Ray Seyfarth

Density profile and flow of miscible fluid with dissimilar constituent masses

A computer simulation model is used to study the density profile and flow of a miscible gaseous fluid mixture consisting of differing constituent masses (mA=mB/3) through an open matrix. The density profile is found to decay with the height ∝exp(−mA(B)h), consistent with the barometric height law. The flux density shows a power-law increase ∝(pc−p)μ with μ≃2.3 at the porosity 1−p above the pore percolation threshold 1−pc.

SELF-ORGANIZED PHASE SEGREGATION IN A DRIVEN FLOW OF DISSIMILAR PARTICLES MIXTURES

Self-organized patterns in an immiscible fluid mixture of dissimilar particles driven from a source at the bottom are examined as a function of hydrostatic pressure bias by a Monte Carlo computer simulation. As the upward pressure bias competes with sedimentation due to gravity, a multi-phase system emerges: a dissociating solid phase from the source is separated from a migrating gas phase towards the top by an interface of mixed (bi-continuous) phase. Scaling of solid-to-gas phase with the altitude is nonuniversal and depends on both the range of the height/depth and the magnitude of the pressure bias. Onset of phase separation and layering is pronounced at low bias range.

Characteristics of the intrinsic modulus as applied to particulate composites with both soft and hard particulates utilizing the generalized viscosity/modulus equation

Recently, four significantly different particulate composite modulus derivations from the literature were found to yield the same theoretical “intrinsic modulus” for a particulate composite. In this article, this new intrinsic modulus was successfully combined with the generalized viscosity/modulus equation to yield a good fit of the shear modulus–particulate concentration data of both Smallwood and Nielsen using a variable intrinsic modulus. Some fillers yielded an intrinsic modulus that was close to the Einstein limiting value ([G] = [η] = 2.5), while other fillers yielded intrinsic moduli that were either somewhat larger or somewhat smaller than this value. The intrinsic modulus for carbon black in rubber was much larger than was Einsteins predicted value. However, intrinsic modulus values for Nielsens data for particulate composites were smaller than were Einsteins prediction at temperatures below the glass transition temperature of the matrix. The explanation for this phenomenon can easily be understood from a review of the properties of the intrinsic modulus. Likewise, the generalized viscosity/modulus equation was also successfully applied to available modulus literature for ceramics where voids were the particulate phase. When applied to Wangs data, the intrinsic modulus was found to be negative when describing the compaction of voids in the hot isostatic pressing of a ceramic. For this application, the modulus of a particulate composite as a function of the volume fraction of particles was modified to describe the modulus as a function of porosity. For the sets of data analyzed, values of the interaction coefficient and the packing fraction were not necessarily unique if the data sets were limited to the lower particulate volume fractions. For applications where a minimum amount of data was found to be available, a new approach was introduced to address a relative measure of the compatibility of the particle and the matrix using a new definition for Kraemers constant.

New Mathematical Method for Computer Graphics

Rendering two-dimensional data in the case of rough, complex surfaces is a challenge in computer graphics. Typically, splines with knots and control points are used, and while they yield useful surfaces they can be of poor quality, or can be difficult to apply. Fundamentally splines are local. An alternative mathematical method is to construct global methods which can be tuned to have polynomial behavior, or behave in ways that are not as restrictive, and which can be local, or not, depending on user input. This study examines a hybrid method of stochastic interpolation built around Bernstein functions. This approach is non-polynomial and global, but readily computable and can successfully fit complex two-dimensional surface data to obtain high quality at low computational cost. The representation of parametric surfaces in 3 dimensions can be achieved using approximation, or interpolation using this method. The generation of computational surfaces rendered using OpenGL, shows that this hybrid method of Bernstein function interpolation is a sound approach to surface rendering, and computational issues in achieving speed with accuracy are discussed. The hybrid method is shown to be robust, and can be selectively adjusted to yield controlled smoothing of the surface data. The method enables use of computational stencils of arbitrary size, and permits the construction of infinitely differentiable surfaces if needed.