Multiscale Modeling and Simulation of Stepped Crystal Surfaces

A primary goal of this dissertation is to understand the links between mathematical models that describe crystal surfaces at three fundamental length scales: The scale of individual atoms, the scale of collections of atoms forming crystal defects, and macroscopic scale. Characterizing connections between different classes of models is a critical task for gaining insight into the physics they describe, a long-standing objective in applied analysis, and also highly relevant in engineering applications. The key concept I use in each problem addressed in this thesis is coarse graining, which is a strategy for connecting fine representations or models with coarser representations. Often this idea is invoked to reduce a large discrete system to an appropriate continuum description, e.g. individual particles are represented by a continuous density. While there is no general theory of coarse graining, one closely related mathematical approach is asymptotic analysis, i.e. the description of limiting behavior as some parameter becomes very large or very small. In the case of crystalline solids, it is natural to consider cases where the number of particles is large or where the lattice spacing is small. Limits such as these often make explicit the nature of links between models capturing different scales, and, once established, provide a means of improving our understanding, or the models themselves. Finding appropriate variables whose limits illustrate the important connections between models is no easy task, however. This is one area where computer simulation is extremely helpful, as it allows us to see the results of complex dynamics and gather clues regarding the roles of different physical quantities. On the other hand, connections between models enable the development of novel multiscale computational schemes, so understanding can assist computation and vice versa. Some of these ideas are demonstrated in this thesis. The important outcomes of this thesis include: (1) a systematic derivation of the step-flow model of Burton, Cabrera, and Frank, with corrections, from an atomistic solid-on-solid-type models in 1+1 dimensions; (2) the inclusion of an atomistically motivated transport mechanism in an island dynamics model allowing for a more detailed account of mound evolution; and (3) the development of a hybrid discrete-continuum scheme for simulating the relaxation of a faceted crystal mound. Central to all of these modeling and simulation efforts is the presence of steps composed of individual layers of atoms on vicinal crystal surfaces. Consequently, a recurring theme in this research is the observation that mesoscale defects play a crucial role in crystal morphological evolution.

Removal of paracetamol on biomass-derived activated carbon: Modeling the fixed bed breakthrough curves using batch adsorption experiments

The remediation of paracetamol (PA), an emerging contaminant frequently found in wastewater treatment plants, has been studied in the low concentration range (0.3–10 mg L−1) using as adsorbent a biomass-derived activated carbon. PA uptake of up to 100 mg g−1 over the activated carbon has been obtained, with the adsorption isotherms being fairly explained by the Langmuir model. The application of Reichemberg and the Vermeulen equations to the batch kinetics experiments allowed estimating homogeneous and heterogeneous diffusion coefficients, reflecting the dependence of diffusion with the surface coverage of PA. A series of rapid small-scale column tests were carried out to determine the breakthrough curves under different operational conditions (temperature, PA concentration, flow rate, bed length). The suitability of the proposed adsorbent for the remediation of PA in fixed-bed adsorption was proven by the high PA adsorption capacity along with the fast adsorption and the reduced height of the mass transfer zone of the columns. We have demonstrated that, thanks to the use of the heterogeneous diffusion coefficient, the proposed mathematical approach for the numerical solution to the mass balance of the column provides a reliable description of the breakthrough profiles and the design parameters, being much more accurate than models based in the classical linear driving force.

A discrete-time queueing system with feedback and optional service

Queueing systems constitute a central tool in modeling and performance analysis. These types of systems are in our everyday life activities, and the theory of queueing systems was developed to provide models for forecasting behaviors of systems subject to random demand. The practical and useful applications of the discrete-time queues make the researchers to con- tinue making an e ort in analyzing this type of models. Thus the present contribution relates to a discrete-time Geo/G/1 queue in which some messages may need a second service time in addition to the rst essential service. In day-to-day life, there are numerous examples of queueing situations in general, for example, in manufacturing processes, telecommunication, home automation, etc, but in this paper a particular application is the use of video surveil- lance with intrusion recognition where all the arriving messages require the main service and only some may require the subsidiary service provided by the server with di erent types of strategies. We carry out a thorough study of the model, deriving analytical results for the stationary distribution. The generating functions of the number of messages in the queue and in the system are obtained. The generating functions of the busy period as well as the sojourn times of a message in the server, the queue and the system are also provided.

Modeling the Effect of Vapor Wall Deposition on the Formation of Secondary Organic Aerosol in Chamber Studies

Laboratory chamber experiments are used to investigate formation of secondary organic aerosol (SOA) from biogenic and anthropogenic precursors under a variety of environmental conditions. Simulations of these experiments test our understanding of the prevailing chemistry of SOA formation as well as the dynamic processes occurring in the chamber itself. One dynamic process occurring in the chamber that was only recently recognized is the deposition of vapor species to the Teflon walls of the chamber. Low-volatility products formed from the oxidation of volatile organic compounds (VOCs) deposit on the walls rather than forming SOA, decreasing the amount of SOA formed (quantified as the SOA yield: mass of SOA formed per mass of VOC reacted). In this work, several modeling studies are presented that address the effect of vapor wall deposition on SOA formation in chambers.

A coupled vapor-particle dynamics model is used to examine the competition among the rates of gas-phase oxidation to low volatility products, wall deposition of these products, and mass transfer to the particle phase. The relative time scales of these rates control the amount of SOA formed by affecting the influence of vapor wall deposition. Simulations show that an effect on SOA yield of changing the vapor-particle mass transfer rate is only observed when SOA formation is kinetically limited. For systems with kinetically limited SOA formation, increasing the rate of vapor-particle mass transfer by increasing the concentration of seed particles is an effective way to minimize the effect of vapor wall deposition.

This coupled vapor-particle dynamics model is then applied to α-pinene ozonolysis SOA experiments. Experiments show that the SOA yield is affected when changing the oxidation rate but not when changing the rate of gas-particle mass transfer by changing the concentration of seed particles. Model simulations show that the absence of an effect of changing the seed particle concentration is consistent with SOA formation being governed by quasi-equilibrium growth, in which gas-particle equilibrium is established much faster than the rate of change of the gas-phase concentration. The observed effect of oxidation rate on SOA yield arises due to the presence of vapor wall deposition: gas-phase oxidation products are produced more quickly and condense preferentially onto seed particles before being lost to the walls. Therefore, for α-pinene ozonolysis, increasing the oxidation rate is the most effective way to mitigate the influence of vapor wall deposition.

Finally, the detailed model GECKO-A (Generator for Explicit Chemistry and Kinetics of Organics in the Atmosphere) is used to simulate α-pinene photooxidation SOA experiments. Unexpectedly, α-pinene OH oxidation experiments show no effect when changing either the oxidation rate or the vapor-particle mass transfer rate, whereas GECKO-A predicts that changing the oxidation rate should drastically affect the SOA yield. Sensitivity studies show that the assumed magnitude of the vapor wall deposition rate can greatly affect conclusions drawn from comparisons between simulations and experiments. If vapor wall loss in the Caltech chamber is of order 10^-5 s^-1, GECKO-A greatly overpredicts SOA during high UV experiments, likely due to an overprediction of second-generation products. However, if instead vapor wall loss in the Caltech chamber is of order 10^-3 s^-1, GECKO-A greatly underpredicts SOA during low UV experiments, possibly due to missing autoxidation pathways in the α-pinene mechanism.

MOLECULAR MODELING OF EPON 862-DETDA / CARBON COMPOSITES

The thermoset epoxy resin EPON 862, coupled with the DETDA hardening agent, are utilized as the polymer matrix component in many graphite (carbon fiber) composites. Because it is difficult to experimentally characterize the interfacial region, computational molecular modeling is a necessary tool for understanding the influence of the interfacial molecular structure on bulk-level material properties. The purpose of this research is to investigate the many possible variables that may influence the interfacial structure and the effect they will have on the mechanical behavior of the bulk level composite. Molecular models are established for EPON 862-DETDA polymer in the presence of a graphite surface. Material characteristics such as polymer mass-density, residual stresses, and molecular potential energy are investigated near the polymer/fiber interface. Because the exact degree of crosslinking in these thermoset systems is not known, many different crosslink densities (degrees of curing) are investigated. It is determined that a region exists near the carbon fiber surface in which the polymer mass density is different than that of the bulk mass density. These surface effects extend ~10 Å into the polymer from the center of the outermost graphite layer. Early simulations predict polymer residual stress levels to be higher near the graphite surface. It is also seen that the molecular potential energy in polymer atoms decreases with increasing crosslink density. New models are then established in order to investigate the interface between EPON 862-DETDA polymer and graphene nanoplatelets (GNPs) of various atomic thicknesses. Mechanical properties are extracted from the models using Molecular Dynamics techniques. These properties are then implemented into micromechanics software that utilizes the generalized method of cells to create representations of macro-scale composites. Micromechanics models are created representing GNP doped epoxy with varying number of graphene layers and interfacial polymer crosslink densities. The initial micromechanics results for the GNP doped epoxy are then taken to represent the matrix component and are re-run through the micromechanics software with the addition of a carbon fiber to simulate a GNP doped epoxy/carbon fiber composite. Micromechanics results agree well with experimental data, and indicate GNPs of 1 to 2 atomic layers to be highly favorable. The effect of oxygen bonded to the surface of the GNPs is lastly investigated. Molecular Models are created for systems with varying graphene atomic thickness, along with different amounts of oxygen species attached to them. Models are created for graphene containing hydroxyl groups only, epoxide groups only, and a combination of epoxide and hydroxyl groups. Results show models of oxidized graphene to decrease in both tensile and shear modulus. Attaching only epoxide groups gives the best results for mechanical properties, though pristine graphene is still favored.

Enzyme Optimization for Lignocellulose Hydrolysis using Mechanistic Modeling

A novel mechanistic model for the saccharification of cellulose and hemicellulose is utilized to predict the products of hydrolysis over a range of enzyme loadings and times. The mechanistic model considers the morphology of the substrate and the kinetics of enzymes to optimize enzyme concentrations for the enzymatic hydrolysis of cellulose and hemicellulose simultaneously. Substrates are modeled based on their fraction of accessible sites, glucan content, xylan content, and degree of polymerizations. This enzyme optimization model takes into account the kinetics of six core enzymes for lignocellulose hydrolysis: endoglucanase I (EG1), cellobiohydrolase I (CBH1), cellobiohydrolase II (CBH2), and endo-xylanase (EX) from Trichoderma reesei; β-glucosidase (BG), and β-xylosidase (BX) from Aspergillus niger. The model employs the synergistic action of these enzymes to predict optimum enzyme concentrations for hydrolysis of Avicel and ammonia fiber explosion (AFEX) pretreated corn stover. Glucan, glucan + xylan, glucose and glucose + xylose conversion predictions are given over a range of mass fractions of enzymes, and a range of enzyme loadings. Simulation results are compared with optimizations using statistically designed experiments. BG and BX are modeled in solution at later time points to predict the effect on glucose conversion and xylose conversion.

Discrete Velocity Models for Mixtures Without Nonphysical Collision Invariants

An important aspect of constructing discrete velocity models (DVMs) for the Boltzmann equation is to obtain the right number of collision invariants. It is a well-known fact that DVMs can also have extra collision invariants, so called spurious collision invariants, in plus to the physical ones. A DVM with only physical collision invariants, and so without spurious ones, is called normal. For binary mixtures also the concept of supernormal DVMs was introduced, meaning that in addition to the DVM being normal, the restriction of the DVM to any single species also is normal. Here we introduce generalizations of this concept to DVMs for multicomponent mixtures. We also present some general algorithms for constructing such models and give some concrete examples of such constructions. One of our main results is that for any given number of species, and any given rational mass ratios we can construct a supernormal DVM. The DVMs are constructed in such a way that for half-space problems, as the Milne and Kramers problems, but also nonlinear ones, we obtain similar structures as for the classical discrete Boltzmann equation for one species, and therefore we can apply obtained results for the classical Boltzmann equation.

Modeling chemistry in massive star forming regions with internal PDRs

Over the past decades star formation has been a very attractive field because knowledge of star formation leads to a better understanding of the formation of planets and thus of our solar system but also of the evolution of galaxies. Conditions leading to the formation of high-mass stars are still under investigation but an evolutionary scenario has been proposed: As a cold pre-stellar core collapses under gravitational force, the medium warms up until it reaches a temperature of 100 K and enters the hot molecular core (HMC) phase. The forming central proto-star accretes materials, increasing its mass and luminosity and eventually it becomes sufficiently evolved to emit UV photons which irradiate the surrounding environment forming a hyper compact (HC) and then a ultracompact (UC) HII region. At this stage, a very dense and very thin internal photon-dominated region (PDR) forms between the HII region and the molecular core. Information on the chemistry allows to trace the physical processes occurring in these different phases of star formation. Formation and destruction routes of molecules are influenced by the environment as reaction rates depend on the temperature and radiation field. Therefore, chemistry also allows the determination of the evolutionary stage of astrophysical objects through the use of chemical models including the time evolution of the temperature and radiation field. Because HMCs host a very rich chemistry with high abundances of complex organic molecules (COMs), several astrochemical models have been developed to study the gas phase chemistry as well as grain chemistry in these regions. In addition to HMCs models, models of PDRs have also been developed to study in particular photo-chemistry. So far, few studies have investigated internal PDRs and only in the presence of outflows cavities. Thus, these unique regions around HC/UCHII regions remain to be examined thoroughly. My PhD thesis focuses on the spatio-temporal chemical evolution in HC/UC HII regions with internal PDRs as well as in HMCs. The purpose of this study is first to understand the impact and effects of the radiation field, usually very strong in these regions, on the chemistry. Secondly, the goal is to study the emission of various tracers of HC/UCHII regions and compare it with HMCs models, where the UV radiation field does not impact the region as it is immediately attenuated by the medium. Ultimately we want to determine the age of a given region using chemistry in combination with radiative transfer.

Aerobic power and lean mass are indicators of competitive sprint performance among elite female cross-country skiers

The purpose of this study was to establish the optimal allometric models to predict International Ski Federation’s ski-ranking points for sprint competitions (FISsprint) among elite female cross-country skiers based on maximal oxygen uptake (V̇O2max) and lean mass (LM). Ten elite female cross-country skiers (age: 24.5±2.8 years [mean ± SD]) completed a treadmill roller-skiing test to determine V̇O2max (ie, aerobic power) using the diagonal stride technique, whereas LM (ie, a surrogate indicator of anaerobic capacity) was determined by dual-emission X-ray anthropometry. The subjects’ FISsprint were used as competitive performance measures. Power function modeling was used to predict the skiers’ FISsprint based on V̇O2max, LM, and body mass. The subjects’ test and performance data were as follows: V̇O2max, 4.0±0.3 L min-1; LM, 48.9±4.4 kg; body mass, 64.0±5.2 kg; and FISsprint, 116.4±59.6 points. The following power function models were established for the prediction of FISsprint: 3.91×105 ∙ VO -6.002maxand 6.95×1010 ∙ LM-5.25; these models explained 66% (P=0.0043) and 52% (P=0.019), respectively, of the variance in the FISsprint. Body mass failed to contribute to both models; hence, the models are based on V̇O2max and LM expressed absolutely. The results demonstrate that the physiological variables that reflect aerobic power and anaerobic capacity are important indicators of competitive sprint performance among elite female skiers. To accurately indicate performance capability among elite female skiers, the presented power function models should be used. Skiers whose V̇O2max differs by 1% will differ in their FISsprint by 5.8%, whereas the corresponding 1% difference in LM is related to an FISsprint difference of 5.1%, where both differences are in favor of the skier with higher V̇O2max or LM. It is recommended that coaches use the absolute expression of these variables to monitor skiers’ performance-related training adaptations linked to changes in aerobic power and anaerobic capacity.

Flow Phenomena: Fluids, Heat and Mass

In this book are published results of high-tech application of computational modeling and simulation the dynamics of different flows, heat and mass transfer in different fields of science and engineering.

Offshore Wind Energy Conversion System Connected to the Electric Grid: Modeling and Simulation

This paper is on modeling and simulation for an offshore wind system equipped with a semi-submersible floating platform, a wind turbine, a permanent magnet synchronous generator, a multiple point clamped four level or five level full-power converter, a submarine cable and a second order filter. The drive train is modeled by three mass model considering the resistant stiffness torque, structure and tower in deep water due to the moving surface elevation. The system control uses PWM by space vector modulation associated with sliding mode and proportional integral controllers. The electric energy is injected into the electric grid either by an alternated current link or by a direct current link. The model is intend to be a useful tool for unveil the behavior and performance of the offshore wind system, especially for the multiple point clamped full-power converter, under normal operation or under malfunctions.

Modeling, Component Selection and Optimization of Servo-controlled Automatic Machinery

A servo-controlled automatic machine can perform tasks that involve synchronized actuation of a significant number of servo-axes, namely one degree-of-freedom (DoF) electromechanical actuators. Each servo-axis comprises a servo-motor, a mechanical transmission and an end-effector, and is responsible for generating the desired motion profile and providing the power required to achieve the overall task. The design of a such a machine must involve a detailed study from a mechatronic viewpoint, due to its electric and mechanical nature. The first objective of this thesis is the development of an overarching electromechanical model for a servo-axis. Every loss source is taken into account, be it mechanical or electrical. The mechanical transmission is modeled by means of a sequence of lumped-parameter blocks. The electric model of the motor and the inverter takes into account winding losses, iron losses and controller switching losses. No experimental characterizations are needed to implement the electric model, since the parameters are inferred from the data available in commercial catalogs. With the global model at disposal, a second objective of this work is to perform the optimization analysis, in particular, the selection of the motor-reducer unit. The optimal transmission ratios that minimize several objective functions are found. An optimization process is carried out and repeated for each candidate motor. Then, we present a novel method where the discrete set of available motor is extended to a continuous domain, by fitting manufacturer data. The problem becomes a two-dimensional nonlinear optimization subject to nonlinear constraints, and the solution gives the optimal choice for the motor-reducer system. The presented electromechanical model, along with the implementation of optimization algorithms, forms a complete and powerful simulation tool for servo-controlled automatic machines. The tool allows for determining a wide range of electric and mechanical parameters and the behavior of the system in different operating conditions.

Analytical methods for modeling elastic metasurfaces

This dissertation aims at developing advanced analytical tools able to model surface waves propagating in elastic metasurfaces. In particular, four different objectives are defined and pursued throughout this work to enrich the description of the metasurface dynamics. First, a theoretical framework is developed to describe the dispersion properties of a seismic metasurface composed of discrete resonators placed on a porous medium considering part of it fully saturated. Such a model combines classical elasticity theory, Biot’s poroelasticity and an effective medium approach to describe the metasurface dynamics and its coupling with the poroelastic substrate. Second, an exact formulation based on the multiple scattering theory is developed to extend the two-dimensional classical Lamb’s problem to the case of an elastic half-space coupled to an arbitrary number of discrete surface resonators. To this purpose, the incident wavefield generated by a harmonic source and the scattered field generated by each resonator are calculated. The substrate wavefield is then obtained as solutions of the coupled problem due to the interference of the incident field and the multiple scattered fields of the oscillators. Third, the above discussed formulation is extended to three-dimensional contexts. The purpose here is to investigate the dynamic behavior and the topological properties of quasiperiodic elastic metasurfaces. Finally, the multiple scattering formulation is extended to model flexural metasurfaces, i.e., an array of thin plates. To this end, the resonant plates are modeled by means of their equivalent impedance, derived by exploiting the Kirchhoff plate theory. The proposed formulation permits the treatment of a general flexural metasurface, with no limitation on the number of plates and the configuration taken into account. Overall, the proposed analytical tools could pave the way for a better understanding of metasurface dynamics and their implementation in engineered devices.

Assessing brain connectivity through electroencephalographic signal processing and modeling analysis

Brain functioning relies on the interaction of several neural populations connected through complex connectivity networks, enabling the transmission and integration of information. Recent advances in neuroimaging techniques, such as electroencephalography (EEG), have deepened our understanding of the reciprocal roles played by brain regions during cognitive processes. The underlying idea of this PhD research is that EEG-related functional connectivity (FC) changes in the brain may incorporate important neuromarkers of behavior and cognition, as well as brain disorders, even at subclinical levels. However, a complete understanding of the reliability of the wide range of existing connectivity estimation techniques is still lacking. The first part of this work addresses this limitation by employing Neural Mass Models (NMMs), which simulate EEG activity and offer a unique tool to study interconnected networks of brain regions in controlled conditions. NMMs were employed to test FC estimators like Transfer Entropy and Granger Causality in linear and nonlinear conditions. Results revealed that connectivity estimates reflect information transmission between brain regions, a quantity that can be significantly different from the connectivity strength, and that Granger causality outperforms the other estimators. A second objective of this thesis was to assess brain connectivity and network changes on EEG data reconstructed at the cortical level. Functional brain connectivity has been estimated through Granger Causality, in both temporal and spectral domains, with the following goals: a) detect task-dependent functional connectivity network changes, focusing on internal-external attention competition and fear conditioning and reversal; b) identify resting-state network alterations in a subclinical population with high autistic traits. Connectivity-based neuromarkers, compared to the canonical EEG analysis, can provide deeper insights into brain mechanisms and may drive future diagnostic methods and therapeutic interventions. However, further methodological studies are required to fully understand the accuracy and information captured by FC estimates, especially concerning nonlinear phenomena.

Jeans modeling of massive early-type galaxies with observed stellar kinematic profiles up to 2-3 effective radii

A recent integral-field spectroscopic (IFS) survey, the MASSIVE survey (Ma et al. 2014), observed the 116 most massive (MK < −25.3 mag, stellar mass M∗ > 10^11.6 M⊙) early-type galaxies (ETGs) within 108 Mpc, out to radii as large as 40 kpc, that correspond to ∼ 2 − 3 effective radii (Re). One of the major findings of the MASSIVE survey is that the galaxy sample is split nearly equally among three groups showing three different velocity dispersion profiles σ(R) outer of a radius ∼ 5 kpc (falling, flat and rising with radius). The purpose of this thesis is to model the kinematic profiles of six ETGs included in the MASSIVE survey and representative of the three observed σ(R) shapes, with the aim of investigating their dynamical structure. Models for the chosen galaxies are built using the numerical code JASMINE (Posacki, Pellegrini, and Ciotti 2013). The code produces models of axisymmetric galaxies, based on the solution of the Jeans equations for a multicomponent gravitational potential (supermassive black hole, stars and dark matter halo). With the aim of having a good agreement between the kinematics obtained from the Jeans equations, and the observed σ and rotation velocity V of MASSIVE (Veale et al. 2016, 2018), I derived constraints on the dark matter distribution and orbital anisotropy. This work suggests a trend of the dark matter amount and distribution with the shape of the velocity dispersion profiles in the outer regions: the models of galaxies with flat or rising velocity dispersion profiles show higher dark matter fractions fDM both within 1 Re and 5 Re. Orbital anisotropy alone cannot account for the different observed trends of σ(R) and has a minor effect compared to variations of the mass profile. Galaxies with similar stellar mass M∗ that show different velocity dispersion profiles (from falling to rising) are successfully modelled with a variation of the halo mass Mh.