Counting degree-constrained subgraphs and orientations

The goal of this short paper to advertise the method of gauge transformations (aka holographic reduction, reparametrization) that is well-known in statistical physics and computer science, but less known in combinatorics. As an application of it we give a new proof of a theorem of A. Schrijver asserting that the number of Eulerian orientations of a $d$--regular graph on $n$ vertices with even $d$ is at least $\left(\frac{\binom{d}{d/2}}{2^{d/2}}\right)^n$. We also show that a $d$--regular graph with even $d$ has always at least as many Eulerian orientations as $(d/2)$--regular subgraphs

Computational Simulation of Explosively Generated Pulsed Power Devices

Technology and size constraints have limited the development of the end game mechanisms of today\u27s modern military weapons. A smaller, more efficient means of powering these devices is needed, and explosive pulsed power devices could be that answer. While most prior research has been in the experimental field, there is a need for more theory-based research and a computer modeling capability. The objective of this research was to use experimental data collected by the US Army at Redstone Arsenal from their ferroelectric generator (FEG) design in combination with the ALEGRA-EMMA code to develop a computer model that can accurately represent an FEG and that can be verified against experimental data and used to predict future experiments. While the ALEGRA code is not capable of simulating the breakdown phenomenon seen in the open circuit cases, the model can accurately reproduce the peak values for the current but has problems reproducing the peak values for the voltage. Overall, the developed model provides a good baseline simulation capability that can be used as a springboard for future development with further research

Investigation of Blast Load Characteristics On Lung Injury

In many parts of the world, civilians and peacekeepers are exposed to potentially serious injury from blasts and explosions. Providing insight into the trauma thresholds for blast injury is necessary for the development of blast protection equipment and identification and subsequent treatment of blast injury. [Phillips, 1988] Blast injury can be categorized as primary, secondary, tertiary, quaternary and quinernary, corresponding to different aspects of the blast loading and injury mechanisms. Primary blast injury occurring in the lungs is of importance, since lung injury results in one of the highest rate of blast mortality. Much of the existing blast injury data was obtained from animal testing with sheep and subsequently extrapolated to humans using scaling techniques. More recently, mathematical, experimental and numerical models have been developed and employed to investigate blast injury. In this study, a detailed finite element model of a sheep thorax and human thorax (developed at the University of Waterloo) was used to predict primary blast lung injury based on a range of blast loading conditions. The models were developed based on available anatomical data and material properties to model the organs and tissues, and were evaluated using the LS-Dyna explicit finite element code. The models were previously validated for the prediction of lung PBI using Friedlander-type blast waves. All results were compared to existing literature to further verify and validate the numerical models as wells as to provide insight on the effect of loading conditions on blast injury. The blast loading input for these simulations used idealized blast waves, based on a blast physics approach. Blast loads were verified using the Chinook CFD software. The effects of idealized blast waves on predicted lung injury were investigated to determine the importance of peak pressure, blast wave duration and impulse. The duration and peak pressures for the waves were selected based on the Bowen and UVa curves, and included a right angle triangular shape and a square wave to allow for the different parameters to be considered. These results were compared to the Bowen and revised Bowen injury models. The results show that the peak overpressure is dominant in predicting injury for blast loads with long durations (>8 ms). The impulse was dominant in predicting injury for blast loads with short durations (<1 ms). For blasts loads with intermediate durations (1 ms < 8 ms) both the shape of the blast load wave and peak overpressure play a role in primary blast lung injury. The effect of orientation of the body position on primary blast lung injury was investigated. Simulations were performed using the sheep and human numerical models along with a model of a commonly used experimental device, the Blast Test Device (BTD) cylinder. These models were oriented in different positions by rotating the body relative to the blast flow. Injury results for the BTD were calculated using the Injury 8.1 injury prediction software. The BTD simulations served several purposes; it was used as a reference for the human and sheep simulations and its effectiveness as a tool to predict body orientation was evaluated. In general, all of the models predicted appropriate and similar levels of injury for the body in its default orientation, and these predictions were comparable to the accepted injury levels for this insult. For other orientations the BTD was not able to predict the appropriate blast injury. This highlighted the importance of proper placement and orientation of the BTD when used in simulations or physical experiments. The overall injury (based on the results from the right and left lung) predicted by the sheep and human thorax was similar for all orientations. However, very different results were obtained when the predicted injury for the right and left lungs was compared. The differences between the sheep and the human were examined and the differences in injury between the right and left lung is a result of the differences in anatomy between the two species. This study has evaluated the importance of blast wave parameters in predicting primary blast injury, an important consideration for the improvement of blast protection, and the effect of body orientation on primary blast injury, an important consideration for experimental testing and a starting point for the evaluation of complex blast loading. Future work will focus on the evaluation of injury in complex blast environments

How to pack trapezoids: exact and evolutionary algorithms

The purposes of this paper are twofold. In the first, we describe an exact polynomial-time algorithm for the pair sequencing problem and show how this method can be used to pack fixed-height trapezoids into a single bin such that interitem wastage is minimised. We then go on to examine how this algorithm can be combined with bespoke evolutionary and local search methods for tackling the multiple-bin version of this problem—one that is closely related to one-dimensional bin packing. In the course of doing this, a number of ideas surrounding recombination, diversity, and genetic repair are also introduced and analysed

Efficient routing of snow removal vehicles

This research addresses the problem of finding a minimum cost set of routes for vehicles in a road network subject to some constraints. Extensions, such as multiple service requirements, and mixed networks have been considered. Variations of this problem exist in many practical applications such as snow removal, refuse collection, mail delivery, etc. An exact algorithm was developed using integer programming to solve small size problems. Since the problem is NP-hard, a heuristic algorithm needs to be developed. An algorithm was developed based on the Greedy Randomized Adaptive Search Procedure (GRASP) heuristic, in which each replication consists of applying a construction heuristic to find feasible and good quality solutions, followed by a local search heuristic. A simulated annealing heuristic was developed to improve the solutions obtained from the construction heuristic. The best overall solution was selected from the results of several replications. The heuristic was tested on four sets of problem instances (total of 115 instances) obtained from the literature. The simulated annealing heuristic was able to achieve average improvements of up to 26.36% over the construction results on these problem instances. The results obtained with the developed heuristic were compared to the results obtained with recent heuristics developed by other authors. The developed heuristic improved the best-known solution found by other authors on 18 of the 115 instances and matched the results on 89 of those instances. It worked specially better with larger problems. The average deviations to known lower bounds for all four datasets were found to range between 0.21 and 2.61%

Fluid structure interactions within a common rail diesel injector.

The internal flow of a high-pressure diesel injector is simulated numerically to investigate the complex transient flow structures and the unsteady forces imparted to the injector needle that result from the asymmetric flow fields developed during operation. The gas-liquid two phase flow is simulated using a mixture model with the cavitation numerically modeled using the Zwart-Gerber-Belamri model. Both the k-ε model and the detached eddy simulation (DES) model are used, and the numerical results are compared. This dissertation looks at the internal flow of a generic injector at different lifts and characterizes the flow parameters at high lift and low lifts. This paper shows that the DES model captures the important unsteady flow features missed by the k-ε model. A DES simulation of a dual gain orifice injector is performed and the impact of a unique vortical structure that is generated by the gain orifices on the flow characteristics is discussed. The fluid-structure interactions of an injector at hover are simulated and the behavior of this injector and the impact of the resulting lateral bending motion of the needle is discussed. This paper identifies the geometric feature that creates the asymmetrical flow that leads to the bending motion. In the final portion of this dissertation the fluid-structure interactions are simulated over the entire injection cycle. This dissertation discusses how the bending motion of the needle is initiated and develops over the injection cycle and discusses the impact of this motion on the fuel quantity injected and the vapor formed during operation by comparing the FSI simulation to a simulation where the lateral motion is artificially limited