The basis of this work is to find how varying the grain size of materials contained in sandbags (sand and crumb rubber) effects the ballistic penetration of the projectiles from both the 7.62x39mm (308-short), and 9mm Luger cartridges. The sandbags were stacked in a pyramidal stacking configuration according to military specifications in order to simulate a section of a sandbag barrier or redoubt as would be seen on the battlefield. The projectiles were fired at the targets, and the velocity and penetration data was recorded. The results concern both military and civilian applications alike. The 7.62x39 round was found to experience more fragmentation as grain size increased, and was also found to have, on average, the least amount of penetration into the largest grains. The 9mm round was found to suffer negligible deformation in all of the various sizes of materials, and when fired at the two types of materials, showed a steady trend of decreasing penetration depth with increasing grain size. The sand had a wearing effect on the projectiles leaving them scared or fragmented and deformed while the rubber kept the rounds in pristine condition.

A descoberta da magnetoresistência (GMR) em materiais granulares gerou um grande interesse no estudo destes materiais, havendo um empenho particular no estudo de grãos de CO em CU e AG. Como as propriedades de transporte estão ligadas intimamente às estruturais, o entendimento da GMR nestes materiais requer uma descrição acurada destas características. Neste trabalho, procurando determinar algumas características magnéticas locais, usamos o método RS-LMTO-ASA para realizar um estudo sistemático dos momentos magnéticos locais e campos hiperfinos com respeito ao tamanho de grãos de CI com até 135 átomos em matrizes de CU e AG fcc. Além disso, estudamos FE e CO nas configurações espaciais seguintes em hospedeiro AG: impurezas isoladas, dímeros FE-FE e FE-CO e precipitados com 13, 19 e 43 átomos. Calculamos o FE enquanto impureza central nos grãos de CO e, para os clusters com 13 e 19 átomos, também consideramos a impureza em posições de interface. Encontramos para os grãos em AG momentos magnéticos bastante estáveis e, para o CU, obtivemos uma ligeira dependência do momento magnético médio com o tamanho do grão. Nossos resultados mostram que há uma diferença significativa no comportamento de grãos e clusters livres. Para os campos hiperfinos, mostramos que este segue comportamentos semelhantes em todos os casos, tendo uma dependência sistemática com relação ao sítio / The discovery of giant magnetoresistance (GMR) in granular materiais generated a great interest in the study of these systems. Special attention has been devoted to Co grains inside Cu and Ag medium. As the transport properties are closely related to structural characteristics, an accurate description is required in order to understand the GMR behavior in these materiais. Here we use the Real Space-LMTO-ASA method to perform a systematic study of the site and grain size dependence of local magnetic moments and hyperfine fields at Co grains ( up to 135 atoms) in fcc Ag and Cu hosts. We have also studied Fe and Co atoms in different spatial configurations in Ag hosts: isolated impurities, Fe-Fe and Fe-Co dimmers and precipitates containing 13, 19 and 43 atoms. Special attention is given to the differences between central and interface positions of Fe atoms in the two smallest Co clusters. We found a very stable value for the local moment at Co atoms in Ag hosts whereas the average local moments for Co grains in Cu tend to be slight ly larger for larger grains. we show that free and embedded Co clusters have very different magnetic behavior. The hyperfine fields present similar values in both matrices and exhibit a systematic site dependence.

A descoberta da magnetoresistência (GMR) em materiais granulares gerou um grande interesse no estudo destes materiais, havendo um empenho particular no estudo de grãos de CO em CU e AG. Como as propriedades de transporte estão ligadas intimamente às estruturais, o entendimento da GMR nestes materiais requer uma descrição acurada destas características. Neste trabalho, procurando determinar algumas características magnéticas locais, usamos o método RS-LMTO-ASA para realizar um estudo sistemático dos momentos magnéticos locais e campos hiperfinos com respeito ao tamanho de grãos de CI com até 135 átomos em matrizes de CU e AG fcc. Além disso, estudamos FE e CO nas configurações espaciais seguintes em hospedeiro AG: impurezas isoladas, dímeros FE-FE e FE-CO e precipitados com 13, 19 e 43 átomos. Calculamos o FE enquanto impureza central nos grãos de CO e, para os clusters com 13 e 19 átomos, também consideramos a impureza em posições de interface. Encontramos para os grãos em AG momentos magnéticos bastante estáveis e, para o CU, obtivemos uma ligeira dependência do momento magnético médio com o tamanho do grão. Nossos resultados mostram que há uma diferença significativa no comportamento de grãos e clusters livres. Para os campos hiperfinos, mostramos que este segue comportamentos semelhantes em todos os casos, tendo uma dependência sistemática com relação ao sítio / The discovery of giant magnetoresistance (GMR) in granular materiais generated a great interest in the study of these systems. Special attention has been devoted to Co grains inside Cu and Ag medium. As the transport properties are closely related to structural characteristics, an accurate description is required in order to understand the GMR behavior in these materiais. Here we use the Real Space-LMTO-ASA method to perform a systematic study of the site and grain size dependence of local magnetic moments and hyperfine fields at Co grains ( up to 135 atoms) in fcc Ag and Cu hosts. We have also studied Fe and Co atoms in different spatial configurations in Ag hosts: isolated impurities, Fe-Fe and Fe-Co dimmers and precipitates containing 13, 19 and 43 atoms. Special attention is given to the differences between central and interface positions of Fe atoms in the two smallest Co clusters. We found a very stable value for the local moment at Co atoms in Ag hosts whereas the average local moments for Co grains in Cu tend to be slight ly larger for larger grains. we show that free and embedded Co clusters have very different magnetic behavior. The hyperfine fields present similar values in both matrices and exhibit a systematic site dependence.

[pt] Neste trabalho estudamos o comportamento dinâmico de um gás granular a baixa densidade do ponto de vista hidrodinâmico. Fizemos também uma análise de instabilidade linear das equações de Navier-Stockes para tais sistemas. Finalmente, construímos um modelo de sistema de celulas dinâmicas para simular computacionalmente esses sistema e o aplicamos a um gás granular, a fim de entender um pouco mais sobre seus comportamentos dinâmicos, sob diversas condições de contornos externos. / [en] In this work we study the dynamic behavior of a granular gas at low density from the hydrodynamic point of view. We also perform a linear instability analysis of the Navier- Stockes for such systems. Finally we construct a cell dynamic systems model to simulate computationally these systems and apply it for a granular gas in order to understand a little more about its dynamic behavior, under several boundary conditions.

Made available in DSpace on 2015-03-26T13:35:25Z (GMT). No. of bitstreams: 1 texto completo.pdf: 4745443 bytes, checksum: e9df978dd48087897127e59c83f364af (MD5) Previous issue date: 2006-03-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work we study the pattern formation in the interface between two types of granular materials in a Hele-Shaw cell. Different types of patterns, ranging from almost circular to fingered ones were observed, varying the ratio between the size of the grains and the cell spacing. The transition from patterns with fingers to rounded patterns seems to be continuous. The Fourier transform was obtained for the patterns with and without fingers. Patterns that present fingers showed mode selection, contrary to what happens for the rounded patterns. The dependence of the gyration radius and the number of particles at the border of the pattern was studied as a function of the number of particles inside the pattern. We observed that the gyration radius as well as the number of particles at the border of the pattern follow power laws. Analyses of the pattern border roughness showed that the Hurst exponent decreases as the patterns become more rounded. The roughness does not obey a power law with time. For the patterns with fingers the roughness increases with time and as the patterns become more regular it seem to tend to a saturation value. Finger formation is explained in terms of force transmission through the grains. / Em nosso trabalho, estudamos a formação de padrões na interface entre dois tipos de materiais granulares em uma célula de Hele-Shaw. Diferentes tipos de padrões, variando de desde quase-circulares a até padrões com dedos, formaram- se variando a razão entre o tamanho dos grãos e o espaçamento da célula. A transição de padrões com dedos para padrões arredondados parece ser contínua. Foi obtida a transformada de Fourier para os padrões com e sem dedos, sendo que padrões com dedos apresentam seleção de modos, ao contrário do que ocorre para os padrões sem dedos. A dependência do raio de giração e do número de partículas na borda do padrão foi estudada em função do número de partículas dentro do padrão. Observamos que tanto o raio de giração quanto o número de partículas na borda do padrão obedecem a leis de potência. A análise da rugosidade da borda dos padrões mostrou que o expoente de Hurst decresce à medida que os padrões se tornam mais arredondados. A rugosidade não obedece a uma lei de potência com o tempo. Para padrões com dedos a rugosidade aumenta com o tempo e à medida que os padrões se tornam mais regulares ela parece tender a um valor de saturação. A formação dos dedos é explicada em termos da transmissão de forças através dos grãos.

[pt] Neste trabalho estudamos o comportamento dinâmico de um gás granular a baixa densidade do ponto de vista hidrodinâmico. Fazemos também uma análise de instabilidade linear das equações de Navier-Stockes para tais sistemas. Finalmente, construímos um modelo de sistema de Células Dinâmicas para simular computacionalmente esses sistemas e o aplicamos a um gás granular, a fim de entender um pouco mais sobre seus comportamentos dinâmicos, inclusive a formação de aglomerados, sob as mais variadas condições de contorno. / [en] In this work we study the dynamic behavior of a granular gas at low density from the hydrodynamic point of view. We also perform a linear instability analysis of the Navier- Stockesfor for such systems. Finally, we construct a cell dynamic systems model to simulate computationally these systems and apply it for a granular gas in order to understand a little more about its dynamic behavior, enclose formation of clusters, under several boundary conditions.

[pt] Estendemos o formalismo de Fokker-Planck que foi usado previamente para descrever, a partir de primeiros princípios, o comportamento de um gás granular em esfriamento, com potencial de contato Hertziano e força de atrito viscoelástica o qual resulta em um sistema com coeficiente de restituição que depende da velocidade. Nesta tese é estudado, também a partir de primeiros princípios, o caso mais geral, o de um estado estacionário com energia cinética finita e fora do equilíbrio, devido ao acoplamento a um mecanismo externo de alimentação de energia. Estende- se assim a validade do resultado prévio. / [en] We extend the Fokker-Planck formalism used previously to describe the behavior of a cooling granular gas, with a Hertzian contact potential and viscoelastic radial friction, giving a velocity dependent coeficient of restitution. In this thesis, we study the more general case of a steady-state with finite kinetic, energy and far from equilibrium, due to the coupling to an external energy- feeding mechanism, also from first-principles, and extend the validity of the former results.

[pt] Neste trabalho estudamos o comportamento dinâmico de uma mistura binária granular submetida a uma equação do tipo Cahn-Hilliard com o objetivo de observar o fenômeno da segregação. Construímos um modelo de sistema de células dinâmicas para simularmos computacionalmente esses sistemas e observarmos o seu comportamento, a fim de comparar nosso modelo com o que é observado experimentalmente. / [en] In this work we study the dynamic behavior of a granular binary mixture with the aim of investigation phenomenom. We construct also a cell dynamic systems model to simulate computationally these systems and observe its behaviour, in order to compare our model with the experiments.

Cette thèse couvre l'auto-assemblage de particules dipolaires (magnétiques/électriques). Ces systèmes sont abondants en physique de la matière condensée (molécules et nanoparticules magnétiques, particules colloïdales magnétiques, bactérie magnétotactique, etc.). Sur un plan fondamental, ils représentent un défi important en raison de l'anisotropie et de la longue portée de l'interaction de paire. Le principal objectif de ce travail de recherche est de prédire les microstructures de ces systèmes en tenant compte de façon adéquate de l'interaction complexe dipôle-dipôle ainsi que des effets stériques et ceux dus à un éventuel confinement. Comprendre et revisiter les interactions de filaments dipolaires tels que des aiguilles et des chaînes faites de billes dipolaires est une première étape importante de cette thèse. En effet, les chaînes sont les constituants élémentaires de nombreux systèmes dipolaires, notamment sous l'effet d'un champ magnétique extérieur appliqué. Ensuite, l'agrégation colonnaire des chaînes dipolaires est examinée, ce qui conduit aussi naturellement à l'étude des cristaux dipolaires massifs où une nouvelle phase est découverte. Le cas plus générique des chaînes hélicoïdales est discuté en considérant les situations limites que sont les chaînes linéaires droites et en zigzag. L'association des chaînes dipolaires, dans le cas bidimensionnel, forme des rubans, puis une monocouche avec un réseau hexagonal. La réponse non triviale d'un tel réseau à un champ magnétique perpendiculaire imposé est aussi étudiée. Il est démontré qu'un réseau rhombique peut être induit de cette façon. Finalement, la sédimentation de particules paramagnétiques dans une monocouche inclinée en présence d'un champ magnétique est explorée via une étude mêlant expériences, théorie et simulations. L'ordre induit par gravité s'avère être une voie prometteuse pour l'élaboration contrôlée de réseaux bidimensionnels / This thesis covers the self-assembly of dipolar (magnetic/dielectric) particles. These systems are abundant in condensed matter physics (magnetic molecules and nanoparticles, magnetic colloidal particles, magnetotactic bacteria, etc). They also represent a fundamental challenge owing to the both long range and anisotropic nature of the pair interaction. The main objective of this research work is to predict the microstructures of these systems by properly handling the intricate dipole-dipole interaction combined with steric and possibly confinement effects. Understanding and revisiting the interaction of dipolar filaments such as needles or chains made up of dipolar beads is a first important achievement in this thesis. Indeed, the chains are the fundamental building blocks of many dipolar systems especially under applied external magnetic field. Then, the columnar aggregation of dipolar chains is investigated which naturally leads to the study of the bulk dipolar crystals. A new phase is discovered there. The more generic case of helical chains is discussed by considering limiting situations such as straight linear chains and zigzag chains. The association of dipolar chains in two-dimensions forms ribbons then a monolayer with triangular lattice symmetry. The interesting response of such a layer to an imposed perpendicular magnetic is addressed as well. It is demonstrated that rhombicity can be induced that way. Finally, sedimenting paramagnetic particles in a tilted monolayer in presence of a magnetic field are investigated by experiments, theory and simulations. The gravity-mediated ordering is found to be a promising route to elaborate tailored two-dimensional patterns

In this thesis we have explored the no equilibrium phase behavior and dynamics of an agitated monolayer of macroscopic rod-like particles. The main objective of this thesis was to highlight the ways in which even the simplest nonequilibrium 2Dliquid-crystallinen system differs qualitatively from its thermal equilibrium counter part. One major finding of ours is the extreme sensitivity to shape in these nonequilibrium systems. In chapter 3 we saw that tapering the ends of the particles induced a change from 2–fold ordering to 4–fold ordering. As far as we know, this is the first experimental observation of ‘tetratic’ correlations in equilibrium or nonequilibrium settings. This shape dependence is also pronounced in the single particle dynamics where, in chapter 5, we saw that similar-shaped objects behave differently even if they have dissimilar aspect ratios. Another important finding of ours is that the density fluctuations in the nonequilibrium nematic are not merely larger than, but qualitatively different from, those seen in their equilibrium counterparts: the fluctuations of the population, in a region containing on average N particles, grow much faster than √N . Then on equilibrium nature of the systems we study is clearly visible even at the single-particle level where we observe violations of equipartition in all the particles we study. The anomalous fluctuations we observe can be under stood in the light of theories of flocking. We have motivated why our system can be thought of as a granular flock and in chapter 4 presented various quantitative observations that justify this claim: we see giant fluctuations that decay only logarithmically in time as predicted by a theory of active nematics. This supports the idea that granular systems can provide a faithful imitation of the collective dynamics of living flocks, thus offering an attractive and easily control able system on which to test the predictions of flocking theories. A part from being a table-top experiment, , our system has the two substantial advantages over living systems that there are no products of metabolism which need removing and that the population remains constant. Our work highlights the fact that the fascinating phenomena of flocking ,coherent motion and large-scale in homogeneity seen in living matter can be obtained in a system in which particles do not communicate except by contact, have no sensing mechanisms and are not influenced by the spatially-varying pressures and incentives of a biological environment. Directions to go from here are aplenty. There is a lot that needs to be done towards understanding the origins of the anomalous fluctuations: do they arise due to the coupling of mass currents to gradients in the nematic director field or is there some other mechanism at play? Though the observed motion of disclinations suggests the former, a thorough hand systematic study of defect behavior is lacking. How defects interact and whether there is any analogy to thermal-equilibrium defect-behavior is completely unexplored, theoretically and experimentally. Indeed, this would be of interest purely as a problem in nonequilibrium statistical mechanics independent of whether or not the system is described by theories of active nematics. A part from settling the important, fundamental issues regarding the giant fluctuations, one can explore the entire spectrum of rod-like particles and study its dynamics and phase behaviour. What happens to collections of javelins that are agitated in 2D geometries? Do they form steadily-moving flocks? What about the short cylinders? We have seen that in the dilute limit they behave in a polar fashion but at high area fractions they form a polar, 4–fold correlated states. At Intermediate densities will they form a polar phase? Why is it that the long cylinders do not show any polar dynamics? What factors govern whether a particle is polar or not? Can one engineer particles to efficiently translate random impulses in to directed motion? Thus, even the single particle dynamics offers many avenues for experimental exploration. However, there is also scope for theoretical work in this direction. A sound theoretical understanding of the individual particle’s behaviour will then pave the way for a microscopic theory for the collective granular-rod state.. This can then be compared to the active and flocking literature which his, largely, of a phenomenological nature as of now. In conclusion, we would like to say that our experiments have revealed many important and fascinating nonequilibrium phenomena. Our experiments demonstrate situations where ‘effective equilibrium’ approaches are in adequate. Such descriptions can accommodate neither the slow, giant, collective fluctuations we observe nor the non-equipartition at the single-particle level. Finally, as is often the case, our studies have thrown open many more questions than they have answered. We hope our experiments stimulate further studies and we believe that we are witnessing the birth of a new subfield at the crossroads of granular physics and the physics of flocks.