# DE Seminars: Fall 2003

#### Monday September 15

Title |
Modeling and a bit of theory for bubble reactors |

Speaker |
Thomas I. Seidman UMBC |

**Abstract:**

We consider the modeling of gas–liquid reactions in cocurrent and countercurrent packed bubble reactors: in a reactor of countercurrent type the liquid is fed in from the top with outflow at the bottom while gas (bubbles) are fed in from the bottom and removed from the top; in a cocurrent bubble reactor both gas and liquid are fed in from the bottom, with pumping of the liquid. The talk starts with some discussion of an approach to modeling these situations and then, for a very simplified version, considers the question of existence of steady-state solutions. [An affirmative answer can be given for the cocurrent case, but the countercurrent case remains open.] This is joint work with Heikki Haario.

#### Monday September 22

Title |
A stable hp mixed finite element method for viscoelasticity problems |

Speaker |
Manil Suri UMBC |

**Abstract:**

Mixed finite element methods are based on casting the underlying PDEs in so-called `mixed’ variational form. In these, an auxiliary unknown is introduced and the solution is found as a saddle point rather than a minimum. One such formulation is the Hellinger-Reissner principle, which casts problems in elasticity as a first-order system by expressing both the stress and the displacement as independent unknowns. This is particularly useful when adapted to problems in plasticity and viscoelasticity, where the stresses cannot be directly recovered from the displacements and both have to be approximated separately. Unfortunately, the price one has to pay is that stability of the finite element approximation is not automatic – one has to satisfy an `inf-sup’ or `Babuska-Brezzi’ condition. In this talk, we review the above ideas and present a choice of finite element spaces which is completely stable both when the mesh size is decreased (h version) or the polynomial degree is increased (p version).

#### Monday September 29

Title |
The Magneto-hydrodynamic Richtmyer-Meshkov Instability |

Speaker |
Ravi Samtaney Princeton Plasma Physics Laboratory |

**Abstract:**

In the past two decades the Richtmyer-Meshkov (RM) instability has become the subject of extensive experimental, theoretical and computational research due to it’s importance in technological applications such as inertial confinement fusion, as well as astrophysical phenomena such as supernovae collapse. In this talk we will present recent results from nonlinear simulations of the Richtmyer-Meshkov instability in the presence of a magnetic field. The seminar will be divided into three segments. In the first segment, we will present a primer on compressible magneto-hydrodynamics (MHD). In the second segment we will present numerical evidence that the growth of the Richtmyer-Meshkov instability is suppressed in the presence of a magnetic field. This is due to a bifurcation which occurs during the refraction of the incident shock on the density interface. The result is that baroclinically generated vorticity is transported away from the interface to a pair of slow or intermediate magnetosonic shocks. Consequently, the density interface is devoid of vorticity and its growth and associated mixing is completely suppressed. The third segment on the talk will focus on the numerical method to obtain the aforementioned results. We will discuss the the implementation of an unsplit upwinding method to solve the ideal MHD equations with adaptive mesh refinement (AMR) using the Chombo framework. The solenoidal property of the magnetic field is enforced using a projection method which is solved using a multigrid technique.

#### Monday October 13

Title |
Configuration and Performance of the Math Department’s SCREMS Cluster |

Speaker |
Matthias Gobbert UMBC |

**Abstract:**

Recently, four PIs from our department on an NSF SCREMS grant (Bell, Potra, Nayakkankuppam, and myself) have taken delivery of “kali”, a 64-processor IBM Beowulf cluster. In short, this cluster has 32 dual-processor nodes connected via a high-performance Myrinet interconnect for computations and a fast ethernet for file serving to a 0.5 TB RAID array. Each node has 2 Intel Xeon 2.0 GHz (512 KB L2 cache) chips and at least 1 GB of memory. With its high-performance interconnect, this machine is arguably the most powerful parallel computer on campus at present. In this talk, I will explain the configuration of the machine in detail, but designed for a general audience. Then I will report on performance studies using two existing parallel research codes. Both codes are true parallel code that require frequent interprocessor communications, hence they are suitable to get a realistic feel for the machine’s capabilities. The codes were run in some different hardware and software configurations, so I will be able to draw some general conclusions on setup issues with machines of this type, some obvious ones and some not so obvious ones. For more information on the machine, you can visit the webpage http://www.math.umbc.edu/~gobbert/kali/.

#### Monday October 27

Title |
Hydrogen fuel cells: modeling and computations |

Speaker |
Rouben Rostamian UMBC |

**Abstract:**

Hydrogen fuel cells are devices that convert hydrogen to electricity through electrochemical reactions. Working prototypes exist, but the technology is still under rapid development. It is predicted that automobiles powered with hydrogen fuel cells will reach the market around 2010. See http://www.howstuffworks.com/fuel-cell.htm for a quick overview of hydrogen fuel cells. I will outline the operating principles of hydrogen fuel cells and describe two mathematical problems related to their design.

#### Monday November 3

Title |
Stability Results for Elastic Rods with Electrostatic Self-Repulsion |

Speaker |
Kathleen Hoffman UMBC |

**Abstract:**

Elastic rod models of DNA that incorporate an electrostatic self-repulsion have not been widely studied due to inherent numerical and analytical difficulties introduced by the singular nature of the problem. In this talk, I will present a representative functional and derive the appropriate first and second variations. In addition, I will outline how the method of constrained conjugate points can be modified to incorporate this singular potential and describe the currently unresolved numerical difficulties in implementing this method for determining stable solutions.

#### Monday November 10

Title |
Flow Control inside Micro-Fluidic Systems: Modeling, Sensing, and Feedback Control Design |

Speaker |
Benjamin Shapiro University of Maryland at College Park |

**Abstract:**

Micro-fluidic technology has the potential to allow hand-held devices with the functionality of existing biological and chemical laboratories, it can be used to create wearable or implantable drug delivery platforms, and it allows direct handling of biological materials such as cells, proteins, and DNA. In our research we have found that feedback control is sometimes required for robust micro-fluidic performance (as in the UCLA electro-wetting devices) and it allows new capabilities in other cases (as in our multi-particle steering system). This talk will address our efforts to integrate research in system design and feedback control with the rapid progress being made in micro-fluidic systems. Results will be shown for two physical systems. The first is the Electro-Wetting-On-Dielectric (EWOD) system developed at UCLA by CJ Kim. Here a grid of electrodes is used to locally change surface tension forces on liquid droplets: by choosing the electrode firing sequence it is possible to move, split, join, and mix liquids in the droplets. I will describe our modeling, vision sensing, and control results for this system. In particular, I will show our algorithms for precision control of droplet splitting and joining, and I will describe how feedback can be used to correct for an unknown external environment. The second system is a micro-fluidic “no-laser tweezer” system that can be used to steer many particles at once. I will show how we use flow control to create an underlying, time-varying fluid flow that carries all the particles at once along their desired trajectories, and I will describe the status of our experiments at Maryland and at NIST. Because the system does not require lasers and high quality optics with long optical path lengths, it is cheap and it can be miniaturized. This system is being used to steer cells for a “cell clinics” project at the University of Maryland. These systems lead to linear and nonlinear partial differential equations that must be controlled through their boundary conditions. Mathematical challenges include: a) resolving the dynamics, b) model reduction, and c) the formulation of tractable control problems. I will close the talk by outlining some of the key motivations, benefits, bottlenecks, and remaining open challenges in integrating feedback control and micro-fluidic systems research.

#### Monday November 17

Title |
Level Set Methods and Fast Marching Methods: Part I |

Speaker |
John Zweck UMBC |

**Abstract:**

I will give a two part expository talk on the Level Set and Fast Marching Methods, based in large part on Sethian’s book on the subject. My aim is to give an introduction to the theory, weaving in applications along the way. Graduate students are encouraged to attend.

#### Monday November 24

Title |
Level Set Methods and Fast Marching Methods: Part II |

Speaker |
John Zweck UMBC |

**Abstract:**

I will give a two part expository talk on the Level Set and Fast Marching Methods, based in large part on Sethian’s book on the subject. My aim is to give an introduction to the theory, weaving in applications along the way. Graduate students are encouraged to attend.

#### Monday December 1

Title |
Rigid Body Dynamics with Contact and Friction |

Speaker |
Bogdan Gavrea UMBC |

**Abstract:**

Constrained mechanical systems involving frictional contacts between rigid bodies have compelling practical applications in various fields, including robotics, virtual reality simulations, collapsing structures and the behavior of granular materials. The talk will focus on time-stepping schemes used to model the rigid body problem. We will also discuss a new second order scheme based on the linearly implicit trapezoidal method.