Allan J. Lichtenberg. / "October, 6, 1954." "This report is based on a thesis submitted to the Department of Electrical Engineering, M.I.T., ... for the degree of Master of Science." / Bibliography: p. 27. / Army Signal Corps Contract DA36-039 sc-42607 Project 132B Dept. of the Army Project 3-99-12-022

As technological advances occur, many conventional materials are incapable of providing the unique multi-functional characteristics demanded thus driving an accelerated focus to create new material systems such as carbon and graphite foams. The improvement of their mechanical stiffness and strength, and tailoring of thermal and electrical conductivities are two areas of multi-functionality with active interest and investment by researchers. The present research focuses on developing models to facilitate and assess multi-functional carbon foams in an effort to expand knowledge. The foundation of the models relies on a unique approach to finite element meshing which captures the morphology of carbon foams. The developed models also include ligament anisotropy and coatings to provide comprehensive information to guide processing researchers in their pursuit of tailorable performance. Several illustrations are undertaken at multiple scales to explore the response of multi-functional carbon foams under coupled field environments providing valuable insight for design engineers in emerging technologies. The illustrations highlight the importance of individual moduli in the anisotropic stiffness matrix as well as the impact of common processing defects when tailoring the bulk stiffness. Furthermore, complete coating coverage and quality interface conditions are critical when utilizing copper to improve thermal and electrical conductivity of carbon foams.

The Wind-Evaporation-Sea Surface Temperature (WES) feedback is believedto play an important role in the tropics, where climate variability is governed byatmosphere-ocean coupled interactions. This dissertation reports on studies to distinctlyisolate the WES feedback mechanism over tropical oceans using a modiedversion of an NCAR-Community Climate Model (CCM3) thermodynamically coupledto a slab ocean model, where the WES feedback is deliberately suppressed inthe bulk aerodynamic formulation for surface heat uxes. A comparison of coupledintegrations using the modified WES-off CCM3 to those carried out using the standardCCM3 conclusively identifies the role of the WES feedback in enhancing theinter-annual variability over deep tropical oceans and the westward propagation ofthe equatorial annual cycle. An important role for near surface humidity in tropicalclimate variability in enhancing inter-annual variability and in sustaining the equatorialannual cycle is also suggested. Statistical analyses over the tropical Atlanticreveal that the free coupled meridional mode of the Atlantic Ocean is amplified in thepresence of the WES feedback. Similar analyses of coupled model integrations, whenforced with an articial El Ni~no Southern Oscillation (ENSO)-like SST cycle in tropicalPacific, reveal that only in the presence of the WES feedback is the meridionalmode the preferred mode of response of the Atlantic to ENSO forcings. It is also foundthat WES feedback reinforces the tendency of the ITCZ to stay north of the equator over the Atlantic during El-Nino events. Comparative studies between Last GlacialMaximum (LGM) equivalent imposed northern hemispheric sea-ice experiments withthe WES-off model and the standard model indicate a dominant role for the WESfeedback in the southward shift of the ITCZ as indicated by paleo-climate records.However, it is found not to be the sole thermodynamic mechanism responsible for thepropagation of high latitude cold SST anomalies to the tropics, suggesting significantroles for other mechanisms in the tropical response to high latitude changes.

Relations between propagators and Green functions of Hamiltonians which are SUSY partners have been obtained. New exact propagators for the family of multi-well, time-dependent and non-hermitian potentials have been calculated. Non-conservative SUSY transformation has been studied in the case of multichannel Schrodinger equation with different thresholds. Spectrum (bound/virtual states and resonances) of the non-conservative SUSY partner of zero potential has been founded. Exactly solvable model of the magnetic induced Feshbach resonance has been constructed. This model was tested in the case of Rb$^{85}$. Conservative SUSY transformations of the first and the second order have been studied in the case of multichannel Schrodinger equation with equal thresholds. Transformations which introduce non-trivial coupling between scattering channels have been founded. The first order SUSY transformation which preserves $S$-matrix eigen-phase shifts and modifies mixing parameter has been founded in the case of two channel scattering with partial waves of different parities. In the case of coinciding parities we have found the second order SUSY transformation which preserves $S$-matrix eigen-phase shifts and modifies mixing parameter. Phenomenological two channel $^3S_1-^3D_1$ neutron-proton potential has been obtained by using single channel, phase equivalent and coupling SUSY transformations applied to zero potential.

The kinetic effects in an inductively coupled plasma (ICP) due to thermal motion of particles modified by self-consistent magnetic fields are studied by using a particle-in-cell (PIC) simulation. In the low pressure, low frequency regime, electron mean free paths are large relative to device size and the trajectories are strongly curved by the induced radio frequency (RF) magnetic field. This causes problems for linear theories, which ignore the influence of the magnetic field on the particles, and are therefore unable to recover effects accumulated along each nonlinear path.<p>The tools to perform high-performance parallel PIC simulations of inductively coupled plasmas were developed to allow rapid scanning of a broad range of the input parameters, such as wave amplitude, frequency, and plasma temperature. Different behavioural regimes are identified by observing the resultant variations in the skin depth, surface impedance, and ponderomotive force (PMF). At low electron-neutral collision rates, these are shown to include the local collisionless regime, the anomalous skin effect regime, and the nonlinear regime.<p>The local collisionless regime occurs at high driving frequencies and is characterized by plasma behaviour independent of both the driving frequency and amplitude: a short skin depth, low energy absorption, and strong PMF. The anomalous skin effect regime occurs at low frequencies and low amplitudes: the plasma varies with driving frequency, but not driving amplitude, the skin depth increases with frequency, the plasma is much more absorptive in the anomalous regime than in the local regime, and the PMF increases with frequency. The nonlinear regime occurs at low frequencies and high amplitudes: the plasma varies with driving amplitude, but not frequency, the skin depth decreases with amplitude, there is low energy absorption, and the PMF increases with wave amplitude.<p>The simulation runs in four modes: linear collisionless, linear collisional, nonlinear collisionless, and nonlinear collisional. The linear modes, in which the particles ignore the magnetic field, are used to validate the results against theory, while the nonlinear modes are used to test actual plasma behaviour. In linear collisionless mode, the plasma was found to exhibit only the local collisionless and anomalous skin effect regimes, as expected by theories. In nonlinear collisionless mode, the plasma exhibits the nonlinear regime in addition to the regimes found in linear mode. Finally, the nonlinear regime disappears in nonlinear collisionless mode because the curved paths caused by the magnetic field are disrupted by collisions.<p>Finally, the regime boundaries are investigated as a function of temperature. Since the plasma properties vary continuously, a boundary exists where two regimes share the same characteristics. From linear theories, it is known that the division between the local collisionless and anomalous skin effect regimes moves to higher frequencies as the plasma temperature is increased. When nonlinear fields are present, this still occurs, but in conjunction with the boundary between the local collisionless and nonlinear regimes moving to higher wave amplitudes. Temperature also effects the boundary between the anomalous skin effect and nonlinear regimes, causing the minimum frequency of the anomalous skin effect regime to be reduced at low wave amplitudes.

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The hippocampus is one of the most intensely studied brain structures and the oscillatory activity of the hippocampal neurons is believed to be involved in learning and memory consolidation. Therefore, studying rhythm generation and modulation in this structure is an important step in understanding its function. In this thesis, these phenomena are studied via mathematical models of networks of hippocampal interneurons. The two types of neural networks considered here are homogenous and heterogenous networks. In homogenous networks, the input current to each neuron is equal, while in heterogenous networks, this assumption is relaxed and there is a specified degree of heterogeneity in the input stimuli. A phase reduction technique is applied to the neural network model of the hippocampal interneurons and attempts are made to understand the implications of heterogeneity to the existence and stability of the synchronized oscillations. The Existence of a critical level of heterogeneity above which the synchronized rhythms are not stable is established, and linear analysis is applied to derive expressions for estimating the perturbations in the network frequency and timing of the neural spikes. The mathematical techniques developed in this thesis are general enough to be applied to models describing other types of neurons not considered here. Possible biological implications include the application of high frequency local stimulation to alleviate the synchronous neural oscillations in pathological conditions such as epilepsy and Parkinson's disease and the possible role of heterogeneity in controlling the rhythm frequency and switching between various cognitive states.

The hippocampus is one of the most intensely studied brain structures and the oscillatory activity of the hippocampal neurons is believed to be involved in learning and memory consolidation. Therefore, studying rhythm generation and modulation in this structure is an important step in understanding its function. In this thesis, these phenomena are studied via mathematical models of networks of hippocampal interneurons. The two types of neural networks considered here are homogenous and heterogenous networks. In homogenous networks, the input current to each neuron is equal, while in heterogenous networks, this assumption is relaxed and there is a specified degree of heterogeneity in the input stimuli. A phase reduction technique is applied to the neural network model of the hippocampal interneurons and attempts are made to understand the implications of heterogeneity to the existence and stability of the synchronized oscillations. The Existence of a critical level of heterogeneity above which the synchronized rhythms are not stable is established, and linear analysis is applied to derive expressions for estimating the perturbations in the network frequency and timing of the neural spikes. The mathematical techniques developed in this thesis are general enough to be applied to models describing other types of neurons not considered here. Possible biological implications include the application of high frequency local stimulation to alleviate the synchronous neural oscillations in pathological conditions such as epilepsy and Parkinson's disease and the possible role of heterogeneity in controlling the rhythm frequency and switching between various cognitive states.

Warm forming of aluminum alloys of has shown promising results for increasing the formability of aluminum alloy sheet. Warm forming is a term that is generally used to describe a sheet metal forming process, where part or all of the blank is formed at an elevated temperature of less than one half of the material’s melting temperature. The focus of this work is to study the effects of warm forming on Novelis X926 clad aluminum brazing sheet. Warm forming of clad aluminum brazing sheet, which is commonly used in automotive heat exchangers has not been studied. This work can be split into three main goals: i) to characterize the material behavior and develop a constitutive model, ii) to experimentally determine the effects of warm forming on deep drawing; and, iii) to create and validate a finite element model for warm forming of Novelis X926. For an accurate warm forming material model to be created, a temperature and rate dependant hardening law as well as an anisotropic yield function are required. Uniaxial isothermal tensile tests were performed on 0.5mm thick Novelis X926at 25°C (room temperature), 100°C, 150°C, 200°C, and 250°C. At each temperature, tests were performed with various strain rates between 7.0 E -4 /sec and 7.0 E -2 /sec to determine the strain rate sensitivity. Tensile tests were also performed at 0° (longitudinal), 45° (diagonal), and 90° (transverse) with respect to the material rolling direction in order to assess the anisotropy of the material. It was found that increasing forming temperature increases elongation to failure by 200%, decreases flow stress by 35%, and increases strain rate sensitivity. Barlat’s Yield 2000 yield function (Barlat et al., 2003a) and the Bergström work hardening law (van den Boogaard and Huétink , 2006) were found to accurately method model the material behavior. Warm deep drawing of 101.6 mm (4”) diameter cylindrical cups was performed using specially designed tooling with heated dies and a cooled punch. Deep drawing was performed on 228.6 mm (9“) and 203.2 mm (8”) diameter blanks of 0.5 mm thick Novelis X926. Deep drawing was performed with die temperatures ranging from 25°C to 300°C with a cooled punch. Teflon sheet and Dasco Cast 1200 lubricants were used in experiments. Different punch velocities were also investigated. 228.6 mm diameter blanks, which could not be drawn successfully at room temperature, were drawn successfully using 200°C dies. Increasing the die temperature further to 250°C and 300°C provided additional improvement in formability and reduced tooling loads. Increasing the punch velocity, increases the punch load when forming at elevated temperatures, reflecting the strong material rate sensitivity at elevated temperatures. A coupled thermal mechanical finite element model was developed using the Bergström hardening rule and the Yield 2000 yield surface using LS-DYNA. The model was found to accurately predict punch force for warm deep drawing using Teflon sheet as a lubricant. Results for Dasco Cast 1200 were not as accurate, due to the difficulties in modeling the lubricant’s behavior. Finite element simulations demonstrated that warm forming can be used to reduce thinning at critical locations, compared to parts formed at room temperature.

The kinetic effects in an inductively coupled plasma (ICP) due to thermal motion of particles modified by self-consistent magnetic fields are studied by using a particle-in-cell (PIC) simulation. In the low pressure, low frequency regime, electron mean free paths are large relative to device size and the trajectories are strongly curved by the induced radio frequency (RF) magnetic field. This causes problems for linear theories, which ignore the influence of the magnetic field on the particles, and are therefore unable to recover effects accumulated along each nonlinear path.<p>The tools to perform high-performance parallel PIC simulations of inductively coupled plasmas were developed to allow rapid scanning of a broad range of the input parameters, such as wave amplitude, frequency, and plasma temperature. Different behavioural regimes are identified by observing the resultant variations in the skin depth, surface impedance, and ponderomotive force (PMF). At low electron-neutral collision rates, these are shown to include the local collisionless regime, the anomalous skin effect regime, and the nonlinear regime.<p>The local collisionless regime occurs at high driving frequencies and is characterized by plasma behaviour independent of both the driving frequency and amplitude: a short skin depth, low energy absorption, and strong PMF. The anomalous skin effect regime occurs at low frequencies and low amplitudes: the plasma varies with driving frequency, but not driving amplitude, the skin depth increases with frequency, the plasma is much more absorptive in the anomalous regime than in the local regime, and the PMF increases with frequency. The nonlinear regime occurs at low frequencies and high amplitudes: the plasma varies with driving amplitude, but not frequency, the skin depth decreases with amplitude, there is low energy absorption, and the PMF increases with wave amplitude.<p>The simulation runs in four modes: linear collisionless, linear collisional, nonlinear collisionless, and nonlinear collisional. The linear modes, in which the particles ignore the magnetic field, are used to validate the results against theory, while the nonlinear modes are used to test actual plasma behaviour. In linear collisionless mode, the plasma was found to exhibit only the local collisionless and anomalous skin effect regimes, as expected by theories. In nonlinear collisionless mode, the plasma exhibits the nonlinear regime in addition to the regimes found in linear mode. Finally, the nonlinear regime disappears in nonlinear collisionless mode because the curved paths caused by the magnetic field are disrupted by collisions.<p>Finally, the regime boundaries are investigated as a function of temperature. Since the plasma properties vary continuously, a boundary exists where two regimes share the same characteristics. From linear theories, it is known that the division between the local collisionless and anomalous skin effect regimes moves to higher frequencies as the plasma temperature is increased. When nonlinear fields are present, this still occurs, but in conjunction with the boundary between the local collisionless and nonlinear regimes moving to higher wave amplitudes. Temperature also effects the boundary between the anomalous skin effect and nonlinear regimes, causing the minimum frequency of the anomalous skin effect regime to be reduced at low wave amplitudes.