Research Interaction Team Website
Applied Partial Differential Equations
Fall 2012

Weekly Meetings: 3:00pm - 3:50pm Mondays in MTH 1311
Team Directors: Stuart Antman (ssa"at"math) Maria Cameron (cameron"at"math)
Sandra Cerrai (cerrai"at"math) Manoussos Grillakis (mng"at"math)
Pierre Emmanuele Jabin (pjabin"at"math) David Levermore (lvrmr"at"math)
Doron Levy (dlevy"at"math) Matei Machedon (mxm"at"math)
Dionisios Margetis (dio"at"math) Antoine Mellet (mellet"at"math)
Eitan Tadmor (tadmor"at"cscamm) Konstantina Trivisa (trivisa"at"math)

Tentative Schedule

Date Speaker Topic
17 September David Levermore Coarsening of Particle Systems
24 September Konstantina Trivisa On the Doi Model for the Suspension of Rod-Like Molecules
1 October Maria Cameron Analysis of the Stochastic Network Associated
with the Lennard-Jones-38 Cluster
8 October Changhui Tan Macroscopic Flocking Models
15 October David Levermore Modeling Profolios with Risky Assets
22 October Matias Delgadino Flocking Modeled by Kinetic Equations
29 October Kanna Nakamura Remnants of Discrete Dynamics at a Free Boundary
in a Continuum Limit
5 November KI-Net Conference Kinetic Description of Social Dynamics: From Consensus to Flocking
12 November Sam Punshon-Smith Fokker-Planck Model of "Integrate and Fire" Neuronal Networks
19 November Sandra Cerrai Pathwise Uniqueness for Stochastic Partial
Differential Equations in Banach Spaces
26 November Doron Levy Crime Models
3 December Wenqing Hu Second-Order Elliptic Equations with a Small Parameter
10 December Dionisios Margetis High-Frequency Asymptotics of Feynman Diagrams
in Quantum Field Theory: Abelian Case

RIT Related Activities

RIT Participants

Faculty:
 
  		Stuart Antman, Maria Cameron, Sandra Cerrai, Manoussos Grillakis,
Pierre Emmanuele Jabin, David Levermore, Doron Levy, Matei Machedon,
Dionisios Margetis, Antoine Mellet, Eitan Tadmor, Konstantina Trivisa
Students:
 
  		Josh Ballew, Matias Delgadino, Stefan Doboszczak, Wenqing Hu, Elif Kuz,
Chunting Lu, Kanna Nakamura, Joshua Parker, Sam Punshon-Smith, Luyu Sun,
Changhui Tan, Jinxin Xue, Dongmian Zou
Updated 11 October 2012

RIT Plan

Research Focus: We will study mathematical aspects of applied partial differential equations. These might include well-posedness, long-time behavior, attractor dynamics, stability of coherent structures, asymptotic limits, and the relationship between chaos and stochasticity. (Presentations from past semesters are listed below.)

Graduate Prerequisites: Analysis (Math 630), or PDEs (Math 673), or ODEs (Math 414 or 670), or numerics (AMSC 666 or 660), or probability (STAT 600). Some knowledge of partial differential equations would be useful. Permission of a Team Director.

Undergraduate Prerequisites: Advanced calculus (Math 410) and differential equations (Math 246). Any of the following are useful but not required: complex variables (Math 463), ODE (Math 414), PDE (Math 462), computation (AMSC 460 or AMSC 466). Permission of a Team Director.

Graduate Program: Team members will make presentations either on readings of fundamental papers or book chapters, or on their own analytical and/or numerical investigations. When appropriate, these may be developed into more formal presentations for seminars, conferences, or publication. Team members will be asked to help mentor more junior team members.

Undergraduate Program: Same as above, as appropriate to the background of the student.

Credit: Students can participate without signing up for credit. Students who sign up for credit typically take one credit; they are expected to attend regularly and to make one presentation. Students who sign up for two credits are expected to attend regularly and to either make three presentations or make one presentation and produce a related written report or project. This last option has been used by AMSC students to prepare for their oral candidacy exam; the written part becomes their AMSC Candidacy Prospectus, and their presentation becomes practice for their oral exam. Students who sign up for three credits will be expected to attend regularly, to make three presentations, and to produce a related written report or project.

Work Schedule: Meetings will be held weekly.

RIT Activity in Past Semesters

Topics Covered During Spring 2012

Date Speaker Topic
20 February David Levermore Global Maxwellians over All Space and Their Relation
to Converved Quantities of Classical Kinetic Equations
27 February Eitan Tadmor Marcinkiewicz Interpolation Theorem and Applications:
An Introduction
5 March Pierre Emmanuele Jabin Velocity Averaging
12 March Sebastien Motsch A Traffic Model for Pedestrians and Its Comparison
with Experimental Data
26 March David Levermore Kaniel-Shinbrot Iteration and Global Solutions
of the Cauchy Problem for the Boltzmann Equation
2 April Hantaek Bae Navier-Stokes with Supercritical Initial Data
9 April Antoine Mellet Equilibrium Capillary Surfaces and Sliding Drops
16 April Eitan Tadmor Compensated Compactness
23 April Josh Ballew Low Mach Number Limits to the Navier-Stokes-Smoluchowski System
30 April Chunting Lu Velocity Averaging in L^1 for the Transport Equation
7 May Pierre Emmanuele Jabin Wasserstein Distance and Optimal Transportation

Spring 2012 RIT Participants

Faculty:
 
  		Stuart Antman, Maria Cameron, Sandra Cerrai, Manoussos Grillakis,
Pierre Emmanuele Jabin, David Levermore, Doron Levy, Matei Machedon,
Antoine Mellet, Eitan Tadmor, Konstantina Trivisa
Postdocs: Hantaek Bae, Sebastien Motsch
Students:
  		Josh Ballew, Xuwen Chen, Matias Delgadino, Stefan Doboszczak, Chen Dong,
Chunting Lu, Ioannis Markou, Changhui Tan, Matthew Temba

Topics Covered During Fall 2011

Date Speaker Topic
19 September David Levermore Model Reduction
26 September Stuart Antman Degree Theory
3 October Konstantina Trivisa Admissibility of Weak Solutions - Entropy
10 October TBA TBA
17 October Ed Yasutake Aymptotics
24 October Xuwen Chen Rigorous Derivation of the 2d Cubic Nonlinear Schroedinger Equation with Anisotropic Switchable Quadratic Traps
31 October TBA TBA
7 November Kanna Nakamura Homogenization of Heterogeneous Materials
14 November Ding Zi Newton Polynomials
21 November Sandra Cerrai Gamma Convergence
28 November Ioannis Markou Hypocoercivity
5 December Dionisios Margetis On High-Frequency Asymptotics of Quantum Field Theories

Fall 2011 RIT Participants

Faculty:
 
  		Stuart Antman, Maria Cameron, Sandra Cerrai, Manoussos Grillakis, Pierre Emmanuele Jabin,
David Levermore, Doron Levy, Matei Machedon, Dionisios Margetis, Antoine Mellet,
Eitan Tadmor, Konstantina Trivisa, Peter Wolfe
Postdocs: Hantaek Bae, Trygve Karper, Sebastien Motsch, Abner Salgado
Students:
  		Josh Ballew, Xuwen Chen, Chunting Lu, Ioannis Markou, Kana Nakamura, Ian Schoch,
Funing Shi, Douglas Ulrich, Ed Yasutake, Ding Zi, Ming Zong

Topics Covered During Spring 2011

Date Speaker Topic
14 February David Levermore Bose-Einstein Condensation and the Kompaneets Equation
21 February no speaker no speaker
28 February no speaker no speaker
7 March Suleyman Ulusoy Keller-Segel Type Systems in Higher Dimensions
14 March Xuwen Chen Uniqueness of Solutions to the Gross-Pitaevskii Hierarchy with a Switchable Quadratic Trap
28 March Knut Waagan Stable Numerical Schemes for Nonlinear Elasticity
4 April Sebastien Motsch Models of Flocking with Asymmetric Interactions
11 April Trygve Karper Convergence of Numerical Methods for Compressible Stokes Flow
18 April Sandra Cerrai Small Mass Asymptotics for a Charged Particle in a Magnetic Field and the Long-Time Influence of Small Perturbations
25 April Hantaek Bae Analyticity and Time Decay of Solutions to the 3D Navier-Stokes Equations and 2D Quasi-Geostrophic Equations
2 May Peter Wolfe Discontinuous Petrov-Galerkin Methods
9 May Alexey Miroshnikov Variational Schemes in Nonlinear Elasticity, Convergence and Relative Entropy

Spring 2011 RIT Participants

Faculty:
 
  		Stuart Antman, Maria Cameron, Sandra Cerrai, Manoussos Grillakis, David Levermore,
Doron Levy, Matei Machedon, Antoine Mellet, Eitan Tadmor,
Konstantina Trivisa, Peter Wolfe
Postdocs: Hantaek Bae, Trygve Karper, Sebastien Motsch, Suleyman Ulusoy, Knut Waagan
Students: Josh Ballew, Xuwen Chen, Chunting Lu, Ioannis Markou

Topics Covered During Fall 2010

Date Speaker Topic
20 September Stuart Antman Formal Aymptotics of Heavily-Burdened, Deformable Bodies
27 September Antoine Mellet Fractional Diffusion Limits for Kinetic Equations
4 October David Levermore Corrections to Diffusion Approximations Derived from Kinetic Equations
11 October Dionisios Margetis Notions of Noise in Material Science
18 October Suleyman Ulusoy Aymptotics of Heavily-Burdened, Deformable Bodies
25 October Ioannis Markou Convergence to Equilibria of Solutions to a Fokker-Planck Equation
1 November Maria Cameron Computing Transition Paths for Rare Events
8 November Josh Ballew Singular Limits of the Compressible Navier-Stokes System
15 November Kanna Nakamura Evolution of Crystal Surface: Boundary Conditions and Decay Estimates
22 November Eitan Tadmor Linear PDEs in Critical Regularity Spaces: Hierarchical Construction of their Nonlinear Solutions
29 November Changhui Tan Hierarchical Construction of Bounded Solutions to div U = f
6 December Konstantina Trivisa Fluid-Particle Interactions (postponed until spring)

Fall 2010 Participants

Faculty:
 
  		Stuart Antman, Maria Cameron, Sandra Cerrai, Manoussos Grillakis, David Levermore,
Doron Levy, Matei Machedon, Dionisios Margetis, Antoine Mellet, Eitan Tadmor,
Konstantina Trivisa, Peter Wolfe
Postdocs: Suleyman Ulusoy
Students:
  		Josh Ballew, Ariel Hafftka, Ioannis Markou, Kanna, Nakamura,
Changhui Tan, Dan Weinberg

Topics Covered During Spring 2010

Date Speaker Topic
8 February Brent Baccala Postponed due to Snow!
15 February Knut Waagan Numerical Solution of Astrophysical Magnetohydrodynamics in Multi-Dimensions
22 February Sandra Cerrai Normal Fluctuations Around the Averaged Motion for a Class of Reaction-Diffusion Equations Perturbed
by a Fast Oscillating Stochastic Term
1 March Hantaek Bae Free Boundary-Value Problem of the Navier-Stokes Equations with Surface Tension
8 March Xuwen Chen Nonlinear Schroedinger Equations
22 March Peter Wolfe An Introduction to Evans Functions
29 March Stu Antman TBA
5 April Brent Baccala A Stress-Free Introduction to Differential Algebra
12 April Antoine Mellet Homogenization of Some Obstacle Problems
19 April Dave Levermore Global Classical Solutions of the Boltzmann Equation with Noncutoff Kernels a'la Gressman and Strain I
26 April Manoussos Grillakis Global Classical Solutions of the Boltzmann Equation with Noncutoff Kernels a'la Gressman and Strain II
3 May Animikh Biswas TBA
10 May Sebastien Motsch Models of Flocking: the Cucker-Smale Model and Beyond

Spring 2010 Participants

Faculty:
  		Stuart Antman, Sandra Cerrai, Manoussos Grillakis, David Levermore, Doron Levy,
Matei Machedon, Antoine Mellet, Eitan Tadmor, Konstantina Trivisa, Peter Wolfe
Visitors: Animikh Biswas
Postdocs: Hantaek Bae, Sebastien Motsch, Suleyman Ulusoy, Knut Waagan
Students: Brent Baccala, Xuwen Chen, Ioannis Markou

Topics Covered During Fall 2009

Date Speaker Topic
14 September Matei Machedon Quantum Dynamics of Many-Body Systems, the Hartree Equation, and Beyond
Joint work with M. Grillakis and D. Margetis
21 September FRG Meeting:
Tai-Ping Liu et. al. 		Kinetic Description of Multiscale Phenomena
Room: CSIC 4122
28 September Dave Levermore Dissperive Corrections to the Compressible Navier-Stokes System
5 October Jae Ryong Kweon Discontinuity of Solutions to the Compressible Navier-Stokes Equations on Bounded Domains with Corners
12 October Aziz Lecture:
Thomas J.R. Hughes 		Isogeometric Analysis: Computational Mechanics based on Modern Developments in Computational Geometry
Room: MATH 3206
19 October Stu Antman Invariance and Computation for Hyperbolic Conservation Laws
26 October Konstantina Trivisa Hyperbolic Balance Laws: Sharp Decay Rates & Consequences
2 November Suleyman Ulusoy Asymptotic Equipartition and Long-Time Behavior of Weak Solutions for the Hele-Shaw Flow Problem
9 November Dio Margetis Metamaterials and Metasurfaces: A Homogenization (PDE) Perspective
16 November Sandra Cerrai postponed to spring due to special seminar
23 November Animikh Biswas Analyticity and Gevrey Class Technique for Navier-Stokes and Related Equations
30 November Hantaek Bae The Littlewood-Paley Theory and Applications to PDEs
7 December Knut Waagan Numerical Solution of Astrophysical Magnetohydrodynamics in Multi-Dimensions
postponed to spring due to special seminar

Fall 2009 RIT Participants

Faculty:
 
  		Stuart Antman, Sandra Cerrai, Manoussos Grillakis, David Levermore, Doron Levy,
Matei Machedon, Dionisios Margetis, Antoine Mellet, Eitan Tadmor, Konstantina Trivisa,
Athanasios Tzavaras, Peter Wolfe
Visitors: Animikh Biswas, J.T. Halbert, Jae Ryong Kweon
Postdocs: Hantaek Bae, Sebastien Motsch, Suleyman Ulusoy, Knut Waagan
Students: Chungting Lu, Ioannis Markou, Karl Schmitt, Rongrong Wang

Topics Covered During Spring 2009

Date Speaker Topic
9 February J.T. Halbert Local Equilibrium for Brownian Particles
16 February David Levermore Classical Kinetic Equations, Gaussian Moment Closures, and Fluid Regimes
23 February Konstantinos Spiliopoulos Large Deviations Principle for Feller Diffusion Processes and Wave Front Propagation
2 March Stuart Antman Invariance and Computation for Hyperbolic Conservation Laws (postponed due to snow)
9 March Ioannis Markou The Rouse and Zimm Models in Polymer Dynamics
23 March Eitan Tadmor A New Approach to the 2D Pressureless Equations
30 March Dionisios Margetis Homogenization of Reconstructed Surfaces and Bose-Einstein Condensates
6 April Sandra Cerrai Quasipotentials and Exit Times
13 April Antoine Mellet Front Propagation in Heterogeneous Media
20 April Konstantina Trivisa Asymptotics and Navier-Stokes
27 April Manoussos Grillakis Bose-Einstein Condensates
4 May Arthur Cheng Two-Phase Euler
11 May Cynthia Bossard Mathematical Models for Stock Prices

Spring 2009 RIT Participants

Faculty:
  		Stuart Antman, Sandra Cerrai, Manoussos Grillakis, David Levermore,
Dionisios Margetis, Antoine Mellet, Eitan Tadmor, Konstantina Trivisa
Postdocs: Arthur Cheng, Weiran Sun
Students: Avanti Athreya, Cynthia Bossard, J.T. Halbert, Ioannis Markou, Hyejin Kim, Karl Schmitt, Konstantinos Spiliopoulos

Topics Covered During Fall 2008

Date Speaker Topic
17 September Konstantinos Spiliopoulos Smoluchowski-Kramers Approximation for the Langevin Equation with Reflection
Sandra Cerrai Smoluchowski-Kramers Approximation for Stochastic PDEs
24 September Alexey Miroshnikov Radial Shocks in Elastodynamics
Stuart Antman Time-Asymptotics for Nonlinear PDEs
1 October Avanti Athreya Metastability for Nearly-Hamiltonian Systems
Weiran Sun Low Mach Number Limits for Dispersive Navier-Stokes Systems
8 October J.T. Halbert Dissipative Particle Dynamics
David Levermore Equations-of-State for Pressure
15 October Konstantinos Spiliopoulos Reaction-Diffusion Equations in Narrow Domains and Wave Front Propagation
22 October Avanti Athreya Large Deviations, Metastability, and Averaging for Diffusion Processes
29 October Arthur Cheng The Interaction between Nonlinear Koiter Shells and Viscous Fluids
5 November Alexey Miroshnikov A Time Approximation Scheme for the Equations of Elastodynamics in the Radial Case
12 November Konstantina Trivisa On the Dynamics of Multicomponent Flows (postponed to 20 November PDE Seminar)
19 November Sandra Cessai Fast Diffusion Asymptotics for Stochastic Reaction-Diffusion Equations with Boundary Noise
3 December Hyejin Kim Weak Convergence of D_v D_u - Processes
10 December Weiran Sun Low Mach Number Limits for Dispersive Navier-Stokes Systems

Fall 2008 RIT Participants

Faculty: Stuart Antman, Sandra Cerrai, David Levermore, Konstantina Trivisa, Athanasios Tzavaras
Postdocs: Arthur Cheng, Weiran Sun
Students: Avanti Athreya, J.T. Halbert, Ioannis Markou, Hyejin Kim, Alexey Miroshnikov, Konstantinos Spiliopoulos