相关论文: Existence of coated inclusions of general shape we…

The neutral inclusion problem in two dimensional isotropic elasticity is considered. The neutral inclusion, when inserted in a matrix having a uniform applied field, does not disturb the field outside the inclusion. The inclusion consists…

We consider the problem of neutral inclusions for two-dimensional conductivity and anti-plane elasticity. The neutral inclusion, when inserted in a matrix having a uniform field, does not disturb the field outside the inclusion. The…

Upon insertion of an inclusion into a medium with the uniform field, if the field is not perturbed at all outside the inclusion, then it is called a neutral inclusion. It is called a weakly neutral inclusion if the field is perturbed…

For certain shapes of inclusions embedded in a body, the field inside the inclusion is uniform for some boundary condition. We provide a construction scheme for inclusions of general shapes having such a uniformity property in two…

An inclusion is said to be neutral to uniform fields if upon insertion into a homogenous medium with a uniform field it does not perturb the uniform field at all. It is said to be weakly neutral if it perturbs the uniform field mildly. Such…

If a neutral inclusion is inserted in a matrix containing a uniform applied electric field, it does not disturb the field outside the inclusion. The well known Hashin coated sphere is an example of a neutral coated inclusion. In this paper,…

The problem of determining nonlinear neutral inclusions in (electrical or thermal)conductivity is considered. Neutral inclusions, inserted in a matrix containing a uniform applied electric field, do not disturb the field outside the…

Singular complex analytic vector fields on the Riemann surfaces enjoy several geometric properties (singular means that poles and essential singularities are admissible). We describe relations between singular complex analytic vector fields…

In this paper we analyze the gradient blow-up of the solution to the conductivity problem in two dimensions in the presence of an inclusion with eccentric core-shell geometry. Assuming that the core and shell have circular boundaries that…

New connections between static elastic cloaking, low frequency elastic wave scattering and neutral inclusions are established in the context of two dimensional elasticity. A cylindrical core surrounded by a cylindrical shell is embedded in…

This paper presents a new concept of geometric multipole expansion for the conductivity or anti-plane elasticity problem in two dimensions by using the Faber polynomials. As an application, we construct semi-neutral inclusions of general…

We present a density-functional study of a binary phase-separating mixture of soft core particles immersed in a random matrix of quenched soft core particles of larger size. This is a model for a binary polymer mixture immersed in a…

Integrable or near-integrable magnetic fields are prominent in the design of plasma confinement devices. Such a field is characterized by the existence of a singular foliation consisting entirely of invariant submanifolds. A regular leaf,…

Let $\Gamma_g$ be the fundamental group of a closed connected orientable surface of genus $g\geq2$. We introduce a combinatorial structure of "core surfaces", that represent subgroups of $\Gamma_g$. These structures are (usually)…

We generalize the compact group approach to conducting systems to give a self-consistent analytical solution to the problem of the effective quasistatic electrical conductivity of macroscopically homogeneous and isotropic dispersions of…

The polarization tensor is a geometric quantity associated with a domain. It is a signature of the small inclusion's existence inside a domain and used in the small volume expansion method to reconstruct small inclusions by boundary…

Eshelby showed that if an inclusion is of elliptic or ellipsoidal shape then for any uniform elastic loading the field inside the inclusion is uniform. He then conjectured that the converse is true, i.e., that if the field inside an…

Stretching, drilling, and bending are the independent deformation modes of a thin shell, each of which has an individual energy content. When the energy content of a mode vanishes, that mode is neutral. We characterize all neutral modes of…

We investigate the problem of planar conductivity inclusion with imperfect interface conditions. We assume that the inclusion is simply connected. The presence of the inclusion causes a perturbation in the incident background field. This…

We prove that any two-dimensional moduli space of stable 2-vector bundles, in the non-filtrable range, on a primary Kodaira surface is a primary Kodaira surface. If a universal bundle exists, then the two surfaces are homeomorphic up to…