Prof. Howard Stone,
Engineering and Applied Mathematics, Harvard University

Multiphase flows in confined systems: (I) A model for separation-driven coalescence and (II) Shear-induced dispersion of nonspherical particles

Microfluidic approaches are proving to be very useful for shedding new insights into multiphase hydrodynamics in confined systems and cellular-scale hydrodynamics. I will survey several multiphase microfluidic contributions from my group, and then focus on two specific problems. First, it was recently shown in microfluidic experiments that drops can be forced to coalescence in a channel flow that forces separation of the drops (Bremond et al., Physical Review Letters 2008). We use a lubrication model of the local dynamics to study this system and so arrive at an analytical criterion for conditions that support near contact of the drops. We also briefly describe electrically driven coalescence, including an observation of noncoalescence if the electric field is large enough. Second, we use a microfluidic approach to experimentally study shear-enhanced dispersion of disk-shaped particles. We analyze the transport process, and obtain experimental results for the concentration dependence of the shear-enhanced dispersion coefficient over a wide range of shear rates.

Prof. Ken Golden ,
Department of Mathematics, University of Utah

Climate Change and the Mathematics of Transport in Sea Ice

Sea ice is both an indicator and agent of climate change. It also hosts extensive
microbial communities which sustain life in the polar oceans. Fluid flow through
porous sea ice mediates a broad range of processes such as the growth and decay of
seasonal ice, the evolution of melt ponds and sea ice reflectance, and biomass
build-up. We'll discuss recent mathematical advances using percolation theory,
hierarchical models, and diffusion processes in understanding the fluid permeability
of sea ice and the thermal evolution of its microstructure. Our work will help in
predicting how global warming may affect Earth's sea ice packs and how polar
ecosystems may respond. Related results on electromagnetic properties will help in
monitoring ice thickness. Video from a 2007 Antarctic expedition where we measured
fluid and electrical transport in sea ice will be shown.

Dr. Clemens Heitzinger,
Department of Mathematics, University of Vienna & Wolfgang Pauli Institute, Vienna

Multiscale Modeling and Stochastics of Field-effect Sensors

In recent experiments, field-effect biosensors based on silicon
nanowires were demonstrated. These sensors can detect various kinds
of biomolecules, such as DNA strands and tumor markers, by the
intrinsic electric charge of the biomolecules. The main advantage of
field-effect sensors is label-free operation, whereas current
technology relies on fluorescent or radioactive markers.

A multiscale problem arises from the different length scales of the
biomolecules (i.e., the microscopic length scale) and of the sensor
structure (i.e., the macroscopic length scale). We have developed
multiscale models for the electrostatics of this type of sensor by
homogenization. Based on these models, a 3D simulator that calculates
the current through the sensor was developed and it has been applied
to published sensor geometries and to recently proposed structures.

The crucial part for the functioning of the sensor is its
biofunctionalized boundary layer. In order to investigate the
electrostatics of the boundary layer, we have developed a 3D
Metropolis Monte-Carlo simulator for functionalized surfaces. It
yields the charge distribution in the boundary layer that serves as
input to the charge-transport simulation.

Noise and fluctuations arise in these nanostructures due to the
Brownian motion of the biomolecules at the sensor surface. To
quantify these limitations, we have developed models for the
expectation value and variance of the electrostatic potential and the
current through the sensor. The models are based on the
Poisson-Boltzmann equation and the stochastic linearized
Poisson-Boltzmann equation. Simulation results are presented.
Finally, a scaling law for the variance of the electrostatic potential
was derived.

This is joint work with Christian Ringhofer (ASU) and Robert W. Dutton
and Yang Liu (Stanford).

Prof. Caroline Japhet,
LAGA, Université Paris 13 and CSCAMM

Discontinuous Galerkin and Nonconforming in Time Optimized Schwarz
Waveform Relaxation for Coupling Heterogeneous Problems

In this talk we present a nonconforming in time domain decomposition method for solving
evolution problems with discontinuous coefficients. The objective is long time computations
in highly discontinuous media such as nuclear waste disposal simulations, or climate modeling.
The strategy is to split the time interval into time windows and to perform, in each window, few
iterations of an Optimized Schwarz Waveform Relaxation algorithm. This type of method have
two strong points: it is global in time and thus allow non conforming space-time discretization in different
subdomains, and second, few iterations are needed to compute an accurate solution, due to optimized
transmission conditions. The subdomain solver is the discontinuous Galerkin method in time in order
to have a high degree of accuracy, time-stepping approaches, and ultimately adaptive control of the time step.
We present the analysis of the method and two-dimensional numerical results to illustrate the performances
of the method.

Prof. Thomas Sterling ,
Department of Computer Science, Louisiana State University

HPC Phase VI - the Final Convergence

Since 2007, high performance computing has been at the beginnings of the most dramatic change in form and function in the last decade and a half. Since the advent of the killer micro and the MPPs and commodity Clusters it spawned supported by message-passing programming techniques, most notably MPI, HPC has been on an exponential curve augmenting performance at historic rates through incremental changes to feature size, clock rate, and architectural complexity. But as always happens with S-curves, HPC is turning towards its final asymptote and is undergoing what may prove to be its 6th and potential final phase change. Most visible is the adoption of multicore heterogeneous system architectures driven by constraints in power, complexity, clock rate, and reliability while continuing to exploit improvements in feature size to achieve growth in performance. To realize this goal and the achievement of Exascale performance by the end of the next decade within practical limitations critical advances in efficiency, scalability, energy, and programmability will be required. In all previous such metamorphoses in HPC, the underlying principles of a new execution model was used to guide the co-design of new architectures, programming methods, and system software. Such is the case for the emerging HPC Phase VI. This presentation will discuss the likely elements the new execution model based on the exploratory ParalleX model of computation, and describe key attributes of architecture, operating, and runtime system software, and programming methods that are likely to gain ascendency over the next decade. Results from recent experiments with HPX prototype runtime system will be presented.

Prof. Victor S. Batista,
Department of Chemistry, Yale University

The MP/SOFT Method for Quantum Dynamics Simulations

The matching pursuit split operator Fourier transform (MP/SOFT) method will be presented as a rigorous and practical methodology for quantum propagation of wave packets and density matrices. MP/SOFT recursively applies the time-evolution operator, as defined by the Trotter expansion to second order accuracy, in dynamically adaptive coherent-state representations generated by a sequential orthogonal decomposition scheme inspired in the matching-pursuit algorithm. Applications will include adiabatic and nonadiabatic dynamics of molecular systems by integration of the time-dependent Schrödinger equation, and calculations of thermal correlation functions by solving the Bloch equation via imaginary-time propagation of the density matrix, and evaluating Heisenberg time-evolution operators through real-time propagation.

Prof. Raghuram Murtugudde,
Department of AOSC & ESSIC, University of Maryland

Earth System Predictions: A regional prototype

As the impacts of climate change manifest themselves in all
components of the Earth System, producing usable information for
Joe, the plumber, on the environment, agro-economics, human health,
energy and water resources, etc., from days to seasons become as
crucial as providing decadal information for policy makers and managers as well as superusers such as transportation, energy, insurance, and other industries. While the national weather service focuses on the physical system out to 8-10 days and national centers focus on global warming projections, the subseasonal to decadal window remains wide open. A prototype regional downscaling system has been developed for Chesapeake Bay Watershed to produce high resolution atmospheric, watershed, and estuarine forecasts which are presently limited to 16-days due to a lack of boundary information from NCEP GENS for longer periods. Experimental seasonal forecasts are made from NASA GMAO forecasts. Linked products include land use scenarios and the impacts on the Bay, Dissolved Oxygen, HABs (Karlodinum, Microcystis, pseudo-nitzschia), Striped Bass, pathogens such as vibrio cholerae, vibrio vulnificus, and vibrio parahaemolyticus. Statistical downscaling is being developed to go from Km scale to meter scale environmental information combined with pollution/pathogen/allergen data to produce personalized, pre-emptive, and predictive health information. Standard suites of products also include waves and inundation with DEMs to track street-level flooding to navigate emergency workers and police. The concept is developed to make the system modular so that it can easily be transplanted to any part of the US or the world.

Prof. Alex Kurganov,
Department of Mathematics, Tulane University

Central-Upwind Schemes for Two-Layer Shallow Water Equations

I will first give a brief review of Godunov-type central-upwind schemes for hyperbolic systems of balance laws. These finite volume methods offer a simple, robust and yet highly accurate alternative to more complicated and problem oriented upwind schemes. The second part of the talk will be devoted to applications of central-upwind schemes to the Saint-Venant system of shallow water equations and related problems. I will show how to construct of the central-upwind scheme, which accurately balances the flux and the source terms and at the same time preserves positivity of the water depth -- both properties are absolutely required for practical applications of the method. The scheme, derived in both one- and two-dimensional cases (in the latter case we use both Cartesian and triangular grids), is applied to a variety of test problems including the model of water waves generated by submarine landslides. Finally, I will discuss an extension of the central-upwind schemes to a more complicated system of two-layer shallow water equations. Developing robust numerical methods for this system is a very challenging task since the two-layer shallow water system contains interlayer exchange terms, which are generically nonconservative. We develop a well-balanced and positivity preserving scheme, which is applied in such a way that the effect of nonconservative product terms is negligible for cases arising in practical applications.

Prof. Richard Kleeman,
Courant Institute of Mathematical Sciences & Center for Atmosphere Ocean Science, New York University

Information transfer: Theory and Applications

The flow of information through a dynamical system is interesting in a purely theoretical way but also because there are many potentially useful applications. In this talk we review the measures that have been proposed in recent years with a particular emphasis on a more rigorous formalism proposed by the speaker and coworkers recently. We then consider important applications in the design of observing networks for prediction and also for the analysis of stochastic models of complex systems.

November 9 *MONDAY*

3.30PM,

AV Williams 3258

Prof. Manuel Tiglio, Physics & CSCAMM, University of Maryland

High Performance Computing Challenges in Black Hole Simulations
The presentation will describe the huge computational and storage demands to numerically study the binary black hole problem and map its configuration space, a key problem for gravitational wave observatories already taking data at design sensitivity. Both “standard” and heterogeneous large-scale parallel simulations of binary black holes will be discussed.

Prof. Henk Dijkstra,
Department of Physics and Astronomy,
Utrecht University

A stochastic dynamical systems view of the Atlantic

A dynamical systems framework, in many ways similar to that of El Nino/Southern Oscillation, is presented to understand the multidecadal variability in the North Atlantic. A so-called minimal primitive equation model is first used to represent the Atlantic ocean circulation. Within this minimal model, we identify a normal mode of multidecadal variability that can destabilize the background climate state through a so-called Hopf bifurcation. Next, it is argued that noise is setting the amplitude of the sea surface temperature variability associated with this normal mode. Finally, it is shown that the mechanism found in the minimal model is likely responsible for the multidecadal variability in GCMs and available observations.

Prof. Pierre-Emmanuel Jabin,
Université de Nice-Sophia Antipolis

Selection-mutation Dynamics for the Evolution of Traits in a Population

This talk aims at introducing some models describing the evolution of a large population of individuals with different biological "traits". The reproduction rate of each individual depends on its trait and on the competition for ressources within the population. In addition mutations may be included, enabling new traits to develop. These models leads to difficult asymptotic problems as the time scale of the mutations is usually much larger than the time scale of births and death. One such asymptotic will in particular be investigated, corresponding to frequent small mutations.

Prof. José Antonio Carrillo de la Plata, ICREA and Departament de Matemàtiques, Universitat Autònoma de Barcelona

Blowup in Multidimensional Aggregation Equations

In this talk I will review recent works in collaboration with A. Bertozzi and T. Laurent and with M. DiFrancesco, A. Figalli, T. Laurent and D. Slepcev in which we prove infinite/finite time blow-up for generic initial data in several models. More precisely, we consider nonlinear friction equations with potentials with a singularity at the origin like the Morse potential in swarming problems.