Far-field approximation for hydrodynamic interactions in parallel-wall geometry

A complete analysis is presented for the far-field creeping flow produced by a multipolar force distribution in a fluid confined between two parallel planar walls. We show that at distances larger than several wall separations the flow field assumes the Hele-Shaw form, i.e., it is parallel to the walls and varies quadratically in the transverse direction. The associated pressure field is a two-dimensional harmonic function that is characterized by the same multipolar number m as the original force multipole. Using these results we derive asymptotic expressions for the Green's matrix that represents Stokes flow in the wall-bounded fluid in terms of a multipolar spherical basis. This Green's matrix plays a central role in our recently proposed algorithm [Physica A xx, {\bf xxx} (2005)] for evaluating many-body hydrodynamic interactions in a suspension of spherical particles in the parallel-wall geometry. Implementation of our asymptotic expressions in this algorithm increases its efficiency substantially because the numerically expensive evaluation of the exact matrix elements is needed only for the neighboring particles. Our asymptotic analysis will also be useful in developing hydrodynamic algorithms for wall-bounded periodic systems and implementing acceleration methods by using corresponding results for the two-dimensional scalar potential.Comment: 28 pages 5 figure

Calculation of the free energy of crystalline solids

The prediction of the packing of molecules into crystalline phases is a key step in understanding the properties of solids. Of particular interest is the phenomenon of polymorphism, which refers to the ability of one compound to form crystals with different structures, which have identical chemical properties, but whose physical properties may vary tremendously. Consequently the control of the polymorphic behavior of a compound is of scientific interest and also of immense industrial importance. Over the last decades there has been growing interest in the development of crystal structure prediction algorithms as a complement and guide to experimental screenings for polymorphs. The majority of existing crystal structure prediction methodologies is based on the minimization of the static lattice energy. Building on recent advances, such approaches have proved increasingly successful in identifying experimentally observed crystals of organic compounds. However, they do not always predict satisfactorily the relative stability among the many predicted structures they generate. This can partly be attributed to the fact that temperature effects are not accounted for in static calculations. Furthermore, existing approaches are not applicable to enantiotropic crystals, in which relative stability is a function of temperature. In this thesis, a method for the calculation of the free energy of crystals is developed with the aim to address these issues. To ensure reliable predictions, it is essential to adopt highly accurate molecular models and to carry out an exhaustive search for putative structures. In view of these requirements, the harmonic approximation in lattice dynamics offers a good balance between accuracy and efficiency. In the models adopted, the intra-molecular interactions are calculated using quantum mechanical techniques; the electrostatic inter-molecular interactions are modeled using an ab-initio derived multipole expansion; a semi-empirical potential is used for the repulsion/dispersion interactions. Rapidly convergent expressions for the calculation of the conditionally and poorly convergent series that arise in the electrostatic model are derived based on the Ewald summation method. Using the proposed approach, the phonon frequencies of argon are predicted successfully using a simple model. With a more detailed model, the effects of temperature on the predicted lattice energy landscapes of imidazole and tetracyanoethylene are investigated. The experimental structure of imidazole is Abstract | ii correctly predicted to be the most stable structure up to the melting point. The phase transition that has been reported between the two known polymorphs of tetracyanoethylene is also observed computationally. Furthermore, the predicted phonon frequencies of the monoclinic form of tetracyanoethylene are in good agreement with experimental data. The potential to extend the approach to predict the effect of temperature on crystal structure by minimizing the free energy is also investigated in the case of argon, with very encouraging results.Open Acces

Nanostructure Modeling in Oxide Ceramics Using Large Scale Parallel Molecular Dynamics Simulations.

The purpose of this dissertation is to investigate the properties and processes in nanostructured oxide ceramics using molecular-dynamics (MD) simulations. These simulations are based on realistic interatomic potentials and require scalable and portable multiresolution algorithms implemented on parallel computers. The dynamics of oxidation of aluminum nanoclusters is studied with a MD scheme that can simultaneously treat metallic and oxide systems. Dynamic charge transfer between anions and cations which gives rise to a compute-intensive Coulomb interaction, is treated by the O(N) Fast Multipole Method. Structural and dynamical correlations and local stresses reveal significant charge transfer and stress variations which cause rapid diffusion of Al and O on the nanocluster surface. At a constant temperature, the formation of an amorphous surface-oxide layer is observed during the first 100 picoseconds. Subsequent sharp decrease in O diffusion normal to the cluster surface arrests the growth of the oxide layer with a saturation thickness of 4 nanometers; this is in excellent agreement with experiments. Analyses of the oxide scale reveal significant charge transfer and variations in local structure. When the heat is not extracted from the cluster, the oxidizing reaction becomes explosive. Sintering, structural correlations, vibrational properties, and mechanical behavior of nanophase silica glasses are also studied using the MD approach based on an empirical interatomic potential that consists of both two and three-body interactions. Nanophase silica glasses with densities ranging from 76 to 93% of the bulk glass density are obtained using an isothermal-isobaric MD approach. During the sintering process, the pore sizes and distribution change without any discernable change in the pore morphology. The height and position of the first sharp diffraction peak (the signature of intermediate-range order) in the neutron static structure factor shows significant differences in the nanophase glasses relative to the bulk silica glass. Enhancement of the low-energy vibrational modes is observed. The effect of densification on mechanical properties is also examined

A fluctuating boundary integral method for Brownian suspensions

We present a fluctuating boundary integral method (FBIM) for overdamped Brownian Dynamics (BD) of two-dimensional periodic suspensions of rigid particles of complex shape immersed in a Stokes fluid. We develop a novel approach for generating Brownian displacements that arise in response to the thermal fluctuations in the fluid. Our approach relies on a first-kind boundary integral formulation of a mobility problem in which a random surface velocity is prescribed on the particle surface, with zero mean and covariance proportional to the Green's function for Stokes flow (Stokeslet). This approach yields an algorithm that scales linearly in the number of particles for both deterministic and stochastic dynamics, handles particles of complex shape, achieves high order of accuracy, and can be generalized to three dimensions and other boundary conditions. We show that Brownian displacements generated by our method obey the discrete fluctuation-dissipation balance relation (DFDB). Based on a recently-developed Positively Split Ewald method [A. M. Fiore, F. Balboa Usabiaga, A. Donev and J. W. Swan, J. Chem. Phys., 146, 124116, 2017], near-field contributions to the Brownian displacements are efficiently approximated by iterative methods in real space, while far-field contributions are rapidly generated by fast Fourier-space methods based on fluctuating hydrodynamics. FBIM provides the key ingredient for time integration of the overdamped Langevin equations for Brownian suspensions of rigid particles. We demonstrate that FBIM obeys DFDB by performing equilibrium BD simulations of suspensions of starfish-shaped bodies using a random finite difference temporal integrator.Comment: Submitted to J. Comp. Phy

Scalable parallel molecular dynamics algorithms for organic systems

A scalable parallel algorithm, Macro-Molecular Dynamics (MMD), has been developed for large-scale molecular dynamics simulations of organic macromolecules, based on space-time multi-resolution techniques and dynamic management of distributed lists. The algorithm also includes the calculation of long range forces using Fast Multipole Method (FMM). FMM is based on the octree data structure, in which each parent cell is divided into 8 child cells and this division continues until the cell size is equal to the non-bonded interaction cutoff length. Due to constant number of operations performed at each stage of the octree, the FMM algorithm scales as O(N). Design and analysis of MMD and FMM algorithms are presented. Scalability tests are performed on three tera-flop machines: 1024-processor Intel Xeon-based Linux cluster, SuperMike at LSU, 1184-processor IBM SP4 Marcellus and the 512-processor Compaq AlphaServer Emerald at the U.S. Army Engineer Research and Development Center (ERDC) MSRC. The tests show that the Linux cluster outperforms the SP4 for the MMD application. The tests also show significant effects of memory- and cache-sharing on the performance

Particle motion between parallel walls: Hydrodynamics and simulation

The low-Reynolds-number motion of a single spherical particle between parallel walls is determined from the exact reflection of the velocity field generated by multipoles of the force density on the particle’s surface. A grand mobility tensor is constructed and couples these force multipoles to moments of the velocity field in the fluid surrounding the particle. Every element of the grand mobility tensor is a finite, ordered sum of inverse powers of the distance between the walls. These new expressions are used in a set of Stokesian dynamics simulations to calculate the translational and rotational velocities of a particle settling between parallel walls and the Brownian drift force on a particle diffusing between the walls. The Einstein correction to the Newtonian viscosity of a dilute suspension that accounts for the change in stress distribution due to the presence of the channel walls is determined. It is proposed how the method and results can be extended to computations involving many particles and periodic simulations of suspensions in confined geometries