Mach Fronts in Random Media with Fractal and Hurst Effects

An investigation of transient second sound phenomena due to moving heat sources on planar random media is conducted. The spatial material randomness of the relaxation time is modeled by Cauchy or Dagum random fields allowing for decoupling of fractal and Hurst effects. The Maxwell–Cattaneo model is solved by a second-order central differencing. The resulting stochastic fluctuations of Mach wedges are examined and compared to unperturbed Mach wedges resulting from the heat source traveling in a homogeneous domain. All the examined cases are illustrated by simulation movies linked to this paper.

Iron/N-doped graphene nano-structured catalysts for general cyclopropanation of olefins

An Fe-based heterogeneous catalyst allows for the synthesis of cyclopropanes via a carbene transfer reaction, a transformation usually belonging to the homogeneous domain.

Analytical representation of the solution of the space kinetic diffusion equation in a one-dimensional and homogeneous domain

In this work we solve the space kinetic diffusion equation in a one-dimensional geometry considering a homogeneous domain, for two energy groups and six groups of delayed neutron precursors. The proposed methodology makes use of a Taylor expansion in the space variable of the scalar neutron flux (fast and thermal) and the concentration of delayed neutron precursors, allocating the time dependence to the coefficients. Upon truncating the Taylor series at quadratic order, one obtains a set of recursive systems of ordinary differential equations, where a modified decomposition method is applied. The coefficient matrix is split into two, one constant diagonal matrix and the second one with the remaining time dependent and off-diagonal terms. Moreover, the equation system is reorganized such that the terms containing the latter matrix are treated as source terms. Note, that the homogeneous equation system has a well known solution, since the matrix is diagonal and constant. This solution plays the role of the recursion initialization of the decomposition method. The recursion scheme is set up in a fashion where the solutions of the previous recursion steps determine the source terms of the subsequent steps. A second feature of the method is the choice of the initial and boundary conditions, which are satisfied by the recursion initialization, while from the first recursion step onward the initial and boundary conditions are homogeneous. The recursion depth is then governed by a prescribed accuracy for the solution.

Bergman–Hartogs domains and their automorphisms

For Cartan–Hartogs domains and also for Bergman–Hartogs domains, the determination of their automorphism groups is given for the cases when the base is any bounded symmetric domain and a general bounded homogeneous domain respectively.

On the holomorphic automorphism group of the Bergman–Hartogs domain

The Bergman–Hartogs domain which can be regarded as a generalization of the Cartan–Hartogs domain provides a large class of bounded pseudoconvex domains which are in general nonhomogeneous. Since the geometry of a domain is determined by its automorphism group to a certain extent, it is meaningful to study the structure of the automorphism group. In this paper, we completely determine the structure of the holomorphic automorphism group of the Bergman–Hartogs domain over a minimal homogeneous domain with center at the origin.