We simplify, to a single integral of dilogarithms, the least tractable O(1/N) contribution to the large-N critical exponent η of the non-linear σ-model, and hence φ-theory, for any spacetime dimensionality, D. It is the sole generator of irreducible multiple zeta values in ε-expansions with D = 2− 2ε, for the σ-model, and D = 4− 2ε, for φ-theory. In both cases we confirm results of Broadhurst, ...

We evaluate the unintegrated gluon distribution of proton starting from a parametrization color dipole cross section including Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) evolution and saturation effects. To this end, we perform Fourier-Bessel transform σ(x,r)/α(r). At large transverse momentum gluons match so-obtained to logarithmic derivative collinear distribution. check our approach ...

With discretized particle velocity space, a unified gas-kinetic scheme for entire Knudsen number flows is constructed based on the BGK model. In comparison with many existing kinetic schemes for the Boltzmann equation, the current method has no difficulty to get accurate solution in the continuum flow regime, such as the solution of the Navier-Stokes (NS) equations with the time step being much...

This paper concerns the development and application of a gas-kinetic scheme based on the Bhatnagar–Gross–Krook (BGK) model for the Navier–Stokes equations in the study of hypersonic viscous flow. Firstly, we extend the gas-kinetic Navier–Stokes solver [K. Xu, A gas-kinetic BGK scheme for the Navier–Stokes equations and its connection with artificial dissipation and Godunov method, J. Comput. Ph...

A discontinuous Galerkin Method based on a Bhatnagar-Gross-Krook (BGK) formulation is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. The idea behind this approach is to combine the robustness of the BGK scheme with the accuracy of the DG methods in an effort to develop a more accurate, efficient, and robust method for numerical simulations of viscous ...

An immersed-boundary (IB) method is proposed and applied in the gas-kinetic BGK scheme to simulate incompressible/compressible viscous flow with stationary/moving boundary. In present method the ghost-cell technique is adopted to fulfill the boundary condition on the immersed boundary. A novel idea “local boundary determination” is put forward to identify the ghost cells, each of which may have...