Minimum error solutions of the Boltzmann equation for shock structure

‘Best’ solutions for the shock-structure problem are obtained by solving the Boltzmann equation for a rigid sphere gas by applying minimum error criteria on the Mott-Smith ansatz. The use of two such criteria minimizing respectively the local and total errors, as well as independent computations of the remaining error, establish the high accuracy of the solutions, although it is shown that the Mott-Smith distribution is not an exact solution of the Boltzmann equation even at infinite Mach number. The minimum local error method is found to be particularly simple and efficient. Adopting the present solutions as the standard of comparison, it is found that the widely used v2x-moment solutions can be as much as a third in error, but that results based on Rosen's method provide good approximations. Finally, it is shown that if the Maxwell mean free path on the hot side of the shock is chosen as the scaling length, the value of the density-slope shock thickness is relatively insensitive to the intermolecular potential. A comparison is made on this basis of present results with experiment, and very satisfactory quantitative agreement is obtained.

High-strain composites and dual-matrix composite structures

Most space applications require deployable structures due to the limiting size of current launch vehicles. Specifically, payloads in nanosatellites such as CubeSats require very high compaction ratios due to the very limited space available in this typo of platform. Strain-energy-storing deployable structures can be suitable for these applications, but the curvature to which these structures can be folded is limited to the elastic range. Thanks to fiber microbuckling, high-strain composite materials can be folded into much higher curvatures without showing significant damage, which makes them suitable for very high compaction deployable structure applications. However, in applications that require carrying loads in compression, fiber microbuckling also dominates the strength of the material. A good understanding of the strength in compression of high-strain composites is then needed to determine how suitable they are for this type of application.

The goal of this thesis is to investigate, experimentally and numerically, the microbuckling in compression of high-strain composites. Particularly, the behavior in compression of unidirectional carbon fiber reinforced silicone rods (CFRS) is studied. Experimental testing of the compression failure of CFRS rods showed a higher strength in compression than the strength estimated by analytical models, which is unusual in standard polymer composites. This effect, first discovered in the present research, was attributed to the variation in random carbon fiber angles respect to the nominal direction. This is an important effect, as it implies that microbuckling strength might be increased by controlling the fiber angles. With a higher microbuckling strength, high-strain materials could carry loads in compression without reaching microbuckling and therefore be suitable for several space applications.

A finite element model was developed to predict the homogenized stiffness of the CFRS, and the homogenization results were used in another finite element model that simulated a homogenized rod under axial compression. A statistical representation of the fiber angles was implemented in the model. The presence of fiber angles increased the longitudinal shear stiffness of the material, resulting in a higher strength in compression. The simulations showed a large increase of the strength in compression for lower values of the standard deviation of the fiber angle, and a slight decrease of strength in compression for lower values of the mean fiber angle. The strength observed in the experiments was achieved with the minimum local angle standard deviation observed in the CFRS rods, whereas the shear stiffness measured in torsion tests was achieved with the overall fiber angle distribution observed in the CFRS rods.

High strain composites exhibit good bending capabilities, but they tend to be soft out-of-plane. To achieve a higher out-of-plane stiffness, the concept of dual-matrix composites is introduced. Dual-matrix composites are foldable composites which are soft in the crease regions and stiff elsewhere. Previous attempts to fabricate continuous dual-matrix fiber composite shells had limited performance due to excessive resin flow and matrix mixing. An alternative method, presented in this thesis uses UV-cure silicone and fiberglass to avoid these problems. Preliminary experiments on the effect of folding on the out-of-plane stiffness are presented. An application to a conical log-periodic antenna for CubeSats is proposed, using origami-inspired stowing schemes, that allow a conical dual-matrix composite shell to reach very high compaction ratios.

ELECTRONIC AND MAGNETIC-STRUCTURE OF THE TERNARY COMPOUND ND2FE17N

The electronic and the magnetic structure of the Nd2Fe17N1 phase in the family of Nd-Fe-N ternary compounds have been calculated using the first-principles, spin-polarized orthogonalized linear-combination-of-atomic-orbitals method. Results are presented in the form of site-decomposed and spin-projected partial density of states. The occupation sites of the three N atoms are determined by an average radial distribution of all possible N site configurations. Both cases of N occupying the 3b and the 18g sites are studied. The results indicate that the 6c Fe sites have the maximum and the 18h Fe sites have the minimum local moments. This is in good agreement with experiment. It is concluded that the influence on the local moment due to lattice expansion is less important compared to that due to interatomic interaction between the N atom and its neighbors. The results also show the important role of N atoms in raising the Curie temperature of this compound.

Optimisation quadratique en variables binaires : quelques résultats et techniques

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Caratérisation de la surface d’énergie potentielle des matériaux complexes et son application sur la cinétique du SiO2/Si

Dans ce rapport de mémoire, nous avons utilisé les méthodes numériques telles que la dynamique moléculaire (code de Lammps) et ART-cinétique. Ce dernier est un algorithme de Monte Carlo cinétique hors réseau avec construction du catalogue d'événements à la volée qui incorpore exactement tous les effets élastiques. Dans la première partie, nous avons comparé et évalué des divers algorithmes de la recherche du minimum global sur une surface d'énergie potentielle des matériaux complexes. Ces divers algorithmes choisis sont essentiellement ceux qui utilisent le principe Bell-Evans-Polanyi pour explorer la surface d'énergie potentielle. Cette étude nous a permis de comprendre d'une part, les étapes nécessaires pour un matériau complexe d'échapper d'un minimum local vers un autre et d'autre part de contrôler les recherches pour vite trouver le minimum global. En plus, ces travaux nous ont amené à comprendre la force de ces méthodes sur la cinétique de l'évolution structurale de ces matériaux complexes. Dans la deuxième partie, nous avons mis en place un outil de simulation (le potentiel ReaxFF couplé avec ART-cinétique) capable d'étudier les étapes et les processus d'oxydation du silicium pendant des temps long comparable expérimentalement. Pour valider le système mis en place, nous avons effectué des tests sur les premières étapes d'oxydation du silicium. Les résultats obtenus sont en accord avec la littérature. Cet outil va être utilisé pour comprendre les vrais processus de l'oxydation et les transitions possibles des atomes d'oxygène à la surface du silicium associée avec les énergies de barrière, des questions qui sont des défis pour l'industrie micro-électronique.

Estimating oceanic heat content change using isotherms

This paper presents a new analysis of ocean heat content changes over the last 50 yr using isotherms by calculating the mean temperature above the 148C isotherm and the depth of the 148C isotherm as separate variables. A new quantity called the ‘‘relative heat content’’ (‘‘RHC’’) is introduced, which represents the minimum local heat content change over time, relative to a fixed isotherm. It is shown how mean temperature and isotherm depth changes make separable and additive contributions to changes in RHC. Maps of RHC change between 1970 and 2000 show similar spatial patterns to a traditional fixed-depth ocean heat content change to 220 m. However, the separate contributions to RHC suggest a more spatially uniform contribution from warming above the isotherm, while isotherm depth changes show wind-driven signals, of which some are identifiable as being related to the North Atlantic Oscillation. The time series show that the warming contribution to RHC dominates the global trend, while the depth contribution only dominates on the basin scale in the North Atlantic. The RHC shows minima associated with the major volcanic eruptions (particularly in the Indian Ocean), and these are entirely contributed by mean temperature changes rather than isotherm depth changes. The depth change contributions to RHC are strongly affected by the recently reported XBT fall-rate bias, whereas the mean temperature contributions are not. Therefore, only the isotherm depth change contributions toRHCwill need to be reassessed as fall-rate-corrected data become available.

Minimum neighbour and extended Kalman filter estimator: a practical distributed channel assignment scheme for dense wireless local area networks

Dense deployments of wireless local area networks (WLANs) are becoming a norm in many cities around the world. However, increased interference and traffic demands can severely limit the aggregate throughput achievable unless an effective channel assignment scheme is used. In this work, a simple and effective distributed channel assignment (DCA) scheme is proposed. It is shown that in order to maximise throughput, each access point (AP) simply chooses the channel with the minimum number of active neighbour nodes (i.e. nodes associated with neighbouring APs that have packets to send). However, application of such a scheme to practice depends critically on its ability to estimate the number of neighbour nodes in each channel, for which no practical estimator has been proposed before. In view of this, an extended Kalman filter (EKF) estimator and an estimate of the number of nodes by AP are proposed. These not only provide fast and accurate estimates but can also exploit channel switching information of neighbouring APs. Extensive packet level simulation results show that the proposed minimum neighbour and EKF estimator (MINEK) scheme is highly scalable and can provide significant throughput improvement over other channel assignment schemes.

Data pertinent to the establishment of minimum wage rates under the Fair labor standards act for newly covered employment in the local transit industry in Puerto Rico /

"WH67-378."

Spatial variation of climate and the impact of disturbances on local climate and forest recovery in northern Finland

The structure and function of northern ecosystems are strongly influenced by climate change and variability and by human-induced disturbances. The projected global change is likely to have a pronounced effect on the distribution and productivity of different species, generating large changes in the equilibrium at the tree-line. In turn, movement of the tree-line and the redistribution of species produce feedback to both the local and the regional climate. This research was initiated with the objective of examining the influence of natural conditions on the small-scale spatial variation of climate in Finnish Lapland, and to study the interaction and feedback mechanisms in the climate-disturbances-vegetation system near the climatological border of boreal forest. The high (1 km) resolution spatial variation of climate parameters over northern Finland was determined by applying the Kriging interpolation method that takes into account the effect of external forcing variables, i.e., geographical coordinates, elevation, sea and lake coverage. Of all the natural factors shaping the climate, the geographical position, local topography and altitude proved to be the determining ones. Spatial analyses of temperature- and precipitation-derived parameters based on a 30-year dataset (1971-2000) provide a detailed description of the local climate. Maps of the mean, maximum and minimum temperatures, the frost-free period and the growing season indicate that the most favourable thermal conditions exist in the south-western part of Lapland, around large water bodies and in the Kemijoki basin, while the coldest regions are in highland and fell Lapland. The distribution of precipitation is predominantly longitudinally dependent but with the definite influence of local features. The impact of human-induced disturbances, i.e., forest fires, on local climate and its implication for forest recovery near the northern timberline was evaluated in the Tuntsa area of eastern Lapland, damaged by a widespread forest fire in 1960 and suffering repeatedly-failed vegetation recovery since that. Direct measurements of the local climate and simulated heat and water fluxes indicated the development of a more severe climate and physical conditions on the fire-disturbed site. Removal of the original, predominantly Norway spruce and downy birch vegetation and its substitution by tundra vegetation has generated increased wind velocity and reduced snow accumulation, associated with a large variation in soil temperature and moisture and deep soil frost. The changed structural parameters of the canopy have determined changes in energy fluxes by reducing the latter over the tundra vegetation. The altered surface and soil conditions, as well as the evolved severe local climate, have negatively affected seedling growth and survival, leading to more unfavourable conditions for the reproduction of boreal vegetation and thereby causing deviations in the regional position of the timberline. However it should be noted that other factors, such as an inadequate seed source or seedbed, the poor quality of the soil and the intensive logging of damaged trees could also exacerbate the poor tree regeneration. In spite of the failed forest recovery at Tunsta, the position and composition of the timberline and tree-line in Finnish Lapland may also benefit from present and future changes in climate. The already-observed and the projected increase in temperature, the prolonged growing season, as well as changes in the precipitation regime foster tree growth and new regeneration, resulting in an advance of the timberline and tree-line northward and upward. This shift in the distribution of vegetation might be decelerated or even halted by local topoclimatic conditions and by the expected increase in the frequency of disturbances.

Optimisation Problems in Wireless Sensor Networks : Local Algorithms and Local Graphs

This thesis studies optimisation problems related to modern large-scale distributed systems, such as wireless sensor networks and wireless ad-hoc networks. The concrete tasks that we use as motivating examples are the following: (i) maximising the lifetime of a battery-powered wireless sensor network, (ii) maximising the capacity of a wireless communication network, and (iii) minimising the number of sensors in a surveillance application. A sensor node consumes energy both when it is transmitting or forwarding data, and when it is performing measurements. Hence task (i), lifetime maximisation, can be approached from two different perspectives. First, we can seek for optimal data flows that make the most out of the energy resources available in the network; such optimisation problems are examples of so-called max-min linear programs. Second, we can conserve energy by putting redundant sensors into sleep mode; we arrive at the sleep scheduling problem, in which the objective is to find an optimal schedule that determines when each sensor node is asleep and when it is awake. In a wireless network simultaneous radio transmissions may interfere with each other. Task (ii), capacity maximisation, therefore gives rise to another scheduling problem, the activity scheduling problem, in which the objective is to find a minimum-length conflict-free schedule that satisfies the data transmission requirements of all wireless communication links. Task (iii), minimising the number of sensors, is related to the classical graph problem of finding a minimum dominating set. However, if we are not only interested in detecting an intruder but also locating the intruder, it is not sufficient to solve the dominating set problem; formulations such as minimum-size identifying codes and locating dominating codes are more appropriate. This thesis presents approximation algorithms for each of these optimisation problems, i.e., for max-min linear programs, sleep scheduling, activity scheduling, identifying codes, and locating dominating codes. Two complementary approaches are taken. The main focus is on local algorithms, which are constant-time distributed algorithms. The contributions include local approximation algorithms for max-min linear programs, sleep scheduling, and activity scheduling. In the case of max-min linear programs, tight upper and lower bounds are proved for the best possible approximation ratio that can be achieved by any local algorithm. The second approach is the study of centralised polynomial-time algorithms in local graphs these are geometric graphs whose structure exhibits spatial locality. Among other contributions, it is shown that while identifying codes and locating dominating codes are hard to approximate in general graphs, they admit a polynomial-time approximation scheme in local graphs.

Bounding Run-Times of Local Adiabatic Algorithms

A common trick for designing faster quantum adiabatic algorithms is to apply the adiabaticity condition locally at every instant. However it is often difficult to determine the instantaneous gap between the lowest two eigenvalues, which is an essential ingredient in the adiabaticity condition. In this paper we present a simple linear algebraic technique for obtaining a lower bound on the instantaneous gap even in such a situation. As an illustration, we investigate the adiabatic un-ordered search of van Dam et al. [17] and Roland and Cerf [15] when the non-zero entries of the diagonal final Hamiltonian are perturbed by a polynomial (in log N, where N is the length of the unordered list) amount. We use our technique to derive a bound on the running time of a local adiabatic schedule in terms of the minimum gap between the lowest two eigenvalues.

A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.

A local 2-approximation algorithm for the vertex cover problem

We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in (Δ + 1)2 synchronous communication rounds, where Δ is the maximum degree of the graph. For Δ = 3, we give a 2-approximation algorithm also for the weighted version of the problem.

Optimal local polynomial regression of noisy time varying signals

We address the problem of local-polynomial modeling of smooth time-varying signals with unknown functional form, in the presence of additive noise. The problem formulation is in the time domain and the polynomial coefficients are estimated in the pointwise minimum mean square error (PMMSE) sense. The choice of the window length for local modeling introduces a bias-variance tradeoff, which we solve optimally by using the intersection-of-confidence-intervals (ICI) technique. The combination of the local polynomial model and the ICI technique gives rise to an adaptive signal model equipped with a time-varying PMMSE-optimal window length whose performance is superior to that obtained by using a fixed window length. We also evaluate the sensitivity of the ICI technique with respect to the confidence interval width. Simulation results on electrocardiogram (ECG) signals show that at 0dB signal-to-noise ratio (SNR), one can achieve about 12dB improvement in SNR. Monte-Carlo performance analysis shows that the performance is comparable to the basic wavelet techniques. For 0 dB SNR, the adaptive window technique yields about 2-3dB higher SNR than wavelet regression techniques and for SNRs greater than 12dB, the wavelet techniques yield about 2dB higher SNR.

Relation between Local Structure and Glass Forming Ability of Liquid Alloys

An attempt has been made to describe the glass forming ability (GFA) of liquid alloys, using the concepts of the short range order (SRO) and middle range order (MRO) characterizing the liquid structure.A new approach to obtain good GFA of liquid alloys is based on the following four main factors: (1) formation of new SRO and competitive correlation with two or more kinds of SROs for crystallization, (2) stabilization of dense random packing by interaction between different types of SRO, (3) formation of stable cluster (SC) or middle range order (MRO) by harmonious coupling of SROs, and (4) difference between SRO characterizing the liquid structure and the near-neighbor environment in the corresponding equilibrium crystalline phases. The atomic volume mismatch estimated from the cube of the atomic radius was found to be a close relation with the minimum solute concentration for glass formation. This empirical guideline enables us to provide the optimum solute concentration for good GFA in some ternary alloys. Model structures, denoted by Bernal type and the Chemical Order type, were again tested in the novel description for the glass structure as a function of solute concentration. We illustrated the related energetics of the completion between crystal embryo and different types of SRO. Recent systematic measurements also provide that thermal diffusivity of alloys in the liquid state may be a good indicator of their GFA.