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General method for exponential-type equations for eight- and nine-point prismatic arrays

Description: The results of three-parameter experiments are commonly interpreted by the trilinear equation for eight data in a prismatic array. Ifa center point estimate is available, the eight-and nine-point arrays can be represented by new exponential-type equations. The equations are easy to generate, they are invariant under data translation, and they estimate curvature coefficients.
Date: January 1, 2009
Creator: Silver, Gary L
Partner: UNT Libraries Government Documents Department

Generalized Monge-Kantorovich optimization for grid generation and adaptation in LP

Description: The Monge-Kantorovich grid generation and adaptation scheme of is generalized from a variational principle based on L{sub 2} to a variational principle based on L{sub p}. A generalized Monge-Ampere (MA) equation is derived and its properties are discussed. Results for p > 1 are obtained and compared in terms of the quality of the resulting grid. We conclude that for the grid generation application, the formulation based on L{sub p} for p close to unity leads to serious problems associated with the boundary. Results for 1.5 {approx}< p {approx}< 2.5 are quite good, but there is a fairly narrow range around p = 2 where the results are close to optimal with respect to grid distortion. Furthermore, the Newton-Krylov methods used to solve the generalized MA equation perform best for p = 2.
Date: January 1, 2009
Creator: Delzanno, G L & Finn, J M
Partner: UNT Libraries Government Documents Department

Strong mobility in weakly disordered systems

Description: We study transport of interacting particles in weakly disordered media. Our one-dimensional system includes (i) disorder, the hopping rate governing the movement of a particle between two neighboring lattice sites is inhomogeneous, and (ii) hard core interaction, the maximum occupancy at each site is one particle. We find that over a substantial regime, the root-mean-square displacement of a particle s grows superdiffusively with time t, {sigma}{approx}({epsilon}t){sup 2/3}, where {epsilon} is the disorder strength. Without disorder the particle displacement is subdiffusive, {sigma} {approx}t{sup 1/4}, and therefore disorder strongly enhances particle mobility. We explain this effect using scaling arguments, and verify the theoretical predictions through numerical simulations. Also, the simulations show that regardless of disorder strength, disorder leads to stronger mobility over an intermediate time regime.
Date: January 1, 2009
Creator: Ben-naim, Eli & Krapivsky, Pavel
Partner: UNT Libraries Government Documents Department

New, higher-order, elasticity-based micromechanics model

Description: The formulation for a new homogenization theory is presented. The theory utilizes a higher-order, elasticity-based cell analysis of a periodic array of unit cells. The unit cell is discretized into subregions or subcells. The displacement field within each subcell is approximated by an (truncated) eigenfunction function expansion of up to fifth order. The governing equations are developed by satisfying the pointwise governing equations of geometrically linear continuum mechanics exactly up through the given order of the subcell displacement fields. The specified governing equations are valid for any type of constitutive model used to describe the behavior of the material in a subcell. The fifth order theory is subsequently reduced to a third order theory. The appropriate reduction of the fifth and third order theories to the first order theory (which corresponds to a variant of the original method of cells (MOC) (Aboudi, 1991) theory) is outlined. The 3D ECM theory correctly reduces to the 2D ECM theory microstructures and the exact 1D theory for bilaminated structures. Comparison of the predicted bulk and local responses with published results indicates that the theory accurately predicts both types of responses. Furthermore, it is shown that the higher order fields introduced coupling effects between the local fields that can result in substantial changes in the predicted bulk inelastic response of a composite.
Date: January 1, 2003
Creator: Williams, T. O. (Todd O.)
Partner: UNT Libraries Government Documents Department

Nonlinearity in modal and vibration testing.

Description: This set of slides describes some aspects of nonlinear Vibration analysis thru use of analytical fromulas and Examples from real or simulated test systems . The Systems are drawn from a set of examples based on Years of vibration testing experience . Both traditional and new methods are used to describe nonlinear vibration.
Date: January 1, 2003
Creator: Hunter, N. F. (Norman F.)
Partner: UNT Libraries Government Documents Department