1. Date of download: 6/3/2016 Copyright © ASME. All rights reserved. From: Stochastic Simulations With Graphics Hardware: Characterization of Accuracy and Performance J. Comput. Inf. Sci. Eng. 2010;10(1):011010-011010-11. doi:10.1115/1.3270248 Conceptual map of the GPU rendering pipeline. The three main stages are physically represented in the center of the figure while examples of their memory models (scatter and gather) are shown at the bottom. Figure Legend:

2. Date of download: 6/3/2016 Copyright © ASME. All rights reserved. From: Stochastic Simulations With Graphics Hardware: Characterization of Accuracy and Performance J. Comput. Inf. Sci. Eng. 2010;10(1):011010-011010-11. doi:10.1115/1.3270248 Calculate z=dx/dt+y using the postprocessing stage. The green squares in the figure are inputs to the program and the orange squares are the outputs. Figure Legend:

3. Date of download: 6/3/2016 Copyright © ASME. All rights reserved. From: Stochastic Simulations With Graphics Hardware: Characterization of Accuracy and Performance J. Comput. Inf. Sci. Eng. 2010;10(1):011010-011010-11. doi:10.1115/1.3270248 Three user-defined programs chained together to implement the velocity Verlet integrator in the postprocessing stage of the GPU Figure Legend:

4. Date of download: 6/3/2016 Copyright © ASME. All rights reserved. From: Stochastic Simulations With Graphics Hardware: Characterization of Accuracy and Performance J. Comput. Inf. Sci. Eng. 2010;10(1):011010-011010-11. doi:10.1115/1.3270248 Log linear plot of normalized energy (ESimulated/ETheoretical) and normalized diffusion constant (DSimulated/DTheoreitcal) against time-step (δt) for an ensemble of 30 glass particles with radius 500 nm suspended in a water bath at 293 K. This data in this plot is used to pick the parameters for the full simulation with 900 particles. Figure Legend:

5. Date of download: 6/3/2016 Copyright © ASME. All rights reserved. From: Stochastic Simulations With Graphics Hardware: Characterization of Accuracy and Performance J. Comput. Inf. Sci. Eng. 2010;10(1):011010-011010-11. doi:10.1115/1.3270248 Log-log plot of the average particle displacement after 1×106 time-steps at δt=0.01τ as a function of particle diameter from Eq.. The gray region shows the effect of ±10% error in the diffusion constant. Smaller particles exhibit larger excursions from their initial positions as a function of particle diameter; however, the average displacement is no larger than 1/10×d for the finite-time simulation. Figure Legend:

6. Date of download: 6/3/2016 Copyright © ASME. All rights reserved. From: Stochastic Simulations With Graphics Hardware: Characterization of Accuracy and Performance J. Comput. Inf. Sci. Eng. 2010;10(1):011010-011010-11. doi:10.1115/1.3270248 Speedup (calculated as the ratio of the GPU simulation time over single-precision CPU simulation time) as a function of the ensemble size. The three curves show the results when the output was sampled after every 10, 100, and 500 simulation time-steps (δt). Figure Legend: