September 24 
Angus I.D. Macnab, CSCAMM
Simulations of Resistive Magnetohydrodynamics Using Lattice Boltzmann Methods
Lattice Boltzmann methods (LBM) provide a novel technique for simulating systems that are governed
by dissipative and dispersive nonlinear partial differential equations. The method avoids the direct
treatment of computationally expensive nonlinear convective derivatives by advectively streaming
mesoscopic particle distribution functions, which describe the macroscopic system. LBMs that use the
linear BGK collision operator produce simple algorithms, which lend themselves to ideal parallelization
on platforms containing multiple processing environments. Moreover, LBMs can incorporate most of the
modern computational techniques used in finite difference simulations, including nonuniform and
adaptive grids. I will present a simple development of LBMs from kinetic theory and will show how
the particle distribution functions can be chosen to describe resistive magnetohydrodynamics (MHD).
I will then present some simulations of one and two dimensional resistive MHD.

October 1 
Margaret S. Cheung, IPST, University of Maryland
Solvation in Protein Folding
Analysis, Combination of Theoretical
and Experimental Approaches
An effort of combining theoretical/computational analyses and protein
engineering methods has been made to probe the folding mechanism of
a modular protein, SH3, utilizing an Energy Landscape Theory and novel
mutagenetic phivalue analysis. Particularly
emphasis was given to core residues and the effect of desolvation during the protein folding
event. Experimentally that was probed by replacing the core valines by
isosteric threonines. These mutations have the advantage of keeping core
structurally invariant while affecting the core stability
relative to the unfolded state. Although the valines that form the core
appear spatially invariant, the folding kinetics of their threonine
mutants varies, indicating their different extent of solvation in the transition state ensemble. Theoretical
and computational studies predicted the distribution of folding kinetics of threonine mutants without previous knowledge of the
measured rates. This initial success encourages further investigations of providing molecular details behind these macroscopic phenomena and on the
role of solvation in the folding reaction.

October 7
11:00AM  12:15PM
CSIC 3118 
Ron DeVore, University of South Carolina
Quasiinterpolants
Note: Special Time and place

October 810 
WORKSHOP
Women of Applied Mathematics: Research and Leadership
CSCAMM Seminar Room 4122 Schedule: [Wednesday 8]
[Thursday 9]
[Friday 10]
Complete Schedule: [Click Here]

October 15 
Lili Ju, IMA at University of Minnesota
Numerical Simulations of the Quantized Vortices in a Thin Superconducting Hollow
Sphere
In this talk, We investigate the vortex nucleation in a thin superconducting
hollow sphere. The problem is studied using a simplified system of
GinzburgLandau equations. We present finite volume methods which preserve the
discrete gauge invariance for the time dependent simulation. The spatial
discretization is based on a spherical centroidal Voronoi tessellation which
offers a very effective high resolution mesh on the sphere for the order
parameter as well as other physically interesting variables such as the
supercurrent and the induced magnetic field. Various vortex configurations and
energy diagrams are computed.

CSCAMM WORKSHOP
Nonequilibrium Interface Dynamics: Tutorials

October 22 
NO SEMINAR SCHEDULED

CSCAMM WORKSHOP
Nonequilibrium Interface Dynamics: Fundamental Physical Issues in Nonequilibrium Interface Dynamics

October 29 
Carsten Carstensen, Institute for Applied Mathematics and Numerical Analysis at Vienna University of
Technology
Adaptive Finite Elements for
Relaxed Methods (FERM) in Computational
Microstructures
Nonconvex minimisation problems are encountered in many applications such as
phase transitions in solids (1) or liquids but also in optimal design tasks (2)
or micromagnetism (3). In contrast to rubbertype elastic materials and many
other variational problems in continuum mechanics, the minimal energy may be not
attained. In the sense of (Sobolev) functions, the nonrankone convex
minimisation problem ($M$) is illposed: As illustrated in the introduction of
FERM, the gradients of infimising sequences are enforced to develop finer and
finer oscillations called microstructures. Some macroscopic or effective
quantities, however, are wellposed and the target of an efficient numerical
treatment. The presentation proposes adaptive meshrefining algorithms for the
finite element method for the effective equations ($R$), i.e. the macroscopic
problem obtained from relaxation theory. For some class of convexified model
problems, a~priori and a~posteriori error control is available with an
reliabilityefficiency gap. Nevertheless, convergence of some adaptive finite
element schemes is guaranteed. Applications involve model situations for (1),
(2), and (3) where the relaxation is provided by a simple convexification.

CSCAMM WORKSHOP
Nonequilibrium Interface Dynamics: Hierarchical Modeling and Multiscale Simulation of Materials Interfaces

November 5 
Xiaoming Wang, Department of Mathematics at Iowa State University
Large Prandtl Number Behavior of the Boussinesq System
of RayleighBenard Convection
One of the useful models in the study of turbulent convection is
the socalled infinite Prandtl number model which is derived by formally
setting the Prandtl number equal to infinity in the Boussinesq
approximation of RayleighBenard convection. The model is particularly
relevant for fluids with large Prandtl number such as the earth's mantle,
silicone oil, and many gases under high pressure. In this talk I will
present a few results in the systematic study of the behavior of solutions
to the Boussinesq system at large Prandtl number. We first establish the
validity of the infinite Prandtl number model as an approximation of the
Boussinesq system at large Prandtl number on any finite but fixed time
interval. Such an approximation is singular involving an initial
transition layer. We then argue that individual trajectories of the
Boussinesq system are not expected to remain close to those of the
infinite Prandtl number model over a long period of time due to
instability. The validity of the infinite Prandtl number model over long
time interval is then studied in terms of the proximity of invariant
measures (stationary statistical solutions) and global attractors which
are commonly used in the study of long time behaviors. Finally we study
the long time behavior of the infinite Prandtl number model. Some
numerical issues will also be discussed.

November 12 
Alina Chertok, North Carolina State University
FiniteVolumeParticle Methods for Models of Transport of Pollutant in Shallow Water
Prediction of a pollution transport in flows is an important
problem in many industrial and environmental projects. Different
mathematical models are used to describe the propagation of the pollutant
and to obtain its accurate location and concentration.
We will consider
the flow modeled by the SaintVenant system of shallow water equations while
the pollutant propagation is described by a transport equation. Designing an
accurate, efficient and reliable numerical method for this model is a
challenging task: solutions are typically nonsmooth, they may contain both
nonlinear shock and rarefaction waves, and linear discontinuities in the
pollution concentration. Moreover, the interaction with a nonflat bottom may
result in very complicated wave structures and nontrivial equilibrium, which are
hard to preserve numerically. In addition, dry states (arising, for example,
in dam break problems) need special attention, since (even small) numerical
oscillations may lead to nonphysical negative values of the water depth
there.
I will present a new hybrid numerical method for computing the
transport of a passive pollutant by a flow. The idea behind the new
finitevolumeparticle method is to use different schemes for the flow and
pollution computations: the shallow water equations are numerically
integrated using a finitevolume scheme, while the transport equation is
solved by a particle method. This way the specific advantages of each scheme are
utilized at the right place. This results in a significantly enhanced
resolution of the computed solution.
This is joint work with A.
Kurganov and G. Petrova.

November 19 
Martin MeierSchellersheim, National Institute of Allergy and Infectious Diseases, NIH
Current Challenges in Computational Cell Biology
Although the wealth and complexity of phenomena in cell biology have raised considerable interest among
theorists the impact of theoretical work on scientific progress in this discipline has been very limited.
I want to discuss two main challenges theorists face when entering the world of biological phenomena: First,
many of the scientific procedures and tools which have proven very useful in the physical sciences and
other classical disciplines of applied mathematics fail or do not yet exist in computational biology. For
example do most biological systems not yield themselves readily to rigorous reductionism. On the other
hand are approaches to solve the problem of biological complexity through the development of effective
theories (akin to the transition from mechanics to statistical mechanics and finally thermodynamics)
still missing. The second challenge results from the difficulty of information exchange between biologists
and theorists. Scientists with theoretical background frequently lack the biological knowledge needed to
understand the work of experimentalists while biologists are not trained in presenting their research in
abstract terms.The modeling and simulation software we are currently developing is an attempt to address
some of these problems. It allows its users (mainly biologists) to define molecular properties and mechanisms
of cellular behavior in much biological detail through a graphical interface. It then transforms the biological
models into a format which makes it possible to analyze the structural properties of the model or to simulate
the model system by numerically integrating reactiondiffusion equations.

Monday November 24 
Alex Mahalov, Department of Mathematics at Arizona State University
Global Regularity of the 3D NavierStokes Equations with Weakly Aligned Large Initial Vorticity
In this talk we review mathematical results on the
3D NavierStokes and Euler Equations with initial
data characterized by uniformly large vorticity.
We prove existence on infinite time intervals
of regular solutions to the 3D NavierStokes Equations
for a class of large initial data both in R3 and
bounded cylindrical domains; as well as long time
existence of smooth solutions for 3D incompressible
Euler Equations. There are no conditional assumptions
on the properties of solutions at later times,
nor are the global solutions close to some 2D manifold.
The approach is based on fast singular oscillating
limits, nonlinear averaging and cancellation of oscillations
in the nonlinear interactions for the vorticity field.
With nonlinear averaging methods in the context
of almost periodic functions, resonance conditions
and a nonstandard small divisor problem, we obtain
fully 3D limit resonant NavierStokes equations.
We establish global regularity of the latter without
any restriction on the size of 3D initial data and
with the help of strong convergence theorems bootstrap
this into the global regularity of the weak solutions
of 3D NavierStokes Equations with weakly aligned
uniformly large vorticity at t=0. For the 3D
incompressible Euler Equations with initial data
characterized by uniformly large vorticity which
induce large vortex stretching in bounded cylindrical
domains we prove existence on arbitrary large time
intervals of regular solutions with large kinetic
energy; the ratio of the large enstrophy to the large
kinetic energy is of order one.
Note Special Day: Monday November 24

December 3 
Dmitry Chalikov, ESSIC at University of Maryland
Precise Numerical Scheme and longterm
Integration the Principal Equations for
Potential Flow with a Free Surface
A method for numerical investigation of nonlinear wave dynamics based on direct
hydrodynamical modeling of 1D potential periodic surface waves is developed. By
a nonstationary conformal mapping, the principal equations are rewritten in a
surfacefollowing coordinate system and reduced to two simple evolutionary
equations for the elevation and the velocity potential of the surface; Fourier
expansion is used to approximate these equations. High accuracy of the method is
confirmed (i) by control of main integral invariants, (ii) by validation of the
nonstationary model against stationary solutions (Stokes? Crappers? and
gravitycapillary waves in a moving coordinate system) and (ii) by comparison
between the results obtained with different resolution in the horizontal. A
number of longterm simulations of gravity, gravitycapillary and pure capillary
waves with various initial conditions, were performed; for the simulated wave
fields, distribution of energy and phase speed over full spectra were analysed.
Numerical experiments with initially monochromatic waves with different
steepness show that the model is able to simulate breaking conditions when the
surface becomes a multivalued function of the horizontal coordinate; an
estimate of the critical initial wave height that divides between nonbreaking
and eventually breaking waves is obtained. Simulations of nonlinear evolution of
a wave field represented initially by two modes with close wave numbers
(amplitude modulation) and a wave field with a phase modulation both result in
appearance of large and very steep waves, which also break if the initial
amplitudes are sufficiently large. The method developed may be applied to a
broad range of problems where the assumption of one dimensionality is
acceptable. The problem of numerical simulation of 2D potential and 3D
nonpotential waves options is also briefly discussed.

December 10 
Alexis Vasseur, Department of Mathematics at University of Texas at Austin
Motion of Particles in a Fluid: an Asymptotic Problem
We modelize the motion of particles in a fluid as the coupling of a fluid equation and a FokkerPlanck
type kinetic equation. This system takes into account both the
Brownian effect and the interactions between the
fluid and the particles. Such system is very costly in a numerical point of view. We investigate how we can
derive a simpler model and show mathematically the convergence from the previous model to the
simpler one.
