Poster Presenters: will be updated as information is received

| A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

A

Computer modeling of microtubules and ion channels in touch receptor neurons of C. elegans

D

Symplectic integration for parallel particle methods

E

Computational Fluid Dynamics on Streaming Processors

J

Discrete Variational Mechanics for Elastic Rods

K

O

Discrete Mechanics and Optimal Control: Its place in the optimal control context and specific properties

Abstract: In order to solve optimal control problems for mechanical systems, the method "Discrete Mechanics and Optimal Control (DMOC)" links the theory of optimal control with concepts from variational mechanics. This poster places the discrete variational approach of DMOC within the context of optimal control theory and compares its strategy to existing solution methods. Additionally, specific properties of DMOC are described that partly arise from the variational approach: The application of discrete variational principles allows for the construction of an optimization algorithm that enables the discrete solution to inherit characteristic structural properties from the continuous problem such as the preservation of the total angular momentum of a falling cat. Furthermore, the order of approximation of the discrete problem to the continuous one is investigated: Due to the symplecticity of the DMOC approach the discretization for the adjoint system, that provides necessary optimality conditions for the optimal control problem, is of the same order as for the state system. Finally, convergence of DMOC can be shown, that is solutions of the discrete optimal control problem converge to solutions of the continuous optimal control problem.

R

A DG-based immersed boundary method

S

Variational Implicit-Explicit Integrators: Multiple Time Scales without Resonance Instability
(Joint work with Eitan Grinspun)

S

Finding Most Probable Transition by Freidlin-Wentzell Theory

Abstract: Freidlin-Wentzell Theory gives probability density of solutions to stochastic dynamical system. If a chemical reaction is modeled as Langevin equation, the most probable reaction trajectory could be obtained by maximizing the conditional probability density, which is equivalent to minimizing the Freidlin-Wentzell rate functional with boundary conditions on configurations. When the potential is quadratic, this variational problem could be solved analytically. One interesting result is on inertia effect, namely that optimal trajectory changes as mass varies. A discrete Freidlin-Wentzell theory is also proposed for solving more generic cases numerically.

As another example of inertia effect, Freidlin-Wentzell Theory also suggests the preference of Channel1 and Channel2 over Channel3 in a Langevin setting of triatomic Morse cluster isomerization reaction, while similar result in a Hamiltonian setting was shown by Yanao et al.

W

Störmer Verlet for Constrained Langevin Equations

Abstract: Langevin type equations are employed in a vast array of applications within the fields of biology, chemistry, physics, and various other fields. Störmer Verlet is a type of integrator that possesses desirable key traits, such as simplicity in implementation, reversibility with respect to time, and the ability to produces results without numerical drift. The extension of Störmer Verlet to the context where Langevin type dynamics are appropriate, is the focus of this study. A Störmer Verlet integrator that is also conformally symplectic and developed from a variational principle, is introduced in this work. This integrator, tailored specifically for constrained Langevin dynamics, admits a convergence of second order in the weak sense, and three-halves in the strong sense. The usefulness of this novel Störmer Verlet integrator, is exhibited through its performance.

Y

Dimension Reduction for Conformational Dynamics of Clusters and Biopolymers