Simulation studies of correlation functions and relaxation in polymeric systems

We investigate the statics and dynamics of a glassy,non-entangled, short bead-spring polymer melt with moleculardynamics simulations. Temperature ranges from slightlyabove the mode-coupling critical temperature to the liquidregime where features of a glassy liquid are absent. Ouraim is to work out the polymer specific effects on therelaxation and particle correlation. We find the intra-chain static structure unaffected bytemperature, it depends only on the distance of monomersalong the backbone. In contrast, the distinct inter-chainstructure shows pronounced site-dependence effects at thelength-scales of the chain and the nearest neighbordistance. There, we also find the strongest temperaturedependence which drives the glass transition. Both the siteaveraged coupling of the monomer and center of mass (CM) andthe CM-CM coupling are weak and presumably not responsiblefor a peak in the coherent relaxation time at the chain'slength scale. Chains rather emerge as soft, easilyinterpenetrating objects. Three particle correlations arewell reproduced by the convolution approximation with theexception of model dependent deviations. In the spatially heterogeneous dynamics of our system weidentify highly mobile monomers which tend to follow eachother in one-dimensional paths forming ``strings''. Thesestrings have an exponential length distribution and aregenerally short compared to the chain length. Thus, arelaxation mechanism in which neighboring mobile monomersmove along the backbone of the chain seems unlikely.However, the correlation of bonded neighbors is enhanced. When liquids are confined between two surfaces in relativesliding motion kinetic friction is observed. We study ageneric model setup by molecular dynamics simulations for awide range of sliding speeds, temperatures, loads, andlubricant coverings for simple and molecular fluids. Instabilities in the particle trajectories are identified asthe origin of kinetic friction. They lead to high particlevelocities of fluid atoms which are gradually dissipatedresulting in a friction force. In commensurate systemsfluid atoms follow continuous trajectories for sub-monolayercoverings and consequently, friction vanishes at low slidingspeeds. For incommensurate systems the velocity probabilitydistribution exhibits approximately exponential tails. Weconnect this velocity distribution to the kinetic frictionforce which reaches a constant value at low sliding speeds. This approach agrees well with the friction obtaineddirectly from simulations and explains Amontons' law on themicroscopic level. Molecular bonds in commensurate systemslead to incommensurate behavior, but do not change thequalitative behavior of incommensurate systems. However,crossed chains form stable load bearing asperities whichstrongly increase friction.

Novel simulation methods for Coulomb and hydrodynamic interactions

This thesis presents new methods to simulate systems with hydrodynamic and electrostatic interactions. Part 1 is devoted to computer simulations of Brownian particles with hydrodynamic interactions. The main influence of the solvent on the dynamics of Brownian particles is that it mediates hydrodynamic interactions. In the method, this is simulated by numerical solution of the Navier--Stokes equation on a lattice. To this end, the Lattice--Boltzmann method is used, namely its D3Q19 version. This model is capable to simulate compressible flow. It gives us the advantage to treat dense systems, in particular away from thermal equilibrium. The Lattice--Boltzmann equation is coupled to the particles via a friction force. In addition to this force, acting on {it point} particles, we construct another coupling force, which comes from the pressure tensor. The coupling is purely local, i.~e. the algorithm scales linearly with the total number of particles. In order to be able to map the physical properties of the Lattice--Boltzmann fluid onto a Molecular Dynamics (MD) fluid, the case of an almost incompressible flow is considered. The Fluctuation--Dissipation theorem for the hybrid coupling is analyzed, and a geometric interpretation of the friction coefficient in terms of a Stokes radius is given. Part 2 is devoted to the simulation of charged particles. We present a novel method for obtaining Coulomb interactions as the potential of mean force between charges which are dynamically coupled to a local electromagnetic field. This algorithm scales linearly, too. We focus on the Molecular Dynamics version of the method and show that it is intimately related to the Car--Parrinello approach, while being equivalent to solving Maxwell's equations with freely adjustable speed of light. The Lagrangian formulation of the coupled particles--fields system is derived. The quasi--Hamiltonian dynamics of the system is studied in great detail. For implementation on the computer, the equations of motion are discretized with respect to both space and time. The discretization of the electromagnetic fields on a lattice, as well as the interpolation of the particle charges on the lattice is given. The algorithm is as local as possible: Only nearest neighbors sites of the lattice are interacting with a charged particle. Unphysical self--energies arise as a result of the lattice interpolation of charges, and are corrected by a subtraction scheme based on the exact lattice Green's function. The method allows easy parallelization using standard domain decomposition. Some benchmarking results of the algorithm are presented and discussed.

Wet bioadhesion in tree frogs

Viele Tiere wie etwa Geckos oder Laubfrösche können mittels ihrer Haftscheiben an Oberflächen kleben. Diese Haftscheiben ermöglichen es den Tieren, sich während ihrerrnFortbewegung an Oberflächen anzuheften und wieder zu lösen unabhängig von denrnvorherrschenden Umweltbedingungen. Frösche besitzen mikro- und nanostrukturierternsowie charakteristisch geformte Haftscheiben an Finger- und Zehenenden. Ihre besonderernevolutionäre Errungenschaft, sich stark und zugleich reversibel in sowohl trockenen alsrnauch feuchten Umgebungen anzuhaften, hat die Wissenschaft zur Nachahmung und Untersuchungrndieser Strukturen inspiriert. Zum besseren Verständnis der Mechanismen vonrnAnhaftung und Loslösung bei Laubfröschen wurden weiche, elastische und mikrostrukturierternOberflächen hergestellt, indem PDMS (Polydimethylsiloxan) auf einer Siliziummaskernmit Hexagonstruktur aufgetragen und vernetzt wurde. Dadurch wurden Anordnungenrnvon hexagonalen Mikrosäulen mit spezifischen geometrischen Eigenschaften undrnunterschiedlichen Kontaktgeometrien (normale, flache Form, T-Form und konkave Formrnder Säulenenden) erhalten. Um den Einfluss der van-der-Waals, hydrodynamischen,rnKapillar-und Adhäsionskräfte zu verstehen, wurden verschiedene experimentelle Ansätzernverfolgt: Die auf eine einzelne Säule wirkenden Adhäsionskräfte wurden mittelsrnRasterkraftmikroskopie gemessen. Dazu wurden speziell hergestellte kolloidale Sensorenrnverwendet. Diese Experimente wurden sowohl mit als auch ohne Flüssigkeitsfilm auf derrnSäule durchgeführt. Die Ergebnisse zeigten den Beitrag von Kapillarkraft und direktenrnKontaktkräften zur Adhäsionskraft bei Vorliegen eines Flüssigkeitsfilms. Die Adhäsionrnfiel umso größer aus, je weniger Flüssigkeit zwischen Sensor und Säule vorhanden war.rnIm Falle einer trockenen Adhäsion zeigte die Säule mit T-Form die höchste Adhäsion. Darndie Haftscheiben der Laubfrösche weich sind, können sie dynamisch ihre Form ändern,rnwas zu einer Änderung der hydrodynamischen Kraft zwischen Scheibe und Oberflächernführt. Der Einfluss der Oberflächenverformbarkeit auf die hydrodynamische Kraft wurderndaher am Modellsystem einer Kugel untersucht, welche sich einer weichen und ebenenrnOberfläche annähert. Dieses System wurde sowohl theoretisch über die Simulation finiterrnElemente als auch experimentell über die Messung mit kolloidalen Sonden untersucht.rnSowohl experimentelle Ergebnisse als auch die Simulationen ergaben eine Abnahme derrnhydrodynamischen Kraft bei Annäherung des kolloidalen Sensors an eine weiche undrnelastische Oberfläche. Beim Entfernen der Sensors von der Oberfläche verstärkte sichrndie hydrodynamische Anziehungskraft. Die Kraft, die zur Trennung eines Partikels von einer Oberfläche in Flüssigkeit notwendig ist, ist für weiche und elastischen Oberflächenrngrößer als für harte Oberflächen. In Bezug zur Bioadhäsion bei Laubfröschen konnternfestgestellt somit festgestellt werden, dass sich der hydrodynamische Anteil zur feuchtenrnBioadhäsion aufgrund der weichen Oberfläche erhöht. Weiterhin wurde der Einflussrndes Aspektverhältnisses der Säulen auf die Reibungskraft mittels eines kolloidalen Sensorsrnuntersucht. Gestreckte Säulen zeigten dabei eine höhere Reibung im Vergleich zu.rnSäulen mit einem gestreckten Hexagon als Querschnitt.

Delamination Arrestment in Bonded-Bolted Composite Structures by Fasteners

Thesis (Ph.D.)--University of Washington, 2016-06

Effects of Drive Speed Modulation on Dynamics of Slender Rotating Structures

Slender rotating structures are used in many mechanical systems. These structures can suffer from undesired vibrations that can affect the components and safety of a system. Furthermore, since some these structures can operate in a harsh environment, installation and operation of sensors that are needed for closed-loop and collocated control schemes may not be feasible. Hence, the need for an open-loop non-collocated scheme for control of the dynamics of these structures. In this work, the effects of drive speed modulation on the dynamics of slender rotating structures are studied. Slender rotating structures are a type of mechanical rotating structures, whose length to diameter ratio is large. For these structures, the torsion mode natural frequencies can be low. In particular, for isotropic structures, the first few torsion mode frequencies can be of the same order as the first few bending mode frequencies. These situations can be conducive for energy transfer amongst bending and torsion modes. Scenarios with torsional vibrations experienced by rotating structures with continuous rotor-stator contact occur in many rotating mechanical systems. Drill strings used in the oil and gas industry are an example of rotating structures whose torsional vibrations can be deleterious to the components of the drilling system. As a novel approach to mitigate undesired vibrations, the effects of adding a sinusoidal excitation to the rotation speed of a drill string are studied. A portion of the drill string located within a borewell is considered and this rotating structure has been modeled as an extended Jeffcott rotor and a sinusoidal excitation has been added to the drive speed of the rotor. After constructing a three-degree-of-freedom model to capture lateral and torsional motions, the equations of motions are reduced to a single differential equation governing torsional vibrations during continuous stator contact. An approximate solution has been obtained by making use of the Method of Direct Partition of Motions with the governing torsional equation of motion. The results showed that for a rotor undergoing forward or backward whirling, the addition of sinusoidal excitation to the drive speed can cause an increase in the equivalent torsional stiffness, smooth the discontinuous friction force at contact, and reduce the regions of negative slope in the friction coefficient variation with respect to speed. Experiments with a scaled drill string apparatus have also been conducted and the experimental results show good agreement with the numerical results obtained from the developed models. These findings suggest that the extended Jeffcott rotordynamics model can be useful for studies of rotor dynamics in situations with continuous rotor-stator contact. Furthermore, the results obtained suggest that the drive speed modulation scheme can have value for attenuating drill-string vibrations.

Mathematical models for cellular aggregation: the chemotactic instability and clustering formation

In this thesis we present a mathematical formulation of the interaction between microorganisms such as bacteria or amoebae and chemicals, often produced by the organisms themselves. This interaction is called chemotaxis and leads to cellular aggregation. We derive some models to describe chemotaxis. The first is the pioneristic Keller-Segel parabolic-parabolic model and it is derived by two different frameworks: a macroscopic perspective and a microscopic perspective, in which we start with a stochastic differential equation and we perform a mean-field approximation. This parabolic model may be generalized by the introduction of a degenerate diffusion parameter, which depends on the density itself via a power law. Then we derive a model for chemotaxis based on Cattaneo's law of heat propagation with finite speed, which is a hyperbolic model. The last model proposed here is a hydrodynamic model, which takes into account the inertia of the system by a friction force. In the limit of strong friction, the model reduces to the parabolic model, whereas in the limit of weak friction, we recover a hyperbolic model. Finally, we analyze the instability condition, which is the condition that leads to aggregation, and we describe the different kinds of aggregates we may obtain: the parabolic models lead to clusters or peaks whereas the hyperbolic models lead to the formation of network patterns or filaments. Moreover, we discuss the analogy between bacterial colonies and self gravitating systems by comparing the chemotactic collapse and the gravitational collapse (Jeans instability).

Transcription-Coupled DNA Supercoiling in Escherichia Coli: Mechanisms and Biological Functions

Transcription by RNA polymerase can induce the formation of hypernegatively supercoiled DNA both in vivo and in vitro. This phenomenon has been explained by a “twin-supercoiled-domain” model of transcription where a positively supercoiled domain is generated ahead of the RNA polymerase and a negatively supercoiled domain behind it. In E. coli cells, transcription-induced topological change of chromosomal DNA is expected to actively remodel chromosomal structure and greatly influence DNA transactions such as transcription, DNA replication, and recombination. In this study, an IPTG-inducible, two-plasmid system was established to study transcription-coupled DNA supercoiling (TCDS) in E. coli topA strains. By performing topology assays, biological studies, and RT-PCR experiments, TCDS in E. coli topA strains was found to be dependent on promoter strength. Expression of a membrane-insertion protein was not needed for strong promoters, although co-transcriptional synthesis of a polypeptide may be required. More importantly, it was demonstrated that the expression of a membrane-insertion tet gene was not sufficient for the production of hypernegatively supercoiled DNA. These phenomenon can be explained by the “twin-supercoiled-domain” model of transcription where the friction force applied to E. coli RNA polymerase plays a critical role in the generation of hypernegatively supercoiled DNA. Additionally, in order to explore whether TCDS is able to greatly influence a coupled DNA transaction, such as activating a divergently-coupled promoter, an in vivo system was set up to study TCDS and its effects on the supercoiling-sensitive leu-500 promoter. The leu-500 mutation is a single A-to-G point mutation in the -10 region of the promoter controlling the leu operon, and the AT to GC mutation is expected to increase the energy barrier for the formation of a functional transcription open complex. Using luciferase assays and RT-PCR experiments, it was demonstrated that transient TCDS, “confined” within promoter regions, is responsible for activation of the coupled transcription initiation of the leu-500 promoter. Taken together, these results demonstrate that transcription is a major chromosomal remodeling force in E. coli cells.

Utilisation d’arbres de faible vigueur provenant de forêts feuillues tempérées comme matière première pour la fabrication de granules de bois

La présente étude avait pour objectif de contribuer à une meilleure compréhension de la granulation des bois feuillus par l’évaluation de la possibilité technique de transformer des bois feuillus de faible vigueur (l’érable à sucre et le bouleau jaune) en granules conventionnels et granules de haute qualité, un type prometteur de transport énergétique. Trois études individuelles ont été réalisées et présentées dans cette thèse. La première étude visait à déterminer s’il y a des changements de teneur en extractibles, cendres, et lignine du bois entre les classes de vigueur des arbres. Les teneurs plus élevées en extractibles et en lignine dans les arbres peu vigoureux ont suggéré que ces derniers sont plus appropriés par rapport aux arbres vigoureux pour la conversion en biocombustibles solides. La deuxième étude visait à optimiser des procédés de granulation des bois feuillus. L’étude a porté sur l’influence des paramètres du procédé (la température et la force de compression) et des caractéristiques de la matière première (la taille des particules et la teneur en humidité) sur les propriétés physiques et mécaniques des granules de bois. Le procédé de granulation doit être effectué à une température d’environ 100 °C pour minimiser la force de friction dans le granulateur et à une teneur en humidité d’environ 11,2% pour maximiser la masse volumique et la résistance mécanique des granules produites. Cette étude a également confirmé que les arbres de faible qualité sont plus appropriés pour la fabrication de granules de bois que les arbres vigoureux. La troisième étude visait l’élaboration de granules de haute qualité. L’eau chaude à température élevée a été utilisée pour modifier les propriétés de la matière première avant granulation. Les caractéristiques de granulation du matériau traité ont été significativement améliorées. Les granules produites ont montré des propriétés améliorées incluant une plus faible teneur en cendres, une plus haute densité énergétique, une meilleure résistance à l’eau, et une meilleure résistance mécanique. Les résultats obtenus de toutes ces études ont démontré la nécessité de bien connaître les fondements de la granulation des bois feuillus et les solutions pratiques pour l’utilisation d’arbres feuillus de faible qualité, le premier peut être applicable pour le développement de procédés de granulation et le dernier peut contribuer à long terme à la restauration des forêts feuillues dégradées en termes de santé des forêts et de leur valeur.

The effect of friction on indenter force and pile-up in numerical simulations of bone nanoindentation

Nanoindentation is a useful technique for probing the mechanical properties of bone, and finite element (FE) modeling of the indentation allows inverse determination of elasto-plastic constitutive properties. However, FE simulations to date have assumed frictionless contact between indenter and bone. The aim of this study was to explore the effect of friction in simulations of bone nanoindentation. Two dimensional axisymmetric FE simulations were performed using a spheroconical indenter of tip radius 0.6m and angle 90°. The coefficient of friction between indenter and bone was varied between 0.0 (frictionless) and 0.3. Isotropic linear elasticity was used in all simulations, with bone elastic modulus E=13.56GPa and Poisson’s ratio =0.3. Plasticity was incorporated using both Drucker-Prager and von Mises yield surfaces. Friction had a modest effect on the predicted force-indentation curve for both von Mises and Drucker-Prager plasticity, reducing maximum indenter displacement by 10% and 20% respectively as friction coefficient was increased from zero to 0.3 (at a maximum indenter force of 5mN). However, friction has a much greater effect on predicted pile-up after indentation, reducing predicted pile-up from 0.27m to 0.11m with a von Mises model, and from 0.09m to 0.02m with Drucker-Prager plasticity. We conclude that it is important to include friction in nanoindentation simulations of bone.

The effect of friction on indenter force and pile-up in numerical simulations of bone nanoindentation

Nanoindentation is a useful technique for probing the mechanical properties of bone, and finite element (FE) modeling of the indentation allows inverse determination of elasto-plastic constitutive properties. However, all but one FE study to date have assumed frictionless contact between indenter and bone. The aim of this study was to explore the effect of friction in simulations of bone nanoindentation. Two dimensional axisymmetric FE simulations were performed using a spheroconical indenter of tip radius 0.6 m and angle 90°. The coefficient of friction between indenter and bone was varied between 0.0 (frictionless) and 0.3. Isotropic linear elasticity was used in all simulations, with bone elastic modulus E=13.56GPa and Poisson‟s ratio f 0.3. Plasticity was incorporated using both Drucker-Prager and von Mises yield surfaces. Friction had a modest effect on the predicted force-indentation curve for both von Mises and Drucker-Prager plasticity, reducing maximum indenter displacement by 10% and 20% respectively as friction coefficient was increased from zero to 0.3 (at a maximum indenter force of 5mN). However, friction has a much greater effect on predicted pile-up after indentation, reducing predicted pile-up from 0.27 to 0.11 m with a von Mises model, and from 0.09 to 0.02 m with Drucker-Prager plasticity. We conclude that it is potentially important to include friction in nanoindentation simulations of bone if pile-up is used to compare simulation results with experiment.

Force chains, friction, and flow: Behavior of granular media across length scales

We study the behavior of granular materials at three length scales. At the smallest length scale, the grain-scale, we study inter-particle forces and "force chains". Inter-particle forces are the natural building blocks of constitutive laws for granular materials. Force chains are a key signature of the heterogeneity of granular systems. Despite their fundamental importance for calibrating grain-scale numerical models and elucidating constitutive laws, inter-particle forces have not been fully quantified in natural granular materials. We present a numerical force inference technique for determining inter-particle forces from experimental data and apply the technique to two-dimensional and three-dimensional systems under quasi-static and dynamic load. These experiments validate the technique and provide insight into the quasi-static and dynamic behavior of granular materials.

At a larger length scale, the mesoscale, we study the emergent frictional behavior of a collection of grains. Properties of granular materials at this intermediate scale are crucial inputs for macro-scale continuum models. We derive friction laws for granular materials at the mesoscale by applying averaging techniques to grain-scale quantities. These laws portray the nature of steady-state frictional strength as a competition between steady-state dilation and grain-scale dissipation rates. The laws also directly link the rate of dilation to the non-steady-state frictional strength.

At the macro-scale, we investigate continuum modeling techniques capable of simulating the distinct solid-like, liquid-like, and gas-like behaviors exhibited by granular materials in a single computational domain. We propose a Smoothed Particle Hydrodynamics (SPH) approach for granular materials with a viscoplastic constitutive law. The constitutive law uses a rate-dependent and dilation-dependent friction law. We provide a theoretical basis for a dilation-dependent friction law using similar analysis to that performed at the mesoscale. We provide several qualitative and quantitative validations of the technique and discuss ongoing work aiming to couple the granular flow with gas and fluid flows.

Direct measurement of plowing friction and wear of a polymer thin film using the atomic force microscope

Nanometer-scale plowing friction and wear of a polycarbonate thin film were directly measured using an atomic force microscope (AFM) with nanoscratching capabilities. During the nanoscratch tests, lateral forces caused discrepancies between the maximum forces for the initial loadings prior to the scratch and the unloading after the scratch. In the case of a nanoscratch test performed parallel to the cantilever probe axis, the plowing friction added another component to the moment acting at the cantilevered end compared to the case of nanoindentation, resulting in an increased deflection of the cantilever. Using free-body diagrams for the cases of nanoindentation and nanoscratch testing, the AFM force curves were analyzed to determine the plowing friction during nanoscratch testing. From the results of this analysis, the plowing friction was found to be proportional to the applied contact force, and the coefficient of plowing friction was measured to be 0.56 +/- 0.02. Also, by the combination of nanoscratch and nanoindentation testing, the energetic wear rate of the polycarbonate thin film was measured to be 0.94 +/- 0.05 mm(3)/(N m).

Force shading and bump mapping using the friction cone algorithm

Previous work has presented the friction cone algorithm, a generalised method to resolve forces on a simulated haptic object when two or more fingers are in contact. Two extensions to the friction cone algorithm are presented: force shading and bump mapping. Force shading removes the discontinuities that are present when transitioning from one face to the next, whilst bump mapping provides a mechanism for rendering haptic textures on polygonal surfaces. Both these extensions can be combined whilst still maintaining the friction cone algorithm's intrinsic ability to simulate arbitrarily complex friction models.