We establish the existence of traveling front solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model with Holling type-II functional response. The traveling front solutions are equivalent to heteroclinic orbits in R(4) and the small amplitude traveling wave train solutions are equivalent to small amplitude periodic orbits in R...

This paper studied effects of ultrasonic treatment during the solidification process on structure formation of low carbon steel. Results showed that with ultrasonic treatment grains were refined and the steel ingot avoided the cast widmanstatten structure. When ultrasonic treatment was employed, pearlite was broken and the average length of pearlite was decreased from 550mm to 140mm. The corres...

Ultrasonic and dielectrophoretic particle manipulation have been studied for particle trajectory modification and particle trapping in microfluidic channels. We report an approach that combines dielectrophoresis (DEP) and ultrasonic fields to trap and concentrate particles and cells in an aqueous suspension. By simultaneously applying electric and ultrasonic fields to the sample, the favorable ...

Using ultrasonic devices in endodontics can enhance the antibacterial and tissue dissolving ability of different root canal irrigants such as sodium hypochlorite (NaOCl) which is the most common irrigant with excellent antibacterial and tissue dissolving abilities. However, due to its high surface tension, its penetration into the irregularities of the root canal system is a challenge. The purp...

Ultrasonic measurements have been performed for comprehensive microstructural characterisation in 9 % Cr ferritic steels. The variation in grain size, the effect of solution annealing temperature on microstructure developed, the variation in microstructure of the weld joints, the effect of post weld heat treatment and precipitation behaviour during thermal ageing and creep testing have been suc...

We present some variants of Burgers-type equations for incompressible and isothermal planar flow of viscous non-Newtonian fluids based on the Cross, the Carreau and the power-law rheology models, and on a symmetry assumption on the flow. We numerically solve the associated traveling wave equations by using industrial data and in order to validate the models we prove existence and uniqueness of ...

We prove that the approximation ratio of the greedy algorithm for the metric Traveling Salesman Problem is Θ(log n). Moreover, we prove that the same result also holds for graphic, euclidean, and rectilinear instances of the Traveling Salesman Problem. Finally we show that the approximation ratio of the ClarkeWright savings heuristic for the metric Traveling Salesman Problem is Θ(log n). keywor...