Dyadic Green’s Function for Multilayered Planar, Cylindrical, and Spherical Structures with Impedance Boundary Condition

The integral equation (IE) method is one of the efficient approaches for solving electromagnetic problems, where dyadic Green’s function (DGF) plays an important role as the Kernel of the integrals. In general, a layered medium with planar, cylindrical, or spherical geometry can be used to model different biomedical media such as human skin, body, or head. Therefore, in this chapter, different approaches for the derivation of Green’s function for these structures will be introduced. Due to the recent great interest in two-dimensional (2D) materials, the chapter will also discuss the generalization of the technique to the same structures with interfaces made of isotropic and anisotropic surface impedances. To this end, general formulas for the dyadic Green’s function of the aforementioned structures are extracted based on the scattering superposition method by considering field and source points in the arbitrary locations. Apparently, by setting the surface conductivity of the interfaces equal to zero, the formulations will turn into the associated problem with dielectric boundaries. This section will also aid in the design of various biomedical devices such as sensors, cloaks, and spectrometers, with improved functionality. Finally, the Purcell factor of a dipole emitter in the presence of the layered structures will be discussed as another biomedical application of the formulation.

Friction analysis of anisotropic surface for viscoelastic material

Purpose The anisotropic surfaces of viscoelastic materials play a role in sliding friction; the purpose of this paper is to study the effect of the anisotropic surfaces on contact area and the friction coefficient. Design/methodology/approach A complex elastic modulus and an anisotropic power spectrum are used to compute the coefficient of friction based on the extension Persson theory which considers the partial contact and the variation in the roughness slopes. Findings The ratios of the relative contact area that varies with velocity are obtained with different angles and eccentricities, and the effect of the elastic modulus needs to be considered. The coefficients of the friction parallel to the direction of motion decrease as the angle increases, or as the eccentricity decreases. The friction coefficients in the vertical direction change irregularly when the angles or eccentricities increase. Originality/value An extension of Persson’s work considering the partial contact and the effective mean square slope of the roughness is applied to study sliding friction, and the effect of the elastic modulus on contact area is considered.

Enhancement of Planar Orientation of Reactive Mesogen Molecules for Optical Retarder Film by Anisotropic Surface Plasma Treatment

We proposed a method for enhancing the planar orientation of reactive mesogen (RM) molecules by means of anisotropic plasma treatment. Anisotropic surface plasma, of which energy density is dependent on the azimuthal angle, was generated by column-shaped ceramic electrodes. The anisotropic plasma was discharged on the surface of a polyvinyl alcohol (PVA) alignment layer before the rubbing process began. The contact angle of the surface was increased from 12° to 83° after plasma treatment, indicating a hydrophobic property of the surface. From the atomic force microscopy (AFM) measurement, it was found that the grain size of the PVA layer was reduced and that the grooved patterns were formed provided that the plasma direction was parallel to the rubbing direction of the surface. Consequently, the planar orientation was enhanced, and the in-plane retardation of the photo-polymerized RM films increased when the parallel plasma was treated on the surface.

$$H^1$$ solutions for a Kuramoto–Sinelshchikov–Cahn–Hilliard type equation

The Kuramoto–Sinelshchikov–Cahn–Hilliard equation models the spinodal decomposition of phase separating systems in an external field, the spatiotemporal evolution of the morphology of steps on crystal surfaces and the growth of thermodynamically unstable crystal surfaces with strongly anisotropic surface tension. In this paper, we prove the well-posedness of the Cauchy problem, associated with this equation.