Mikyoung Lim

Abstract The electric field increases toward infinity in the narrow region between closely adjacent perfect conductors as they approach each other. Much attention has been devoted to the blow-up estimate, especially in two dimensions, for the practical relevance to high stress concentration in fiber-reinforced elastic composites. In this paper, we establish optimal estimates for the electric field associated with the distance between two spherical conductors in n-dimensional spaces for n ≥ 2. Th

Let U be an ^-dimensional vector space over an algebraically closed field F of characteristic zero, and let V r U denote the rth symmetric product space of U. Let T be a linear transformation on V r U which sends nonzero decomposable elements to nonzero decomposable elements. We prove the following:

If $\ohm$ is a ball in $\Real ^n$ $(n\geq 2)$, then the boundary integral operator of the double layer potential for the Laplacian is self-adjoint on $L^2({\partial}{\ohm})$. In this paper we prove that the ball is the only bounded Lipschitz domain on which the integral operator is self-adjoint.

Using Maxwell's field equations, an analytical investigation is presented of the modal characteristics for a step-index plastic clad tapered optical fiber operating in the infrared region of the electromagnetic spectrum. Following rigorous analytical approach, dispersion relations are developed, and a study is presented of the fiber characteristics for different lower order modes. The cutoff situation is also discussed. Attention is also paid to the characteristics of dispersion curves for the t

We consider the plane elasticity problem for two circular holes. When two holes are close to touching, the stress concentration happens in the narrow gap region. In this paper, we characterize the stress singularity between the two holes by an explicit function. A new method of a singular asymptotic expansion for the Fourier series with slowing decaying coefficients is developed to investigate the asymptotic behavior of the stress.

Abstract We consider the conductivity problem with a simply connected or multi-coated inclusion in two dimensions. The potential perturbation due to an inclusion admits a classical multipole expansion whose coefficients are the so-called generalized polarization tensors (GPTs). The GPTs have been fundamental building blocks in conductivity inclusion problems. In this paper, we present a new concept of geometric multipole expansion and its expansion coefficients, named the Faber polynomial polari

The electric field for an infinite array of conducting nanosized objects in two-dimensional space has been calculated. The mirror symmetry for this physical problem has been introduced. By taking into account this symmetry, we transform the original problem into an infinite two-dimensional array of nanosized objects with the same solution. The electric field equation of the model has been successfully constructed using a single-layer potential of the periodic Green function. The electric field o

We consider the enhancement of electric field in the presence of two perfectly conducting spheres. When the two spheres get closer, the electric field have a much larger magnitude compared to the external field in the small gap region between the two spheres. The enhanced field can be arbitrary large with the generic blow-up rate $|ε\lnε|^{-1}$ in three dimensional space, where $ε$ is the distance between the spheres. In this paper we derive rigorously an asymptotic formula of the electric field

In this paper we develop an iterative approach for reconstructing fine shape details of an inclusion using higher-order EMTs. Starting from the integral equation formulation, we derive an asymptotic formula for the perturbation in the EMTs that are due to small changes in the interface of the inclusion. Based on this formula, we propose an optimization algorithm to find fine shape details. We perform some numerical experiments to demonstrate the validity of the proposed method. AMS subject class

A cylindrical plasmonic structure with a concentric core exhibits an anomalous localized resonance which results in cloaking effects. Here we show that if the structure has an eccentric core, a new kind of shielding effect can happen. In contrast to conventional shielding devices, our proposed structure can block the effect of external electrical sources, even in a region which is not enclosed by any conducting materials. In fact, the shielded region is located at a distance from the device. We