In this thesis, I propose a general stochastic simulation algorithm for particle based lattice model using the concepts of Gillespie's stochastic simulation algorithm, which was originally designed for well-stirred systems. I describe the details about this method and analyze its complexity compared with the StochSim algorithm, another simulation algorithm originally proposed to simulate stochastic lattice model. I compare the performance of both algorithms with application to two different examples: the May-Leonard model and Ziff-Gulari-Barshad model. Comparison between the simulation results from both algorithms has validate our claim that our new proposed algorithm is comparable to the StochSim in simulation accuracy. I also compare the efficiency of both algorithms using the CPU cost of each code and conclude that the new algorithm is as efficient as the StochSim in most test cases, while performing even better for certain specific cases. / Computer simulation has been developed for almost one century. Stochastic lattice model, which follows the physics concept of lattice, is defined as a kind of system in which individual entities live on grids and demonstrate certain random behaviors according to certain specific rules. It is mainly studied using computer simulations. The most widely used simulation method to for stochastic lattice systems is the StochSim algorithm, which just randomly pick an entity and then determine its behavior based on a set of specific random rules. Our goal is to develop new simulation methods so that it is more convenient to simulate and analyze stochastic lattice system. In this thesis I propose another type of simulation methods for the stochastic lattice model using totally different concepts and procedures. I developed a simulation package and applied it to two different examples using both methods, and then conducted a series of numerical experiment to compare their performance. I conclude that they are roughly equivalent and our new method performs better than the old one in certain special cases.

Ferroelectric materials have been an area of keen interest for researchers due to their useful electro-mechanical coupling properties for a range of modern applications, such as sensing, precision actuation, or energy harvesting. The distribution of the piezoelectric coefficients, which corresponds to the piezoelectric properties, in traditional crystalline ferroelectric materials are determined by their inherent crystalline structure. This restriction limits the tunability of their piezoelectric properties. In the present work, ferroelectric lattice materials capable of a wide range of rationally designed piezoelectric coefficients are achieved through lattice micro-architecture design. The piezoelectric coefficients of several lattice designs are analyzed and predicted using an analytical volume-averaging approach. Finite element models were used to verify the analytical predictions and strong agreement between the two sets of results were found. Select lattice designs were additively manufactured using projection microstereolithography from a PZT-polymer composite and their piezoelectric coefficients experimentally verified and also found to be in agreement with the analytical and numerical predictions. The results show that the use of lattice micro-architecture successfully decouples the dependency of the piezoelectric properties on the material's crystalline structure, giving the user a means to tune the piezoelectric properties of the lattice materials. Real-world application of a ferroelectric lattice structure is demonstrated through application as a multi-directional stress sensor. / Master of Science / Ferroelectric materials have been an area of keen interest for researchers due to their useful electro-mechanical coupling properties for a range of modern applications, such as sensing, precision actuation, or energy harvesting. However, the piezoelectric properties of traditional materials are not easily augmented due to their dependency on material crystalline structure. In the present work, material architecture is investigated as a means for designing new piezoelectric materials with tunable sets of piezoelectric properties. Analytical predictions of the properties are first obtained and then verified using finite element models and experimental data from additively manufactured samples. The results indicate that the piezoelectric properties of a material can in fact be tuned by varying material architecture. Following this, real-world application of a ferroelectric lattice structure is demonstrated through application as a multi-directional stress sensor.

Yes / Traditional Lattice-Boltzmann modelling of advection–diffusion flow is affected by numerical instability if the advective term becomes dominant over the diffusive (i.e., high-Péclet flow). To overcome the problem, two 3D one-way coupled models are proposed. In a traditional model, a Lattice-Boltzmann Navier–Stokes solver is coupled to a Lattice-Boltzmann advection–diffusion model. In a novel model, the Lattice-Boltzmann Navier–Stokes solver is coupled to an explicit finite-difference algorithm for advection–diffusion. The finite-difference algorithm also includes a novel approach to mitigate the numerical diffusivity connected with the upwind differentiation scheme.

This paper presents a framework for tuning, validating, and quantifying uncertainties for flight loads. The flight loads are computed using a Nastran doublet lattice model and are validated using measured data from a flight loads survey for a Cessna Model 525B business jet equipped with Tamarack® Aerospace Group’s active winglet modification, ATLAS® (Active Technology Load Alleviation System). ATLAS® allows for significant aerodynamic improvements to be realized by reducing loads to below the values of the original, unmodified airplane. Flight loads are measured using calibrated strain gages and are used to tune and validate a Nastran doublet-lattice flight loads model. Methods used to tune and validate the model include uncertainty quantification of the Nastran model form and lead to an uncertainty quantified model which can be used to estimate flight loads at any given flight condition within the operating envelope of the airplane. The methods presented herein improve the efficiency of the loads process and reduce conservatism in design loads through improved prediction techniques. Regression techniques and uncertainty quantification methods are presented to more accurately assess the complexities in comparing models to flight test results. / Master of Science / This paper presents a process for correlating analytical airplane loads models to flight test data and validating the results. The flight loads are computed using Nastran, a structural modeling tool coupled with an aerodynamic loads solver. The flight loads models are correlated to flight test data and are validated using measured data from a flight loads survey for a Cessna Model 525B business jet equipped with Tamarack ® Aerospace Group’s active winglet modification, ATLAS ® (Active Technology Load Alleviation System). ATLAS ® allows for significant aerodynamic improvements and efficiency gains to be realized by reducing loads to below the values of the original, unmodified airplane. Flight loads are measured using a series of strain gage sensors mounted on the wing. These sensors are calibrated to measure aerodynamic loads and are used to tune and validate the Nastran flight loads model. Methods used to tune and validate the model include quantification of error and uncertainties in the model. These efforts lead to a substantially increased understanding of the model limitations and uncertainties, which is especially valuable at the corners of the operating envelope of the airplane. The methods presented herein improve the efficiency of the loads process and reduce conservatism in design loads through improved prediction techniques. The results provide a greater amount of guidance for decision making throughout the design and certification of a load alleviation system and similar airplane aerodynamic improvements.

Millions of years of evolution have led to a wealth of highly adapted functional surfaces in nature. Among the most fascinating are superhydrophobic surfaces which are highly water-repellent and shed drops very easily owing to their chemical hydrophobicity combined with micropatterning. Superhydrophobic materials have attracted a lot of attention due to their practical applications as ultra-low friction surfaces for ships and pipes, water harvesters, de-humidifiers and cooling systems. At small length scales, where surface tension dominates over gravity, these surfaces show a wealth of phenomena interesting to physicists, such as directional flow, rolling, and drop bouncing. This thesis focuses on two examples of dynamic drop interactions with micropatterned surfaces and studies them by means of a lattice Boltzmann simulation approach. Inspired by recent experiments, we investigate the phenomenon of the self-propelled bouncing of coalescing droplets. On highly hydrophobic patterned surfaces drop coalescence can lead to an out-of-plane jump of the composite drop. We discuss the importance of energy dissipation to the jumping process and identify an anisotropy of the jumping ability with respect to surface features. We show that Gibbs' pinning is the source of this anisotropy and explain how it leads to the inhibition of coalescence-induced jumping. The second example we study is the novel phenomenon of pancake bouncing. Conventionally, a drop falling onto a superhydrophobic surface spreads due to its inertia, retracts due to its surface tension, and bounces off the surface. Here we explain a different pathway to bouncing that has been observed in recent experiments: A drop may spread upon impact, but leave the surface whilst still in an elongated shape. This new behaviour, which occurs transiently for certain impact and surface parameters, is due to reversible liquid imbibition into the superhydrophobic substrate. We develop a theoretical model and test it on data from experiments and simulations. The theoretical model is used to explain pancake bouncing in detail.

Precise predictions of hadronic matrix elements in heavy meson decays are important to constrain the fundamental parameters in the Standard Model of particle physics. The CKM matrix element Vub can be extracted from experimental data on the decay B → πℓν if the hadronic form factor is known. In addition, loop suppressed rare decays of B-mesons, such as B → K∗γ and B → K(∗)ℓℓ, provide valuable insight into new physics models. Hadronic form factors for exclusive meson decays can be calculated in the framework of lattice QCD. As the wavelength of heavy quarks is not resolved on currently available lattices I use an effective nonrelativistic theory to discretise the heavy degrees of freedom. In addition, the discretisation errors in the final state meson are reduced by working in a moving frame. I review the phenomenology of rare B decays and describe how lattice QCD can contribute to calculating the relevant form factors. As the short distance physics in the effective theory is different from that of QCD, the Lagrangian and decay currents need to be renormalised. I show how this can be achieved in the framework of lattice perturbation theory. I calculate the perturbative renormalisation constants of the leading order operators in the heavy quark Lagrangian. Motivated by nonperturbative studies I extend this approach to higher order kinetic terms which break rotational invariance. In combination with simulations in the weak coupling regime of the theory, results from diagrammatic lattice perturbation theory are used to calculate the heavy quark selfenergy corrections and predict the fundamental parameters of QCD. I calculate the one loop correction on a finite lattice with twisted boundary conditions which is used for the extraction of higher order perturbative corrections. I renormalise the heavy-light current to one loop order in lattice mNRQCD and present results from nonperturbative studies. Finally, I discuss how the results are used in the calculation of hadronic form factors.

Association rule mining (ARM) is the task of identifying meaningful implication rules exhibited in a data set. Most research has focused on extracting frequent item (FI) sets and thus fallen short of the overall ARM objective. The FI miners fail to identify the upper covers that are needed to generate a set of association rules whose size can be exploited by an end user. An alternative to FI mining can be found in formal concept analysis (FCA), a branch of applied mathematics. FCA derives a concept lattice whose concepts identify closed FI sets and connections identify the upper covers. However, most FCA algorithms construct a complete lattice and therefore include item sets that are not frequent. An iceberg lattice, on the other hand, is a concept lattice whose concepts contain only FI sets. Only three algorithms to construct an iceberg lattice were found in literature. Given that an iceberg concept lattice provides an analysis tool to succinctly identify association rules, this study investigated additional algorithms to construct an iceberg concept lattice. This report presents the development and analysis of the Quick Iceberg Concept Lattice (QuICL) algorithms. These algorithms provide incremental construction of an iceberg lattice. QuICL uses recursion instead of iteration to navigate the lattice and establish connections, thereby eliminating costly processing incurred by past algorithms. The QuICL algorithms were evaluated against leading FI miners and FCA construction algorithms using benchmarks cited in literature. Results demonstrate that QuICL provides performance on the order of FI miners yet additionally derive the upper covers. QuICL, when combined with known algorithms to extract a basis of association rules from a lattice, offer a "best known" ARM solution. Beyond this, the QuICL algorithms have proved to be very efficient, providing an order of magnitude gains over other incremental lattice construction algorithms. For example, on the Mushroom data set, QuICL completes in less than 3 seconds. Past algorithms exceed 200 seconds. On T10I4D100k, QuICL completes in less than 120 seconds. Past algorithms approach 10,000 seconds. QuICL is proved to be the "best known" all around incremental lattice construction algorithm. Runtime complexity is shown to be O(l d i) where l is the cardinality of the lattice, d is the average degree of the lattice, and i is a mean function on the frequent item extents.

Discutimos um modelo de calibre com simetria Z (N) na rede, sendo as variáveis dinâmicas definidas em faces de cubos. Mostramos a dualidade com um sistema de spins Z (N) em quatro dimensões e a autodualidade em seis dimensões para este modelo, utilizando o formalismo da matriz de transferência. Analisamos as funções de correlação invariantes por transformações de calibre, constatando os decaimentos exponenciais com o volume (para altas temperaturas e d &#8805 3) e com a área (para baixas temperaturas e d > 3). Para três dimensões, o modelo não apresenta transição de fase sendo exatamente solúvel. Estudamos também a versão U (1) do modelo e mostramos sua equivalência com uma teoria de campos clássica livre na região de baixas temperaturas / We discussus a model with a Z (N) gauge symmetry on a lattice, the dynamical variables being defined on faces of cubes. The duality with a Z (N) spin system in four dimensions and the selfduality in six dimensions is shown for this model, using the transfer matrix formalism. The gauge invariant correlation functions have been analysed and we verify their exponential decay with volume (at high temperatures and d &#8805 3) and with the área (at low temperatures and d > 3). For three dimensions, the model exhibits no phase transition, being exactly soluble. We also study a U (I) version o four model and show its equivalence with a free classical field theory in the low temperature region

In this thesis, we study several different renormalization group (RG) methods, including the conventional Wilson renormalization group, Monte Carlo renormalization group (MCRG), exact renormalization group (ERG, or sometimes called functional RG), and tensor renormalization group (TRG). We use the two dimensional nearest neighbor Ising model to introduce many conventional yet important concepts. We then generalize the model to Dyson's hierarchical model (HM), which has rich phase properties depending on the strength of the interaction. The partition function zeros (Fisher zeros) of the HM model in the complex temperature plane is calculated and their connection with the complex RG flows is discussed. The two lattice matching method is used to construct both the complex RG flows and calculate the discrete β functions. The motivation of calculating the discrete β functions for various HM models is to test the matching method and to show how physically relevant fixed points emerge from the complex domain. We notice that the critical exponents calculated from the HM depend on the blocking parameter b. This motivated us to analyze the connection between the discrete and continuous RG transformation. We demonstrate numerical calculations of the ERG equations. We discuss the relation between Litim and Wilson-Polchinski equation and the effect of the cut-off functions in the ERG calculation. We then apply methods developed in the spin models to more complicated and more physically relevant lattice gauge theories and lattice quantum chromodynamics (QCD) like theories. Finite size scaling (FSS) technique is used to analyze the Binder cumulant of the SU(2) lattice gauge model. We calculate the critical exponent nu and omega of the model and show that it is in the same universality class as the three dimensional Ising model. Motivated by the walking technicolor theory, we study the strongly coupled gauge theories with conformal or near conformal properties. We compare the distribution of Fisher zeros for lattice gauge models with four and twelve light fermion flavors. We also briefly discuss the scaling of the zeros and its connection with the infrared fixed point (IRFP) and the mass anomalous dimension. Conventional numerical simulations suffer from the critical slowing down at the critical region, which prevents one from simulating large system. In order to reach the continuum limit in the lattice gauge theories, one needs either large volume or clever extrapolations. TRG is a new computational method that may calculate exponentially large system and works well even at the critical region. We formulate the TRG blocking procedure for the two dimensional O(2) (or XY ) and O(3) spin models and discuss possible applications and generalizations of the method to other spin and lattice gauge models. We start the thesis with the introduction and historical background of the RG in general.

Electromagnetic properties of the octet and decuplet baryons are calculated in quenched QCD on a 20 ³ x40 lattice with a lattice spacing of 0.128 fm using the fat - link irrelevant clover ( FLIC ) fermion action. FLIC fermions enable simulations to be performed efficiently at quark masses as low as 300 MeV. By combining FLIC fermions with an improved conserved vector current we ensure that discretization errors occur only at Ο ( α ² ) while maintaining current conservation. Magnetic moments, charge radii and magnetic radii are extracted from the electric and magnetic form factors for each individual quark sector. From these the corresponding baryon properties are constructed. Our results for the octet baryons are compared with the predictions of Quenched Chiral Perturbation Theory ( Q χ PT ) and experimental values where available. Results for the charge radii and magnetic moments of the octet baryons are in accord with the predictions of the Q χ PT, suggesting that the sum of higher order terms makes only a small contribution to the chiral expansion. The regime where chiral physics dominates remains to be explored. We establish the non - analytic behavior of the charge radii and magnetic moment in the case of octet baryons. The neutron charge radius suggests that the chiral regime is still far away. We establish substantial environment sensitivity in the quark behavior in the low mass region. We establish that the u and d quarks make substantial and important contribution to the magnetic moment of the Λ contradicting the predictions of the Simple Quark Model. We present the E0 and M1 form factors of the decuplet baryons and the charge radii and magnetic moments. We compare the decuplet baryon results with the lattice calculation of charge radii and magnetic moments of octet baryons. We establish that the environment sensitivity is far less pronounced in the case of the decuplet baryons compared to that in the octet baryons. A surprising result is that the charge radii of the decuplet baryons are generally smaller than that of the octet baryons. Magnetic moment of the Δ + shows a turn over in the low quark mass region, making it smaller than the proton magnetic moment. This is consistent with the expectations of the Quenched Chiral Perturbation Theory. A similar turn over is also noticed in the magnetic moment of the ∑ * [superscript 0], but not for Ξ * where only kaon loops can appear in Quenched QCD. We present results for the higher order moments of the decuplet baryons, i.e., the electric quadrupole moment E2 and the magnetic octupole moment M3. With these results we provide the first conclusive analysis which shows that decuplet baryons are deformed. The electric quadrupole moment of the The electric quadrupole moment of the Ω ‾ baryon is postive when the negative charge factor is included, and is equal to 0.014 ± 0.0005 fm ², indicating an oblate shape. / Thesis (Ph.D.)--School of Chemistry and Physics, 2006.