Runx2 and phosphatidylinositol 3-kinase (PI3K)–Akt signaling play important roles in osteoblast and chondrocyte differentiation. We investigated the relationship between Runx2 and PI3K-Akt signaling. Forced expression of Runx2 enhanced osteoblastic differentiation of C3H10T1/2 and MC3T3-E1 cells and enhanced chondrogenic differentiation of ATDC5 cells, whereas these effects were blocked by treatment with IGF-I antibody or LY294002 or adenoviral introduction of dominant-negative (dn)–Akt. Forced expression of Runx2 or dn-Runx2 enhanced or inhibited cell migration, respectively, whereas the enhancement by Runx2 was abolished by treatment with LY294002 or adenoviral introduction of dn-Akt. Runx2 up-regulated PI3K subunits (p85 and p110β) and Akt, and their expression patterns were similar to that of Runx2 in growth plates. Treatment with LY294002 or introduction of dn-Akt severely diminished DNA binding of Runx2 and Runx2-dependent transcription, whereas forced expression of myrAkt enhanced them. These findings demonstrate that Runx2 and PI3K-Akt signaling are mutually dependent on each other in the regulation of osteoblast and chondrocyte differentiation and their migration.

Two-dimensional, unsteady, compressible flow fields produced by the interactions between a single vortex or a pair of vortices and a shock wave are simulated numerically. The Navier–Stokes equations are solved by a finite difference method. The sixth-order-accurate compact Padé scheme is used for spatial derivatives, together with the fourth-order-accurate Runge–Kutta scheme for time integration. The detailed mechanics of the flow fields at an early stage of the interactions and the basic nature of the near-field sound generated by the interactions are studied. The results for both a single vortex and a pair of vortices suggest that the generation and the nature of sounds are closely related to the generation of reflected shock waves. The flow field differs significantly when the pair of vortices moves in the same direction as the shock wave than when opposite to it.

Artificial neural network (ANN) is tested as a tool for finding a new subgrid model of the subgridscale (SGS) stress in large-eddy simulation. ANN is used to establish a functional relation between the grid-scale (GS) flow field and the SGS stress without any assumption of the form of function.Data required for training and test of ANN are provided by direct numerical simulation (DNS) of a turbulent channel flow. It is shown that ANN can establish a model similar to the gradient model.The correlation coefficients between the real SGS stress and the output of ANN are comparable to or larger than similarity models, but smaller than a two-parameter dynamic mixed model. *

A new instability mechanism is found for Kelvin's vortex ring, which may surpass the Widnall instability. The effect of ring curvature emerges at O() in the asymptotic solution of the Euler equations in powers , the ratio of core to ring radii. We show that the O() field causes a parametric resonance between a pair of Kelvin waves whose azimuthal wavenumbers are separated by 1. A closed-form solution enables us to calculate the maximum growth rate to be 165/256 and to make headway to nonlinear stability. MOTIVATION AND MAIN RESULT Vortex rings are invariably susceptible to wavy distortions, leading to violent wiggles and sometimes to disruption. It has been widely accepted that the Moore-Saffman-Tsai-Widnall instability (the MSTW instability) is responsible for genesis of unstable waves [1]-[5]. Remember that this is an instability for a straight vortex tube subjected to a straining field.

We study numerically the reconnection of quantized vortices and the concurrent acoustic emission by the analysis of the Gross-Pitaevskii equation. Two quantized vortices reconnect following the process similar to classical vortices; they approach, twist themselves locally so that they become anti-parallel at the closest place, reconnect and leave separately.The investigation of the motion of the singular lines where the amplitude of the wave function vanishes in the vortex cores confirms that they follow the above scenario by reconnecting at a point. This reconnection is not contradictory to the Kelvin's circulation theorem, because the potential of the superflow field becomes undefined at the reconnection point. When the locally anti-parallel part of the vortices becomes closer than the healing length, it moves with the velocity comparable to the sound velocity, emits the sound waves and leads to the pair annihilation or reconnection; this phenomena is concerned with the Cherenkov resonance. The vortices are broken up to smaller vortex loops through a series of reconnection, eventually disappearing with the acoustic emission. This may correspond to the final stage of the vortex cascade process proposed by Feynman. The change in energy components, such as the quantum, the compressible and incompressible kinetic energy is analyzed for each dynamics. The propagation of the sound waves not only appears in the profile of the amplitude of the wave function but also affects the field of its phase, transforming the quantum energy due to the vortex cores to the kinetic energy of the phase field.

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Abstract

The stability of stably stratified vortices is studied by local stability analysis. Three base flows that possess hyperbolic stagnation points are considered: the two-dimensional (2-D) Taylor–Green vortices, the Stuart vortices and the Lamb–Chaplygin dipole. It is shown that the elliptic instability is stabilized by stratification; it is completely stabilized for the 2-D Taylor–Green vortices, while it remains and merges into hyperbolic instability near the boundary or the heteroclinic streamlines connecting the hyperbolic stagnation points for the Stuart vortices and the Lamb–Chaplygin dipole. More importantly, a new instability caused by hyperbolic instability near the hyperbolic stagnation points and phase shift by the internal gravity waves is found; it is named the strato-hyperbolic instability; the underlying mechanism is parametric resonance as unstable band structures appear in contours of the growth rate. A simplified model explains the mechanism and the resonance curves. The growth rate of the strato-hyperbolic instability is comparable to that of the elliptic instability for the 2-D Taylor–Green vortices, while it is smaller for the Stuart vortices and the Lamb–Chaplygin dipole. For the Lamb–Chaplygin dipole, the tripolar instability is found to merge with the strato-hyperbolic instability as stratification becomes strong. The modal stability analysis is also performed for the 2-D Taylor–Green vortices. It is shown that global modes of the strato-hyperbolic instability exist; the structure of an unstable eigenmode is in good agreement with the results obtained by local stability analysis. The strato-hyperbolic mode becomes dominant depending on the parameter values.