This paper shows the unique solvability of elliptic problems associated with two-phase incompressible flows, which are governed by Navier-Stokes equations a sharp moving interface, in unbounded domains such as whole space separated compact interface and non-compact interface. As by-product, we obtain Helmholtz-Weyl decomposition for flows.

In this present study, volume of fluid method in OpenFOAM open source CFD package will be extended to consider phase change phenomena with modified model due to condensation and boiling processes. This model is suitable for the case in which both unsaturated phase and saturated phase are present and for beginning boiling and condensation process needn't initial interface. Both phases (liquid-va...

<abstract><p>We consider the Cauchy problem for heat diffusion equation in whole Euclidean space consisting of two media with different constant conductivities, where initially one medium has temperature 0 and other 1. Under assumptions that is bounded interface class $ C^{2, \alpha} $, we show if stationary isothermic, then it must be a sphere. The method moving planes due to Serri...

One proves that the moving interface of a two-phase Stefan problem on Ω⊂Rd, d=1,2,3, is controllable at end time T by Neumann boundary controller u. The phase-transition region mushy {σtu;0≤t≤T} modified and main result amounts to saying that, for each Lebesgue measurable set Ω∗ with positive measure, there u∈L2((0,T)×∂Ω) such Ω∗⊂σTu. To this aim, one uses an optimal control approach combined C...

A new finite element level set method is developed to simulate the interface motion. The normal velocity of the moving interface can depend on both the local geometry, such as the curvature, and the external force such as that due to the flux from both sides of the interface of a material whose concentration is governed by a diffusion equation. The key idea of the method is to use an interface-...

Model identification is an important and complicated step within the autoregressive integrated moving average (ARIMA) methodology framework. This step is especially difficult for integrated series. In this article first investigate Box-Jenkins methodology and its faults in detecting model, and hence have discussed the problem of outliers in time series. By using this optimization method, we wil...

Gestures on an interactive surface are mostly hard to discover and therefore difficult to learn. That is the major drawback which should be resolved for allowing gesture-based input to develop into an easy and widely used input-technique. A well known gesture is in average faster, than moving to a small button. Gestures do not consume place of an interface and you can apply them on the whole su...

The problem of several finite moving cracks in a functionally graded material is solved by dislocation technique under the condition of anti-plane deformation. By using the Fourier transform the stress fields are obtained for a functionally graded strip containing a screw dislocation. The stress components reveal the familiar Cauchy singularity at the location of dislocation. The solution is em...