We construct a 4d Lorentzian spin foam model capable of describing both spacelike and timelike surfaces. To do so we use a coherent state approach inspired by the Riemannian FK model. Using the coherent state method we reproduce the results of the EPRL model for Euclidean tetrahedra and extend the model to include Lorentzian tetrahedra. The coherent states of spacelike/timelike triangles are found to correspond to elements of the discrete/continuous series of SU(1,1). It is found that the area spectrum of both spacelike and timelike surfaces is quantized. A path integral for the quantum theory is defined as a product of vertex amplitudes. The states corresponding to timelike triangles are constructed in a basis diagonalised with respect to a noncompact generator. A derivation of the matrix elements of the generators of SL(2,C) in this basis is provided.

No description available.

The macroscopic behaviour of a two-phase foam depends on chemical properties such as surface tension, and physical properties such as the shape and size of the bubbles in the foam. The chemical properties of a foaming material may be deduced from experiments on the material in the single phase, for example surface tension or viscosity measurements. However, in order to measure structure the foam must clearly be present. This presents a difficult problem, especially for liquid foams which are often fast-moving and liable to collapse or rearrange on coming into contact with a probe. Optical techniques for examining foam structures can be non-invasive and take advantage of the semi-transparent nature of many liquid and solid foams. In particular, the application of confocal and axial tomography systems to real three-dimensional cellular foams can resolve their local geometric structure. This thesis covers the application of new optical tomographic techniques to the imaging of foams and presents the first three-dimensional models of bubble structure in liquid and solid foams. Complete descriptions of the hardware and software are included; imaging systems are based on a personal computer with an inexpensive video digitising card and a CCD camera. A clear advantage of optical systems is that the high data bandwidth required for tomography is available even on relatively slow computers by modern standards. Typically, all the data for a sixteen-million (256³) voxel model covering a world volume of 64mm³ can be acquired in a period of 30 seconds. Results from this work include the first three-dimensional solid models of observed foams, both aqueous and polyurethane-based, including volume models of minimal energy cellular foam configurations. In particular, Kelvin's proposed minimal cell and also bubbles from the Weaire-Phelan structure have been resolved by the system.

The rheological properties of polymer melts and polymer/blowing agent (BA) solutions are determined experimentally and the influences of material rheological properties and crystallization on low-density foaming behaviour of polylactic acid (PLA) are investigated. Understanding the rheological properties of foaming polymers allows the optimization of polymer chemical structure and the development of technologies that produce desired cell morphologies. Although the technology for producing CO2-blown polystyrene (PS) foams is well established, the rheological properties of a PS/CO2 solution, especially its extensional property, are not well understood. In this study, these properties are determined with an in-house developed, online technique, and the measured data are compared with those from commercial rheometers. The online measurement system consists of a tandem foam extrusion system and a die for measuring pressure drops. Shear viscosity is determined from the pressure drop over a straight rectangular channel, while planar extensional viscosity from the pressure drop over a thin hyperbolic channel, taking into account the pressure drop due to shearing. Measured viscosities of the polystyrene without CO2 compare well with those from commercial rheometers. With the presence of dissolved CO2, both the shear and extensional viscosities of the polystyrene are significantly reduced. The influence of CO2 on the two viscosities is found to be similar to an increase of temperature. Polylactic acid is the first mass-produced biodegradable polymer, and has potential to replace petroleum-based polymers in foaming applications. In this study, the influences of material rheological properties and crystallization on the low-density, microcellular extrusion foaming behaviour of polylactic acids (PLAs) are investigated. Comparisons are made between linear and branched PLAs and between amorphous and crystalline PLAs. The branched PLAs are found to produce foams with higher expansion ratios and reduced open-cell content compared to the linear PLA. The foaming behaviour of the linear PLA, then, is significantly improved by adding a small amount of long-chain-branched PLA. The improved cell structure with branched PLAs is attributed to their relatively high melt strength and strain to break. For the first time, it is shown that crystallization, induced by cooling and macroscopic flow during processing, increases melt strength, which aids the production of low-density foams.

Dielectric materials are used as spacers in antennas. The design of the dielectric determines the properties of the antenna. The insertion of high dielectric materials in a specific pattern into a low dielectric matrix material is one means to accomplish this. This thesis studies the means to insert metal cylinders (wire or nails) into polymer foams to produce such a material. Depending on the antenna properties desired, the patterns and number of nails varies tremendously. To decrease the manufacturing time and, therefore, the cost of creating these materials, an automatic machine capable of rapidly inserting wires to a predetermined pattern is developed. This thesis has two parts. In the first part, the ballistic impact of nails into foam is modeled. Experimental observations of the nails impacting the foam are used to verify the model. Penetration equations are developed to express the penetration capability of a nail into foam. All of this allows one to predict the forces required for a nail to be inserted into foam to a desired depth, thereby facilitating manufacture of these dielectric materials. In the second part, a fully automatic nail insertion device is designed, fabricated, and tested with the experimental tests used as control settings.

Dissertation (Ph.D.)--Auburn University, / Abstract. Vita. Includes bibliographic references (p.114-125).

Physical properties and morphology of extruded semicrystalline polymers can be significantly affected by modification and change in die design and melt viscosity of the molten polymer. Further modifications to physical properties (i.e. density and open cell fraction) of foamed material occur, following the modification of melt viscosity by melt blending of polypropylene and high density polyethylene). The main object of this research project was to carry out a systematic examination of rheological properties of polymer/gas mixture, affect of die design, polymer molecular weight (melt viscosity), and processing conditions on density, open cell fraction, cell morphology (i.e. cell size and cell size distribution) and micromorphology of polyolefin foams. Also attention was given to method of stabilisation of extruded foam, where, it was found support of the extrudated foam (by adding a specially designed die adapter to the end of the die) prior to entering the cooling tank could result not only to a specimen with uniform cross section, but also due to drop in melt temperature, the cell walls are to some extent rigidized, hence, the collapse of bubbles are limited. From commercial point of view control of cell collapse, density and open cell fraction, will make these foamed materials valuable for their filtration characteristics. Microstructural analysis of polypropylene (unfoamed state) by X-ray diffraction and Differential Scanning Calorimetry revealed 13-spherulites are only formed in skin layer, and beneath the thickness of 500 pm from the surface, the crystal structure of this polymer is only consist of B-spherulites. On the other hand, the chemical blowing agent (Hydrocerol CF-20), was found to have nucleating affect on microstructure of polypropylene, where, it has resulted in reduction of size of spherulites together with a drop in recrystallisation temperature and formation of P and a spherulites through the thickness of extrudated foam. The foregoing chemical blowing agent was found to have no significant affect on the crystal structure of the high density polyethylene.

Ceramic and refractory metal foams have a potential for use in extreme environments, such as in fuel elements within nuclear reactors both in space and terrestrial applications. In addition, infiltrating an open-cell ceramic foam with a continuous second phase can create an interpenetrating phase composite (IPC), consisting of a three-dimensional reinforcement structure. One aspect of investigation within this study was the influence of foam pore/strut size, foam composition, and foam density on neutronic and mechanical properties. Neutron transmission through open-cell tantalum carbide foams was measured using experimental techniques and modeled with Monte Carlo N-Particle (MCNP) transport code. Neutron transmission decreased linearly within tantalum carbide (TaC)/reticulated vitreous carbon (RVC) foams as areal TaC density increased. All MCNP modeling runs predicted slightly higher neutron transmission than what was experimentally measured, potentially indicating that the foam structure had a small influence on neutron transmission. Compressive strength and Young's moduli of tantalum carbide foams were measured for foam specimens that were exposed to thermal cycling and thermal shock, as well as for baseline specimens. Extensive micro-cracking was observed in the foams after 18 thermal cycles to 2100°C. However, thermal shock in liquid nitrogen did not produce observable micro-cracking in the TaC foams. The average strengths of baseline TaC/RVC foams ranged from 1.97 MPa - 3.82 MPa. The baseline TaC/PyC/RVC foams exhibited strengths ranging from 4.57 MPa - 12.60 MPa. The compressive strength of thermally cycled foams tended to be 1/3-1/2 that of baseline specimens. Another aspect of this study investigated the infiltration of RVC foams with tungsten powder in an attempt to form a tungsten-ceramic foam interpenetrating phase composite (IPC). It was found that tungsten particle size influenced infiltrated densities more than foam pore size. Significantly lower infiltrated densities were obtained using sub-micron tungsten than with 5-10 micron tungsten as a result of particle agglomeration. Infiltrated 5-10 micron tungsten achieved densities ranging from 23-25% theoretical within RVC foams, whereas sub-micron tungsten densities ranged from 11-16% theoretical. Constrained densification was observed during sintering of tungsten-infiltrated foams. / Ph. D.

The dissertation presents two distinct but related studies of foam. The initial investigation involves the evaluation of a method of controlling foaming in aerated fermenters; the second involves the evaluation of a method of characterization of durable foams. Since foaming has frequently been a problem of considerable magnitude in aerated waste treatment and various other aerated cultures, a method was conceived which involved the disruption of foam at the liquid-foam interface during carriage as a result of an accelerated converging flow through a down flow draft tube. The principles of the method were based on the creation of differential shearing forces at the foam-liquid interface to cause disruption of foam at the interface and subsequent re-entrainment during the convergence of flow through the down flow draft tube. The geometry of the inlet to the draft tube, recirculation rate, and hydraulic head over the inlet were principal variables affecting the degree of foam control. Foam control performance increased with increased diameter of the inlets as a result of the reduced tendencies of foam to span or 2 bridge inlets of larger size. Increased recirculation rate and low hydraulic head over the inlet offered the greatest potential relative to foam re-entrainment; however, the conditions of increased recirculation rate and low hydraulic head resulted in air being drawn into the draft tube in addition to the foam-liquid mixture. The foam subsequently re-appearlng at the liquid surface possessed a dense, fine hubble structure which was resistant to control. The method proved successful on a short-term basis in as much as operational times were extended to about six times those required to generate comparable volumes of foam while employing aeration only. For extended operational periods, the method resulted in resistant foams which defied control by the process. During the course of the foam control investigation a method was sought which could practically be employed to evaluate the durability properties of foams for routine characterization measurements.The natural collapse periods for foams resulting from the employed alkyl benzene sulfonate (ABS) solutions were of such duration to be impractical for repetitive measurements. A method was conceived whereby the destruction of teams could be accelerated by application of an external force. The method involved application of a weighted disc assembly to a definite volume of foam confined in a 3.75-inch inside diameter foam generation column. The principle of the method was based on the hypothesis that a measure of the durability properties of teams could he obtained relative to the rate of collapse under applied stress, The method was evaluated on foams generated from solutions containing ABS concentrations ranging from 20 to 120 ppm employing aeration rates of 0.75, 1.5, and 2.45 l/min, Measurements consisted of recording the level of disc descent at one-minute intervals until the disc reached the liquid surface, The results were presented as disc descent rates or slopes of the disc descent curves for each measurement. Experiments employing static decay methods were performed to observe the behavior of foams subjected to destruction due to natural causes, Measurements consisted of observing the remaining foam level at one-half hour intervals for a total period of eight hours. The results were presented graphically as foam collapse vs time curves and quantitatively in terms of the average lifetime of the teams. The results of the experiments employing the weighted disc and the experiments employing static decay methods agreed insofar as the durability properties of foam were enhanced by increased ABS concentration and low aeration rate. The results of both methods indicated that, on a comparative basis of the data and by a statistical analysis of the data, aeration rate had a more pronounced effect on foam character than ABS concentration for the ranges of the variables employed in the investigation. The periods required for completion of the measurements of the weighted disc experiment: ranged from about 10 to 25 minutes which represent a considerable saving in time in comparison to the length of experiments employing static decay procedures. The rapidity and simplicity of the method employing the weighted disc appear to make this method applicable for routine characterization measurements of durable foams. / Ph. D.

This thesis examines potential improvements to current coal mine fire response measures. In the event of a fire scenario, indirect testing and analysis of the exhausting air is needed to characterize changes in the fire. The application of multiple passive source tracers provides improved detail of complex ventilation interactions over an extended period of time. The first work in this thesis details the testing of the passive release rates for three Perfluorocarbon tracer compounds over a 180-day period. The results of this study demonstrate the ability for the permeation plug release vessel design to release Perfluorocarbon tracers at a steady rate. Current response methods for a fire in a coal mine gob consist of injection of inert gas and sealing of the mine openings. Injection of high expansion foam into the gob from the surface has potential to improve extinguishment of the fire and reduce the time needed to bring the mine back to an operational state. The applicability of this method requires computational modeling and field testing. The second part of this thesis determines the Darcy and Forchheimer values for high expansion foam flow in simulated gob material with a lab experiment. The experiment was replicated in the CFD software, OpenFOAM, to validate the methods for calculation of the Darcy and Forchheimer values. The results of this study provide a tested methodology for a future full scale modeling of high expansion foam injection in a coal mine gob. / Master of Science