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CNA Publications


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Recent Publications:

2025

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

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

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

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

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

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

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, (download paper)

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, (download paper)

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

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

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

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, (download paper)

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, (download paper)

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

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, (download paper)

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

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

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

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

25-CNA-001, Exploiting instabilities to enable large shape transformations in dielectric elastomers, Daniel Katusele, Carmel Majidi, Pradeep Sharma, Kaushik Dayal, (download paper)

2024

24-CNA-020, Phase-Field Modeling of Fracture under Compression and Confinement in Anisotropic Geomaterials, Maryam Hakimzadeh, Carlos Mora-Corral, Noel J. Walkington, Giuseppe Buscarnera, Kaushik Dayal, (download paper)

24-CNA-019, The Second Law as a constraint and admitting the approximate nature of constitutive assumptions, Amit Acharya, (download paper)

24-CNA-018, Motion of Islands of Elastic Thin Films in the Dewetting Regime, Gianni Dal Maso, Irene Fonseca, Giovanni Leoni, (download paper)

24-CNA-017, Variational formulation based on duality to solve partial differential equations: Use of B-splines and machine learning approximants, N. Sukumar, Amit Acharya, (download paper)

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: