A model fermion has been produced in a theory of quantum gravity that establishes the existence of a mass gap and half-integral spin. The third requirement for the fermion is electric charge. We herein develop a duali...A model fermion has been produced in a theory of quantum gravity that establishes the existence of a mass gap and half-integral spin. The third requirement for the fermion is electric charge. We herein develop a dualism-based analysis that explains the origin of charge at the fermion scale in a primordial field theory of quantum gravity.展开更多
The main aspects of a gauge-invariant approach to the description of quark dynamics in the nonperturbative regime of quantum chromodynamics （QC, D） are first reviewed. The role of the parallel transport operation in...The main aspects of a gauge-invariant approach to the description of quark dynamics in the nonperturbative regime of quantum chromodynamics （QC, D） are first reviewed. The role of the parallel transport operation in constructing gauge-invariant Green＇s functions is then presented, and the relevance of Wilson loops for the representation of the interaction is emphmsized. Recent developments, based on the use of polygonal lines for the parallel transport operation, are presented. An integro-differential equation, obtained for the qua.rk Green＇s function defined with a phase factor along a single, straight line segment, is solved exactly and analytically in the case of two-dimensional QCD in the large-Nc, limit. The solution displays the dynamical mass generation phenomenon for quarks, with an infinite number of branch-cut singularities that are stronger than simple poles.展开更多
In this paper, the Cartan tensors of the(α, β)-norms are investigated in detail. Then an equivalence theorem of(α, β)-norms is proved. As a consequence in Finsler geometry, general(α, β)-metrics on smooth manifo...In this paper, the Cartan tensors of the(α, β)-norms are investigated in detail. Then an equivalence theorem of(α, β)-norms is proved. As a consequence in Finsler geometry, general(α, β)-metrics on smooth manifolds of dimension n 4 with vanishing Landsberg curvatures must be Berwald manifolds.展开更多
We have simulated a time varying wind field using the lattice Boltzmann model, and its effect on blades of grass with a simple mass-spring model. We present a global illumination model for multiple scattering of incid...We have simulated a time varying wind field using the lattice Boltzmann model, and its effect on blades of grass with a simple mass-spring model. We present a global illumination model for multiple scattering of incident sun and sky illumination within the field of grass. We model the grass as a continuous distribution of infinitesimal colored scattering flakes and solve a system of differential equations for the radiance transport. We repeat this for a collection of grass bending directions and amounts, and then interpolate the solutions when rendering animations of blowing grass.展开更多
文摘A model fermion has been produced in a theory of quantum gravity that establishes the existence of a mass gap and half-integral spin. The third requirement for the fermion is electric charge. We herein develop a dualism-based analysis that explains the origin of charge at the fermion scale in a primordial field theory of quantum gravity.
文摘The main aspects of a gauge-invariant approach to the description of quark dynamics in the nonperturbative regime of quantum chromodynamics （QC, D） are first reviewed. The role of the parallel transport operation in constructing gauge-invariant Green＇s functions is then presented, and the relevance of Wilson loops for the representation of the interaction is emphmsized. Recent developments, based on the use of polygonal lines for the parallel transport operation, are presented. An integro-differential equation, obtained for the qua.rk Green＇s function defined with a phase factor along a single, straight line segment, is solved exactly and analytically in the case of two-dimensional QCD in the large-Nc, limit. The solution displays the dynamical mass generation phenomenon for quarks, with an infinite number of branch-cut singularities that are stronger than simple poles.
基金supported by National Natural Science Foundation of China (Grant Nos. 11221091, 11271062, 11501067, 11571184, 11871126 and 11931007)China Scholarship Council Visiting Scholar Program+1 种基金the Fundamental Research Funds for the General UniversitiesNankai Zhide Foundation。
文摘In this paper, the Cartan tensors of the(α, β)-norms are investigated in detail. Then an equivalence theorem of(α, β)-norms is proved. As a consequence in Finsler geometry, general(α, β)-metrics on smooth manifolds of dimension n 4 with vanishing Landsberg curvatures must be Berwald manifolds.
基金the Japan Society for the Promotion of Science for financial support.
文摘We have simulated a time varying wind field using the lattice Boltzmann model, and its effect on blades of grass with a simple mass-spring model. We present a global illumination model for multiple scattering of incident sun and sky illumination within the field of grass. We model the grass as a continuous distribution of infinitesimal colored scattering flakes and solve a system of differential equations for the radiance transport. We repeat this for a collection of grass bending directions and amounts, and then interpolate the solutions when rendering animations of blowing grass.
