Mesoscale fluid simulation with the Lattice Boltzmann method

PhDThis thesis describes investigations of several complex fluid effects., including hydrodynamic spinodal decomposition, viscous instability. and self-assembly of a cubic surfactant phase, by simulating them with a lattice Boltzmann computational model. The introduction describes what is meant by the term "complex fluid", and why such fluids are both important and difficult to understand. A key feature of complex fluids is that their behaviour spans length and time scales. The lattice Boltzmann method is presented as a modelling technique which sits at a "mesoscale" level intermediate between coarse-grained and fine-grained detail, and which is therefore ideal for modelling certain classes of complex fluids. The following chapters describe simulations which have been performed using this technique, in two and three dimensions. Chapter 2 presents an investigation into the separation of a mixture of two fluids. This process is found to involve several physical mechanisms at different stages. The simulated behaviour is found to be in good agreement with existing theory, and a curious effect, due to multiple competing mechanisms, is observed, in agreement with experiments and other simulations. Chapter 3 describes an improvement to lattice Boltzmann models of Hele-Shaw flow, along with simulations which quantitatively demonstrate improvements in both accuracy and numerical stability. The Saffman-Taylor hydrodynamic instability is demonstrated using this model. Chapter 4 contains the details and results of the TeraGyroid experiment, which involved extremely large-scale simulations to investigate the dynamical behaviour of a self-assembling structure. The first finite- size-effect- free dynamical simulations of such a system are presented. It is found that several different mechanisms are responsible for the assembly; the existence of chiral domains is demonstrated, along with an examination of domain growth during self-assembly. Appendix A describes some aspects of the implementation of the lattice Boltzmann codes used in this thesis; appendix B describes some of the Grid computing techniques which were necessary for the simulations of chapter 4. Chapter 5 summarises the work, and makes suggestions for further research and improvement.Huntsman Corporation Queen Mary University Schlumberger Cambridge Researc

A molecular dymanics view of structure and reactivity

2009 - 2010The eld of computer simulations has developed into a very important branch of science providing a guess at the interactions between molecules to obtain predictions of properties as accurate as required, subject to the limitations imposed by the computer power and of the chosen and feasible theory level. Quantum chemical methods are predominantly applied to isolated molecules, which corresponds to the state of an ideal gas. Most chemical processes, however, take place in condensed phase, and the interaction of a molecule with its environment: the dimension and the huge amount of degrees of freedom of the system preclude the possiblity of quantum-level calculations. In this PhD thesis di erent approaches to treat several aspects of structure and reactivity, through the use of molecular dynamics techniques have been used. In the rst part, behaviour of Ru complexes relevant as (pre)catalysts for ole n metathesis have been inves- tigated. In particular, it has shed light on a so far underestimated key feature, i.e. the exibility around the N substituent: this allows NHCs to modulate their encumbrance in the rst coordination sphere of the metal to allow the coordination even for incoming bulky substrates. Furthermore, the reduced electron density on the MO of the methylidene group, due to the presence of a acid ligand trans have been analyzed, showing that it allows for a favorable interaction with the aromatic system of the proximal mesityl group of the NHC ligand, which leads to metallacycle rst and subsequently in the formation of a tensioned cyclopropane structure that nally evolves to the experimental product via a Buchner type ring expansion. Since the presence of a transition metal and the bonds breaking/formation the quantum approach is mandatory. On the other hand, the structure description of a Metal/polymer interface have been treated with classical coarse grained molecular dynamics approach. The calculated radial density pro les allowed to get atomistic insights in the Metal/polymer interface. In both cases of non coated and coated gold nanoparticles the polystyrene chains expose the phenyl rings to the nanoparticle surface. In the case of coated nanoparticles there is some penetration of the polystyrene phenyl rings into nanoparticle coating layer. When it is present, the third organic component (8 hydroxyquinoline) is closer to the nanoparticle surface and when in contact with a coated nanoparticle shows a deeper penetration into the thiols layer. The orientation of 8 hydroxyquinoline results short range and parallel with respect to the surface of non coated gold nanoparticles. Di erent is the 8 hydroxyquinoline orientation in the case of a coated gold nanoparticle. In this case the orientation results perpendicular to the nanoparticle surface.[edited by author]IX n.s

Efficient numerical algorithms for surface formulations of mathematical models for biomolecule analysis and design

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 179-183).This thesis presents a set of numerical techniques that extend and improve computational modeling approaches for biomolecule analysis and design. The presented research focuses on surface formulations of modeling problems related to the estimation of the energetic cost to transfer a biomolecule from the gas phase to aqueous solution. The thesis discusses four contributions to modeling biomolecular interactions. First, the thesis presents an approach to allow accurate discretization of the most prevalent mathematical definitions of the biomolecule-solvent interface; also presented are a number of accurate techniques for numerically integrating possibly singular functions over the discretized surfaces. Such techniques are essential for solving surface formulations numerically. The second part of the thesis presents a fast multiscale numerical algorithm, FFTSVD, that efficiently solves large boundary-element method problems in biomolecule electrostatics. The algorithm synthesizes elements of other popular fast algorithms to achieve excellent efficiency and flexibility. The third thesis component describes an integral-equation formulation and boundary-element method implementation for biomolecule electrostatic analysis.(cont.) The formulation and implementation allow the solution of complicated molecular topologies and physical models. Furthermore, by applying the methods developed in the first half of the thesis, the implementation can deliver superior accuracy for competitive performance. Finally, the thesis describes a highly efficient numerical method for calculating a biomolecular charge distribution that minimizes the free energy' change of binding to another molecule. The approach, which represents a novel PDE-constrained methodology, builds on well-developed physical theory. Computational results illustrate not only the method's improved performance but also its application to realistic biomolecule problems.by Jaydeep Porter Bardhan.Ph.D

Interdisciplinary Reasoning about Energy in an Introductory Physics Course for the Life Sciences

Energy is a unifying concept that cuts across physics, chemistry, and biology. However, students who study all three disciplines can end up with a fragmented understanding of energy. This dissertation sits at the intersection of two active areas of current research: the teaching and learning of energy, and interdisciplinary science education (particularly the intersection of physics and biology). The context for this research is an introductory physics course for undergraduate life sciences majors that is reformed to build stronger interdisciplinary connections between physics, biology, and chemistry. An approach to energy that incorporates chemical bonds and chemical reactions is better equipped to meet the needs of life sciences students than a traditional introductory physics approach that focuses primarily on mechanical energy, and so we present a curricular thread for chemical energy in the physics course. Our first set of case studies examines student reasoning about ATP hydrolysis, a biochemically significant reaction that powers various processes in the cell. We observe students expressing both that an energy input is required to break a chemical bond (which they associate with physics) and that energy is released when the phosphate bond is broken in ATP (which they associate with biology). We use these case studies to articulate a model of interdisciplinary reconciliation: building coherent connections between concepts from different disciplines while understanding each concept in its own disciplinary context and justifying the modeling choices in deciding when to use each disciplinary model. Our second study looks at ontological metaphors for energy: metaphors about what kind of thing energy is. Two ontological metaphors for energy that have previously been documented include energy as a substance and energy as a location. We argue for the use of negative energy in modeling chemical energy in an interdisciplinary context, and for the use of a blended substance/location ontology in reasoning about negative energy. Our data show students and experts using the blended ontology productively when the two ontologies are combined in a coherent structure, as well as students getting confused when the ontologies are not coherently combined

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

Feasibility studies of promising stability and gravity /including zero-G/ experiments for manned orbiting missions Final report, 17 Dec. 1964 - 17 Dec. 1965

Feasibility of stability and gravity experiments for manned orbiting mission

Large-scale parallelised boundary element method electrostatics for biomolecular simulation

Large-scale biomolecular simulations require a model of particle interactions capable of incorporating the behaviour of large numbers of particles over relatively long timescales. If water is modelled as a continuous medium then the most important intermolecular forces between biomolecules can be modelled as long-range electrostatics governed by the Poisson- Boltzmann Equation (PBE). We present a linearised PBE solver called the "Boundary Element Electrostatics Program"(BEEP). BEEP is based on the Boundary Element Method (BEM), in combination with a recently developed O(N) Fast Multipole Method (FMM) algorithm which approximates the far-�field integrals within the BEM, yielding a method which scales linearly with the number of particles. BEEP improves on existing methods by parallelising the underlying algorithms for use on modern cluster architectures, as well as taking advantage of recent progress in the �field of GPGPU (General Purpose GPU) Programming, to exploit the highly parallel nature of graphics cards. We found the stability and numerical accuracy of the BEM/FMM method to be highly dependent on the choice of surface representation and integration method. For real proteins we demonstrate the critical level of surface detail required to produce converged electrostatic solvation energies, and introduce a curved surface representation based on Point-Normal G1-continuous triangles which we �find generally improves numerical stability compared to a simpler surface constructed from planar triangles. Despite our improvements upon existing BEM methods, we �find that it is not possible to directly integrate BEM surface solutions to obtain intermolecular electrostatic forces. It is, however, practicable to use the total electrostatic solvation energy calculated by BEEP to drive a Monte-Carlo simulation

PSA 2018

These preprints were automatically compiled into a PDF from the collection of papers deposited in PhilSci-Archive in conjunction with the PSA 2018