CNA Publications

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Recent Publications:

2024
• 24-CNA-015, Nonlocal Phase Transitions with Singular Heterogeneous Kernels, Wes Caldwell, (download paper)

• 24-CNA-014, Rigidly breaking potential flows and a countable Alexandrov theorem for polytopes, Jian-Guo Liu, Robert L. Pego, (download paper)

• 24-CNA-013, A Finite Deformation Theory of Dislocation Thermomechanics, Gabriel D. Lima-Chaves, Amit Acharya, Manas V. Upadhyaya, (download paper)

• 24-CNA-012, Residual Diffusivity For Noisy Bernoulli Maps, Gautam Iyer, James Nolen, (download paper)

• 24-CNA-011, Impact of Grain Boundary Energy Anisotropy on Grain Growth, Kiana Naghibzadeh, Zipeng Xu, David Kinderlehrer, Robert Suter, Kaushik Dayal, Gregory S. Rohrer, (download paper)

• 24-CNA-010, Variational Dual Solutions for Incompressible Fluids, Amit Acharya, Bianca Stroffolini, Arghir Zarnescu, (download paper)

• 24-CNA-009, Interplay between Nucleation and Kinetics in Dynamic Twinning, Janel Chua, Vaibhav Agrawal, Noel J. Walkington, George Gazonas, Kaushik Dayal, (download paper)

• 24-CNA-008, Nonuniqueness in Defining the Polarization: Nonlocal Surface Charges and the Electrostatic, Energetic, and Transport Perspectives, Shoham Sen, Yang Wang, Timothy Breitzman, Kaushik Dayal, (download paper)

• 24-CNA-007, Existence of solitary waves in particle lattices with power-law forces, Benjamin Ingimarson, Robert L. Pego, (download paper)

• 24-CNA-006, Statistical Field Theory of Polarizable Polymer Chains with Nonlocal Dipolar Interactions, Pratik Khandagale, Carlos Garcia-Cervera, Gal deBotton, Timothy Breitzman, Carmel Majidi, Kaushik Dayal, (download paper)

• 24-CNA-005, Coupled Dislocations and Fracture dynamics at finite deformation: model derivation, and physical questions, Amit Acharya, (download paper)

• 24-CNA-004, A Harris Theorem for Enhanced Dissipation, and an Example of Pierrehumbert, William Cooperman, Gautam Iyer, Seungjae Son, (download paper)

• 24-CNA-003, Mid-surface scaling invariance of some bending strain measures, Amit Acharya, (download paper)

• 24-CNA-002, Inviscid Burgers as a degenerate elliptic problem, Uditnarayan Kouskiya, Amit Acharya, (download paper)

• 24-CNA-001, A Hidden Convexity of Nonlinear Elasticity, Siddharth Singh, Janusz Ginster, Amit Acharya, (download paper)

2023

• 23-CNA-019, Emergent fault friction and supershear in a continuum model of geophysical rupture, Abhishek Arora, Amit Acharya, (download paper)

• 23-CNA-018, An Experimentally Informed Continuum Grain Boundary Model, Syed Ansari, Amit Acharya, Alankar Alankar, (download paper)

• 23-CNA-017, Ideal Magnetohydrodynamics and Field Dislocation Mechanics, Amit Acharya, (download paper)

• 23-CNA-016, A Dimensionally-Reduced Nonlinear Elasticity Model for Liquid Crystal Elastomer Strips with Transverse Curvature, Kevin LoGrande, M. Ravi Shankar, Kaushik Dayal, (download paper)

• 23-CNA-015, Modeling of experimentally observed topological defects inside bulk polycrystals, Siddharth Singh, He Liu, Rajat Arora, Robert Suter, Amit Acharya, (download paper)

• 23-CNA-014, A Hidden Convexity in Continuum Mechanics, with application to classical, continuous-time, rate-(in)dependent plasticity, Amit Acharya, (download paper)

• 23-CNA-013, On long waves and solitons in particle lattices with forces of infinite range, Benjamin Ingimarson, Robert L. Pego, (download paper)

• 23-CNA-012, Deformation Decomposition versus Energy Decomposition for Chemo- and Poro- Mechanics, Janel Chua, Mina Karimi, Patrick Kozlowski, Mehrdad Massoudi, Santosh Narasimhachary, Kai Kadau, George Gazonas, Kaushik Dayal, (download paper)

• 23-CNA-011, Convergence and non-convergence in a nonlocal gradient flow, Sangmin Park, Robert L. Pego, (download paper)

 

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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:
  • Irene Fonseca - dvi, ps, pdf
  • Richard James - ppt
  • Dal Maso - dvi
  • Luc Tartar - Lecture 1: dvi, ps ; Lecture 2: dvi, ps
  • Lev Truskinovsky - Lect 1: 1-1, 1-2; Lect 2: 2-1, 2-2; Lect 3: 3-1, 3-2 ; Lect 4: 4-1, 4-2
  • Noel Walkington - ps
  
  
• 2004 CNA Summer School Lecture Notes:
  • Luigi Ambrosio - ps, pdf
  • Maria-Carme Calderer - pdf
  • Wilfrid Gangbo - pdf
  • Nassif Ghoussoub - Lecture 1: pdf, Lecture 2: pdf
  • David Kinderlehrer - pdf
  • Stefan Müller - ps, pdf
  
  
• 2006 CNA Summer School Lecture Notes:
  • Krzysztof Burdzy - Lecture 1: pdf, Reference 1: pdf, Lecture 2: pdf, Reference 2: pdf, Lecture 3: pdf, Lecture 4: pdf, Lecture 5: pdf
  • Carlos Kenig - pdf
  • Ricardo Nochetto - Lecture 1: pdf, Lecture 2: pdf, Lecture 3: pdf, Lecture 4: pdf
  • Panagiotis Souganidis - pdf
  • Srinivasa Varadhan - Lecture 1: pdf, Lecture 2: pdf, Lecture 3: pdf, Lecture 4: pdf, Lecture 5: pdf
  
  
• 2008 CNA Summer School Lecture Notes:
  • Robert Kohn - Overview: pdf, Lecture 1: pdf, Lecture 2 and 3: pdf, Lecture 4: pdf, Lecture 5: pdf
  • Perhame - pdf