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 Royal Society Open Science 11: 231537 (2024).

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.