Dielectric function for a material containing hyperspherical inclusions toO(c2): I. Multipole expansions

Choy, T. C.; Alexopoulos, Aris; Thorpe, M. F.

doi:10.1098/rspa.1998.0244

Cited by 13 publications

(7 citation statements)

References 16 publications

(26 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A concrete example will be discussed below. In dielectric materials, an equivalent non-linearity occurs when the pair correlation supersedes those of the individual particles (Jeffrey 1973;Choy et al 1998) Similar arguments were made for elastic media by Chen and Acrivos (1978) and Willis and Acton (1976). Even in the simplest case of a solution of simple spheres in a matrix the average dielectric function depends strongly on f 2 even in the dilute limit (Jeffrey 1973;Willis and Acton 1976).…”

Section: Scaling Of the Volume Fractionmentioning

confidence: 60%

An empirical scaling model for averaging elastic properties including interfacial effects

Salje¹

2007

American Mineralogist

View full text Add to dashboard Cite

429 1963;Hill 1963). The Hashin-Shtrikman bounds are based on the assumption that each phase in the composite is in its minimum energy state and is described by a positive defi nite energy function. Therefore, this approach does not apply to materials in the vicinity of phase transformations (for elastic instabilities, see Salje 1993). In addition, more specifi c schemes have been developed. The shear-lag approach has seen a multitude of versions, which are all best justifi ed for fi brous inclusions rather than in case of rocks where the individual mineral grains have LETTER ABSTRACTThe elastic properties of ceramics and a mix of minerals can be calculated in a simple way including some properties of the interfaces between grains. While the Hashin Shtrikman averaging method has bounds, which are strictly correct for many realistic physical conditions, one fi nds empirical data which lie outside these bonds. One possible interpretation is that the scaling of the volume proportions in mineral assemblies is not truly represented by the nominal volume proportion f of each phase. It is argued that interfacial effects scale with f(1-f). In the case of certain assemblies, it is shown that the scaling is entirely with f 2 rather than f. For intermediate cases, a more realistic scaling replaces f in the relevant averaging schemes by f(1-S) + S f 2 where S weighs the effect of the non-linearities in the volume expansion of the averaging schemes.

show abstract

Section: Scaling Of the Volume Fractionmentioning

confidence: 60%

An empirical scaling model for averaging elastic properties including interfacial effects

Salje¹

2007

American Mineralogist

View full text Add to dashboard Cite

show abstract

“…To put our approach in the context of composite particles, we have performed a mean-field approach in the spirit of Choy et al [35,36], i.e., treating inhomogeneous particles as effectively homogeneous ones which are embedded in a uniform field. In particular, it is worth noting that well-known Tartar formula [37] can be used to exactly calculate the effective complex dielectric constant of a single graded particle.…”

Section: Discussionmentioning

confidence: 99%

Electrokinetic behavior of two touching inhomogeneous biological cells and colloidal particles: Effects of multipolar interactions

Huang

Karttunen²,

et al. 2004

Phys. Rev. E

View full text Add to dashboard Cite

We present a theory to investigate electrokinetic behavior, namely, electrorotation and dielectrophoresis under alternating current (ac) applied fields for a pair of touching inhomogeneous colloidal particles and biological cells. These inhomogeneous particles are treated as graded ones with physically motivated model dielectric and conductivity profiles. The mutual polarization interaction between the particles yields a change in their respective dipole moments, and hence in the ac electrokinetic spectra. The multipolar interactions between polarized particles are accurately captured by the multiple images method. In the point-dipole limit, our theory reproduces the known results. We find that the multipolar interactions as well as the spatial fluctuations inside the particles can affect the ac electrokinetic spectra significantly.

show abstract

“…The review [10] and the last two chapters of the book [11] provide some indication of the work that is available in this area. Also [12,13] and [14] involve some interesting material on images for spherical boundaries. For the use of the ellipsoidal harmonics in the solution of boundary value problems, we refer to [15,16] and [17] among many others.…”

Section: Introductionmentioning

confidence: 99%

On the Neumann function and the method of images in spherical and ellipsoidal geometry

Dassios

Stén

2012

Math Methods in App Sciences

View full text Add to dashboard Cite

The invention of an image system for a boundary value problem adds to a significant understanding of the structure of the problem, both at the mathematical and at the physical level. In this paper, the interior and exterior Neumann functions for the Laplacian in the cases of spherical and ellipsoidal domains are represented in terms of images. Besides isolated images, the presence of the normal derivative in the Neumann condition demands an additional continuous distribution of images, which in the spherical cases, can be restricted to a one-dimensional manifold, whereas for the ellipsoid, both a one-dimensional and a two-dimensional distribution of images is needed.

show abstract

Dielectric function for a material containing hyperspherical inclusions toO(c²): I. Multipole expansions

Cited by 13 publications

References 16 publications

An empirical scaling model for averaging elastic properties including interfacial effects

An empirical scaling model for averaging elastic properties including interfacial effects

Electrokinetic behavior of two touching inhomogeneous biological cells and colloidal particles: Effects of multipolar interactions

On the Neumann function and the method of images in spherical and ellipsoidal geometry

Contact Info

Product

Resources

About