### Dallas R. Trinkle

#### Research Group

## Stochastic / Statistical Methods

Stochastic-based methods—both **Bayesian** statistics and **kinetic Monte Carlo** techniques—provide powerful techniques for integrating over variability in models, and extending time-scales of DFT or classical potential approaches.

### Bayesian statistics

Given a mathematical model to describe a set of data (experimental measurements, or even other computational predictions), an **ensemble** of model parameters can be found that describe that model description of the data. This ensemble of parameters give models that reproduce the data “similarly well,” and the ensemble also gives a variance of model predictions. This variance is an estimate of the error *in the absence* of experimental validation.

### Kinetic Monte Carlo

Rather than integrating time forward with equally spaced steps—as in molecular dynamics—we can evolve time forward from state to state, provided we can (a) enumerate the possible transitions from a given state, and (b) find the individual rates for each transition in a computationally efficient way. We use methods, such as **dimer search** and **nudged elastic-band method** with DFT and atomistics to find states, transitions, and energy barriers.

#### Publications

- “Mechanism of a prototypical synthetic membrane-active antimicrobial: Efficient hole-punching via interaction with negative intrinsic curvature lipids”

L. Yang, V. D. Gordon, D. R. Trinkle, N. W. Schmidt, A. Davis, C. DeVries, A. Som, J. E. Cronan, Jr., G. N. Tew, G. C. L. Wong.*Proc. Nat. Acad. Sci.***105**, 20595 (2008): publication, PDF, doi - “Contribution to size effect of yield strength from the stochastics of dislocation source lengths in finite samples”

T. A. Parthasarathy, S. I. Rao, D. M. Dimiduk, M. D. Uchic and D. R. Trinkle.*Scripta Mater.***56**, 313-316 (2007): publication, PDF, doi

This work in collaboration with Yuguo Chen, UIUC Statistics.