Active contour driven by scalable local regional information on expandable kernel

An active contour that uses the pixel’s intensity on a set of expandable kernels along the propagating contour for image segmentation is presented in this paper. The objective is this study is to employ the scalable kernels to attract the contour to meet the desired boundary. The key characteristics of this scheme is that the kernels gradually expand to find an object’s boundary. So this scheme could penetrate to the concave boundary more effective and efficient than some other schemes. If a Gaussian kernel is applied, it could trace the object with a blurred or smooth boundary. Moreover, the directional selectivity feature enables in capturing two edge’s types with just one initial position. Its performance showed more desirable segmentation outcomes compared to the other existing active contours using regional information when segmenting the noisy image and the non-uniform (or heterogeneous) textures. Meanwhile, the level set implementation enables topological flexibility to our active contour scheme.

Constant sign and nodal solutions for superlinear (p, q)–equations with indefinite potential and a concave boundary term

We consider a nonlinear elliptic equation driven by the (p, q)–Laplacian plus an indefinite potential. The reaction is (p − 1)–superlinear and the boundary term is parametric and concave. Using variational tools from the critical point theory together with truncation, perturbation and comparison techniques and critical groups, we show that for all small values of the parameter, the problem has at least five nontrivial smooth solutions, all with sign information and which are linearly ordered.

The amplification of large-scale motion in a supersonic concave turbulent boundary layer and its impact on the mean and statistical properties

Direct numerical simulation is conducted to uncover the response of a supersonic turbulent boundary layer to streamwise concave curvature and the related physical mechanisms at a Mach number of 2.95. Streamwise variations of mean flow properties, turbulence statistics and turbulent structures are analysed. A method to define the boundary layer thickness based on the principal strain rate is proposed, which is applicable for boundary layers subjected to wall-normal pressure and velocity gradients. While the wall friction grows with the wall turning, the friction velocity decreases. A logarithmic region with constant slope exists in the concave boundary layer. However, with smaller slope, it is located lower than that of the flat boundary layer. Streamwise varying trends of the velocity and the principal strain rate within different wall-normal regions are different. The turbulence level is promoted by the concave curvature. Due to the increased turbulence generation in the outer layer, secondary bumps are noted in the profiles of streamwise and spanwise turbulence intensity. Peak positions in profiles of wall-normal turbulence intensity and Reynolds shear stress are pushed outward because of the same reason. Attributed to the Görtler instability, the streamwise extended vortices within the hairpin packets are intensified and more vortices are generated. Through accumulations of these vortices with a similar sense of rotation, large-scale streamwise roll cells are formed. Originated from the very large-scale motions and by promoting the ejection, sweep and spanwise events, the formation of large-scale streamwise roll cells is the physical cause of the alterations of the mean properties and turbulence statistics. The roll cells further give rise to the vortex generation. The large number of hairpin vortices formed in the near-wall region lead to the improved wall-normal correlation of turbulence in the concave boundary layer.

Propagation characteristics of rotating detonation wave in plane–radial structure with different pressure conditions

This paper simulates the propagation characteristics of rotating detonation wave in the plane–radial structure for mixtures of 2H2 + O2 + 3.76N2. Two-dimensional numerical simulation was modeled, and two kinds of typical flow field and corresponding operating range were obtained under various pressure conditions. Due to the influence of curvature, the detonation wave is strengthened near the outer concave boundary and weakened near the inner convex one. The pressure ratio was varied from 1.6 to 10 by varying both stagnation and back pressure for detonation parameters and flow parameters. It is found that these parameters are dependent only on stagnation pressure for higher pressure ratio. While the pressure ratio is low, the back pressure also has an effect on them. The detonation wave height initially increases and then decreases as stagnation pressure increases, and the pressure ratio has a significant effect on it for lower pressure ratio. The inlet block ratio varies slightly from 14% to 21%. The exit average Mach number has small fluctuations between 0.89 and 1.05. The exit supersonic flow ratio varies from 14% to 74%, and the peak value is gained when pressure ratio is 6. The exit pressure amplifying ratio varies from 1.45 to 1.95, and the maximum value is obtained when pressure ratio is 2.5.

Elliptic equations with indefinite and unbounded potential and a nonlinear concave boundary condition

We consider an elliptic problem driven by the negative Laplacian plus an indefinite and unbounded potential and a superlinear reaction. The boundary condition is parametric, nonlinear and superlinear near zero. Thus, the problem is a new version of the classical “convex–concave” problem (problem with competing nonlinearities). First, we prove a bifurcation-type result describing the set of positive solutions as the parameter [Formula: see text] varies. We also show the existence of a smallest positive solution [Formula: see text] and investigate the properties of the map [Formula: see text]. Finally, by imposing bilateral conditions on the reaction we generate two more solutions, one of which is nodal.