Alexei Novikov

Blow-up of Solutions to a

Consider two perfectly conducting spheres in a homogeneous medium where the current-electric field relation is the power law. Electric field

p

E

-Laplace Equation

blows up in the

Discrete Network Approximation for Highly-Packed Composites with Irregular Geometry in Three Dimensions

L^\infty

Illumination Strategies for Intensity-Only Imaging

-norm as

Optimal mixing and optimal stirring for fixed energy, fixed power, or fixed palenstrophy flows

\delta

EXIT TIMES OF DIFFUSIONS WITH INCOMPRESSIBLE DRIFT

, the distance between the conductors, tends to zero. We give here a concise rigorous justification of the rate of this blow-up in terms of

Ad ifferential equations approach tol 1 -minimization with applications to array imaging

\delta

Coherent Imaging without Phases

. If the current-electric field relation is linear, see similar results obtained earlier in [E. S. Bao, Y. Y. Li, and B. Yin, Arch. Ration. Mech. Anal., 193 (2009), pp. 195--226; H. Kang, M. Lim, and K. H. Yun, preprint, http://arxiv.org/abs/1105.4328v1, 2011; M. Lim and K. Yun, Comm. Partial Differential Equations, 34 (2009), pp. 1287--1315; K. Yun, SIAM J. Appl. Math., 67 (2007), pp. 714--730; K. Yun, J. Math. Anal. Appl., 350 (2009), pp. 306--312].

Modulational stability of cellular flows

We introduce a discrete network approximation to the problem of the effective conductivity of a high contrast, densely packed composite in three dimensions. The inclusions are irregularly (randomly) distributed in a host medium. For this class of arrays of inclusions we derive a discrete network approximation for effective conductivity and obtain a priori error estimates. We use a variational duality approach to provide rigorous mathematical justification for the approximation and its error estimate.