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Using the field theoretic renormalization group technique the simultaneous influence of the compressibility and finite time correlations of the non-solenoidal Gaussian velocity field on the advection of a passive scalar field is studied within the generalized Kraichnan model in three spatial dimensions up to the second-order approximation in the corresponding perturbative expansion. All possible infrared stable fixed points of the model, which drive the corresponding scaling regimes of the model, are identified and their regions of the infrared stability in the model parametric space are discussed. It is shown that, depending on the value of the parameter that drives the compressibility of the system, there exists a gap in the parametric space between the regions where the model with the frozen velocity field and the model with finite-time correlations of the velocity field are stable or there exists an overlap between them. [ABSTRACT FROM AUTHOR]

We report an upgrade of the program KANTBP 4M implemented in the computer algebra system MAPLE for solving, with a given accuracy, the multichannel scattering problem, which is reduced to a boundary-value problem for a system of ordinary differential equations of the second order with continuous or piecewise continuous real or complex-valued coeffcients. The solution over a finite interval is subject to mixed homogeneous boundary conditions: Dirichlet and/or Neumann, and/or of the third kind. The discretization of the boundary problem is implemented by means of the finite element method with the Lagrange or Hermite interpolation polynomials. The effciency of the proposed algorithm is demonstrated by solving a multichannel scattering problem with coupling of channels in both the reaction region and the asymptotic one. [ABSTRACT FROM AUTHOR]

A new algorithm for constructing multivariate interpolation Hermite polynomials in analytical form in a multidimensional hypercube is presented. These polynomials are determined from a specially constructed set of values of the polynomials themselves and their partial derivatives with continuous derivatives up to a given order on the boundaries of the finite elements. The effciency of the finite element schemes, algor thms and programs is demonstrated by solving the Helmholtz problem for a cube. [ABSTRACT FROM AUTHOR]