Photonic crystals are artificial low-loss either two-dimensional (2D) or three-dimensional (3D) dielectric structures with a periodic modulation of the refractive index. Due to Bragg reflection, electromagnetic (optical) waves cannot propagate through such structures in certain directions, at certain frequencies. Hence, photonic crystals can exhibit bandgaps (even omnidirectional bandgaps in ce...

It is a highly nonlinear problem of 3-D elastoplastic contact with friction. To obtain the key information about the real size, displacement and traction in contact zone, the elements in contact and plastic zone should be subdivided. However, the increase of degrees of freedom is limited by the problem-solving scale when traditional BEM is used, for a larger memory size is required and the solu...

The paper presents analysis of two-dimensional non-Newtonian incompressible viscous flow between parallel plates. The governing problem of momentum equations are reduced to NODE using similarity transformations. The resulting equation is solved using series solution and homotopy analysis method. These methods have advantages over pure numerical methods for obtaining the derived quantities accur...

S U M M A R Y Many unresolved questions in geodynamics revolve around the physical behaviour of the two-phase system of a silicate melt percolating through and interacting with a tectonically deforming host rock. Well-accepted equations exist to describe the physics of such systems and several previous studies have successfully implemented various forms of these equations in numerical models. T...

We consider a variational problem for three-dimensional (3D) classical lattice models. We construct the trial state as a two-dimensional product of local variational weights that contain auxiliary variables. We propose a stable numerical algorithm for the maximization of the variational partition function per layer. Numerical stability and efficiency of the new method is examined through its ap...

This work advances the approximation error model approach for inverse analysis of biodiesel synthesis using soybean oil and methanol in 3D-microreactors. Two hybrid numerical-analytical approaches reduced computational cost are considered to offer an approximate forward problem solution a three-dimensional nonlinear coupled diffusive-convective-reactive model. First, Generalized Integral Transf...