CMU Applied and Computational Mathematics Seminar

Spring 2022

Organizers

If you would like to give a talk, please email any one of us.

Meeting Times

Fridays, 3:00pm – 4:00pm, on Webex

Past seminars: Fall 2014, ...

Schedule

Date

Speaker

Title

1/21/22   

TBA

TBA

1/28/22 

TBA

TBA

2/4/22 

TBA

TBA

2/11/22 

TBA

TBA

2/18/22 

TBA

TBA

2/25/22

TBA

TBA

3/4/22

TBA

TBA

3/11/22

TBA

TBA

3/18/22

TBA

TBA

3/25/22
WebEx link:
https://cmich.webex.com/cmich/j.php?MTID=mf67d220dc2bc772fd842af400d578122
Meeting number:2624 301 8787
Password: hNPcEg25h2a

Walter G. Chapman (Rice University)

Density Gradient Theory for Interfacial Properties of Fluids: Stabilized and Mass Conserved Algorithms for Associating Solvents to Surfactants 

4/1/22

TBA

TBA

4/8/22

TBA

TBA

4/15/22

TBA

TBA

4/22/22

TBA

TBA

4/29/22
WebEx link:
https://cmich.webex.com/meet/rakes1l

Miranda Holmes (Courant Mathematical Institute, NYU)

Numerically simulating particles with short-ranged interactions

Speaker: Walter G. Chapman
Title: Density Gradient Theory for Interfacial Properties of Fluids: Stabilized and Mass Conserved Algorithms for Associating Solvents to Surfactants
Abstract:
Density gradient theory (DGT) is a form of density functional theory (DFT) that allows prediction of the interfacial tension and density profile of molecules through a fluid-fluid interface. In DFT, the free energy is minimized as a function of the density distribution of molecules to obtain the equilibrium structure and properties of the fluid. DGT has roots that trace back to van der Waals. In this talk, we introduce several recent extensions of the theory and algorithms for practical calculations. While conventional algorithms require a reference substance of the system, we have developed a “stabilized density gradient theory” (SDGT) algorithm to solve DGT equations for multiphase pure and mixed systems that is robust and enables other generalizations. This algorithm makes it possible to calculate interfacial properties accurately at any domain size larger than the interface thickness without choosing a reference substance or assuming the functional form of the density profile. Further, we extend DGT to enable calculations for surfactant systems. For the first time, the surfactant head group and tail group are described separately in the DGT. Finally, these extensions are applied using a mass conserved DGT. This is a true mass conserved algorithm rather than being mass constrained. Applications of the approach are demonstrated using our SAFT equation of state.

 

Speaker: Miranda Holmes
Title: Numerically simulating particles with short-ranged interactions
Abstract:
Particles with diameters of nanometres to micrometres form the building blocks of many of the materials around us, and can be designed in a multitude of ways to form new ones. Such particles commonly live in fluids, where they jiggle about randomly because of thermal fluctuations in the fluid, and interact with each other via numerous mechanisms. One challenge in simulating such particles is that the range over which they interact attractively is often much shorter than their diameters, so the equations describing the particles’ dynamics are stiff, requiring timesteps much smaller than the timescales of interest. I will introduce methods to accelerate these simulations, which instead solve the limiting equations as the range of the attractive interaction goes to zero. In this limit a system of particles is described by a diffusion process on a collection of manifolds of different dimensions, connected by “sticky” boundary conditions. I will show how to simulate low-dimensional sticky diffusion processes, and then discuss some ongoing challenges such as extending these methods to high dimensions and incorporating hydrodynamic interactions.

 

Speaker: TBA
Title:
Abstract: