,Huelva,Spainthe Chair d'excellence within the program d'Alembert supporting a visiting professorship in the Universitéde Paris-Saclay,France。
文摘Several aspects of the internal structure of pseudoscalar mesons,accessible through generalized parton distri-butions in their zero-skewness limit,are examined.These include electromagnetic and gravitational form factors related to charge and mass densities;and distributions in the impact parameter space.To this end,we employ an algebraically viable framework that is based upon the valence-quark generalized parton distribution expressed explicitly in terms of the associated distribution function and a profile function that governs the off-forward dynamics.The predominantly analytical nature of this scheme yields several algebraic results and relations while also facilitating the exploration of insightful limiting cases.With a suitable input distribution function,guided either by experiment or theory,and with an appropriate choice of the profile function,it is possible to provide testable predictions for spatial distributions of valence quarks inside pseudoscalar mesons.When comparison is possible,these predictions align well with existing experimental data as well as the findings of reliable theoretical approaches and lattice QCD.
基金supported by the Nature Science Foundation of China(12171140).
文摘In this paper,we prove that for certain fiber bundles there is a k-Futaki-Ono conformally Kahler metric related to a metric in any given Kahler class for any k≥2.
文摘Solving the Dirac equation has played an important role in many areas of fundamental physics.In this work,we present the Dirac equation solver DiracSVT,which solves the Dirac equation with scalar,vector,and tensor nuclear potentials in spherical coordinate space.The shooting method was used with a Runge–Kutta 4 integration scheme.The potentials are parameterized in a Woods–Saxon form,which reproduce well the known single-particle states around all doubly magic nuclei and can be applied to study the shell evolution of exotic nuclei.The code can be easily extended to the study of other systems,including atomic,hadron,and molecular physics.
