Department of Mathematical Sciences

CMU Campus

Department Home Undergraduate Graduate CNA Math Finance Giving

Center for Nonlinear Analysis

CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact

CNA Publications


*Search by Year, Author, and Title (Sorts Chronologically)*
Year	Author	Search Titles	Submit


All Authors

Recent Publications:

2026

26-CNA-017, How Does Hard Magnetic Soft Matter Deform?, Daniel Katusele, Carmel Majidi, Liping Liu, Pradeep Sharma, Kaushik Dayal

26-CNA-016, Spectral Alignment of Mesogens for Three-Dimensional Disclination Localization in Liquid Crystals, Saptarshi Saha, Amit Acharya, Gerald J. Wang

26-CNA-015, The Adaptive Variational Dual Method for Nonlinear Nonsquare Algebraic Equations, Amit Acharya, Soummya Kar, N. Sukumar

26-CNA-014, Compressive Splitting in Brittle Solids: The Inverse of Wrinkling in Sheets, Maryam Khodadad, Francois Barthelat, John D. Clayton, George Gazonas, Kaushik Dayal

26-CNA-013, Anisotropic Thermalization in Far-from-Equilibrium Flows, Arnab Debnath, Timothy Breitzman, Kaushik Dayal

26-CNA-012, Dual Variational Principles for Curl Forces, Arash Yavari, Amit Acharya

26-CNA-011, Solving the Dissipation Inequality not as a Constitutive Restriction, Maximiliano Larrain Silva, Amit Acharya

26-CNA-010, A New Perspective in Linear Cauchy Elasticity: Variational Minimum Principles for Statics, Dynamics, and Heterogeneous Materials, Amit Acharya

26-CNA-009, Dynamic Micromagnetism a la Ericksen-Leslie, and the Constrained Polar Continuum Mechanics of Hard Magnetic Soft Materials, Amit Acharya, Siladitya Pal

26-CNA-008, Finite-width Adiabatic Shear Banding and Dislocation Patterning in Mesoscale Polycrystalline Aggregates, Siddharth Singh, Rajat Arora, Janith Wanni, Charles Adkins, Raymond Rasmussen, Noah J. Schmelzer, Dan J. Thoma, Curt A. Bronkhorst, Amit Acharya

26-CNA-007, Convergence of Langevin AIS for Multimodal Distributions, Akshat Agarwal, Gautam Iyer, Aidan Jameson, Seungjae Son, Wyatt Wimmer

26-CNA-005, Averaging Molecular Dynamics Simulations to Study the Slow-strain Rate Behavior of Metals, Sarthok Kumar Baruah, Sabyasachi Chatterjee, Amit Acharya, Gerald J. Wang

26-CNA-004, Stress Asymmetry in Hard Magnetic Soft Materials, H. Gökçen Güner, Francois Barthelat, John D. Clayton, Carlos Mora-Corral, Noel J. Walkington, Kaushik Dayal

26-CNA-003, Asymptotic analysis of higher-order perturbations of the Perona–Malik functional, Andrea Braides, Irene Fonseca

26-CNA-002, A Kinetic Phase-Field Model of Diffusion Bonding: A Nonlocal Approach to Interface Coalescence, Maryam Khodadad, Noel J. Walkington, Suresh Kalyanam, Matteo Pozzi, Kaushik Dayal

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

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: