Although the flow of granular material in silos and the pressure acting on the silo walls have been studied for over a century, many challenges still remain in silo design. In particular, during the discharge process some dynamic phenomena in silos can often be observed to display large, self-induced and dynamic pulsations which may endanger the stability of the silo structure. The aim of this thesis is to study the flow and pressure in silos using numerical modelling and analytical methods, and to further understand the mechanical behaviour of granular material and mechanism of dynamic phenomena during silo discharge. The Finite Element (FE) method can be used to analyse the behaviour of the granular material in silos by considering the material as a continuum. In this thesis, FEM modelling of silo flow was developed using the Arbitrary Lagrangian-Eulerian (ALE) formulation in the Abaqus/Explicit program and the key parameters that affect the predictions of the flow and pressure during discharge were identified. Using the ALE technique, almost the entire silo discharge process can be simulated without mesh distortion problems. The mass flow rate and temporally averaged discharge pressure predicted by the FE model were first investigated in a conical hopper and were found to be in good agreement with those from the most commonly quoted theoretical solutions. The transient dynamic pressure fluctuations during incipient silo discharge were predicted and the causes for these dynamic events have been investigated which led to the conclusion that the stress wave propagation and the moving shear zone phenomena within the bulk solid were responsible for the dominant higher and lower frequencies effects respectively. A one-dimensional dynamic model of granular columns subject to Coulomb wall friction was developed to investigate the propagation of stress waves, focusing on the effect of geometry by examining converging and diverging tapered columns. The analytical solutions of this model are compared to the FE model based on the ALE formulation. This FE model was first validated using the known behaviour for cylindrical columns. In all cases, the stress impulse set off by incipient discharge at the silo outlet grew with the distance travelled up the column, however the rate was shown to depend on the halfangle of the taper. Over a range of small angles, the proposed analytical model was found to accurately predict this behaviour. After the successful application of the ALE technique for a conical hopper, the FE model was extended to simulate the granular flow in a flat-bottomed model silo. The FE predictions were compared with the silo pressure measurements in a model silo (Rotter et al, 2004). Pressure cells mounted along a vertical line on the silo walls were used to measure the pressure distribution in the silo tests using dry sand. The FE model was further extended to simulate the granular flow in a model silo consisting of a cylindrical section with a conical hopper. The prediction was compared with the experimental observations from a model silo (Munch-Andersen et al, 1992), together with the well-known theoretical solutions. Two numerical issues were addressed in some detail: one is the numerical treatment of the abrupt transition between the cylinder section and the conical hopper, the other is the interaction between the granular solid and the silo walls that was modelled using a dynamic friction model. In addition, the dynamic pressure events during discharge were examined and plausible explanations were given. Finally, this thesis deployed a non-coaxial elastoplastic constitutive model to explore the effect of non-coaxiality on silo phenomena. The non-coaxial FE modelling was performed on three problems: a simple shear test under various initial conditions, a steep hopper and a flat-bottomed silo. The results show that non-coaxiality did not influence the prediction of wall pressure during filling and storing, on the other hand, the discharge pressure was predicted to be larger when non-coaxiality is considered.

Logistics play a vital role in the prosperity of today’s cities, but current urban logistics delivery practices have proven problematic and to be causing various negative effects in cities. This study proposes an alternative method for delivering cargo with the leasing of a network of logistics hubs within urban areas for designated daily time intervals and handcart last-mile deliveries. The objective of the study is the development of a mathematical programming model for identifying the optimal number and locations of hubs for serving demand with the minimum cost, as well as the optimal times during the day for leasing the facilities, while also allocating hubs to customers. The problem is effectively solved by applying a Lagrangian relaxation and subgradient optimization approach. Numerical examples and a sensitivity analysis provide evidence of the robustness of the model and its ability to be effectively applied to address real problems. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2018. / FAU Electronic Theses and Dissertations Collection

Entrainment velocity, salt flux and the turbulent diffusivity of salt are estimated in the outflow of a small, radially spreading buoyant outflow, just outside of the Teign Estuary mouth, as a means to compare mixing dynamics between very small and larger-scale estuarine and river plumes, and build on a scant knowledge base regarding the former. The analysis was made using a control volume approach, based on the conservation of momentum, volume and salt, from a Lagrangian perspective. Drifting buoys were used to accomplish this. The analysis was based on that employed by McCabe et al. (2008), with some modifications to fit a small-scale outflow, namely: repeat deployments, shorter drifter tracks, and deployment-specific criteria used for choosing the plume base, a step in the analysis used to calculate vertical entrainment, flux and diffusivity. In addition, temperature was used as a proxy for salinity, and this is evaluated in the results. Overall results were compared to a similar study, which was conducted in the Columbia River plume, a system much larger in scale to the Teign. Drifter experiments were conducted on multiple days, under different conditions (i.e. wind, tides, river flow), and those results are discussed briefly, but the focus is on one specific day, April 3, 2014, where conditions most closely matched those of the comparison study, and those results are compared between the two systems. Entrainment velocity was measured along the drifter tracks, in the near-field plume, where shear-induced mixing dominates. Drifter track subsections were chosen so as to avoid source or frontal dynamics, the plume base was chosen for individual deployments as the plume dynamics could change relatively quickly, and repeat deployments were conducted as a way to look at near-field plume evolution over the course of the ebb (and with a smaller plume, time allowed for this) . On April 3, the mean value for entrainment velocity for the four deployments chosen in the Teign outflow was 4.3 x 10-4 ms-1. The mean cast value was slightly higher at 7.6 x 10-4 ms-1, as casts values were typically measured at the beginning of the drifter tracks. Entrainment values at the cast sites were calculated in the same way as the track values, taking plume thickness from hydrographic casts, as a means to evaluate accuracy of track values, which are based on a modelled plume thickness. A rough estimate for the mean entrainment velocity for one pair of drifters used in the Columbia River was 9 x 10-4 ms-1, approximately double that of the Teign, but within the same order of magnitude. Salt flux values ranged from 0-5 x 10-2 psu ms-1 and from 0-3 x 10-2 psu ms-1 for the Teign and the Columbia, respectively, and diffusivities ranged from 0.5-5.8 x 10-2 m2s-1 and from 0.2-9.6 x 10-3 m2s-1. With a similar range of entrainment and salt flux values, and almost an order of magnitude difference between diffusivity values, it was determined that weaker density gradients in the Teign are responsible for the latter, and that this increased level of mixing results in a larger horizontal horizontal salinity gradient, which balances out the terms in the entrainment equation that are related solely to the physical size of the system (i.e. plume thickness, velocity and the vertical salinity gradient). This higher level of mixing of a smaller physical entity, supports the view that smaller plumes mix more thoroughly over a shorter timescale, resulting in a larger impact to the local environment into which they flow.

This thesis considers one-dimensional moving mesh (MM) methods coupled with semi-Lagrangian (SL) discretisations of partial differential equations (PDEs) for meteorological applications. We analyse a semi-Lagrangian numerical solution to the viscous Burgers’ equation when using linear interpolation. This gives expressions for the phase and shape errors of travelling wave solutions which decay slowly with increasing spatial and temporal resolution. These results are verified numerically and demonstrate qualitative agreement for high order interpolants. The semi-Lagrangian discretisation is coupled with a 1D moving mesh, resulting in a moving mesh semi-Lagrangian (MMSL) method. This is compared against two moving mesh Eulerian methods, a two-step remeshing approach, solved with the theta-method, and a coupled moving mesh PDE approach, which is solved using the MATLAB solver ODE45. At each time step of the SL method, the mesh is updated using a curvature based monitor function in order to reduce the interpolation error, and hence numerical viscosity. This MMSL method exhibits good stability properties, and captures the shape and speed of the travelling wave well. A meteorologically based 1D vertical column model is described with its SL solution procedure. Some potential benefits of adaptivity are demonstrated, with static meshes adapted to initial conditions. A moisture species is introduced into the model, although the effects are limited.

One of the most important tools to study the geometry of irreducible holomorphic symplectic manifolds is the monodromy group. The first part of this dissertation concerns the construction and studyof monodromy operators on irreducible holomorphic symplectic manifolds which are deformation equivalent to the 10-dimensional example constructed by O'Grady. The second part uses the knowledge of the monodromy group to compute the number of connected components of moduli spaces of bothmarked and polarised irreducible holomorphic symplectic manifolds which are deformationequivalent to generalised Kummer varieties.

In this thesis we study the self-Floer theory of a monotone Lagrangian submanifold $L$ of a closed symplectic manifold $X$ in the presence of various kinds of symmetry. First we consider the group $\mathrm{Symp}(X, L)$ of symplectomorphisms of $X$ preserving $L$ setwise, and extend its action on the Oh spectral sequence to coefficients of arbitrary characteristic, working over an enriched Novikov ring. This imposes constraints on the differentials in the spectral sequence which force them to vanish in certain situations. We then specialise to the case where $L$ is $K$-homogeneous for a compact Lie group $K$, meaning roughly that $X$ is Kaehler, $K$ acts on $X$ by holomorphic automorphisms, and $L$ is a Lagrangian orbit. By studying holomorphic discs with boundary on $L$ we compute the image of low codimension $K$-invariant subvarieties of $X$ under the length zero closed-open string map. This places restrictions on the self-Floer cohomology of $L$ which generalise and refine the Auroux-Kontsevich-Seidel criterion. These often result in the need to work over fields of specific positive characteristics in order to obtain non-zero cohomology. The disc analysis is then developed further, with the introduction of the notion of poles and a reflection mechanism for completing holomorphic discs into spheres. This theory is applied to two main families of examples. The first is the collection of four Platonic Lagrangians in quasihomogeneous threefolds of $\mathrm{SL}(2, \mathbb{C})$, starting with the Chiang Lagrangian in $\mathbb{CP}^3$. These were previously studied by Evans and Lekili, who computed the self-Floer cohomology of the latter. We simplify their argument, which is based on an explicit construction of the Biran-Cornea pearl complex, and deal with the remaining three cases. The second is a family of $\mathrm{PSU}(n)$-homogeneous Lagrangians in products of projective spaces. Here the presence of both discrete and continuous symmetries leads to some unusual properties: in particular we obtain non-displaceable monotone Lagrangians which are narrow in a strong sense. We also discuss related examples including applications of Perutz's symplectic Gysin sequence and quilt functors. The thesis concludes with a discussion of directions for further research and a collection of technical appendices.

Ma, Man Shun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 75-76). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 2 --- Basic notions in Riemannian geometry --- p.10 / Chapter 2.1 --- Basic manifold theory --- p.11 / Chapter 2.2 --- "Connection, curvature" --- p.19 / Chapter 2.3 --- Submanifold theory --- p.29 / Chapter 3 --- Basic facts in symplectic and complex geometry --- p.33 / Chapter 3.1 --- "Symplectic manifolds, Lagrangian submanifolds" --- p.34 / Chapter 3.2 --- Kahler and Calabi-Yau manifolds --- p.39 / Chapter 3.3 --- Calibration --- p.49 / Chapter 4 --- Mean curvature flow --- p.52 / Chapter 4.1 --- Basic equations in Lagrangian immersions --- p.53 / Chapter 4.2 --- Evolution equation for --- p.57 / Chapter 4.3 --- Evolution equations for H and θ --- p.62 / Chapter 5 --- Lagrangian angle of a foliation --- p.67 / Chapter 5.1 --- "Proof of equation (5.1), (5.2)" --- p.68 / Chapter 5.2 --- Main theorem --- p.70 / Chapter 5.3 --- Examples of invariant solution --- p.73 / Bibliography --- p.75

Li, Xing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 76-80). / Abstract also in Chinese. / Introduction --- p.4 / Chapter 1 --- Preliminary --- p.6 / Chapter 1.1 --- Notations --- p.6 / Chapter 1.2 --- On Properties of Epigraphs --- p.10 / Chapter 1.3 --- Subdifferential Calculus --- p.14 / Chapter 1.4 --- Conical Approximations --- p.16 / Chapter 2 --- Duality in the Cone-convex System --- p.20 / Chapter 2.1 --- Introduction --- p.20 / Chapter 2.2 --- Various of Constraint Qualifications --- p.28 / Chapter 2.2.1 --- Slater´ةs Condition Revisited --- p.28 / Chapter 2.2.2 --- The Closed Cone Constrained Qualification --- p.31 / Chapter 2.2.3 --- The Basic Constraint Qualification --- p.38 / Chapter 2.3 --- Lagrange Multiplier and the Geometric Multiplier --- p.45 / Chapter 3 --- Stable Lagrangian Duality --- p.48 / Chapter 3.1 --- Introduction --- p.48 / Chapter 3.2 --- Stable Farkas Lemma --- p.48 / Chapter 3.3 --- Stable Duality --- p.57 / Chapter 4 --- Sequential Lagrange Multiplier Conditions --- p.63 / Chapter 4.1 --- Introduction --- p.63 / Chapter 4.2 --- The Sequential Lagrange Multiplier --- p.64 / Chapter 4.3 --- Application in Semi-Infinite Programs --- p.71 / Bibliography --- p.76 / List of Symbols --- p.80

Les effets des opérateurs liés aux anomalies axiale et de trace de QCD et de QED dans les désintégrations faibles des mésons sont analysés dans deux régimes extrêmes: tout d'abord lorsque les densités anomales de gluons et de photons sont générées à courte distance par une boucle de quark lourd, ensuite lorsqu'elles sont générées à longue distance par des corrections fortes associées aux quarks légers u, d et s. A courte distance, l'ensemble des corrections de type pingouin à une interaction effective à quatre quarks arbitraire est obtenu à partir de l'expansion en la masse inverse du propagateur d'un quark lourd plongé dans un champ de jauge classique. Une suppression des effets anomaux est ainsi mise en évidence dans le Modèle Standard. Un nouvel ensemble d'opérateurs de dimension huit décrivant les effets du quark charmé dans les désintégrations des kaons est également établi. A longue distance, les effets anomaux associés aux quarks légers dans les désintégrations faibles hadroniques et radiatives des kaons sont analysés dans le formalisme des Lagrangiens chiraux. Une contribution potentiellement importante de l'opérateur d'anomalie de trace est ainsi mise en évidence. Les implications d'une éventuelle dominance des anomalies sont également étudiées.

We study a generic minimization problem with separable non-convex piecewise linear costs, showing that the linear programming (LP) relaxation of three textbook mixed integer programming formulations each approximates the cost function by its lower convex envelope. We also show a relationship between this result and classical Lagrangian duality theory.