Stationary Transfer Equation Research Articles

Rayleigh wave on the half-space with a gradient piezoelectric layer and imperfect interface

In this study, we consider the propagation of a Rayleigh wave on an anisotropic half-space with a piezoelectric gradient covering layer and imperfect interface. First, the state transfer equation is derived from the governing equations and constitutive relations. The transfer matrix of the state vector is then obtained by solving the state transfer equation and the stiffness matrix is obtained. The total surface stiffness matrix is obtained by combining the transfer matrices and the stiffness matrices of the piezoelectric half-space, the gradient covering layer, and the imperfect interface. Finally, the application of the electrically open circuit, short circuit conditions, and mechanically traction-free conditions gives the frequency dispersive relation. We investigate five types of gradient profiles for the covering layer where the material parameters vary gradually from the top to the bottom, and two types of imperfect interfaces, i.e., dielectrically weakly and highly conducting but mechanically compliant interfaces. The numerical results show that the surface wave speed is sensitive to the gradient profile of the covering layer with the mechanically and dielectrically imperfect interfaces between the covering layer and the substrate.

Dispersion relations of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with functionally graded interlayers

The effects of functionally graded interlayers on dispersion relations of elastic waves in a one-dimensional piezoelectric/piezomagnetic phononic crystal are studied in this paper. First, the state transfer equation of the functionally graded interlayer is derived from the motion equation by the reduction of order (from second order to first order). The transfer matrix of the functionally graded interlayer is obtained by solving the state transfer equation with the spatial-varying coefficient. Based on the transfer matrixes of the piezoelectric slab, the piezomagnetic slab and the functionally graded interlayers, the total transfer matrix of a single cell is obtained. Further, the Bloch theorem is used to obtain the resultant dispersion equations of in-plane and anti-plane Bloch waves. The dispersion equations are solved numerically and the numerical results are shown graphically. Five kinds of profiles of functionally graded interlayers between a piezoelectric slab and a piezomagnetic slab are considered. It is shown that the functionally graded interlayers have evident influences on the dispersion curves and the band gaps.

Formalization of Matrix Theory in HOL4

Matrix theory plays an important role in modeling linear systems in engineering and science. To model and analyze the intricate behavior of complex systems, it is imperative to formalize matrix theory in a metalogic setting. This paper presents the higher-order logic (HOL) formalization of the vector space and matrix theory in the HOL4 theorem proving system. Formalized theories include formal definitions of real vectors and matrices, algebraic properties, and determinants, which are verified in HOL4. Two case studies, modeling and verifying composite two-port networks and state transfer equations, are presented to demonstrate the applicability and effectiveness of our work.

Passive tracking from the combined set of bearings and frequency measurements by single satellite

In this paper, a new passive modified iterated extended Kalman filter (MIEKF) using the combined set of bearings and frequency measurements in Earth Centered Inertial (ECI) coordinate is proposed. A new measurement update equation of MIEKF is derived by modifying the objective function of the Gauss-Newton iteration. A new gain equation and iteration termination criteria are acquired by applying the property of the maximum likelihood estimate. The approximated second order linearized state propagation equation, Jacobian matrix of state transfer and measurement equations are derived in satellite two-body movement. The tracking performances of MIEKF, iterated extended Kalman filter (IEKF) and extended Kalman filter (EKF) are compared via Monte Carlo simulations through simulated data from STK8.1. Simulation results indicate that the proposed MIEKF is possible to passively track low earth circular orbit satellite by a high earth orbit satellite, and has higher tracking precision than the IEKF and EKF.

Design of Aircraft Circuit Modelling Based on Treble Transitions Petri Nets

This paper presents an approach to modeling aircraft airline maintenance circuit through a particular Petri Nets structures, called Treble transitions Petri Nets. In order to meet the requirements of the simulation of aircraft airline maintenance circuit, several enhancements were proposed. The first of them consider the characteristic of circuit, the places, transitions and arcs of classical Petri Nets are extended. In the Second enhancement, the rules of transitions were modified. Finally, the relating matrix and the state transfer equation are redefined. One case is included illustrating the applicability and efficiency of the proposed modeling method.

Modeling of the radiation transfer under partial frequency redistribution

A model is developed of the resonance radiation transfer under partial redistribution over frequencies. The media’s condition is described via the rate population balance equations for the two-level atom. The spectral intensity of the scattered radiation is calculated according to the stationary transfer equation. The light scattering by the atoms is modeled by a linear combination of the angle-averaged redistribution functions, RII and RIII. The obtained integro-differential equation system is solved numerically taking into account the radiation transfer in a cylindrical gas containing volume. The influence is investigated of the partial frequency redistribution on the sodium atom resonance line (λ = 589 nm) profile as well as on the efficient vapor afterglow duration depending on its optical thickness.

On nonstationary radiative transfer in a spectral line in stellar atmospheres

We consider nonstationary radiative transfer in a line in stellar atmospheres simulated as a stationary semi-infinite plane-parallel medium. We assume complete frequency redistribution in the elementary act of scattering. We assume that the time a photon spends in the medium is determined only by the mean time spent in the absorbed state. We obtain an explicit expression for the resolvent of the nonstationary integral equation of transfer, which is a bilinear expansion with respect to the eigenfunctions found in [12] for the corresponding stationary transfer equation.

Ca II resonance lines in non-homogeneous chromospheres

Profiles of the K line of Caii are computed for a two component solar chromosphere, chosen to simulate with a simple geometry the chromospheric supergranular network. Each component rises above the BCA photosphere, the boundary component representing the bright network with a sharp temperature rise and the cell component representing the darker region with an extended temperature minimum. Theoretical intensity profiles of the Can K core, calculated as weighted averages over the projected areas of the components, are produced for μ = 0.6 and 0.3. The line source function and the optical depth are obtained from a self-consistent treatment of the steady state and radiative transfer equations, with complete redistribution assumed for scattering in the line. The atomic model consists of two bound levels and a continuum. It is found that a 4600 K minimum can lead to the successful theoretical prediction of the observed limb darkening and 4300 K radiation temperature of the K1 feature only when very large values of turbulent velocity are assumed to exist in the cell region.