Publications

Cahn-Hilliard and Isoperimetric Problems with Long-Range Interactions: Self-Assembly of Diblock Copolymers and Liquid Drop Models.

R. Choksi, R. Neumayer, and I. Topaloglu: Anisotropic Liquid Drop Models, Advances in Calculus of Variations 15-1, pp 109-131 (2022).

S. Alama, L. Bronsard, R. Choksi and I. Topaloglu: Droplet Phase In a Nonlocal Isoperimetric Problem Under Confinement, Communications in Pure and Applied Analysis 19-1 175-202 (2020).

S. Alama, L. Bronsard, R. Choksi and I. Topaloglu: Droplet Breakup in the Liquid Drop Model with Background Potential, Communications in Contemporary Mathematics 21-3:1850022 (2019).

R. Choksi, C. Muratov and I. Topaloglu: An Old Problem Resurfaces Nonlocally: Gamow's Liquid Drops Inspire Today's Research and Applications Notices of the American Mathematical Society 64-11 1275-1283 (2017).

S. Alama, L. Bronsard, R. Choksi and I. Topaloglu: Ground-States for the Liquid Drop and TFDW Models with Long-Range Attraction, Journal of Mathematical Physics 58-10 103503 (2017).

D. Shirokoff, R. Choksi and J.C. Nave: Sufficient Conditions for Global Minimality of Metastable States in a Class of Non-Convex Functionals: a Simple Approach via Quadratic Lower Bounds, Journal of Nonlinear Science Volume 25-3 (2015), pp 539-582

R. Choksi, I. Topaloglu and G. Tsogtgerel: Axisymmetric Critical Points of a Nonlocal Isoperimetric Problem on the Two-Sphere, ESAIM: Control, Optimisation and Calculus of Variations 21 (2015) pp. 247-270

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.

Voronoi Tessellations, Optimal Quantization, Generalizations, and Applications

I. Gonzalez, J. Tisdell, R. Choksi, and J.C. Nave: Emergence of Diverse Collective Behaviors from Local Voronoi Topological Perception to appear in Royal Society Open Science (2024).
VTP Appendix
Jack and Ivan's VTP Interactive Github Site

I. Gonzalez, R. Choksi, and J.C. Nave: A Simple Geometric Method for Navigating the Energy Landscape of Centroidal Voronoi Tesselations SIAM J. on Scientific Computing Vol. 43 no. 2 , pp. A1527-A1554 (2021).

R. Choksi and X.Y. Lu: Bounds on the Geometric Complexity of Optimal Centroidal Voronoi Tesselations in 3D Comm. Math. Phys Vol. 377 no. 3 (2020), pp 2429-2450.

L. Larsson, R. Choksi, and J.C. Nave: Geometric Self-assembly of Rigid Shapes: A Simple Voronoi Approach SIAM J. on Applied Math Vol. 76 no. 3 (2016), pp 1101-1125.

L. Larsson, R. Choksi, and J.C. Nave: An Iterative Algorithm for Computing Measures of Generalized Voronoi Regions SIAM J. on Scientific Computing Vol. 36 no. 2 (2014), pp. A792-A827.

Inverse Problems and Variational Approaches to Image Processing

Y. Vaisbourd, R. Choksi, A. Goodwin, T. Hoheisel, and C-Bibiane Schonlieb : Maximum Entropy on the Mean and the Cramer Rate Function in Statistical Estimation and Inverse Problems: Properties, Models, and Algorithms submitted (2023) .
Yakov's Interactive Github Site

G. Rioux, R. Choksi, T. Hoheisel, P. Marechal, and C. Scarvelis: The Maximum Entropy on the Mean Method for Image Deblurring Inverse Problems Vol 37-1 (2021) 015011 .

G. Rioux, C. Scarvelis, R. Choksi, T. Hoheisel, and P. Marechal: Blind Deblurring of Barcodes via Kullback-Leibler Divergence IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI) Vol. 43 no.1 (2021), pp 77-88 .

Y. van Gennip, P. Athavale, J. Gilles, and R. Choksi: A Regularization Approach to Blind Deblurring and Denoising of QR Barcodes IEEE Transactions on Image Processing Vol. 24-9 (2015) pp. 2864-2873.

R. Choksi, I. Fonseca, and B. Zwicknagl : A Few Remarks on Variational Models for Denoising Comm. Math. Sci. Vol. 12-5 (2014) pp. 843-857.

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 .

Nonlocal Interaction Functionals

A. Burchard, R. Choksi and E. Hess-Childs: On the Strong Attraction Limit for a Class of Nonlocal Interaction Energies, Nonlinear Analysis Vol. 198, 111844, (2020)

A. Burchard, R. Choksi and I. Topaloglu: Nonlocal Shape Optimization Via Interactions of Attractive and Repulsive Potentials, Indiana University Mathematics Journal , Vol. 67-1 (2018), pp. 375-395.

R. Choksi, R. Fetecau, and I. Topaloglu: On Minimizers of Interaction Functionals with Competing Attractive and Repulsive Potentials, Annales de l'Institut Henri Poincare -- Non Linear Analysis Vol. 32-6 (2015), pp. 1283-1305.

Anisotropic Surface Tensions and Homogenization

R. Choksi, I. Fonseca, J. Lin, and R. Venkatraman: Anisotropic Surface Tensions for Phase Transitions in Periodic Media, Calculus of Variations and Nonlinear PDE Vol 61:107 (2022).

Grain Growth: Imaging, Statistics and the Phase Field Crystal Model

G. M. La Boissoniere, R. Choksi, J.P. Lessard: Microscopic Patterns in the 2D Phase-Field-Crystal Model Nonlinearity Vol. 35-3, pp. 1500-1520, (2022).

G. M. La Boissoniere, R. Choksi, K. Barmak, and S. Esedoglu: Statistics of Grain Growth: Experiment versus the Phase-Field-Crystal and Mullins Models Materialia Vol. 6, 100280 (2019).

G. M. La Boissoniere and R. Choksi: Atom Based Grain Extraction and Measurement of Geometric Properties, Modelling and Simulation in Materials Science and Engineering Volume 26-3 (2018).

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 Vol. 48 (2013), pp. 337-366.

R. Choksi, M. Morandotti, and M. Veneroni: Global minimizers for axisymmetric multiphase membranes ESAIM: Control, Optimisation and Calculus of Variations Volume 19 (2013), pp. 1014-1029.

Type 1 Superconductors and Ferromagnets: Scaling Laws and Branching of Domain Structures

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.

Miscellaneous: Continuum Mechanics, Geometric Measure Theory, Conservation Laws.

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

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.