On the solution arising in two-cylinders electrostatics.

The electrostatics of two cylinders charged to the symmetrical or anti-symmetrical potential is investigated by using the null-field boundary integral equation (BIE) in conjunction with the degenerate kernel of the bipolar coordinates. The undetermined coefficient is obtained according to the Fredholm alternative theorem. The uniqueness of solution, infinite solution, and no solution are examined therein. A single cylinder (circle or ellipse) is also provided for comparison. The link to the general solution space is also done. The condition at infinity is also correspondingly examined. The flux equilibrium along circular boundaries and the infinite boundary is also checked as well as the contribution of the boundary integral (single and double layer potential) at infinity in the BIE is addressed. Ordinary and degenerate scales in the BIE are both discussed. Furthermore, the solution space represented by the BIE is explained after comparing it with the general solution. The present finding is compared to those of Darevski[2] and Lekner[4] for identity.

Analysis of the boundary integral equation for the growth of a parabolic/paraboloidal dendrite with convection.

The growth of a parabolic/paraboloidal dendrite streamlined by viscous and potential flows in an undercooled one-component melt is analyzed using the boundary integral equation. The total melt undercooling is found as a function of the Péclet, Reynolds, and Prandtl numbers in two- and three-dimensional cases. The solution obtained coincides with the modified Ivantsov solution known from previous theories of crystal growth. Varying Péclet and Reynolds numbers we show that the melt undercooling practically coincides in cases of viscous and potential flows for a small Prandtl number, which is typical for metals. In cases of water solutions and non-metallic alloys, the Prandtl number is not small enough and the melt undercooling is substantially different for viscous and potential flows. In other words, a simpler potential flow hydrodynamic model can be used instead of a more complicated viscous flow model when studying the solidification of undercooled metals with convection.

Numerical study on the impulsive growth of a gaseous plug inside a cylindrical vein with compliant coating.

Introduction : Employing of gaseous plugs inside a vein for preventing of blood flow to the damaged or cancerous tissues has been known as a gas embolism in the medicine. In this research, a numerical investigation has been carried out on the delivery of the liquid drug DDFP, encapsulated in the microlipidcoated spheres (MLCSs), to target the human vein for construction of the gaseous plug inside the veins. Methods : The encapsulated liquid drug DDFP were delivered to the vein by injection of an emulsion. Releasing of the liquid drug DDFP results in an explosive growth of a gaseous plug inside the vein. The targeted vein was served as a rigid cylinder with a compliant coating. The boundary integral equation method has been employed for the numerical simulation of the hydrodynamic behavior of the gaseous plug inside the vein. Results : Numerical results showed that in the case of a rigid cylinder vein with an internal compliant coating, the maximum volume of the gaseous plug was smaller than the case of just a rigid cylinder vein. Furthermore, its elapsed time from the instant of bubble generation to the instant when the bubble reaches its maximum volume was shorter. Numerical results also showed that the compliant coating on the internal wall of the rigid cylindrical vein had a tendency of reducing the impact of the explosive growth of the gaseous plug. Conclusion : This numerical research showed that the compliant coating on the internal wall of the rigid cylindrical vein had the tendency of reducing the impact of the impulsive growth of the gaseous plug. Therefore, in the case of having severed arteriosclerosis, treatment of the cancerous or damaged tissues by use of the gaseous embolism must be done very carefully in order to prevent the hazardous effects of the gaseous plug's impulsive growth.

Analytical results regarding electrostatic resonances of surface phonon/plasmon polaritons: separation of variables with a twist.

The boundary integral equation (BIE) method ascertains explicit relations between localized surface phonon and plasmon polariton resonances and the eigenvalues of its associated electrostatic operator. We show that group-theoretical analysis of the Laplace equation can be used to calculate the full set of eigenvalues and eigenfunctions of the electrostatic operator for shapes and shells described by separable coordinate systems. These results not only unify and generalize many existing studies, but also offer us the opportunity to expand the study of phenomena such as cloaking by anomalous localized resonance. Hence, we calculate the eigenvalues and eigenfunctions of elliptic and circular cylinders. We illustrate the benefits of using the BIE method to interpret recent experiments involving localized surface phonon polariton resonances and the size scaling of plasmon resonances in graphene nanodiscs. Finally, symmetry-based operator analysis can be extended from the electrostatic to the full-wave regime. Thus, bound states of light in the continuum can be studied for shapes beyond spherical configurations.

Boundary regularized integral equation formulation of the Helmholtz equation in acoustics.

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals.

Nonlinear continuum growth model of multiscale reliefs as applied to rigorous analysis of multilayer short-wave scattering intensity. I. Gratings.

It is shown that taking into proper account certain terms in the nonlinear continuum equation of thin-film growth makes it applicable to the simulation of the surface of multilayer gratings with large boundary profile heights and/or gradient jumps. The proposed model describes smoothing and displacement of Mo/Si and Al/Zr boundaries of gratings grown on Si substrates with a blazed groove profile by magnetron sputtering and ion-beam deposition. Computer simulation of the growth of multilayer Mo/Si and Al/Zr gratings has been conducted. Absolute diffraction efficiencies of Mo/Si and Al/Zr gratings in the extreme UV range have been found within the framework of boundary integral equations applied to the calculated boundary profiles. It has been demonstrated that the integrated approach to the calculation of boundary profiles and of the intensity of short-wave scattering by multilayer gratings developed here opens up a way to perform studies comparable in accuracy to measurements with synchrotron radiation, at least for known materials and growth techniques.