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CNA Publications


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Recent Publications:

2026

26-CNA-001, Two-scale Analysis of the Electrostatics of Dielectric Crystals: Emergence of Polarization Density and Boundary Charges, Shoham Sen, Yang Wang, Timothy Breitzman, Kaushik Dayal

2025

25-CNA-024, Convergence of Empirical Measures for I.I.D. Samples in $W^{-\alpha, p}$, Gautam Iyer, Raghavendra Venkatraman

25-CNA-023, On the Variational Dual Formulation of the Nash System and an Adaptive Convex Gradient-Flow Approach to Nonlinear PDEs, Dmitry Vorotnikov, Amit Acharya

25-CNA-022, Hamilton-Jacobi as Model Reduction, Extension to Newtonian Particle Mechanics, and a Wave Mechanical Curiosity, Amit Acharya

25-CNA-021, Incompressible 2D Euler Equations With Non-Decaying Random Initial Vorticity, Gautam Iyer, Milton C. Lopes Filho, Helena J. Nussenzveig Lopes

25-CNA-020, Emergent Electronic Flat Bands Through Dislocation Defect Phase Patterning: Effective One-Dimensional Model, Aziz Fall, Kaushik Dayal

25-CNA-019, Nonlocal Electrostatics and Boundary Charges in Continuum Limits of Two-Dimensional Materials, Shoham Sen, Yang Wang, Timothy Breitzman, Kaushik Dayal

25-CNA-018, Nonlocal Dipolar Self-Interactions Drive Polymer Chain Collapse in Electric Fields, Pratik Khandagale, Gal deBotton, Timothy Breitzman, Carmel Majidi, Kaushik Dayal

25-CNA-017, $\Gamma$-Convergence and Stochastic Homogenization for Functionals in the $\mathcal{A}$-Free Setting, Gianni Dal Maso, Rita Ferreira, Irene Fonseca

25-CNA-016, Polynomial Complexity Sampling From Multimodal Distributions Using Sequential Monte Carlo, Ruiyu Han, Gautam Iyer, Dejan Slepčev

25-CNA-015, Exponentially Mixing Flows With Slow Enhanced Dissipation, William Cooperman, Gautam Iyer, Keefer Rowan, Seungjae Son

25-CNA-014, An experimentally informed grain boundary model in 2–D: addressing triple junctions and invariance of misorientation, Syed Ansari, Amit Acharya, Rajat Arora, Alankar Alankar

25-CNA-013, Impact of Gas/Liquid Phase Change of CO₂ during Injection for Sequestration, Mina Karimi, Elizabeth Cochran, Mehrdad Massoudi, Noel J. Walkington, Matteo Pozzi, Kaushik Dayal

25-CNA-012, Residual Diffusivity For Expanding Bernoulli Maps, William Cooperman, Gautam Iyer, James Nolen

25-CNA-011, Soft Electromechanical Elastomers Impervious to Instability, Daniel Katusele, Carmel Majidi, Kaushik Dayal, Pradeep Sharma

25-CNA-010, Traveling Wave Profiles for a Semi-discrete Burgers Equation, Uditnarayan Kouskiya, Robert L. Pego, Amit Acharya

25-CNA-009, Crack Face Contact Modeling is Essential to Predict Crack-Parallel Stresses, Maryam Hakimzadeh, Noel J. Walkington, Carlos Mora-Corral, George Gazonas, Kaushik Dayal

25-CNA-008, The Roles of Size, Packing, and Cohesion in the Emergence of Force Chains in Granular Packings, Ankit Shrivastava, Kaushik Dayal, Hae Young Noh

25-CNA-007, Dislocation Patterning as a Mechanism for Flat Band Formation, Aziz Fall, Kaushik Dayal

25-CNA-006, Accretion and Ablation in Deformable Solids using an Eulerian Formulation: A Finite Deformation Numerical Method, Kiana Naghibzadeh, Anthony D. Rollett, Noel J. Walkington, Kaushik Dayal

25-CNA-005, A convex variational principle for the necessary conditions of classical optimal control, Amit Acharya, Janusz Ginster

25-CNA-004, Field Dislocation Mechanics, Conservation of Burgers vector, and the augmented Peierls model of dislocation dynamics, Amit Acharya

25-CNA-003, Second-Order $\Gamma$-Limit for the Cahn-Hilliard Functional with Dirichlet Boundary Conditions, II, Irene Fonseca, Leonard Kreutz, Giovanni Leoni

25-CNA-002, Second-Order $\Gamma$-Limit for the Cahn-Hilliard Functional with Dirichlet Boundary Conditions, I, Irene Fonseca, Leonard Kreutz, Giovanni Leoni

Untitled Document

Lecture Notes:

Introduction to Oceanography by Luc Tartar: tex, dvi, postscript, pdf
An Introduction to the Homogenization Method in Optimal Design by Luc Tartar: pdf
An introduction to Sobolev spaces and interpolation spaces by Luc Tartar: dvi, pdf, postscript
2001 CNA Summer School Lecture Notes:
2004 CNA Summer School Lecture Notes:
2006 CNA Summer School Lecture Notes:
2008 CNA Summer School Lecture Notes: