## Nucleation Studies on Graphics Processing Units

Johannes Gutenberg-Universitat Mainz

Johannes Gutenberg-Universitat Mainz, 2014

@article{block2014nucleation,

title={Nucleation studies on graphics processing units},

author={Block, Benjamin J},

year={2014}

}

A system in a metastable state needs to overcome a certain free energy barrier to form a droplet of the stable phase. Standard treatments assume spherical droplets, but this is not appropriate in the presence of an anisotropy, such as for crystals. The anisotropy of the system has a strong effect on their surface free energies at low temperatures, while this effect is less important above the roughening transition temperature T_R . A simple model that features such an anisotropy is the Ising model. We perform large scale simulations of the Ising model to overcome finite-size effects and statistical inaccuracies. The scale of the simulations that are needed to produce meaningful results led us to the development of a versatile and scalable simulation code which can be used across different parallel computation devices such as graphics processing units (GPUs). Platform independence is achieved through abstract interfaces that hide platform specific implementation details. We prepare a system geometry that allows for the investigation of a flat interface with a tunable angle to the crystal plane, which touches an external wall. The contact angle Theta can be adjusted via a surface field H. A differential equation describing the behavior of the surface free energy in the presence of anisotropy for our system is discussed. Combined with thermodynamic integration methods, this equation is used to integrate the anisotropic surface tension over a large range of temperatures from well below T_R up to the vicinity of the bulk critical temperature T_C and is compared with prior predictions. Comparison with previous measurements in different geometries and with different methods shows good agreement and accuracy, which is achieved especially through the ability to simulate much larger systems than was possible in previous studies. The temperature dependence of the surface stiffness k above T_R is extracted by measuring the curvature of the surface free energy near Theta=90 degrees. This measurement is comparable to the simulation data obtained in the literature and is in fact in better agreement with theoretical predictions regarding the scaling behavior of k. We develop a low temperature model to explain the small angle behavior of the system far below T_R , where the angle stays virtually zero up to a critical field H C , which only has a small system size dependency. When this critical field is overcome, the angle increases rapidly. H C is linked to the Step Free Energy, which allows us to to analyze the critical behavior of this quantity. The effect of the hard wall has to be incorporated into the investigation. By comparing free energies at different system sizes, we are able to extract the free energy contribution of the contact line as a function of Theta. The temperature dependence is investigated by repeating this analysis at different temperatures. In the last chapter, a parametric simulation of 2D flow phenomena is accelerated using GPUs which can be used to simulate dynamics e.g. in the atmosphere. In particular we implement a parallel Evolution Galerkin operator and obtain a significant speedup in comparison to a serial implementation.

February 6, 2015 by hgpu