Abstract. The problem of Rayleigh–Bénard convection with internal heat sources and a variable gravity field is treated. For the case of stress-free boundary conditions, it is proved that the principle of exchange of stabilities holds as long as the product of gravity field and the integral of the heat sources is nonnegative throughout the layer. The proof is based on the idea of a positive oper...

in this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $dsubset mathbb{r}^{n}$ with smooth boundary‎. ‎we give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of caffarelli and friedman regarding the representation of functions whose ...

For implementation of the free surface boundary condition, a new subroutine has been introduced to an existing steady 3-D body fitted code. This code was previously written for steady flow simulation in closed ducts. The algorithm used in this subroutine reduces the instability problem according to the free surface wave generation. For code validation, it was applied to two different open cha...

in this paper, installment options on the underlying assetwhich evolves according to black-scholes model and pays constant dividendto its owner will be considered. applying arbitrage pricing theory,the non-homogeneous parabolic partial differential equation governingthe value of installment option is derived. then, penalty method is usedto value the european continuous installment call option.

The objective of this work is to develop deep theoretical methods that are based on the solution of the integral boundary layer equations for investigating film cooling in liquid rocket engine. The integral model assumes that heat is transferred from hot free stream gas to the liquid film both by convection and radiation. The mass is transferred to the free srteam gas by the well-known blowing ...

We study the influence of von Karman nonlinearity, van der Waals force, and a athermal stresses on pull-in instability and small vibrations of electrostatically actuated mi-croplates. We use the Galerkin method to develop a tractable reduced-order model for elec-trostatically actuated clamped rectangular microplates in the presence of van der Waals forcesand thermal stresses. More specifically,...

Using differential quadrature method (DQM), this study investigated pull-in instability of beam-type nano-switches under the effects of small-scale and intermolecular forces including the van der Waals (vdW) and the Casimir forces. In these nano-switches, electrostatic forces served as the driving force, and von-Karman type nonlinear strain was used to examine nonlinear geometric effects. To de...

[1] We analyze the role of slab pull acting on the Pacific plate during its early Tertiary change in motion. Slab pull forces are estimated by integrating the negative buoyancy of a 700 km long slab along a revised subduction boundary model adopting the Müller et al. (2008) seafloor age reconstructions. Our results indicate that torques predicted from a simple slab pull model match the Pacific ...