@article{ly_ito_banks_jolly_reitich_2001, title={Dynamic simulation of the temporal response of microstructure formation in magnetorheological fluids}, volume={15}, ISSN={["0217-9792"]}, DOI={10.1142/s0217979201005416}, abstractNote={ Efficient numerical simulations of microstructure development in magnetorheological (MR) fluids are conducted. The simulations, which are based upon a fast multipole algorithm, treat the magnetic inclusions as two-dimensional continuum magnetic entities. The development of microstructure is quantified by computing and recording the time evolution of the effective permeability of the composite fluid. Such a principle has been previously exploited for the experimental measurements of microstructure development [Jolly, Bender and Mathers, ERMR'97, Yonezawa, Japan 1997]. As was observed experimentally, numerical simulations reveal the evolution of microstructure to be multimodal in nature. Unlike the experiments, the numerical simulations afford us the ability to observe the physical mechanisms associated with various modes. }, number={6-7}, journal={INTERNATIONAL JOURNAL OF MODERN PHYSICS B}, author={Ly, HV and Ito, K and Banks, HT and Jolly, MR and Reitich, F}, year={2001}, month={Mar}, pages={894–903} }
 @article{lee_reitich_jolly_banks_2001, title={Piecewise linear model for field-responsive fluids}, volume={37}, ISSN={["1941-0069"]}, DOI={10.1109/20.914377}, abstractNote={The Frohlich-Kennelly model provides a constitutive law for saturation that is field dependent and has been widely used for studying nonlinear properties for a variety of electric and magnetic applications. Under the Frohlich-Kennelly model, saturation begins to occupy the entire conducting domain even at low-moderate applied fields, in this paper, we first present a new nonlinear constitutive law for field-responsive fluids that depends on the local fields and allows regions where the fields have not reached a critical value to remain unsaturated. We then study numerically the nonlinear saturated model and compare the results to the Frohlich-Kennelly model and experiments performed at the Lord Corporation, Cary, NC.}, number={1}, journal={IEEE TRANSACTIONS ON MAGNETICS}, author={Lee, CH and Reitich, F and Jolly, MR and Banks, HT}, year={2001}, month={Jan}, pages={558–560} }
 @article{simon_reitich_jolly_ito_banks_2001, title={The effective magnetic properties of magnetorheological fluids}, volume={33}, ISSN={["0895-7177"]}, DOI={10.1016/S0895-7177(00)00244-2}, abstractNote={Magnetorheological (MR) fluids represent a class of smart materials whose rheological properties change in response to the application of a magnetic field. These fluids typically consist of small (μm) magnetizable particles dispersed in a nonmagnetic carrier fluid that generally contains additives such as surfactants and antiwear agents [1]. Due to such additives, there is an outer nonmagnetic layer on the particles that keeps them from touching. The goal of this paper is to study the effective magnetic behavior of an MR composite as a function of the interparticle distance. To this end, we present and employ a model for the effective magnetic properties of MR fluids with periodic microstructure that is based on the theory of homogenization. Finally, we discuss an interpolating formula for the effective permeability of MR fluids as an extension of the work of Keller [2] and Doyle [3].}, number={1-3}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Simon, TM and Reitich, F and Jolly, MR and Ito, K and Banks, HT}, year={2001}, pages={273–284} }
 @article{ito_reitich_1999, title={A high-order perturbation approach to profile reconstruction: I. Perfectly conducting gratings}, volume={15}, ISSN={["0266-5611"]}, DOI={10.1088/0266-5611/15/4/315}, abstractNote={A new method for the reconstruction of two-dimensional periodic structures from scattered far-field data is presented. The approach is based on the recently developed `methods of variation of boundaries' (MVB) for the solution of forward-scattering problems. Here, the inverse problem is formulated as that of minimization of an appropriate nonlinear least-squares cost functional J. The analytic continuation ideas inherent to MVB are then advanced to enable a global line search at each step of a proposed conjugate gradients algorithm. Through a number of numerical examples it is demonstrated that such globalization may be necessary to overcome the non-convexity of J which, in turn, is shown to persist even when the global minimizer is known to be unique.}, number={4}, journal={INVERSE PROBLEMS}, author={Ito, K and Reitich, F}, year={1999}, month={Aug}, pages={1067–1085} }