Compact finite difference - Fourier spectral method for three-dimensional incompressible Navier-Stokes equations

A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.

Spectral-line profile of turbulent gas

phases should be specified when the particle Reynolds number is higher than

Fixed Points of Closed and Compact Composite Sequences of Operators and Projectors in a Class of Banach Spaces

Some results on fixed points related to the contractive compositions of bounded operators in a class of complete metric spaces which can be also considered as Banach's spaces are discussed through the paper. The class of composite operators under study can include, in particular, sequences of projection operators under, in general, oblique projective operators. In this paper we are concerned with composite operators which include sequences of pairs of contractive operators involving, in general, oblique projection operators. The results are generalized to sequences of, in general, nonconstant bounded closed operators which can have bounded, closed, and compact limit operators, such that the relevant composite sequences are also compact operators. It is proven that in both cases, Banach contraction principle guarantees the existence of unique fixed points under contractive conditions.

On Best Proximity Point Theorems and Fixed Point Theorems for p-Cyclic Hybrid Self-Mappings in Banach Spaces

This paper relies on the study of fixed points and best proximity points of a class of so-called generalized point-dependent (K-Lambda)hybrid p-cyclic self-mappings relative to a Bregman distance Df, associated with a Gâteaux differentiable proper strictly convex function f in a smooth Banach space, where the real functions Lambda and K quantify the point-to-point hybrid and nonexpansive (or contractive) characteristics of the Bregman distance for points associated with the iterations through the cyclic self-mapping.Weak convergence results to weak cluster points are obtained for certain average sequences constructed with the iterates of the cyclic hybrid self-mappings.

Development of kelp rockfish, Sebastes atrovirens (Jordan and Gilbert 1880), and brown rockfish, S. auriculatus (Girard 1854), from birth to pelagic juvenile stage, with notes on early larval development of black-and-yellow rockfish, S. chrysomelas (Jordan and Gilbert 1880), reared in the laboratory (Pisces: Sebastidae).

Larval kelp (Sebastes atrovirens), brown (S. auriculatus), and blackand-yellow (S. chrysomelas) rockfish were reared from known adults, to preflexion stage, nine days after birth for S. chrysomelas, to late postflexion stage for S. atrovirens, and to pelagic juvenile stage for S. auriculatus. Larval S. atrovirens and S. chrysomelas were about 4.6 mm body length (BL) and S. auriculatus about 5.2 mm BL at birth. Both S. atrovirens and S. auriculatus underwent notochord flexion at about 6–9 mm BL. Sebastes atrovirens transform to the pelagic juvenile stage at about 14–16 mm BL and S. auriculatus transformed at ca. 25 mm BL. Early larvae of all three species were characterized by melanistic pigment dorsally on the head, on the gut, on most of the ventral margin of the tail, and in a long series on the dorsal margin of the tail. Larval S. atrovirens and S. auriculatus developed a posterior bar on the tail during the flexion or postflexion stage. In S. atrovirens xanthic pigment resembled the melanistic pattern throughout larval development. Larval S. auriculatus lacked xanthophores except on the head until late preflexion stage, when a pattern much like the melanophore pattern gradually developed. Larval S. chrysomelas had extensive xanthic pigmentation dorsally, but none ventrally, in preflexion stage. All members of the Sebastes subgenus Pteropodus (S. atrovirens, S. auriculatus, S. carnatus, S. caurinus, S. chrysomelas, S. dalli, S. maliger, S. nebulosus, S. rastrelliger) are morphologically similar and all share the basic melanistic pigment pattern described here. Although the three species reared in this study can be distinguished on the basis of xanthic pigmentation, it seems unlikely that it will be possible to reliably identify field-collected larvae to species using traditional morphological and melanistic pigmentation characters. (PDF file contains 36 pages.)