Brown University
Joint Materials/Solid Mechanics Seminar Series
Abstract: Mechanical deformation can be used to induce critical changes in the structure of materials, thereby coupling the mechanical state to the functional behavior and properties of the macrostructure. By investigating such processes at the length and force scales of atomistic/molecular deformation, we can understand the physical basis of such mechanical coupling. This knowledge can be applied toward both the prevention of undesirable material changes - such as the uncontrolled nucleation of defects in an electromagnetic structure - and the exploitation of mechanical coupling for sensing, actuating, and transduction of mechanical signals - such as in the evolution of phenotype in living cells.
Here, we will discuss the development of an atomistic defect nucleation criterion, through the use of nanomechanical experiments, simple models and ophisticated simulations, and what this tells us about the integrity and performance of evershrinking films and lines in integrated circuits. We will also discuss how nanoscale mechanical stimuli can be used to induce and to measure changes in cell function.
A B C
A. Nanoindentation-induced nucleation of a dislocation
dipole (circle) in a 2D bubble raft model of a metallic
crystal.
B. Molecular dynamics simulation of nanoindentation in
3D Cu shows heterogeneous nucleation of prismatic loops.
C. Atomic force microscopy of a living endothelial cell
shows subsurface cytoskeletal proteins and surface-
localized molecules.
Special Joint LCDS & PDE Seminar
***Please Note Special Day, Time and Place for This Week Only |
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: Now that full genomes have been sequenced for a variety of species, one question being asked by researchers is the extent to which we may be able to reconstruct ancestral genomes that no longer exist in nature. This leads to questions about which subset of present-day species would be most informative about a particular ancestor. We address a simple 3-species example using information theory and find results that are quite surprising and counter-intuitive. One consequence of these results is that correlated data is sometimes more informative than independent data.
Brown Analysis Seminar
Brown University, Division of Applied Mathematics Dissertation Defense
Applied Mathematics Colloquium
Abstract: Certain conservation laws of ideal fluids prohibit topological change of tangled vortex lines in the absence of singularities. In real fluids this change is quite common and occurs without singularities. I will present some calculations and some mathematical thoughts related to the subject.
Scientific Computing Seminar
Abstract: A new parallel computer code called SEL has been developed for modeling magnetically confined plasmas, using advanced computational methods. The code is designed to solve systems of fluid equations with multiple length and time scales and the high degrees of anisotropy characteristic of fusion plasmas. Spatial discretization uses high-order spectral elements on a logically rectangular grid.
In collaboration with mathematician Vladimir Liseikin of Novosibirsk, Russia, a new method of adaptive grid generation is being developed to align the grid with the evolving magnetic field and pack it normal to magnetic flux surfaces to resolve regions of sharp gradients. The time advance is fully implicit, allowing for efficient, accurate treatment of multiple time scales and strong flow. Large, sparse nonlinear systems are preconditioned with static condensation, unique to the spectral element method, then solved by Newton-Krylov methods with the PETSc library to achieve efficient parallel operation. There is a clean separation between sections of code specifying the physics from methods of dicretization and solution.
Application are being developed to magnetic reconnection in laboratory and space plasmas and to modeling the turbulent plasma in the pedestal and scrape-off regions at the edge of a tokamak fusion reactor.
PDE Seminar
Department of Mathematics Colloquium
Abstract: I will present new work with Sylvia Serfaty. The main focus is motion by curvature in two space dimensions. The level-set formulation of this interface evolution law is a degenerate parabolic equation. We show it can be interpreted as the value function of a deterministic two-person game. More precisely, we give a family of discrete-time, two-person games whose value functions converge in the continuous-time limit to the solution of the motion-by-curvature PDE. This result is unexpected, because the value function of a deterministic control problem is normally a first-order Hamilton-Jacobi equation.
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