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## Full-Text Articles in Physics

Spectral Densities Of Embedded Interfaces In Composite Materials, A. R. Mcgurn, Anthony Roy Day, D. J. Bergman, L. C. Davis, M. F. Thorpe

#### Spectral Densities Of Embedded Interfaces In Composite Materials, A. R. Mcgurn, Anthony Roy Day, D. J. Bergman, L. C. Davis, M. F. Thorpe

*Anthony Roy Day*

The effective resistivity and conductivity of two media that meet at a randomly rough interface are computed in the quasistatic limit. The results are presented in the spectral density representations of the Bergman-Milton formulation for the properties of two-component composite materials. The spectral densities are extracted from computer simulations of resistor networks in which the random interface separates two regions containing different types of resistors. In the limit that the bond lengths in the resistor network are small compared to parameters characterizing the surface roughness, the resistor network simulation approximates the continuum limit of the two-component composite. The Bergman-Milton formulation ...

Spectral Function Of Composites From Reflectivity Measurements, Anthony Day, A. Grant, A. Sievers, M. Thorpe

#### Spectral Function Of Composites From Reflectivity Measurements, Anthony Day, A. Grant, A. Sievers, M. Thorpe

*Anthony Roy Day*

We demonstrate a method of calculating the spectral function of a composite from measured reflectivity data. To solve this inverse problem it is necessary for the reflectivity data to be taken through a strong, high Q, resonance. By analyzing the reststrahlen region of different fill fraction KCl-diamond composites at three different temperatures, we find accurate spectral functions that are independent of temperature with the low temperature data giving the best resolution. These spectral functions are then used to successfully predict the optical response of RbCl-diamond composites.

Resistivity Of Boron-Doped Diamond Microcrystals, M. D. Jaeger, S. Hyun, Anthony Roy Day, M. F. Thorpe, B. Golding

#### Resistivity Of Boron-Doped Diamond Microcrystals, M. D. Jaeger, S. Hyun, Anthony Roy Day, M. F. Thorpe, B. Golding

*Anthony Roy Day*

We describe measurements of the electrical resistivity of micron-size crystallites of boron-doped diamond. Electron-beam lithography was employed for writing sample-specific contacts on small, well-faceted diamond crystals grown by chemical-vapor deposition on silicon substrates. After generating a three-dimensional computer model of the crystallite, a finite-element analysis was used to calculate the internal electrostatic potential distribution. Multiterminal resistance measurements, in conjunction with a computed geometrical factor, enabled the absolute resistivity to be determined. We find that the resistivities obtained from two different crystallites agree to better than 10%. The results are compared with transport measurements on a large-area homoepitaxial diamond film grown ...

Resistivity Determination From Small Crystallites, S. Hyun, M. Thorpe, B. Golding, M. Jaeger, Anthony Day

#### Resistivity Determination From Small Crystallites, S. Hyun, M. Thorpe, B. Golding, M. Jaeger, Anthony Day

*Anthony Roy Day*

We determine the resistivity of small micrometer-sized conductors with arbitrary shapes. It is shown that with n terminals attached to the sample, there are n(n1)/2 independent measurements of the resistance that can be made; from which the sample resistivity and the contact resistances can be extracted. An image of the sample is digitized and a finite element analysis is used to determine the geometrical factors that arise from the nonuniform current flow and hence control the resistance measurements. It is shown that all the elements of the resistance matrix for the sample are generated from the diagonal ...

The Elastic Moduli Of Simple Two-Dimensional Isotropic Composites: Computer Simulation And Effective Medium Theory, K. A. Snyder, E. J. Garboczi, Anthony Roy Day

#### The Elastic Moduli Of Simple Two-Dimensional Isotropic Composites: Computer Simulation And Effective Medium Theory, K. A. Snyder, E. J. Garboczi, Anthony Roy Day

*Anthony Roy Day*

An algorithm, combining digital-image with spring network techniques, has been developed that enables computation of the elastic moduli of random two-dimensional multiphase composites. This algorithm is used to study the case of isotropic, randomly centered, overlapping circular inclusions in an isotropic elastic matrix. The results of the algorithm for the few-inclusion limit, as well as the case where both phases have the same shear moduli, agree well with the exact results for these two problems. The case where the two phases have the same Poisson’s ratio, but different Young’s moduli, is also studied, and it is shown that ...

Universal Conductivity Curve For A Plane Containing Random Holes., E. J. Garboczi, M. F. Thorpe, M. S. Devries, Anthony Roy Day

#### Universal Conductivity Curve For A Plane Containing Random Holes., E. J. Garboczi, M. F. Thorpe, M. S. Devries, Anthony Roy Day

*Anthony Roy Day*

This paper examines the general percolation problem of cutting randomly centered insulating holes in a two-dimensional conducting sheet, and explores how the electrical conductivity sigma decreases with the remaining area fraction. This problem has been studied in the past for circular, square, and needlelike holes, using both computer simulations and analog experiments. In this paper, we extend these studies by examining cases where the insulating hole is of arbitrary shape, using digital-image-based numerical techniques in conjunction with the Y- [nabla] algorithm. We find that, within computational uncertainty, the scaled percolation threshold, xc=nc=5.9±0.4, is a universal ...

Comment On "Percolation In Isotropic Elastic Media.", Anthony Day, M. Thorpe

#### Comment On "Percolation In Isotropic Elastic Media.", Anthony Day, M. Thorpe

*Anthony Roy Day*

No abstract provided.

Spectral Dimensionality Of Random Superconducting Networks, Anthony Roy Day, W. Xia, M. F. Thorpe

#### Spectral Dimensionality Of Random Superconducting Networks, Anthony Roy Day, W. Xia, M. F. Thorpe

*Anthony Roy Day*

We compute the spectral dimensionality d-tilde of random superconducting-normal networks by directly examining the low-frequency density of states at the percolation threshold. We find that d-tilde=4.1±0.2 and 5.8±0.3 in two and three dimensions, respectively, which confirms the scaling relation d-tilde=2d/(2-s/ nu ), where s is the superconducting exponent and nu the correlation-length exponent for percolation. We also consider the one-dimensional problem where scaling arguments predict, and our numerical simulations confirm, that d-tilde=0. A simple argument provides an expression for the density of states of the localized high-frequency modes in this special ...

Stability Of Networks Under Tension And Pressure, Anthony Roy Day, H. Yan, M. F. Thorpe

#### Stability Of Networks Under Tension And Pressure, Anthony Roy Day, H. Yan, M. F. Thorpe

*Anthony Roy Day*

The number of zero-frequency modes of an elastic network is an important quantity in determining the stability of the network. We present a constraint-counting method for finding this number in general central-force networks that are under an external tension. The technique involves isolating the backbone and then counting constraints in the same way as for free standing networks. A detailed example of this counting is given for a random two-dimensional network subject to an external tension. The results are shown to agree with the number of zero-frequency modes as determined by a direct matrix diagonalization.

Rigid Backbone: A New Geometry For Percolation, Anthony Roy Day, R. R. Tremblay, A.-M. S. Tremblay

#### Rigid Backbone: A New Geometry For Percolation, Anthony Roy Day, R. R. Tremblay, A.-M. S. Tremblay

*Anthony Roy Day*

It is shown that the diluted two-dimensional central-force problem belongs to a new class of percolation problems. Geometric properties such as the fractal dimension of the backbone, the correlation-length exponent, and the connectivity are completely different from those of previously studied percolation problems. Explicit calculations of the backbone and the construction of an algorithm which identifies the infinite rigid cluster clearly demonstrate the absence of singly connected bonds, the overwhelming importance of loops, and the long-range nature of the rigidity.

The Rigid Backbone: A New Geometry For Percolation., Anthony Day, R. Tremblay, A.-M. Tremblay

#### The Rigid Backbone: A New Geometry For Percolation., Anthony Day, R. Tremblay, A.-M. Tremblay

*Anthony Roy Day*

It is shown that the diluted two-dimensional central-force problem belongs to a new class of percolation problems. Geometric properties such as the fractal dimension of the backbone, the correlation-length exponent, and the connectivity are completely different from those of previously studied percolation problems. Explicit calculations of the backbone and the construction of an algorithm which identifies the infinite rigid cluster clearly demonstrate the absence of singly connected bonds, the overwhelming importance of loops, and the long-range nature of the rigidity.

Splay Rigidity In The Diluted Central Force Elastic Network, Anthony Roy Day, A.-M. S. Tremblay, R. R. Tremblay

#### Splay Rigidity In The Diluted Central Force Elastic Network, Anthony Roy Day, A.-M. S. Tremblay, R. R. Tremblay

*Anthony Roy Day*

A Comment on the Letter by Wang and Harris, Phys. Rev. Lett. 55, 2459 (1985).

Guage Invariant De Gennes Model, Anthony Day, T. Lubensky

#### Guage Invariant De Gennes Model, Anthony Day, T. Lubensky

*Anthony Roy Day*

A gauge-invariant formulation of the de Gennes model for the nematic—to—smectic-A transition is presented. In this formulation the energy associated with the gauge field A⃗ reduces to the Frank elastic energy with the application of the constraint n⃗0·A⃗=0 where n⃗0 is the uniform equilibrium director and A⃗ is to be identified with deviations δn⃗ of the director from equilibrium. It is shown that thermodynamic quantities and renormalization-group recursion relations are gauge invariant. All gauge dependence appears in the exponent η describing order-parameter correlations. The gauge invariance of a negative dielectric anisotropy smectic-A in an ...

Dislocations And The Nematic To Smectic-A Transition For Arbitrary Values Of K1, Anthony Day, T. Lubensky, A. Mckane

#### Dislocations And The Nematic To Smectic-A Transition For Arbitrary Values Of K1, Anthony Day, T. Lubensky, A. Mckane

*Anthony Roy Day*

The de Gennes model is used to derive the energy of interacting dislocations in smectic-A liquid crystals. This energy reduces to the energy of interacting vortices in type-II superconductors when the splay elastic constant K1 is zero and to that derived from the Landau-Peierls elastic energy when spatial variations are slow on a scale of the bend and twist penetration depths. Furthermore, it has a well-defined K1→∞ limit. The dislocation energy is used to study the nematic—to—smectic-A transition as a function of K1 in two dimensions and in 4-ε dimensions. No evidence for the Nelson-Toner, anisotropic critical point ...

Imaging Of Paramagnetic Centres In Diamond, M.J. R. Hoch, Anthony Roy Day

#### Imaging Of Paramagnetic Centres In Diamond, M.J. R. Hoch, Anthony Roy Day

*Anthony Roy Day*

An imaging method for determining the spatial distribution of paramagnetic nitrogen centres in diamond is described. Results are presented for a sample consisting of two small type IB diamonds.