The purpose of this research is to develop a heuristic algorithm to minimize total costs in multi-commodity, multi-mode generalized networks with time windows problems. The proposed mathematical model incorporates features of the congestion of vehicle flows and time restriction of delivering commodities. The heuristic algorithm, HA, has two phases. Phase 1 provides lower and upper bounds based on Lagrangian relaxations with subgradient methods. Phase 2 applies two methods, early due date with overdue-date costs and total transportation costs, to search for an improved upper bound. Two application networks are used to test HA for small and medium-scale problems. A different number of commodities and various lengths of planning time periods are generated. Results show that HA can provide good feasible solutions within the reasonable range of optimal solutions. If optimal solutions are unknown, the average gap between lower and upper bounds is 0.0239. Minimal and maximal gaps are 0.0007 and 0.3330. If optimal solutions are known, the maximal gap between upper bounds and optimal solutions is less than 10% ranges of optimal solutions.

Theoretical and numerical studies of chaotic mixing are performed to circumvent the difficulties of efficient mixing, which come from the lack of turbulence in microfluidic devices. In order to carry out efficient and accurate parametric studies and to identify a fully chaotic state, a spectral element algorithm for solution of the incompressible Navier-Stokes and species transport equations is developed. Using Taylor series expansions in time marching, the new algorithm employs an algebraic factorization scheme on multi-dimensional staggered spectral element grids, and extends classical conforming Galerkin formulations to nonconforming spectral elements. Lagrangian particle tracking methods are utilized to study particle dispersion in the mixing device using spectral element and fourth order Runge-Kutta discretizations in space and time, respectively. Comparative studies of five different techniques commonly employed to identify the chaotic strength and mixing efficiency in microfluidic systems are presented to demonstrate the competitive advantages and shortcomings of each method. These are the stirring index based on the box counting method, Poincare sections, finite time Lyapunov exponents, the probability density function of the stretching field, and mixing index inverse, based on the standard deviation of scalar species distribution. Series of numerical simulations are performed by varying the Peclet number (Pe) at fixed kinematic conditions. The mixing length (lm) is characterized as function of the Pe number, and lm ∝ ln(Pe) scaling is demonstrated for fully chaotic cases. Employing the aforementioned techniques, optimum kinematic conditions and the actuation frequency of the stirrer that result in the highest mixing/stirring efficiency are identified in a zeta potential patterned straight micro channel, where a continuous flow is generated by superposition of a steady pressure driven flow and time periodic electroosmotic flow induced by a stream-wise AC electric field. Finally, it is shown that the invariant manifold of hyperbolic periodic point determines the geometry of fast mixing zones in oscillatory flows in two-dimensional cavity.

There is a long terms of developement for academics theoretical analyzing and experimental researching by using the Lagrangian method. But for such trajectory experimentalists still have interference with reflected waves because of the length of the water tank is too short or the diameter and the density of the simulate particle , in spite of measuring the trajectory of the fluid particle have done. For there is no quite completed quantification data for the trajectory of fluid particle, this study is aiming at researching the truly movement of the flow field under wave-current interaction by trajectory measuring. This research choosing the simulate particle¡¦s diameter for 1 mm , collocating with a high-speed vedio camera to record the particle¡¦s moving characteristics while the wave-current interaction occured, to proceed a series of qualitative and quantitative testing. And to comple with all these data and improve the modification by using Image Processing to derive and orientate the coordinates . According to the experimental results of the flow field,it has proved that mass transport occured at the same-depth and no-flow condition through the wave progressing direction.The trajectory of the fluid particle of wave-current interaction in co-flow , its curve presenting the cross-convolution increasing and even presenting the cuspidal locus. And the trajectory of the fluid particle of wave-current interaction in inverse ¡Vflow is opposite to the trajectory of the no-flow movement. The results of the experiment is quite accord with to the 3rd order the theoretical analyzing of Chen ¡]1994¡^and Shu¡BChen¡]2006¡^¡CThe fluid particle reproducting the moving period of the high-elevation is greater than the wave¡¦s and increasing by the sharpness of the wave. The mass transport velocity is the same theory results ,and decreased deviation of artificiality in estimating particle position. According to the ratio of the experimental results, root mean square of error Ex and total mass transport displacement. The experimental results compared to the theoretical results obtained by Chen (1994)and Hsu¡BChen(2006) has the similar results as well.

<p>The work is focused on experimental study and modelling of spacer grid influence on single- and two-phase flow. In the experimental study a mock-up of a realistic fuel bundle with five spacer grids of thin plate spring construction was investigated. A special pressure measuring technique was used to measure pressure distribution inside the spacer. Five pressure taps were drilled in one of the rods, which could exchange position with other rods, in this way providing a large degree of freedom. Laser Doppler Velocimetry was used to measure mean local axial velocity and its fluctuating component upstream and downstream of the spacer in several subchannels with differing spacer part. The experimental study revealed an interesting behaviour. Subchannels from the interior part of the bundle display a different effect on the flow downstream of the spacer compared to subchannels close to the box wall, even if the spacer part is the same. This behaviour is not reflected in modern correlations. The modelling part, first, consisted in comparing the present experimental data to Computational Fluid Dynamics calculations. It was shown that stand-alone subchannel models could predict the local velocity, but are unreliable in prediction of turbulence enhancement due to spacer. The second part of the modelling consisted in developing a deposition model for increase due to spacer. In this study Lagrangian Particle Tracking (LPT) coupled to Discrete Random Walk (DRW) technique was used to model droplet movements through turbulent flow. The LPT technique has an advantage to model the influence of turbulence structure effect on droplet deposition, in this way presenting a generalized model in view of spacer geometry change. The verification of the applicability of LPT DRW method to model deposition in annular flow at Boiling Water Reactor conditions proved that the method is unreliable in its present state. The model calculations compare reasonably well to air-water deposition data, but display a wrong trend if the fluids have a different density ratio than air-water.</p>

Augmentation of the impact of an explosive is routinely achieved by packing metal particles in the explosive charge. When detonated, the particles in the charge are ejected and dispersed. The ejecta influences the post-detonation combustion processes that bolster the blast wave and determines the total impact of the explosive. Thus, it is vital to understand the dispersal and the combustion of the particles in the post-detonation flow, and numerical simulations have been indispensable in developing important insights. Because of the accuracy of Eulerian-Lagrangian (EL) methods in capturing the particle interaction with the post-detonation mixing zone, EL methods have been preferred over Eulerian-Eulerian (EE) methods. However, in most cases, the number of particles in the flow renders simulations using an EL method unfeasible. To overcome this problem, a combined EE-EL approach is developed by coupling a massively parallel EL approach with an EE approach for granular flows. The overall simulation strategy is employed to simulate the interaction of ambient particle clouds with homogenous explosions and the dispersal of particles after detonation of heterogeneous explosives. Explosives packed with aluminum particles are also considered and the aluminum particle combustion in the post-detonation flow is simulated. The effect of particles, both reactive and inert, on the combustion processes is analyzed. The challenging task of solving for clouds of micron and sub-micron particles in complex post-detonation flows is successfully addressed in this thesis.

The safety and security of liquefied natural gas (LNG) facilities has prompted the need for continued study of LNG mitigation systems. Water spray systems are widely recognized as an effective measure for dispersing LNG vapor clouds. Currently, there are no engineering guidelines available for water curtain applications in the LNG industry due to a lack of understanding of the complex interactions between the LNG vapor cloud and water droplets. This research applies computational fluid dynamics (CFD) modeling to investigate the forced dispersion of LNG vapor using upward-oriented full-cone spray nozzles. A Eulerian-Lagrangian approach was applied to simulate the energy and momentum exchange between the continuous (gas flow) and discrete (droplets) phases. Discussed are the physical parameters that are essential inputs to the CFD simulation of the water spray-LNG system. The experimental data collected from the Mary Kay O’Connor Process Safety Center’s outdoor LNG spill work in March 2009 at the Brayton Fire Training Field were used to calibrate the physical parameters. The physical mechanisms of the water spray application were investigated using LNG forced dispersion modeling. The effects of momentum imparting from the droplets to the air- vapor mixture, thermal transfer between the two phases (droplet/vapor) and effects of various levels of air entrainment rates on the behavior of the LNG vapors are evaluated. Lastly, the key parametric dependences of the design elements for an effective water curtain system are investigated. The effects of different droplet sizes, droplet temperatures, nozzle cone angles, and installation configurations of water spray applications on LNG vapor behavior are analyzed. This work aims to investigate the complex interaction of the water droplet-LNG vapor system, which will serve in developing guidelines and establishing engineering criteria for a site-specific LNG mitigation system. Finally, the potentials of applying CFD modeling in providing guidance for setting up the design criteria for an effective forced mitigation system as an integrated safety element for LNG facilities are discussed.

With the advances in process technology, comes the domination of interconnect in the overall propagation delay in modern VLSI designs. Hence, interconnect synthesis techniques, such as buffer insertion, wire sizing and layer assignment play critical roles in the successful timing closure for EDA tools. In this thesis, while our aim is to satisfy timing constraints, accounting for the overhead caused by these optimization techniques is of another primary concern. We utilized a Lagrangian relaxation method to minimize the usage of buffers and metal resources to meet the timing constraints. Compared with the previous work that extended traditional Van Ginneken’s algorithm, which allows for bumping up the wire from thin to thick given significant delay improvement, our approach achieved around 25% reduction in buffer + wire capacitance under the same timing budget.

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In this master thesis we study calibrated geometries, a family of Riemannian or Hermitian manifolds with an associated differential form, φ. We show that it isuseful to introduce the concept of proper calibrated manifolds, which are in asense calibrated manifolds where the geometry is derived from the calibration. In particular, the φ-Grassmannian is considered in the case of proper calibratedmanifolds. The impact of proper calibrated manifolds as a model is studied, aswell as the usefulness of pluripotential theory as tools for the model. The specialLagrangian calibration is an example of an important calibration introduced byHarvey and Lawson, which leads to the definition of the special Lagrangian differentialequation. This partial differential equation can be formulated in threeand four dimensions as det(H(u)) = Δu, where H(u) is the Hessian matrix of some potential u. We prove the existence of solutions and some other propertiesof this nonlinear differential equation and present the resulting 6- and 8-dimensional manifolds defined by the graph {x + i<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cnabla" />u(x)}. We also considerthe physical applications of calibrated geometry, which have so far largely beenrestricted to string theory. However, we consider the manifold (M,g,F), whichis calibrated by the scaled Maxwell 2-form. Some geometrical properties of relativisticand classical electrodynamics are translated into calibrated geometry.

To be