Monday, April 16, 2012 - 14:00 , Location: Skiles 006 , Margaret Cheney , Rensselaer Polytechnic Institute , Organizer: Haomin Zhou
Radar imaging is a technology that has been developed, verysuccessfully, within the engineering community during the last 50years. Radar systems on satellites now make beautiful images ofregions of our earth and of other planets such as Venus. One of thekey components of this impressive technology is mathematics, and manyof the open problems are mathematical ones.This lecture will explain, from first principles, some of the basicsof radar and the mathematics involved in producing high-resolutionradar images.
Monday, April 9, 2012 - 14:00 , Location: Skiles 006 , Xiaolin Wang , GT Math , Organizer:
The Glezer lab at Georgia Tech has found that vorticity can improve heat transfer efficiency in electronic hardware. Vortices are able to enhance the forced convection in the boundary layer and fully mix the heated fluid with cooler core flow. Some recent experiments showed the possibility of using a vibrated reed to produce vortices in heat sinks. In this work, we simulate both the fluid and the heat transfer process in a 3-dimensional plate fin heat sink. We propose a simplified model by considering flow and temperature in a 2-D channel, and extend the model to the third dimension using a 1-D heat fin model. We simulate periodically steady-state solutions. We show that the total heat flux transferred from the plate to the fluid can be improved with vortices given the same input power. A possible optimal solution for the largest heat transfer efficiency is proposed for the physical parameters of a real computer heat sink. We discuss the effect of the important parameters such as Reynolds number and thermal conductivities.
Monday, April 2, 2012 - 14:00 , Location: Skiles 006 , Elizabeth Cherry , School of Mathematical Sciences, Rochester Institute of Technology , Organizer:
The heart is an excitable system in which electrical waves normally propagate in a coordinated manner to produce an effective mechanical contraction. Rapid pacing can lead to the development of alternans, a period-doubling bifurcation in electrical response in which successive beats have long and short responses despite a constant pacing period. Alternans can develop into higher-order rhythms as well as spatiotemporally complex patterns that reflect large regions of dispersion in electrical response. These states disrupt synchrony and compromise the heart's mechanical function; indeed, alternans has been observed clinically as a precursor to dangerous arrhythmias, including ventricular fibrillation. In this talk, we will show experimental examples of alternans, describe how alternans develops using a mathematical and computational approach, and discuss the nonlinear dynamics of several possible mechanisms for alternans as well as the conditions under which they are likely to be important in initiating dangerous cardiac arrhythmias.
Monday, March 26, 2012 - 14:00 , Location: Skiles 006 , Edmond Chow , School of Computational Science and Engineering, Georgia Institute of Technology , Organizer: Sung Ha Kang
Brownian dynamics (BD) is a computational technique for simulating the motions of molecules interacting through hydrodynamic and non-hydrodynamic forces. BD simulations are the main tool used in computational biology for studying diffusion-controlled cellular processes. This talk presents several new numerical linear algebra techniques to accelerate large BD simulations, and related Stokesian dynamics (SD) simulations. These techniques include: 1) a preconditioned Lanczos process for computing Brownian vectors from a distribution with given covariance, 2) low-rank approximations to the hydrodynamic tensor suitable for large-scale problems, and 3) a reformulation of the computations to approximate solutions to multiple time steps simultaneously, allowing the efficient use of data parallel hardware on modern computer architectures.
Monday, March 5, 2012 - 14:00 , Location: Skiles 006 , Prof. Di Liu , Depatment of Mathematics, Michigan State Univeristy , Organizer: Haomin Zhou
Multiscale and stochastic approaches play a crucial role in faithfully capturing the dynamical features and making insightful predictions of cellular reacting systems involving gene expression. Despite theiraccuracy, the standard stochastic simulation algorithms are necessarily inefficient for most of the realistic problems with a multiscale nature characterized by multiple time scales induced by widely disparate reactions rates. In this talk, I will discuss some recent progress on using asymptotic techniques for probability theory to simplify the complex networks and help to design efficient numerical schemes.
Monday, February 27, 2012 - 14:05 , Location: Skiles 006 , Marcus Roper , UCLA Mathematics Dept. , Organizer:
Although fungi are the most diverse eukaryotic organisms, we have only a very fragmentary understanding of their success in so many niches or of the processes by which new species emerge and disperse. I will discuss how we are using math modeling and perspectives from physics and fluid mechanics to understand fungal life histories and evolution: #1. A growing filamentous fungi may harbor a diverse population of nuclei. Increasing evidence shows that this internal genetic flexibility is a motor for diversification and virulence, and helps the fungus to utilize nutritionally complex substrates like plant cell walls. I'll show that hydrodynamic mixing of nuclei enables fungi to manage their internal genetic richness. #2. The forcibly launched spores of ascomycete fungi must eject through a boundary layer of nearly still air in order to reach dispersive air ﬂows. Individually ejected microscopic spores are almost immediately brought to rest by fluid drag. However, by coordinating the ejection of thousands or hundreds of thousands of spores fungi, such as the devastating plant pathogen Sclerotinia sclerotiorum are able to create a flow of air that carries spores across the boundary layer and around any intervening obstacles. Moreover the physical organization of the jet compels the diverse genotypes that may be present within the fungus to cooperate to disperse all spores maximally.
Monday, February 20, 2012 - 14:00 , Location: Skiles 006 , Benjamin Berkels , South Carolina University , Organizer: Sung Ha Kang
Image registration is the task of transforming different images, or more general data sets, into a common coordinate system. In this talk, we employ a widely used general variational formulation for the registration of image pairs. We then discuss a general gradient flow based minimization framework suitable to numerically solve the arising minimization problems. The registration framework is next extended to handle the registration of hundreds of consecutive images to a single image. This registration approach allows us to average numerous noisy scanning transmission electron microscopy (STEM) images producing an improved image that surpasses the quality attainable by single shot STEM images.We extend these general ideas to develop a joint registration and denoising approach that allows to match the thorax surface extracted from 3D CT data and intra-fractionally recorded, noisy time-of-flight (ToF) range data. This model helps track intra-fractional respiratory motion with the aim of improving radiotherapy for patients with thoracic, abdominal and pelvic tumors.
Monday, January 30, 2012 - 14:00 , Location: Skiles 006 , David Mao , Institute for Mathematics and Its Applications (IMA) at University of Minnesota , Organizer: Sung Ha Kang
Binary function is a class of important function that appears in many applications e.g. image segmentation, bar code recognition, shape detection and so on. Most studies on reconstruction of binary function are based on the nonconvex double-well potential or total variation. In this research we proved that under certain conditions the binary function can be reconstructed from incomplete frequency information by using only simple linear programming, which is far more efficient.
Monday, January 23, 2012 - 14:05 , Location: Skiles 006 , Alper Erturk , Georgia Tech, School of Mechanical Engineering , Organizer:
The transformation of vibrations into low-power electricity has received growing attention over the last decade. The goal in this research field is to enable self-powered electronic components by harvesting the vibrational energy available in their environment. This talk will be focused on linear and nonlinear vibration-based energy harvesting using piezoelectric materials, including the modeling and experimental validation efforts. Electromechanical modeling discussions will involve both distributed-parameter and lumped-parameter approaches for quantitative prediction and qualitative representation. An important issue in energy harvesters employing linear resonance is that the best performance of the device is limited to a narrow bandwidth around the fundamental resonance frequency. If the excitation frequency slightly deviates from the resonance condition, the power output is drastically reduced. Energy harvesters based on nonlinear configurations (e.g., monostable and bistable Duffing oscillators with electromechanical coupling) offer rich nonlinear dynamic phenomena and outperform resonant energy harvesters under harmonic excitation over a range of frequencies. High-energy limit-cycle oscillations and chaotic vibrations in strongly nonlinear bistable beam and plate configurations are of particular interest. Inherent material nonlinearities and dissipative nonlinearities will also be discussed. Broadband random excitation of energy harvesters will be summarized with an emphasis on stochastic resonance in bistable configurations. Recent efforts on aeroelastic energy harvesting as well as underwater thrust and electricity generation using fiber-based flexible piezoelectric composites will be addressed briefly.
Monday, November 28, 2011 - 14:00 , Location: Skiles 006 , Christel Hohenegger , Mathematics, Univ. of Utah , Organizer:
One of the challenges in modeling the transport properties of complex fluids (e.g. many biofluids, polymer solutions, particle suspensions) is describing the interaction between the suspended micro-structure with the fluid itself. Here I will focus on understanding the dynamics of semi-dilute active suspensions, like swimming bacteria or artificial micro-swimmers modeled via a simple kinetic model neglecting chemical gradients and particle collisions. I will then present recent results on the linearized structure of such an active system near a state of uniformity and isotropy and on the onset of the instability as a function of the volume concentration of swimmers, both for a periodic domain. Finally, I will discuss the role of the domain geometry in driving the flow and the large-scale flow instabilities, as well as the appropriate boundary conditions.