Everyone interested in the theme of this workshop is welcome to attend with or without a contributed poster presentation.
If you would like to present a poster, send the title and abstract to hliu@iastate.edu.
( Chiu-Yen Kao* and Fadil Santosa, IMA)
Optimization of the quality factor of an acoustic resonator
Resonance is a solution to the time-dependent wave equation which is spatially localized while its time dependence is harmonic except for decay due to radiation. Such a solution occurs in a medium that is inhomogeneous. In this work, the problem of designing a resonator which has low losses (high quality factor) is considered. High quality resonators are desirable in a variety of applications, including photonic bandgap devices. Finding resonance in a linear wave equation involves solving a nonlinear eigenvalue problem. The magnitude of the ratio between real and imaginary part of the eigenvalue is proportional to the quality factor. The optimization we perform is finding a structure which possesses an eigenvalue with largest possible magnitude of the ratio. The challenges in this problem are that (i) it is large, (ii) it is highly nonlinear. We present a numerical approach for solving this problem. The method consists of first finding a resonance eigenvalue for a non-optimal structure. The gradient for the magnitude of the ratio is calculated. Ascent steps are taken in order to increase the magnitude of the ratio. We demonstrate how this approach can be implemented and present numerical examples of optimal structures.
( Ajith Gunaratne* and Zhijun Wu, Department of Mathematics & Program on Bioinformatics and Computational Biology, Iowa State University)
A Penalty Function Method for Constrained Molecular Dynamics Simulation
A penalty function method for constrained molecular dynamics simulation is proposed and applied to systems with distance constraints. The penalty parameter is increased gradually as the simulation proceeds. The constraints are thus enforced progressively as the system moves toward its equilibrium. The algorithm is tested on molecular clusters and small proteins. Results are presented and discussed.
(Maozhi Li and Jim Evans, Iowa State University )
MOUND FORMATION IN UNSTABLE MULTILAYER THIN FILM GROWTH:
EXACT EVOLUTION EQUATIONS FROM STEP DYNAMICS MODELS
In homoepitaxial film growth, deposited atoms initially aggregate into 2D islands. Downward transport of atoms subsequently deposited on top of these islands is often inhibited. This results in unstable film growth characterized by the formation of mounds (multilayer stacks of 2D islands). Local relaxation processes associated with the dynamics of deposition near step edges result in selection of the slopes of the mound sides. This process has been described by atomistic simulations [1], and also by phenomenological continuum equations for evolution of the film height, h [2]. The latter fail to exactly describe such features as slope selection. Thus, we derive an exact continuum evolution equation for h with appropriate boundary conditions starting from a step dynamics model (sharp moving steps separating discrete layers).
[1] PRB 65 (2002) 193407; PRL 75 (1995) 4250; [2] PRL 81 (1998) 5481.
( Dajiang Liu* and Jim Evans, Ames Laboratory USDOE and Iowa State University )
FROM ATOMIC SCALE ORDERING TO MESOSCALE PATTERNS IN SURFACE REACTION-DIFFUSION SYSTEMS: HCLG MULTISCALE SIMULATION APPROACH
The rich variety of spatiotemporal patterns observed in reactions on flat single-crystal surfaces is typically described by mean-field reaction-diffusion equations. These assume reaction kinetics corresponding to well-stirred adsorbed reactants and a simplistic description of surface diffusion. In reality, ordering or islanding of reactants invalidates this mean-field description of kinetics, and diffusion is non-trivial (each reactant must diffuse percolatively through a complex disordered environment created by the co-reactants). We have developed a Heterogeneous Coupled Lattice-Gas (HCLG) simulation approach to connect a realistic atomistic description of reactant ordering, diffusion and reaction kinetics to mesoscale reaction-diffusion front propagation phenomena [1].
[1] J CHEM PHYS 103 (1995) 10277; PRB 70 (2004) 193408; SIAM MMS 4 (2005) 424.
( Hailiang Liu and Zhongming Wang* Iowa State Univeristy)
Computing Multi-valued Velocity and Electrical Fields in Euler-Poisson Equations
We develop a level set method for the computation of multi-valued velocity and electric fields of one-dimensional Euler-Poisson equations. The system of these equations arises in the semi-classical approximation of Schr\"{o}dinger-Poisson equations and the semiconductor modeling. This method uses an implicit Eulerian formulation in an extended space --- called field space, which incorporates both velocity and electric fields into the configuration space. Multi-valued velocity and electric fields are captured through common zeros of two level set functions, which solve a linear homogeneous transport equation in the field space. Numerical examples are presented to validate the proposed level set method.
( Brian Moore, University of Iowa)
Multi-Symplectic Integration for Linear PDEs
Excellent long-time simulation is one major reason for using symplectic integrators to numerically solve Hamiltonian systems. Thus, a natural question arises. What are the merits in numerically preserving the spatial symplectic structure of a Hamiltonian PDE? The idea of multi-symplectic integration is to preserve the symplectic structure of a Hamiltonian PDE in both space and time, and the purpose of this poster is to present the theory behind such methods for linear PDEs. In this context, one is able to consider numerical dispersion relations which completely describe the numerical solution behavior, and recent results suggest that important aspects of the exact solution behavior may be lost if the symplectic structure in space is not also preserved. In particular, we present a class of methods that preserve the sign of the group velocity, a property not necessarily held by other non-symplectic schemes.
( Peter Vedell* and Zhijun Wu, Department of Mathematics & Program on Bioinformatics and Computational Biology, Iowa State University)
Shooting Methods for the Solution of the Boundary-Value Problems in Molecular Dynamics Simulation
Boundary-value problems in molecular dynamics simulation are introduced. Applications to the study of transition of protein conformation including protein folding are
described. Methods for the solution of the problems based on multiple shooting are proposed. Results from simulation of conformational transitions of molecular clusters
and protein polypeptides are presented.