Current Issue : April-June Volume : 2023 Issue Number : 2 Articles : 5 Articles
In this article, we numerically investigate a two-dimensional (2D) droplet deformation and breakup in simple shear flow using a phase-field model for two-phase fluid flows. The dominant driving force for a droplet breakup in simple shear flow is the three-dimensional (3D) phenomenon via surface tension force and Rayleigh instability, where a liquid cylinder of certain wavelengths is unstable against surface perturbation and breaks up into individual droplets to reduce the total surface energy. A 2D droplet breakup does not occur except in special cases because there is only one curvature direction of the droplet interface, which resists breakup. However, there have been many numerical simulation research works on the 2D droplet breakups in simple shear flow. This study demonstrates that the 2D droplet breakup phenomenon in simple shear flow is due to the lack of space resolution of the numerical grid....
For the collapse of the working layer of dry vibrating material during preheating, the four-strand tundish of a steel plant was taken as a prototype for numerical simulation. The software ANSYS was used to calculate the temperature field and stress and strain field on the working layer under three preheating stages through the indirect coupling method. The results show that during the preheating process, the temperature field distribution on the hot surface of the working layer gradually develops toward uniformity with the increase in preheating temperature. However, the temperature gradient between the cold and hot surfaces increases subsequently, and the highest temperature between the cold and hot surfaces reaches 145.31 ◦C in the big fire stage. The stress on the top of the working layer is much larger than in other areas, and the maximum tensile stress on the top reaches 39.06 MPa in the third stage of preheating. Therefore, the damage to the working layer starts from the top of the tundish. In addition, the strain of the area near the sidewall burner nozzle in the casting area is much larger than that in the middle burner area with the increase in preheating temperature. Thus, the working layer near the sidewall burner nozzle is more prone to damage and collapse compared with the middle burner nozzle....
In this paper, we deal with the existence of solution for a class of quasilinear Schrödinger equations with a nonlocal term ( ( ) ) ( ) ( ) ( ) ( ( )) ( ) 2 2 3 div , , g u u g u g u u V x u x KF u Kf u x −μ − ∇ + ′ ∇ + = ∗ ∈ where μ ∈(0,3) , the function K,V ∈C(3 ,+ ) and V (x) may be vanish at infinity, g is a C1 even function with g′(t ) ≤ 0 for all t ≥ 0 , g (0) = 1, lim ( ) t g t a →+∞ = , 0 < a < 1 , and F is the primitive function of f which is superlinear but subcritical at infinity in the sense of Hardy-littlewood- Sobolev inequality. By the mountain pass theorem, we prove that the above equation has a nontrivial solution....
The use of signals of different frequencies determines the geometrical deviation with respect to the optical axes of a given beam. This angle can be determined by Sympletic Map (SM), a powerful and simple mathematical tool for the characterization and construction of images in Geometrical Optics. The Sympletic Map constitutes a Lie Group, with an algebra associated: the Lie Algebra. In general, the SM can be expressed as an infinite series, where each term corresponds to different contributions produced by the optical devices that constitute the optical system (lenses, apertures, bandwidth cutoff, etc.). The level of correction to be performed on the image to recover the original object is clear and controllable by SM. This formalism can be extended easily to physical optics to describe diffraction and interference phenomena....
The resource network is a non-linear threshold model where vertices exchange resource in infinite discrete time. The model is represented by a directed weighted graph. At each time step, all vertices send their resources along all output edges following one of two rules. For each vertex, the threshold value for changing the operation rule is equal to the total weight of its outgoing edges. If all vertices have resources less than their thresholds, the network is completely described by a homogeneous Markov chain. If at least one of the vertices has a resource above the threshold, the network is described by a non-homogeneous Markov chain. The purpose of this article is to describe and investigate non-homogeneous Markov chains generated by the resource network model. It is proven that they are strongly ergodic. In addition, stochastic matrices of a special form were studied. A number of new properties were revealed for them. The results obtained were generalized to arbitrary stochastic matrices....
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