The scaling of specific cutting energy is studied when micro-cutting ductile metals. A unified framework for understanding the scaling in specific cutting energy is first presented by viewing the cutting force as a combination of constant, increasing, and decreasing force components, the independent variable being the uncut chip thickness. Then, an attempt is made to isolate the constant force component by performing high rake angle orthogonal cutting experiments on OFHC Copper. The data shows a trend towards a constant cutting force component as the rake angle is increased. In order to understand the source of this constant force component the chip-root is investigated. By quickly stopping the spindle at low cutting speeds, the chip is frozen and the chip-workpiece interface is examined in a scanning electron microscope. Evidence of ductile tearing ahead of the cutting tool is seen at low and high rake angles. At higher cutting speeds a quick-stop device is used to obtain chip-roots. These experiments also clearly indicate evidence of ductile fracture ahead of the cutting tool in both OFHC Copper and Al-2024 T3. To model the cutting process with ductile fracture leading to material separation the finite element method is used. The model is implemented in a commercial finite element software using the explicit formulation. Material separation is modeled via element failure. The model is then validated using the measured cutting and thrust forces and used to study the energy consumed in cutting. As the thickness of layer removed is reduced the energy consumed in material separation becomes important. Simulations also show that the stress state ahead of the tool is favorable for ductile fracture to occur. Ductile fracture in three locations in an interface zone at the chip root is seen while cutting with edge radius tool. A hypothesis is advanced wherein an element gets wrapped around the tool edge and is stretched in two directions leading to fracture. The numerical model is then used to study the difference in stress state and energy consumption between a sharp tool and a tool with a non-zero edge radius.

In this thesis the entanglement properties of atom-atom, atom-photon, and photon-photon are investigated. The recent developments of quantum computation as well as quantum information and communication have attracted much interest in the generation of these entanglements in the laboratory. To generate atom-photon entanglement, I discuss a model system in the cavity QED setup. By using a four-level atom and two resonant cavity modes, we can generate atom-photon entanglement almost deterministically. An extension of the above model to a six-level atom and again two resonant cavity modes can generate entangled photon pairs by appropriately adjusting system parameters. I then investigate the atom-atom entanglement in a 1D harmonic trap. I show the dependence of the pair entanglement on the scattering length and temperature, as well as the particle symmetry requirement (bosons or fermions). Among many peculiar properties in a 1D system, we briefly discuss the Fermi-Bose duality". While the entanglement properties of a single-channel model have recently been obtained for 1D and 3D systems, I thus study the entanglement of a multi-channel process in a cylindrical harmonic trap. I discuss the dependence of entanglement on the trap geometry. Finally I present detailed studies of the spin mixing between two Rb87 atoms in a single lattice site. The topic is emphasized on various motional state approximations and dipolar effect. Various motional state approximations can cause up to 20% error to experimental data. I also find that the dipolar interaction can lead to an experimentally observable frequency shift in a cylindrical harmonic trap with very large aspect ratio. The spin mixing of spin-2 manifold has also been discussed.

Thesis (M.S.)--University of Central Florida, 2009. / Adviser: Kuo-Chi Lin. Includes bibliographical references (p. 84-92).

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This thesis presents four investigations into mechanical aspects of soft thin structures, focusing on the effects of stochastic and thermal fluctuations and of material inhomogeneities. First, we study the self-organization of arrays of high-aspect ratio elastic micropillars into highly regular patterns via capillary forces. We develop a model of capillary mediated clustering of the micropillars, characterize the model using computer simulations, and quantitatively compare it to experimental realizations of the self-organized patterns. The extent of spatial regularity of the patterns depends on the interplay between cooperative enhancement and history-dependent stochastic disruption of order during the clustering process. Next, we investigate the influence of thermal fluctuations on the mechanics of homogeneous, elastic spherical shells. We show that thermal fluctuations give rise to temperature- and size-dependent corrections to shell theory predictions for the mechanical response of spherical shells. These corrections diverge as the ratio of shell radius to shell thickness becomes large, pointing to a drastic breakdown of classical shell theory due to thermal fluctuations for extremely thin shells. Finally, we present two studies of the mechanical properties of thin spherical shells with structural inhomogeneities in their walls. The first study investigates the effect of a localized reduction in shell thickness—a soft spot—whereas the second studies shells with a smoothly varying thickness. In both cases, the inhomogeneity significantly alters the response of the shell to a uniform external pressure, revealing new ways to control the strength and shape of initially spherical elastic capsules. / Engineering and Applied Sciences

Over the last few years there has been a surge of activity within the physics community in the emerging field of Econophysics—the study of economic systems from a physicist's perspective. Physicists tend to take a different view than economists and other social scientists, being interested in such topics as phase transitions and fluctuations. In this dissertation two simple models of stock exchange are developed and simulated numerically. The first is characterized by centralized trading with a market maker. Fluctuations are driven by a stochastic component in the agents' forecasts. As the scale of the fluctuations is varied a critical phase transition is discovered. Unfortunately, this model is unable to generate realistic market dynamics. The second model discards the requirement of centralized trading. In this case the stochastic driving force is Gaussian-distributed "news events" which are public knowledge. Under variation of the control parameter the model exhibits two phase transitions: both a first- and a second-order (critical). The decentralized model is able to capture many of the interesting properties observed in empirical markets such as fat tails in the distribution of returns, a brief memory in the return series, and long-range correlations in volatility. Significantly, these properties only emerge when the parameters are tuned such that the model spans the critical point. This suggests that real markets may operate at or near a critical point, but is unable to explain why this should be. This remains an interesting open question worth further investigation. One of the main points of the thesis is that these empirical phenomena are not present in the stochastic driving force, but emerge endogenously from interactions between agents. Further, they emerge despite the simplicity of the modeled agents; suggesting complex market dynamics do not arise from the complexity of individual investors but simply from interactions between (even simple) investors. Although the emphasis of this thesis is on the extent to which multi-agent models can produce complex dynamics, some attempt is also made to relate this work with empirical data. Firstly, the trading strategy applied by the agents in the second model is demonstrated to be adequate, if not optimal, and to have some surprising consequences. Secondly, the claim put forth by Sornette et al. that large financial crashes may be heralded by accelerating precursory oscillations is also tested. It is shown that there is weak evidence for the existence of log-periodic precursors but the signal is probably too indistinct to allow for reliable predictions.

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