We propose a formal expansion of multiple relaxation times lattice Boltzmann schemes in terms single infinitesimal numerical variable. The result is system partial differential equations for the conserved moments scheme. presented nonlinear case up to fourth order accuracy. asymptotic corrections nonconserved are developed equilibrium values and differentials moments. Both expansions coupled co...

We discuss effects of chemical potential on the dynamics of chiral transition by the Taylor expansion method in lattice QCD. Operators and their Taylor expansions which characterise the chiral dynamics are related through Maxwell’s relations and Chiral Ward identities. This reduces the computation to just measuring the renormalized expectation values of the chiral condensate and its Taylor coef...

Properties of QCD at finite chemical potential (μ) are extracted using Taylor series expansions. The continuum limits of lattice results are presented. The result of expanding the free energy density, i. e., the pressure, to 6th order in the expansion is shown. The Taylor coefficients of the chiral condensate are also shown. Relations between various Taylor coefficients are demonstrated. All th...

Elongated bubbles which are constrained by the walls of a pipe are commonly known as Taylor bubbles. Taylor bubbles are prevalent in industrial gas-liquid flow, where they are commonly found in buoyancy driven fermenters, the production and transportation of hydrocarbons in the oil and gas industry, the boiling and condensing process in thermal power plants, and the emergency cooling of nuclear...

We describe a formula for the Taylor series expansion of the Gaussian kernel around the origin of Rn × R.

The generalized Taylor expansion including a secret auxiliary parameter h which can control and adjust the convergence region of the series is the foundation of the homotopy analysis method proposed by Liao. The secret of h can’t be understood in the frame of the homotopy analysis method. This is a serious shortcoming of Liao’s method. We solve the problem. Through a detailed study of a simple ...