An improved unified solver for compressible and incompressible fluids involving free surfaces. II. Multi-time-step integration and applications

An improved numerical solver for the unified solution of compressible and incompressible fluids involving interfaces is proposed. The present method is based on the CIP-CUP (Cubic Interpolated Propagation / Combined, Unified Procedure) method, which is a pressure-based semi-implicit solver for the Euler equations of fluid flows. In Part I of this series of articles [M. Ida, Comput. Phys. Commun. 132 (2000) 44], we proposed an improved scheme for the convection terms in the equations, which allowed us discontinuous descriptions of the density interface by replacing the cubic interpolation function used in the CIP scheme with a quadratic extrapolation function only around the interface. In this paper, as Part II of this series, the multi-time-step integration technique is adapted to the CIP-CUP integration. Because the CIP-CUP treats different-nature components in the fluid equations separately, the adaptation of the technique is straightforward. This modification allows us flexible determinations of the time interval, which results in an efficient and accurate integration. Furthermore, some additional discussion on our methods is presented. Finally, the application results to composite flow problems such as compressible and incompressible Kelvin-Helmholtz instabilities and the dynamics of two acoustically coupled deformable bubbles in a viscous liquid are provided.Comment: 34 pages, 13 figures, elsart; Typo in Eq.25 corrected; Publishe

Limiting Distribution of the Score Statistic under Moderate Deviation from a Unit Root in MA(1)

This paper derives the asymptotic distribution of Tanaka's score statistic under moderate deviation from a unit root in a moving average model of order one or MA(1). We classify the limiting distribution into three types depending on the order of deviation. In the fastest case, the convergence order of the asymptotic distribution continuously changes from the invertible process to the unit root. In the slowest case, the limiting distribution coincides with the invertible process in a distributional sense. This implies that these cases share an asymptotic property. The limiting distribution in the intermediate case provides the boundary property between the fastest and slowest cases.

Low temperature annealing of the ultrasonic attenuation in prestrained lif after co60 gamma irradiation at liquid nitrogen temperature

Ultrasonic pulse study of lithium fluorid

A Combinatorial Formula for Principal Minors of a Matrix with Tree-metric Exponents and Its Applications

Let $T$ be a tree with a vertex set $\{ 1,2,\dots, N \}$. Denote by $d_{ij}$ the distance between vertices $i$ and $j$. In this paper, we present an explicit combinatorial formula of principal minors of the matrix $(t^{d_{ij}})$, and its applications to tropical geometry, study of multivariate stable polynomials, and representation of valuated matroids. We also give an analogous formula for a skew-symmetric matrix associated with $T$.Comment: 16 page

A Three-Term Conjugate Gradient Method with Sufficient Descent Property for Unconstrained Optimization

Conjugate gradient methods are widely used for solving large-scale unconstrained optimization problems, because they do not need the storage of matrices. In this paper, we propose a general form of three-term conjugate gradient methods which always generate a sufficient descent direction. We give a sufficient condition for the global convergence of the proposed general method. Moreover, we present a specific three-term conjugate gradient method based on the multi-step quasi-Newton method. Finally, some numerical results of the proposed method are given

Pfaffian Systems from Twistor Fibrations

Canonical twistor fibrations lead to Pfaffian systems by means of their superhorizontal distribution. The aim of this note is to identify explicitly the Pfaffian systems of five or less variables that arise in this way in terms of the classification given by A.Awane and M.Goze.Comment: 18 page