Publications

Cahn-Hilliard and Isoperimetric Problems with Long-Range Interactions and Self-Assembly of Diblock Copolymers

R. Choksi: On Global Minimizers for a Variational Problem with Long-range Interactions, Quart. Appl. Math. 70-3 (2012) pp. 517-537

R. Choksi, M. Maras, and J.F. Williams: 2D Phase Diagram for Minimizers of a Cahn-Hilliard Functional with Long-range Interactions SIAM J. Applied Dynamical Systems, 10-4 (2011) pp. 1344-1362

R. Choksi and M.A. Peletier: Small Volume Fraction Limit of the Diblock Copolymer Problem: II Diffuse Inteface Functional SIAM J. Math Analysis, 43-2 (2011) pp. 739-763

R. Choksi and M.A. Peletier: Small Volume Fraction Limit of the Diblock Copolymer Problem: I Sharp Inteface Functional SIAM J. Math Analysis 42-3 (2010) pp. 1334-1370

K. Glasner and R. Choksi: Coarsening and Self-Organization in Dilute Diblock Copolymer Melts and Mixtures Physica D Vol. 238 (2009) pp. 1241-1255.

R. Choksi, M.A. Peletier, and J.F. Williams: On the Phase Diagram for Microphase Separation of Diblock Copolymers: an Approach via a Nonlocal Cahn-Hilliard Functional SIAM J. Appl. Math. 69-6 (2009) pp. 1712-1738.

G. Alberti, R. Choksi, and F. Otto: Uniform Energy Distribution for an Isoperimetric Problem With Long-range Interactions Journal Amer. Math. Soc. , 22-2 (2009) pp. 569-605.

R. Choksi: Nonlocal Cahn-Hilliard and Isoperimetric Problems: Periodic Phase Separation Induced by Competing Long- and Short-range Interactions CRM Proc. Lecture Notes, AMS 44 (2008) pp. 33-46.

R. Choksi and P. Sternberg: On the First and Second Variations of a Nonlocal Isoperimetric Problem Journal fur die Reine und Angewandte Mathematik Vol. 611 (2007) pp. 75-108.

R. Choksi and P. Sternberg: Periodic Phase Separation: the Periodic Isoperimetric and Cahn-Hilliard Problems Interfaces and Free Boundaries Vol. 8 (2006) pp. 371-392.4

R. Choksi and X. Ren: Diblock Copolymer / Homopolymer Blends: Derivation of a Density Functional Theory Physica D Vol. 203 (2005) , pp. 100 - 119.

R. Choksi and X. Ren: On the Derivation of a Density Functional Theory for Microphase Separation of Diblock Copolymers Journal of Statistical Physics Vol 113 (2003) , pp. 151-176.

R. Choksi: Mathematical Aspects of Microphase Separation of Diblock Copolymers Conference Proceedings, RIMS, Kyoto, Nov. 2002. Surikaisekikenkyusko Kokyuroku Vol 1330 (2003) , pp. 10-17.

R. Choksi: Scaling Laws in Microphase Separation of Diblock Copolymers Journal of Nonlinear Science 11-3 (2001), pp. 223-236.

Variational Problems Associated with the Shape of Biological Membranes

R. Choksi and M. Veneroni: Global minimizers for the doubly-constrained Helfrich energy: the axisymmetric case Calculus of Variations and Nonlinear PDE in press, published electronically (2012).

R. Choksi, M. Morandotti, and M. Veneroni: Global minimizers for axisymmetric multiphase membranes ESAIM: Control, Optimisation and Calculus of Variations to appear (2013).

Variational Approaches to Image Processing

R. Choksi, I. Fonseca, and B. Zwicknagl : A Few Remarks on Variational Models for Denoising submitted (2012). .

R. Choksi, Y. van Gennip, and A. Oberman : Anisotropic Total Variation Regularized $L^1$-Approximation and Denoising/Deblurring of 2D Bar codes Inverse Problems and Imaging, Vol 5-3 (2011), pp. 591-617.

R. Choksi and Y. van Gennip: Deblurring of One Dimensional Bar Codes via Total Variation Energy Minimisation SIAM J. on Imaging Sciences, Vol. 3-4 (2010), pp. 735-764 .

Generalized centroidal Voronoi tessellations and applications of the eikonal equation and distance function in computational geometry

L. Larsson, R. Choksi, and J.C. Nave: An Iterative Algorithm for Computing Measures of Generalized Voronoi Regions submitted (2012). .

Scaling Laws, Branching and Domain Structures in Type 1 Superconductors and Ferromagnets

R. Choksi, S. Conti, R. Kohn, and F. Otto: Ground State Scaling Laws During the Onset and Destruction of the Intermediate State in a Type-I Superconductor Comm. Pure Appl. Math., 61-5 (2008) pp. 595-626.

R. Choksi, R.V. Kohn, and F. Otto: Energy Minimization and Flux Domain Structure in the Intermediate State of a Type-I Superconductor Journal of Nonlinear Science Vol 14-2 (2004) , pp. 119 - 171.

R. Choksi, R.V. Kohn, and F. Otto: Domain Branching in Uniaxial Ferromagnets: a Scaling Law for the Minimum Energy Comm. Math. Phys. 201 (1999) , pp. 61 - 79.

R. Choksi and R.V. Kohn: Bounds on the Micromagnetic Energy of a Uniaxial Ferromagnet Comm. Pure Appl. Math. 51 (1998) pp. 259 - 289.

Continuum Mechanics

R. Choksi, G. Del Piero, I. Fonseca, and D. Owen: Structured Deformations as Energy Minimizers in Models for Fracture and Hysteresis Mathematics and Mechanics of Solids 4 (1999) , pp. 321 - 356.

R. Choksi and I. Fonseca: Bulk and Interfacial Energies for Structured Deformations of Continua Arch. Rational Mech. Anal. 138 (1997) , pp. 37 - 103.

R. Choksi and I. Fonseca: A Change of Variables Formula for Mappings in BV Proc. Amer. Math. Soc. 125-7 (1997) , pp. 2065 - 2072.

R. Choksi: The Conservation Law $ u_y + (\sqrt{1 - u^2})_x = 0 $ and Deformations of Fibre Reinforced Materials SIAM J. Appl. Math. 56-6 (1996) , pp. 1539 - 1560.

R. Choksi: The Singular Limit of a Hyperbolic System and the Incompressible Limit of Solutions with Shocks and Singularities in Nonlinear Elasticity Quart. Appl. Math LV-3 (1997) , pp. 485-504.

Other Interests

J. Restrepo, R. Choksi, J.M. Hyman, and Y. Jiang: Improving the Damage Accumulation in a Biomechanical Bone Remodeling Model Computer Methods in Biomechanics and Biomedical Engineering Vol. 12-3 (2009) pp. 341-352.

J. Borwein, R. Choksi, and P. Marechal: Probability Distributions of Assets Inferred from Option Prices via the Principle of Maximum Entropy SIAM J. Optimization 14-2 (2003) , pp. 464-478.