Scalar Forcing Methodology for Direct Numerical Simulations of Turbulent Stratified Mixture Combustion

Scalar forcing in the context of turbulent stratified flame simulations aims to maintain the fuel-air inhomogeneity in the unburned gas. With scalar forcing, stratified flame simulations have the potential to reach a statistically stationary state with a prescribed mixture fraction distribution and root-mean-square value in the unburned gas, irrespective of the turbulence intensity. The applicability of scalar forcing for Direct Numerical Simulations of stratified mixture combustion is assessed by considering a recently developed scalar forcing scheme, known as the reaction analogy method, applied to both passive scalar mixing and the imperfectly mixed unburned reactants of statistically planar stratified flames under low Mach number conditions. The newly developed method enables statistically symmetric scalar distributions between bell-shaped and bimodal to be maintained without any significant departure from the specified bounds of the scalar. Moreover, the performance of the newly proposed scalar forcing methodology has been assessed for a range of different velocity forcing schemes (Lundgren forcing and modified bandwidth forcing) and also without any velocity forcing. It has been found that the scalar forcing scheme has no adverse impact on flame-turbulence interaction and it only maintains the prescribed root-mean-square value of the scalar fluctuation, and its distribution. The scalar integral length scale evolution is shown to be unaffected by the scalar forcing scheme studied in this paper. Thus, the scalar forcing scheme has a high potential to provide a valuable computational tool to enable analysis of the effects of unburned mixture stratification on turbulent flame dynamics.

Hypergeometric expression for a three-loop vacuum integral

Using the corresponding Mellin–Barnes representation, we derive holonomic hypergeometric system of linear partial differential equations (PDEs) satisfied by Feynman integral of a three-loop vacuum with five propagators. Through the multidimensional residue theorem in dimensional regularization, the scalar integral can be written as the summation of multiple hypergeometric functions, whose convergent regions can be obtained by the Horn’s convergent theory. The numerical continuation of the scalar integral from convergent regions to whole kinematic regions can be accomplished with the finite element methods, when the system of PDEs can be treated as the stationary conditions of a functional under the restrictions.

Growth conditions and regularity, an optimal local boundedness result

We prove local boundedness of local minimizers of scalar integral functionals [Formula: see text], [Formula: see text] where the integrand satisfies [Formula: see text]-growth of the form [Formula: see text] under the optimal relation [Formula: see text].

THE INFLUENCE OF RATE OF DAMAGE ACCUMULATION IS USED IN THE CALCULATION OF DUCTILITY RESOURCE

In assessing marginal change in the process of metal forming, plasticity is significantly affected by the rate of damage accumulation and their healing as derivatives of the stress state indicators. It is shown that under complex loading conditions, when the damage accumulation rate (the first derivative of the stress state indicators) is more than 5 and the curvature of the material deformation trajectories (the second derivative of the stress state indicators) is greater than 1, the scalar integral criteria give the most reliable results destruction, taking into account the influence of the history of deformation on plasticity.

FACTORIZATION OF OPERATORS THROUGH SUBSPACES OF -SPACES

We analyze domination properties and factorization of operators in Banach spaces through subspaces of$L^{1}$-spaces. Using vector measure integration and extending classical arguments based on scalar integral bounds, we provide characterizations of operators factoring through subspaces of$L^{1}$-spaces of finite measures. Some special cases involving positivity and compactness of the operators are considered.

Acoustic Scattering of 3D Complex Systems Having Random Rough Surfaces by Scalar Integral Equations

We propose a numerical surface integral method to study complex acoustic systems, for interior and exterior problems. The method is based on a parametric representation in terms of the arc’s lengths in curvilinear orthogonal coordinates. With this method, any geometry that involves quadric or higher order surfaces, irregular objects or even randomly rough surfaces can be considered. In order to validate the method, the modes in cubic, spherical and cylindrical cavities are calculated and compared to analytical results, which produced very good agreement. In addition, as examples, we calculated the scattering in the far field and the near field by an acoustic sphere and a cylindrical structure with a rough cross-section.