10 citations · 15 across the 12 of their papers we have counts for
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Regularity of Solutions for Peridynamics Equilibrium and Evolution Equations on Periodic Distributions
Thinh Dang, Bacim Alali, Nathan Albin
Results on the peridynamics equilibrium and evolution equations over the space of periodic vector-distributions in multi-spatial dimensions are presented. The associated operator c…
Regularity of Solutions for the Nonlocal Wave Equation on Periodic Distributions
Thinh Dang, Bacim Alali, Nathan Albin
This work addresses the regularity of solutions for a nonlocal wave equation over the space of periodic distributions. The spatial operator for the nonlocal wave equation is given…
Regularity of Solutions for the Nonlocal Diffusion Equation on Periodic Distributions
Ilyas Mustapha, Bacim Alali, Nathan Albin
This work addresses the regularity of solutions for a nonlocal diffusion equation over the space of periodic distributions. The spatial operator for the nonlocal diffusion equation…
Linear peridynamics Fourier multipliers and eigenvalues
Bacim Alali, Nathan Albin
A characterization for the Fourier multipliers and eigenvalues of linear peridynamic operators is provided. The analysis is presented for state-based peridynamic operators for isot…
Peridynamics and Material Interfaces
Bacim Alali, Max Gunzburger
The convergence of a peridynamic model for solid mechanics inside heterogeneous media in the limit of vanishing nonlocality is analyzed. It is shown that the operator of linear per…
Effective Conductivities of Thin-Interphase Composites
Bacim Alali, Graeme W. Milton
A method is presented for approximating the effective conductivity of composite media with thin interphase regions, which is exact to first order in the interphase thickness. The a…
Multiscale Analysis of Heterogeneous Media in the Peridynamic Formulation
Bacim Alali, Robert Lipton
A methodology is presented for investigating the dynamics of heterogeneous media using the nonlocal continuum model given by the peridynamic formulation. The approach presented her…