sysnetwebmailadmin

Upcoming Seminars

Seminars are held Tuesdays and Thursdays in POB 6.304 from 3:30-5:00 pm, unless otherwise noted. Speakers include scientists, researchers, visiting scholars, potential faculty, and ICES/UT Faculty or staff. Everyone is welcome to attend. Refreshments are served at 3:15 pm.

 

ICES Seminar - Applied Mathematics Group/Center for Numerical Analysis Group Series
Tuesday, Sep 22, 2015 from 3:30PM to 5PM
POB 6.304

Nonlocal transport modeling: fundamentals, applications, and numerical methods (first of four 1.5 hour lectures)
by Diego de Castillo-Negrete

Senior Research Scientist, Oak Ridge National Laboratory; and Faculty member, University of Tennessee

Transport modeling is a key element of applied sciences and engineering, and a fertile area of applied mathematics. In the past, a significant amount of work has been devoted to models formulated in terms of local partial differential equations (e.g., linear and nonlinear advection-diffusion type equations). However, relatively recently there has been growing experimental and theoretical evidence that these models fail to describe anomalous non-diffusive transport (e.g., super-diffusive and sub-diffusive transport). To describe these phenomena, nonlocal models introduce nonlocal flux-gradient relations and formulate transport in terms of partial integro-differential equations. The goal of these lectures is to present an introduction to the state of art of nonlocal transport modeling with emphasis on basic mathematical aspects and practical numerical methods. Applications will play a prominent role throughout the lectures in motivating the need for nonlocality, and in guiding the mathematical and numerical developments. Although the main focus will be on fractional diffusion type models, we will devote time to other nonlocal descriptions. Following an overview of nonlocal transport, the first part of the lectures will cover the fundamentals including the statistical foundation of nonlocal models (based on the theory of continuous time random walks driven by general Levy processes) and the basic mathematical properties of fractional derivatives including the fundamental solutions of fractional diffusion equations. Both, spatial nonlocality (resulting, e.g. from large non-Gaussian jumps) and temporal nonlocality (resulting, e.g. from non-Markovian memory effects) will be considered in one and higher dimensions. The second part of the lectures will focus on practical numerical algorithms based on finite-difference continuum methods and stochastic Langevin particle-based methods. A careful discussion of the nontrivial role played by boundary conditions when solving nonlocal models in finite-size domains will be presented. Although applications will be mentioned throughout the first two parts of lectures, the third part will be devoted to an in-depth discussion of some specific applications including: (i) Nonlocal particle and heat transport in fluids and plasmas; (ii) Fluctuation-driven transport in the nonlocal Fokker-Planck equation (e.g., Levy ratchets); (iii) Nonlocal reaction diffusion systems (e.g., front acceleration in the nonlocal Fisher-Kolmogorov equation); (iv) Nonlocal models of option prices in markets with jumps based on the fractional Black-Scholes equation.

Hosted by Luis Caffarelli and Irene Gamba

 

ICES Seminar - Applied Mathematics Group/Center for Numerical Analysis Lecture series
Thursday, Sep 24, 2015 from 3:30PM to 5PM
POB 6.304

Nonlocal transport modeling: fundamentals, applications, and numerical methods (2nd of four 1.5 hour lectures)
by Diego de Castillo-Negrete

Senior Research Scientist, Oak Ridge National Laboratory; and Faculty member, University of Tennessee

Transport modeling is a key element of applied sciences and engineering, and a fertile area of applied mathematics. In the past, a significant amount of work has been devoted to models formulated in terms of local partial differential equations (e.g., linear and nonlinear advection-diffusion type equations). However, relatively recently there has been growing experimental and theoretical evidence that these models fail to describe anomalous non-diffusive transport (e.g., super-diffusive and sub-diffusive transport). To describe these phenomena, nonlocal models introduce nonlocal flux-gradient relations and formulate transport in terms of partial integro-differential equations. The goal of these lectures is to present an introduction to the state of art of nonlocal transport modeling with emphasis on basic mathematical aspects and practical numerical methods. Applications will play a prominent role throughout the lectures in motivating the need for nonlocality, and in guiding the mathematical and numerical developments. Although the main focus will be on fractional diffusion type models, we will devote time to other nonlocal descriptions. Following an overview of nonlocal transport, the first part of the lectures will cover the fundamentals including the statistical foundation of nonlocal models (based on the theory of continuous time random walks driven by general Levy processes) and the basic mathematical properties of fractional derivatives including the fundamental solutions of fractional diffusion equations. Both, spatial nonlocality (resulting, e.g. from large non-Gaussian jumps) and temporal nonlocality (resulting, e.g. from non-Markovian memory effects) will be considered in one and higher dimensions. The second part of the lectures will focus on practical numerical algorithms based on finite-difference continuum methods and stochastic Langevin particle-based methods. A careful discussion of the nontrivial role played by boundary conditions when solving nonlocal models in finite-size domains will be presented. Although applications will be mentioned throughout the first two parts of lectures, the third part will be devoted to an in-depth discussion of some specific applications including: (i) Nonlocal particle and heat transport in fluids and plasmas; (ii) Fluctuation-driven transport in the nonlocal Fokker-Planck equation (e.g., Levy ratchets); (iii) Nonlocal reaction diffusion systems (e.g., front acceleration in the nonlocal Fisher-Kolmogorov equation); (iv) Nonlocal models of option prices in markets with jumps based on the fractional Black-Scholes equation.

A Joint ICES/Applied Mathematics Group/Center for Numerical Analysis Lecture series - four 1.5 hour lectures.

Nonlocal transport modeling: fundamentals, applications, and numerical methods (a series of four 1.5 hour lectures)
Diego de Castillo-Negrete, Senior Research Scientist, Oak Ridge National Laboratory; and Faculty member, University of Tennessee

Hosted by Luis Caffarelli and Irene Gamba

 

ICES Seminar - Applied Mathematics Group/Center for Numerical Analysis Lecture series
Tuesday, Sep 29, 2015 from 1:30PM to 3PM
POB 4.304

Nonlocal transport modeling: fundamentals, applications, and numerical methods (3rd of four 1.5 hour lectures)
by Diego de Castillo-Negrete

Senior Research Scientist, Oak Ridge National Laboratory; and Faculty member, University of Tennessee

Transport modeling is a key element of applied sciences and engineering, and a fertile area of applied mathematics. In the past, a significant amount of work has been devoted to models formulated in terms of local partial differential equations (e.g., linear and nonlinear advection-diffusion type equations). However, relatively recently there has been growing experimental and theoretical evidence that these models fail to describe anomalous non-diffusive transport (e.g., super-diffusive and sub-diffusive transport). To describe these phenomena, nonlocal models introduce nonlocal flux-gradient relations and formulate transport in terms of partial integro-differential equations. The goal of these lectures is to present an introduction to the state of art of nonlocal transport modeling with emphasis on basic mathematical aspects and practical numerical methods. Applications will play a prominent role throughout the lectures in motivating the need for nonlocality, and in guiding the mathematical and numerical developments. Although the main focus will be on fractional diffusion type models, we will devote time to other nonlocal descriptions. Following an overview of nonlocal transport, the first part of the lectures will cover the fundamentals including the statistical foundation of nonlocal models (based on the theory of continuous time random walks driven by general Levy processes) and the basic mathematical properties of fractional derivatives including the fundamental solutions of fractional diffusion equations. Both, spatial nonlocality (resulting, e.g. from large non-Gaussian jumps) and temporal nonlocality (resulting, e.g. from non-Markovian memory effects) will be considered in one and higher dimensions. The second part of the lectures will focus on practical numerical algorithms based on finite-difference continuum methods and stochastic Langevin particle-based methods. A careful discussion of the nontrivial role played by boundary conditions when solving nonlocal models in finite-size domains will be presented. Although applications will be mentioned throughout the first two parts of lectures, the third part will be devoted to an in-depth discussion of some specific applications including: (i) Nonlocal particle and heat transport in fluids and plasmas; (ii) Fluctuation-driven transport in the nonlocal Fokker-Planck equation (e.g., Levy ratchets); (iii) Nonlocal reaction diffusion systems (e.g., front acceleration in the nonlocal Fisher-Kolmogorov equation); (iv) Nonlocal models of option prices in markets with jumps based on the fractional Black-Scholes equation.

Hosted by Irene Gamba and Luis Caffarelli

 

ICES Seminar - Applied Mathematics Group/Center for Numerical Analysis Lecture series
Thursday, Oct 1, 2015 from 1:30PM to 3PM
POB 4.304

Nonlocal transport modeling: fundamentals, applications, and numerical methods (4th of four 1.5 hour lectures)
by Diego de Castillo-Negrete

Senior Research Scientist, Oak Ridge National Laboratory; and Faculty member, University of Tennessee

Transport modeling is a key element of applied sciences and engineering, and a fertile area of applied mathematics. In the past, a significant amount of work has been devoted to models formulated in terms of local partial differential equations (e.g., linear and nonlinear advection-diffusion type equations). However, relatively recently there has been growing experimental and theoretical evidence that these models fail to describe anomalous non-diffusive transport (e.g., super-diffusive and sub-diffusive transport). To describe these phenomena, nonlocal models introduce nonlocal flux-gradient relations and formulate transport in terms of partial integro-differential equations. The goal of these lectures is to present an introduction to the state of art of nonlocal transport modeling with emphasis on basic mathematical aspects and practical numerical methods. Applications will play a prominent role throughout the lectures in motivating the need for nonlocality, and in guiding the mathematical and numerical developments. Although the main focus will be on fractional diffusion type models, we will devote time to other nonlocal descriptions. Following an overview of nonlocal transport, the first part of the lectures will cover the fundamentals including the statistical foundation of nonlocal models (based on the theory of continuous time random walks driven by general Levy processes) and the basic mathematical properties of fractional derivatives including the fundamental solutions of fractional diffusion equations. Both, spatial nonlocality (resulting, e.g. from large non-Gaussian jumps) and temporal nonlocality (resulting, e.g. from non-Markovian memory effects) will be considered in one and higher dimensions. The second part of the lectures will focus on practical numerical algorithms based on finite-difference continuum methods and stochastic Langevin particle-based methods. A careful discussion of the nontrivial role played by boundary conditions when solving nonlocal models in finite-size domains will be presented. Although applications will be mentioned throughout the first two parts of lectures, the third part will be devoted to an in-depth discussion of some specific applications including: (i) Nonlocal particle and heat transport in fluids and plasmas; (ii) Fluctuation-driven transport in the nonlocal Fokker-Planck equation (e.g., Levy ratchets); (iii) Nonlocal reaction diffusion systems (e.g., front acceleration in the nonlocal Fisher-Kolmogorov equation); (iv) Nonlocal models of option prices in markets with jumps based on the fractional Black-Scholes equation.

Hosted by Luis Caffarelli and Irene Gamba

 

ICES Seminar
Tuesday, Nov 24, 2015 from 3:30PM to 5PM
POB 6.304

The Time Dimension, “iIntegrators” and Next Generation State-of-the-Art for First/Second Order ODE/DAE Systems
by Kumar K. Tamma

Professor, Department of Mechanical Engineering; University of Minnesota

Each computational science and engineering simulation, whether it is the analysis of a single discipline or a multi-physics application involving, first or second order system or combination thereof, has its own emphasis and analysis requirements; wishful thinking is that a “wish list” of desired attributes by the analyst to meet certain required analysis needs is desirable. Optimal design developments of algorithms are not trivial; and alternately, how to foster, select, and determine such optimal designs for a targeted application if such an optimal algorithm does not readily exist, is a desirable goal and a challenging and daunting task; not to mention the added complexity of additionally designing a general purpose unified framework – a one size fits all philosophy. Under the notion of Algorithms by Design and the theoretical basis emanating from a generalized time weighted residual philosophy, we have developed under the umbrella of "isochronous time integrators [iIntegrators]" representing the use of the "same time integration framework/architecture", novel designs for first/second order ODE /DAE transient/dynamic systems for the general class of LMS methods . The framework not only encompasses most of the research to-date developed over the past 50 years or so, but additionally encompasses more new and novel schemes and solution procedures with improved physics such as energy-momentum or symplectic-momentum conservation and other optimal attributes with/without controllable numerical dissipation. All formulations within the "iIntegration framework of individual or mixed algorithms and designs" yield the much coveted second-order time accuracy in all kinematic and algebraic variables for ODE’s and DAE’s of any index. Under the umbrella of a single unified architecture, the iIntegration framework is envisioned as the next generation toolkit; and illustrative examples are highlighted as well for computational science and engineering.

Bio:
Dr. Kumar K. Tamma, is currently - Professor in the Dept. of Mechanical Engineering, College of Science and Engineering at the University of Minnesota. He has published over 200 research papers in archival journals and book chapters; and over 300 in refereed conference proceedings, and conference abstracts. His primary areas of research encompass: Computational mechanics with emphasis on multi-scale/multi-physics and fluid-thermal-structural interactions; structural dynamics and contact-impact-penetration; computational aspects of microscale/nanoscale heat transfer; composites and manufacturing processes and solidification; computational development of finite element technology and time dependent algorithms by design; and development of techniques for applications to large-scale problems and high performance parallel computing environments; and virtual surgery applications in medicine. He serves on the editorial boards for over 20 archival national/international journals, Editor-in-Chief (co-shared) of an online journal, and is the Fellow of IACM, USACM, and the Minnesota Supercomputing Institute. He is the recipient of numerous research awards including the “ICCES Outstanding Research Medal for Contributions to Computational Structural Dynamics, June 2014”; and the "George Taylor Research Award" and selected for the University of Minnesota/Institute of Technology Award for Significant and Exceptional Contributions to Research. He is also the recipient of numerous Outstanding Teaching and other national and university awards. His recent book is titled “Advances in Computational Dynamics of Particles, Materials and Structures”, John Wiley & Sons publication.

Hosted by Leszek Demkowicz