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Atomistic Visualization: On-the-fly Data Extraction and Rendering

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Atomistic Visualization: On-the-fly Data Extraction and Rendering

DipeshBhattarai

Dr. Bijaya B. Karki

Department of Computer Science

Louisiana State University

ACMSE 2007: The 45th ACM Southeast ConferenceWinston-Salem, North Carolina, USA March 23-24, 2007

- Atomistic Visualization and Molecular Visualization
- Steps in Atomistic Visualization
- Radial Distribution Function (RDF)
- Coordination Environment
- Diffusion
- Implementation and Outputs
- Conclusion

- A molecule can be most properly defined as a group of atoms joined in a specific structure. (Answers.com)
- The difference: a specific structure

- Molecular Visualization: visualization of molecular structure
- Atomistic Visualization: visualization of atomic structure
- We are working in Atomistic Visualization within the context of Earth Minerals.

Source: Protein Data Bank

Connectivity information is implicitly assumed in a molecule.

- Atomistic Visualization
- Dataset contains information about atoms only
- In the context of earth minerals, there are two kind of minerals of interest: Crystal Minerals and Liquid Minerals
- Crystals Minerals
- discrete and deterministic
- are easier to visualize and are very structured.

- Liquids
- Probabilistic
- harder to visualize.
- Structure of the liquid has to be inferred from various other analytical data
- Inferring structure of a liquid has been one of the very old problems.

- Three types of structures:
- short range structure
- medium range structure, and
- long range structure

- Liquids lack in long range structure
- Medium range structures contain many interesting features.
- Our focus:
- short range structure and diffusion characteristics.

- We felt a need to integrate analysis with visualization
- Providing analytical results and visualization capability in one place enhances the capability to understand the dataset.

- Computation of Radial Distribution Functions (RDFs)
- Computation of Critical Distance from RDFs
- Use of those critical distances to calculate structural properties of the system
- Compute Covariance Matrix for each atom, and find their eigenvalues and eigenvectors

Radial Distribution Function (RDF)

- Gives the radial distribution of atoms around each other
- Total RDF
- Distribution of the atoms irrespective of type of atoms

- Partial RDF
- Distribution of certain type of atoms around another type of atoms

- Computation is time consuming:
- computed only once at the beginning

Coordination Environment

- Coordination Environment is the distribution of atoms around each other
- Gives us the local structure of the system around atoms
- Consists of a specific set of atoms
- Number of atoms in CE is the major characteristics we are looking for

- Varies with the cut-off distance that is used for the computation
- Cut-off distances from RDF are significant

Coordination Environment (contd…)

Formulation:

Total Coordination Number:

Set of all the atoms that coordinated with atom i in the time period T

Partial Coordination Number: Coordination number of atoms of type α with respect to atoms of type β

Set of all the atoms of type β that coordinated with atom i of type α over the time period T

Stability of the coordination environment

A coordination environment exists only when all the bonds forming the environment exist simultaneously.

Coordination Environment (contd…)

- In some systems, the coordination environment can be represented as convex hull with the coordinating atoms forming the vertices of the surface
- For example: In a Magnesium Silicate system, Silicon-Oxygen coordination can be represented as a tetrahedron

- Problem: not generalizable to all the systems
- This is specially true for a liquid mineral system
- continuous coordination environments
- do not result regular polyhedral hull

Coordination Environment (contd…)

- Non-unique Convex hulls
- Even when number of coordinated atoms are same, their polyhedral representation can vary according to their spatial distribution.

- Even when we construct a convex hull for n atoms, it is not guaranteed that the resulting convex hull will contain n vertices.
- This can happen when some of the atoms fall within the convex hull

- Computed polyhedra are color coded to represent the coordination number the polyhedra represent

Covariance Matrix:

- Covariance Matrices are computed for each atom in the system
- 3x3 square matrix has three eigenvalues and three eigenvector
- Covariance Matrix is Positive Semi-definite, so its eigenvalues are non-negative
- Ellipsoid is used to visualize the covariance matrix
- Three Eigenvalues are used as the length of three axes of the ellipsoid
- Three eigenvectors are normalized and are used to orient the ellipsoid giving the direction of diffusion

(left) spherical representation of diffusion of individual atom over the time T

(right) ellipsoidal representation of diffusion of individual atom over the time T

- Spherical representation that we used earlier failed to capture the anisotropy in the atomic movement
- Ellipsoidal representation captures that anisotropy effectively

- Graphics Libraries: OpenGL, GLUT, and GLUI
- For rendering, event handling and user interface

- Other Libraries:
- Matlab
- For eigenvalue, eigenvector calculation

- Qhull
- For convex hull computation

- Matlab
- Programming Language: C++

Coordination environmnet of Silicon(blue) atoms with respect to Oxygen (greenish) atoms: (left) number of outgoing lines from the Silicon atoms gives the coordination number of the atom, (middle) the coordination number if encoded in the Silicon atom and the bond-length between Silicon and Oxygen at also encoded, (right) stability of the coordination environment of Silicon atoms are encoded in the size of the sphere and stability of bond between Silicon and Oxygen are encoded in the width of the bond. Bonds are color-coded similar to the middle figure.

Polyhedral representation of Si-O coordination magnesium silicate liquid. The color and shapes of the polyhedra give the coordination numbers. Red spheres at the corners are Oxygen atoms involved in coordination. The size of the spheres represents the fraction of time the atom is coordinated to the Si atom, and the intensity of the polyhedral color encodes the stability of the coordination.

Polyhedral representation of Silicon and Oxygen coordination in a Magnesium Silicate (MgSiO3) system.

Even simple color coding become effective in showing the spatial distribution of Si-O coordination environment

Diffusion ellipsoids for Magnesium Oxide system at 3000 K temperature (left) and the same system at 7000 K temperature (right)

Both the system contained 64 atoms (32 Magnesium Atoms and 32 Oxygen atoms)

Future Works

- Improving the quality of rendering
- Removing dependencies on external libraries that are not freely available
- Creating a complete application for atomistic visualization targeting Earth mineral scientists
Conclusion

- Integration of Analysis with Visualization is effective
- Atomistic visualization is interesting and still has challenging problems