The relative dispersion of one fluid particle with respect to another is fundamentally related to the transport and mixing of contaminant species in turbulent flows. The most basic consequence of Kolmogorov's 1941 similarity hypotheses for relative dispersion, the Richardson-Obukhov law that mean-square pair separation distance grows with the cube of time at intermediate times in the inertial subrange, is notoriously difficult to observe in the environment, laboratory, and direct numerical simulations (DNS). Inertial subrange scaling in size parameters like the mean-square pair separation requires careful adjustment for the initial conditions of the dispersion process as well as a very wide range of scales (high Reynolds number) in the flow being studied. However, the statistical evolution of the shapes of clusters of more than two particles has already exhibited statistical invariance at intermediate times in existing DNS. This invariance is identified with inertial-subrange scaling and is more readily observed than inertial-subrange scaling for seemingly simpler quantities such as the mean-square pair separation Results from dispersion of clusters of four particles (called tetrads) in large-scale DNS at grid resolutions up to 4096 points in each of three directions and Taylor-scale Reynolds numbers from 140 to 1000 are used to explore the question of statistical universality in measures of the size and shape of tetrahedra in homogeneous isotropic turbulence in distinct scaling regimes at very small times (ballistic), intermediate times (inertial) and very late times (diffusive). Derivatives of fractional powers of the mean-square pair separation with respect to time normalized by the characteristic time scale at the initial tetrad size constitute a powerful technique in isolating cubic time scaling in the mean-square pair separation. This technique is applied to the eigenvalues of a moment-of-inertia-like tensor formed from the separation vectors between particles in the tetrad. Estimates of the proportionality constant "g" in the Richardson-Obukhov law from DNS at a Taylor-scale Reynolds number of 1000 converge towards the value g=0.56 reported in previous studies. The exit time taken by a particle pair to first reach successively larger thresholds of fixed separation distance is also briefly discussed and found to have unexplained dependence on initial separation distance for negative moments, but good inertial range scaling for positive moments. The use of diffusion models of relative dispersion in the inertial subrange to connect mean exit time to "g" is also tested and briefly discussed in these simulations. Mean values and probability density functions of shape parameters including the triangle aspect ratio "w," tetrahedron volume-to-gyration radius ratio, and normalized moment-of-inertia eigenvalues are all found to approach invariant forms in the inertial subrange for a wider range of initial separations than size parameters such as mean-square gyration radius. These results constitute the clearest evidence to date that turbulence has a tendency to distort and elongate multiparticle configurations more severely in the inertial subrange than it does in the diffusive regime at asymptotically late time. Triangle statistics are found to be independent of initial shape for all time beyond the ballistic regime. The development and testing of different schemes for parallelizing the cubic spline interpolation procedure for particle velocities needed to track particles in DNS is also covered. A "pipeline" method of moving batches of particles from processor to processor is adopted due to its low memory overhead, but there are challenges in achieving good performance scaling.

CSIR (INDIA), IFCPAR / The physics of turbulence is the study of the chaotic and irregular behaviour in driven fluids. It is ubiquitous in cosmic, terrestrial and laboratory environments. To describe the properties of a simple incompressible fluid it is sufficient to know its velocity at all points in space and as a function of time. The equation of motion for the velocity of such a fluid is the incompressible Navier–Stokes equation. In more complicated cases, for example if the temperature of the fluid also fluctuates in space and time, the Navier–Stokes equation must be supplemented by additional equations. Incompressible fluid turbulence is the study of solutions of the Navier–Stokes equation at very high Reynolds numbers, Re, the dimensionless control parameter for this problem. The chaotic nature of these solutions leads us to characterise them by their statistical properties. For example, statistical properties of fluid turbulence are characterised often by structure functions of velocity. For intermediate range of length scales, that is the inertial range, these structure functions show multiscaling. Most studies concentrate on equal-time structure functions which describe the equal-time statistical properties of the turbulent fluid. Dynamic properties can be measured by more general time-dependent structure functions. A major challenge in the field of fluid turbulence is to understand the multiscaling properties of both the equal-time and time-dependent structure functions of velocity starting from the Navier–Stokes equation. In this thesis we use numerical and analytical techniques to study scaling and multiscaling of equal-time and time-dependent structure functions in turbulence not only in fluids but also in advection of passive-scalars and passive vectors, and in randomly forced Burgers equation.

<p>This thesis studies the allocation of stock in a two-level inventory system with stochastic demand. The system consists of one central warehouse which supplies N non-identical retailers with one single product. Customer demand occurs solely at the retailers and follows independent Poisson processes. The purpose is to investigate the value of using a more advanced allocation policy than First Come-First Serve at the central warehouse. The focus is on evaluating how well the simple First Come-First Serve assumption works in a system where the warehouse has access to real-time point-of-sale data, and where shipments are time based and consolidated for all retailers. The considered allocation policy is a myopic policy where the solution to a minimization problem, formulated as a constrained newsvendor problem, determines how the warehouse allocates its stock to the retailers. The minimization problem is solved using (a heuristic method based on) Lagrangian relaxation, and simulation is used to evaluate the average inventory holding costs and backorder costs per time unit when using the considered policy. The simulation study shows that cost savings around 1-4 percent can be expected for most system configurations. However, there were cases where savings were as high as 5 percent, as well as cases where the policy performed worse than First Come-First Serve. The study also shows that the highest cost savings are found in systems with relatively low demand, few retailers, short transportation times and a short time interval between shipments.</p>

The use of hazardous toxic substances is very common in the industrial sector. The substances are often stored in tanks in storage compartments or transported between industrial premises. In case of an accident involving these substances, severe harm can affect both population and the environment. This leaves a demand for an accurate prediction of the substance concentration distribution to mitigate the risks as much as possible and in advance create suitable safety measures. Toxic gases and vapors are often denser than air making it affected by negative buoyancy forces. This will make the gas descend and spread horizontally when reaching the ground. Swedish Defence Research Agency (FOI) carries today a model called LillPello for simulating the dispersion of gases, yet it does not account for the specific case of a dense gas. Therefore, this thesis aims to implement the necessary effects needed to accurately simulate the dispersion of a dense gas. These effects were implemented in Fortran 90 by solving five conservation equations for energy, momentum (vertical and horizontal) and mass. The model was compared against experimental data of a leak of ammonia (NH3). By analyzing the result of the simulations in this thesis, we can conclude that the overall result is satisfactory. We can notice a small concentration underestimation at all measurement points and the model produced a concentration power law coefficient which lands inside the expected range. Two out of the three statistical quantities Geometric Mean (MG), Geometric Variance (VG) and Factor of 2 (FA2) produced values within the ranges of acceptable values. The drawback of the model as it is implemented today is its efficiency, so the main priority for the future of this thesis is to improve this. The model should also be analyzed on more experiments to further validate its accuracy. / Användandet av giftiga ämnen är vanligt inom den industriella sektorn. Ämnena är oftast lagrade i behållare positionerade i lagringsutrymmen eller så transporteras ämnena mellan industrilokaler. I samband med en olycka innehållande dessa substanser kan stora skador drabba både befolkning och miljön. Detta leder till ett behov av att noggrant kunna förutspå koncentrationsfördelningen för att minska riskerna, samt i förväg kunna skapa lämpliga säkerhetsåtgärder. Giftiga gaser och ångor är oftast tyngre än luft vilket gör att gasen blir påverkad av negativ bärkraft. Detta gör att gasen sjunker och sprids horisontalt när den når marken. Totalförsvarets Forskningsinstitut (FOI) besitter idag en modell kallad LillPello som simulerar spridning av gaser, men den hanterar inte det specifika fallet av en tunggas. Därför siktar detta projekt på att, in i LillPello, implementera de nödvändiga effekterna som behövs för att korrekt kunna simulera spridningen av en tunggas. Dessa effekter är implementerad i Fortran 90 genom att lösa fem konserveringsekvationer för energi, momentum (vertikal och horisontell) samt massa. Modellen jämfördes mot data från ett fältexperiment där ammoniak (NH3) släpptes ut. Genom att analysera resultatet från simuleringar kan vi dra slutsatsen att det övergripande resultatet är tillfredsställande. Vi kan notera en underskattning för alla koncentrationsmätningar i simuleringarna och modellen producerade en potenslagsexponent vars värde hamnade innanför den accepterade gränsen. Två utav de tre beräknade statistiska kvantiteterna: Geometriskt medelvärde (MG), Geometrisk varians (VG) och Faktor av 2 (FA2) producerade värden inom de acceptabla gränserna. Största nackdelen med modellen är dess effektivitet och därför är största prioritet för det fortsatta arbetet inom detta projekt att effektivisera implementeringen. Modellen ska även bli vidare analyserad mot fler experiment för att validera dess noggrannhet.

Currently, the US Environmental Protection Agency primarily regulates the discharge of dissolved nitrogen and phosphorous from wastewater treatment plants in the United States. A recent study has shown that the treated effluent of many plants contains concentrations of dissolved carbon dioxide well above the expected theoretical equilibrium concentration of 0.6 mg/L, indicating that carbon dioxide may have been overlooked as a possible pollutant in receiving waters. For this reason, it is necessary to examine the possible presence of a discharge plume containing high levels of dissolved CO2 downstream from the outfall of a major wastewater treatment plant in Tampa, Florida. To examine this possibility, discharge data at the Howard F. Curren Advanced Wastewater Treatment Plant was collected over a two-week period and fed into the UM3 submerged discharge model to simulate discharge conditions at peak ebb tide. In all, five separate runs of the model were performed and compared to examine plume rise, spreading rate, average dissolved CO2 concentration, and plume path. The model predicts that, for this scenario, the plume rises fairly rapidly and is also quickly diluted to near-ambient concentrations of dissolved carbon dioxide within a short distance of being discharged. While this would seem to indicate that the effects of Howard F. Curren on Tampa Bay, in terms of dissolved CO2, are negligible major limitations of the UM3 model make it difficult to say this with a great deal of certainty.

Lean distribution networks have been facing an increased exposure to the risk of unpredicted disruptions causing significant economic forfeitures. At the same time, the existing literature contains very few studies that examine the impact of fortification of facilities for improving network reliability. This dissertation presents three related classes of models that support the design of reliable distribution networks. The models extend the uncapacitated P-median and fixed-charge location models by considering heterogeneous facility failure probabilities, supplier backups, and facility fortification within a finite budget. The first class of models considers binary fortification via linear fortification functions. The second class of models extends binary fortification to partial (continuous) reliability improvement with linear fortification. This extension allows a more efficient utilization of limited fortification resources. The third class of models generalizes linear fortification to nonlinear to reflect the effect of diminishing marginal reliability improvement from fortification investment. For each of the models, we develop solution algorithms and demonstrate their computational efficiency. We present a detailed discussion on the novelty of the proposed models. The models are intended to support corporate decisions on the design of robust distribution networks using limited fortification resources.

Inter-turbine burners are useful devices for increasing engine power. To reduce the size of these combustion devices, ultra-compact combustor (UCC) concepts are necessary. One such UCC concept is the centrifugal-force based high-g combustor design. Here, a model ultra-compact combustor (UCC) with fuel spray injection is simulated using large eddy simulation (LES) and Reynolds-Averaged Navier-Stokes (RANS) methodologies to understand mixing and spray dispersion inside centrifugal-based combustion systems. Both non-evaporating and evaporating droplet simulations were carried, as well as the tracking of a passive scalar, to explore this multiphase system. Simulation results show that mixing of fuel and oxidizer is based on a jet-in-crossflow system, with the fuel jet issuing into a circulating oxidizer flow stream. It is seen that a a high velocity vortex-like ring develops in the inner core of the combustor, which has enough momentum to obstruct the path of combustion products. There is minimal fuel droplet and vapor segregation inside the combustor and enhanced turbulent mixing is seen at mid-radius. / text

In today's world, it is becoming increasingly important to be able to design high performance integrated circuits (ICs) and have them run at as low power as possible. Gate sizing and threshold voltage (Vt) assignment optimizations are one of the major contributors to such trade-offs for power and performance of ICs. In fact, the ever increasing design sizes and more aggressive timing requirements make gate sizing and Vt assignment one of the most important CAD problems in physical synthesis. A promising gate sizing optimization algorithm has to satisfy requirements like being scalable to tackle very large design sizes, being able to optimally utilize a large (but finite) number of possible gate configurations available in standard cell library based on different gate sizes and/or threshold voltages (Vt) and/or gate lengths (Lg), and also, being able to handle non-convex cell delays in modern cell libraries. The work in this thesis makes use of the research-oriented infrastructure made available as part of the ISPD (International Symposium on Physical Design) 2012 Gate Sizing Contest that addresses the issues encountered in modern gate sizing problems. We present a two-phase optimization approach where Lagrangian Relaxation is used to formulate the optimization problem. In the first phase, the Lagrangian relaxed subproblem is iteratively solved using a greedy algorithm, while in the second phase, a cell downsizing and Vt upscaling heuristic is employed to further recover power from the timing-feasible and power-optimized sizing solution obtained at the end of first phase. We also propose a multi-core implementation of the first-phase optimizations, which constitute majority of the total runtime, to take advantage of multi-core processors available today. A speedup of the order of 4 to 9 times is seen on different benchmarks as compared to serial implementation when run on a 2 socket 6-core machine. Compared to the winner of ISPD 2012 contest, we further reduce leakage power by 17.21% and runtime by 87.92%, on average, while obtaining feasible sizing solutions on all the benchmark designs. / text

We study the Hitchin component in the space of representations of the fundamental group of a Riemann surface into a split real Lie group in the rank 2 case. We prove that such representations are described by a conformal structure and class of Higgs bundle we call cyclic and we show cyclic Higgs bundles correspond to a form of the affine Toda equations. We also relate various real forms of the Toda equations to minimal surfaces in quadrics of arbitrary signature. In the case of the Hitchin component for PSL(3,R) we provide a new proof of the relation to convex RP²-structures and hyperbolic affine spheres. For PSp(4,R) we prove such representations are the monodromy for a special class of projective structure on the unit tangent bundle of the surface. We prove these are isomorphic to the convex-foliated projective structures of Guichard and Wienhard. We elucidate the geometry of generic 2-plane distributions in 5 dimensions, work which traces back to Cartan. Nurowski showed that there is an associated signature (2,3) conformal structure. We clarify this as a relationship between a parabolic geometry associated to the split real form of G₂ and a conformal geometry with holonomy in G₂. Moreover in terms of the conformal geometry we prove this distribution is the bundle of maximal isotropics corresponding to the annihilator of a spinor satisfying the twistor-spinor equation. The moduli space of deformations of a compact coassociative submanifold L in a G₂ manifold is shown to have a natural local embedding as a submanifold of H2(L,R). We consider G2-manifolds with a T^4-action of isomorphisms such that the orbits are coassociative tori and prove a local equivalence to minimal 3-manifolds in R^{3,3} = H²(T⁴,R) with positive induced metric. By studying minimal surfaces in quadrics we show how to construct minimal 3-manifold cones in R^{3,3} and hence G₂-metrics from equations that are a set of affine Toda equations. The relation to semi-flat special Lagrangian fibrations and the Monge-Ampere equation is explained.

This report provides an introduction to geometric mechanics, which seeks to model the behavior of physical mechanical systems using differential geometric objects. In addition to its elegance as a method of representation, this formulation also admits the application of powerful analytical techniques from geometry as an aid to understanding these systems. In particular, it reveals the fundamental role that symplectic geometry plays in mechanics (something which is not at all obvious from the traditional Newtonian formulation), and in the case of systems exhibiting symmetry, leads to an elucidation of conservation and reduction laws which can be used to simplify the analysis of these systems. The contribution here is primarily one of exposition. Geometric mechanics was developed as an aid to understanding physics, and we have endeavored throughout to highlight the physical principles at work behind the mathematical formalism. In particular, we show quite explicitly the entire development of mechanics from first principles, beginning with Newton's laws of motion and culminating in the geometric reformulation of Lagrangian and Hamiltonian mechanics. Self-contained presentations of this entire range of material do not appear to be common in either the physics or the mathematics literature, but we feel very strongly that this is essential in order to understand how the more abstract mathematical developments that follow actually relate to the real world. We have also attempted to make many of the proofs contained herein more explicit than they appear in the standard references, both as an aid in understanding and simply to make them easier to follow, and several of them are original where we feel that their presentation in the literature was unacceptably opaque (this occurs primarily in the presentation of the geometric formulation of Lagrangian mechanics and the appendix on symplectic geometry). Finally, we point out that the fields of geometric mechanics and symplectic geometry are vast, and one could not hope to get more than a fragmentary glimpse of them in a single work, which necessiates some parsimony in the presentation of material. The subject matter covered herein was chosen because it is of particular interest from an applied or engineering perspective in addition to its mathematical appeal. / text