Relativistic quark models and the current algebra

In this thesis we are concerned with finding representations of the algebra of SU(3) vector and axial-vector charge densities at infinite momentum (the "current algebra") to describe the mesons, idealizing the real continua of multiparticle states as a series of discrete resonances of zero width. Such representations would describe the masses and quantum numbers of the mesons, the shapes of their Regge trajectories, their electromagnetic and weak form factors, and (approximately, through the PCAC hypothesis) pion emission or absorption amplitudes.

We assume that the mesons have internal degrees of freedom equivalent to being made of two quarks (one an antiquark) and look for models in which the mass is SU(3)-independent and the current is a sum of contributions from the individual quarks. Requiring that the current algebra, as well as conditions of relativistic invariance, be satisfied turns out to be very restrictive, and, in fact, no model has been found which satisfies all requirements and gives a reasonable mass spectrum. We show that using more general mass and current operators but keeping the same internal degrees of freedom will not make the problem any more solvable. In particular, in order for any two-quark solution to exist it must be possible to solve the "factorized SU(2) problem," in which the currents are isospin currents and are carried by only one of the component quarks (as in the K meson and its excited states).

In the free-quark model the currents at infinite momentum are found using a manifestly covariant formalism and are shown to satisfy the current algebra, but the mass spectrum is unrealistic. We then consider a pair of quarks bound by a potential, finding the current as a power series in 1/m where m is the quark mass. Here it is found impossible to satisfy the algebra and relativistic invariance with the type of potential tried, because the current contributions from the two quarks do not commute with each other to order 1/m³. However, it may be possible to solve the factorized SU(2) problem with this model.

The factorized problem can be solved exactly in the case where all mesons have the same mass, using a covariant formulation in terms of an internal Lorentz group. For a more realistic, nondegenerate mass there is difficulty in covariantly solving even the factorized problem; one model is described which almost works but appears to require particles of spacelike 4-momentum, which seem unphysical.

Although the search for a completely satisfactory model has been unsuccessful, the techniques used here might eventually reveal a working model. There is also a possibility of satisfying a weaker form of the current algebra with existing models.

Estimation of catalyst activity profiles and deactivation parameters from reactor operating data with applications to naphtha reforming

Techniques are developed for estimating activity profiles in fixed bed reactors and catalyst deactivation parameters from operating reactor data. These techniques are applicable, in general, to most industrial catalytic processes. The catalytic reforming of naphthas is taken as a broad example to illustrate the estimation schemes and to signify the physical meaning of the kinetic parameters of the estimation equations. The work is described in two parts. Part I deals with the modeling of kinetic rate expressions and the derivation of the working equations for estimation. Part II concentrates on developing various estimation techniques.

Part I: The reactions used to describe naphtha reforming are dehydrogenation and dehydroisomerization of cycloparaffins; isomerization, dehydrocyclization and hydrocracking of paraffins; and the catalyst deactivation reactions, namely coking on alumina sites and sintering of platinum crystallites. The rate expressions for the above reactions are formulated, and the effects of transport limitations on the overall reaction rates are discussed in the appendices. Moreover, various types of interaction between the metallic and acidic active centers of reforming catalysts are discussed as characterizing the different types of reforming reactions.

Part II: In catalytic reactor operation, the activity distribution along the reactor determines the kinetics of the main reaction and is needed for predicting the effect of changes in the feed state and the operating conditions on the reactor output. In the case of a monofunctional catalyst and of bifunctional catalysts in limiting conditions, the cumulative activity is sufficient for predicting steady reactor output. The estimation of this cumulative activity can be carried out easily from measurements at the reactor exit. For a general bifunctional catalytic system, the detailed activity distribution is needed for describing the reactor operation, and some approximation must be made to obtain practicable estimation schemes. This is accomplished by parametrization techniques using measurements at a few points along the reactor. Such parametrization techniques are illustrated numerically with a simplified model of naphtha reforming.

To determine long term catalyst utilization and regeneration policies, it is necessary to estimate catalyst deactivation parameters from the the current operating data. For a first order deactivation model with a monofunctional catalyst or with a bifunctional catalyst in special limiting circumstances, analytical techniques are presented to transform the partial differential equations to ordinary differential equations which admit more feasible estimation schemes. Numerical examples include the catalytic oxidation of butene to butadiene and a simplified model of naphtha reforming. For a general bifunctional system or in the case of a monofunctional catalyst subject to general power law deactivation, the estimation can only be accomplished approximately. The basic feature of an appropriate estimation scheme involves approximating the activity profile by certain polynomials and then estimating the deactivation parameters from the integrated form of the deactivation equation by regression techniques. Different bifunctional systems must be treated by different estimation algorithms, which are illustrated by several cases of naphtha reforming with different feed or catalyst composition.

Electrical, electrochemical, and optical characterization of ceria films

Acceptor-doped ceria has been recognized as a promising intermediate temperature solid oxide fuel cell electrode/electrolyte material. For practical implementation of ceria as a fuel cell electrolyte and for designing model experiments for electrochemical activity, it is necessary to fabricate thin films of ceria. Here, metal-organic chemical vapor deposition was carried out in a homemade reactor to grow ceria films for further electrical, electrochemical, and optical characterization. Doped/undoped ceria films are grown on single crystalline oxide wafers with/without Pt line pattern or Pt solid layer. Deposition conditions were varied to see the effect on the resultant film property. Recently, proton conduction in nanograined polycrystalline pellets of ceria drew much interest. Thickness-mode (through-plane, z-direction) electrical measurements were made to confirm the existence of proton conductivity and investigate the nature of the conduction pathway: exposed grain surfaces and parallel grain boundaries. Columnar structure presumably favors proton conduction, and we have found measurable proton conductivity enhancement. Electrochemical property of gas-columnar ceria interface on the hydrogen electrooxidation is studied by AC impedance spectroscopy. Isothermal gas composition dependence of the electrode resistance was studied to elucidate Sm doping level effect and microstructure effect. Significantly, preferred orientation is shown to affect the gas dependence and performance of the fuel cell anode. A hypothesis is proposed to explain the origin of this behavior. Lastly, an optical transmittance based methodology was developed to obtain reference refractive index and microstructural parameters (thickness, roughness, porosity) of ceria films via subsequent fitting procedure.

The search for gravitational waves from the coalescence of black hole binary systems in data from the LIGO and Virgo detectors. Or: A dark walk through a random forest

The LIGO and Virgo gravitational-wave observatories are complex and extremely sensitive strain detectors that can be used to search for a wide variety of gravitational waves from astrophysical and cosmological sources. In this thesis, I motivate the search for the gravitational wave signals from coalescing black hole binary systems with total mass between 25 and 100 solar masses. The mechanisms for formation of such systems are not well-understood, and we do not have many observational constraints on the parameters that guide the formation scenarios. Detection of gravitational waves from such systems — or, in the absence of detection, the tightening of upper limits on the rate of such coalescences — will provide valuable information that can inform the astrophysics of the formation of these systems. I review the search for these systems and place upper limits on the rate of black hole binary coalescences with total mass between 25 and 100 solar masses. I then show how the sensitivity of this search can be improved by up to 40% by the the application of the multivariate statistical classifier known as a random forest of bagged decision trees to more effectively discriminate between signal and non-Gaussian instrumental noise. I also discuss the use of this classifier in the search for the ringdown signal from the merger of two black holes with total mass between 50 and 450 solar masses and present upper limits. I also apply multivariate statistical classifiers to the problem of quantifying the non-Gaussianity of LIGO data. Despite these improvements, no gravitational-wave signals have been detected in LIGO data so far. However, the use of multivariate statistical classification can significantly improve the sensitivity of the Advanced LIGO detectors to such signals.

Searches for new symmetries in pp collisions with the razor kinematic variables at √s = 7 TeV

The construction and LHC phenomenology of the razor variables M_R, an event-by-event indicator of the heavy particle mass scale, and R, a dimensionless variable related to the transverse momentum imbalance of events and missing transverse energy, are presented.  The variables are used  in the analysis of the first proton-proton collisions dataset at CMS  (35 pb^-1) in a search for superpartners of the quarks and gluons, targeting indirect hints of dark matter candidates in the context of supersymmetric theoretical frameworks. The analysis produced the highest sensitivity results for SUSY to date and extended the LHC reach far beyond the previous Tevatron results.  A generalized inclusive search is subsequently presented for new heavy particle pairs produced in √s = 7 TeV proton-proton collisions at the LHC using 4.7±0.1 fb^-1 of integrated luminosity from the second LHC run of 2011.  The selected events are analyzed in the 2D razor-space of M_R and R and the analysis is performed in 12 tiers of all-hadronic, single and double leptons final states in the presence and absence of b-quarks, probing the third generation sector using the event heavy-flavor content.   The search is sensitive to generic supersymmetry models with minimal assumptions about the superpartner decay chains. No excess is observed in the number or shape of event yields relative to Standard Model predictions. Exclusion limits are derived in the CMSSM framework with  gluino masses up to 800 GeV and squark masses up to 1.35 TeV excluded at 95% confidence level, depending on the model parameters. The results are also interpreted for a collection of simplified models, in which gluinos are excluded with masses as large as 1.1 TeV, for small neutralino masses, and the first-two generation squarks, stops and sbottoms are excluded for masses up to about 800, 425 and 400 GeV, respectively.

With the discovery of a new boson by the CMS and ATLAS experiments in the γ-γ and 4 lepton final states, the identity of the putative Higgs candidate must be established through the measurements of its properties. The spin and quantum numbers are of particular importance, and we describe a method for measuring the J^PC of this particle using the observed signal events in the H to ZZ^* to 4 lepton channel developed before the discovery. Adaptations of the razor kinematic variables are introduced for the H to WW^* to 2 lepton/2 neutrino channel, improving the resonance mass resolution and increasing the discovery significance. The prospects for incorporating this channel in an examination of the new boson J^PC is discussed, with indications that this it could provide complementary information to the H to ZZ^* to 4 lepton final state, particularly for measuring CP-violation in these decays.

Trapped ion magnetic resonance: concepts and designs

A novel spectroscopy of trapped ions is proposed which will bring single-ion detection sensitivity to the observation of magnetic resonance spectra. The approaches developed here are aimed at resolving one of the fundamental problems of molecular spectroscopy, the apparent incompatibility in existing techniques between high information content (and therefore good species discrimination) and high sensitivity. Methods for studying both electron spin resonance (ESR) and nuclear magnetic resonance (NMR) are designed. They assume established methods for trapping ions in high magnetic field and observing the trapping frequencies with high resolution (<1 Hz) and sensitivity (single ion) by electrical means. The introduction of a magnetic bottle field gradient couples the spin and spatial motions together and leads to a small spin-dependent force on the ion, which has been exploited by Dehmelt to observe directly the perturbation of the ground-state electron's axial frequency by its spin magnetic moment.

A series of fundamental innovations is described m order to extend magnetic resonance to the higher masses of molecular ions (100 amu = 2x 10^5 electron masses) and smaller magnetic moments (nuclear moments = 10^(-3) of the electron moment). First, it is demonstrated how time-domain trapping frequency observations before and after magnetic resonance can be used to make cooling of the particle to its ground state unnecessary. Second, adiabatic cycling of the magnetic bottle off between detection periods is shown to be practical and to allow high-resolution magnetic resonance to be encoded pointwise as the presence or absence of trapping frequency shifts. Third, methods of inducing spindependent work on the ion orbits with magnetic field gradients and Larmor frequency irradiation are proposed which greatly amplify the attainable shifts in trapping frequency.

The dissertation explores the basic concepts behind ion trapping, adopting a variety of classical, semiclassical, numerical, and quantum mechanical approaches to derive spin-dependent effects, design experimental sequences, and corroborate results from one approach with those from another. The first proposal presented builds on Dehmelt's experiment by combining a "before and after" detection sequence with novel signal processing to reveal ESR spectra. A more powerful technique for ESR is then designed which uses axially synchronized spin transitions to perform spin-dependent work in the presence of a magnetic bottle, which also converts axial amplitude changes into cyclotron frequency shifts. A third use of the magnetic bottle is to selectively trap ions with small initial kinetic energy. A dechirping algorithm corrects for undesired frequency shifts associated with damping by the measurement process.

The most general approach presented is spin-locked internally resonant ion cyclotron excitation, a true continuous Stern-Gerlach effect. A magnetic field gradient modulated at both the Larmor and cyclotron frequencies is devised which leads to cyclotron acceleration proportional to the transverse magnetic moment of a coherent state of the particle and radiation field. A preferred method of using this to observe NMR as an axial frequency shift is described in detail. In the course of this derivation, a new quantum mechanical description of ion cyclotron resonance is presented which is easily combined with spin degrees of freedom to provide a full description of the proposals.

Practical, technical, and experimental issues surrounding the feasibility of the proposals are addressed throughout the dissertation. Numerical ion trajectory simulations and analytical models are used to predict the effectiveness of the new designs as well as their sensitivity and resolution. These checks on the methods proposed provide convincing evidence of their promise in extending the wealth of magnetic resonance information to the study of collisionless ions via single-ion spectroscopy.

Sensor networks for geospatial event detection - theory and applications

This thesis presents theories, analyses, and algorithms for detecting and estimating parameters of geospatial events with today's large, noisy sensor networks. A geospatial event is initiated by a significant change in the state of points in a region in a 3-D space over an interval of time. After the event is initiated it may change the state of points over larger regions and longer periods of time. Networked sensing is a typical approach for geospatial event detection. In contrast to traditional sensor networks comprised of a small number of high quality (and expensive) sensors, trends in personal computing devices and consumer electronics have made it possible to build large, dense networks at a low cost. The changes in sensor capability, network composition, and system constraints call for new models and algorithms suited to the opportunities and challenges of the new generation of sensor networks. This thesis offers a single unifying model and a Bayesian framework for analyzing different types of geospatial events in such noisy sensor networks. It presents algorithms and theories for estimating the speed and accuracy of detecting geospatial events as a function of parameters from both the underlying geospatial system and the sensor network. Furthermore, the thesis addresses network scalability issues by presenting rigorous scalable algorithms for data aggregation for detection. These studies provide insights to the design of networked sensing systems for detecting geospatial events. In addition to providing an overarching framework, this thesis presents theories and experimental results for two very different geospatial problems: detecting earthquakes and hazardous radiation. The general framework is applied to these specific problems, and predictions based on the theories are validated against measurements of systems in the laboratory and in the field.

Fundamental Studies of Carbon Oxygen Bond Activation in Nickel Diphosphine Ether Complexes. And, Metallomacrocycles as Ligands: Synthesis and Characterization of Aluminum-Bridged Bisglyoximato Complexes of Iron and Cobalt

In order to develop better catalysts for the cleavage of aryl-X bonds fundamental studies of the mechanism and individual steps of the mechanism have been investigated in detail. As the described studies are difficult at best in catalytic systems, model systems are frequently used. To study aryl-oxygen bond activation, a terphenyl diphosphine scaffold containing an ether moiety in the central arene was designed. The first three chapters of this dissertation focus on the studies of the nickel complexes supported by this diphosphine backbone and the research efforts in regards to aryl-oxygen bond activation.

Chapter 2 outlines the synthesis of a variety of diphosphine terphenyl ether ligand scaffolds. The metallation of these scaffolds with nickel is described. The reactivity of these nickel(0) systems is also outlined. The systems were found to typically undergo a reductive cleavage of the aryl oxygen bond. The mechanism was found to be a subsequent oxidative addition, β-H elimination, reductive elimination and (or) decarbonylation.

Chapter 3 presents kinetic studies of the aryl oxygen bond in the systems outlined in Chapter 2. Using a series of nickel(0) diphosphine terphenyl ether complexes the kinetics of aryl oxygen bond activation was studied. The activation parameters of oxidative addition for the model systems were determined. Little variation was observed in the rate and activation parameters of oxidative addition with varying electronics in the model system. The cause of the lack of variation is due to the ground state and oxidative addition transition state being affected similarly. Attempts were made to extend this study to catalytic systems.

Chapter 4 investigates aryl oxygen bond activation in the presence of additives. It was found that the addition of certain metal alkyls to the nickel(0) model system lead to an increase in the rate of aryl oxygen bond activation. The addition of excess Grignard reagent led to an order of magnitude increase in the rate of aryl oxygen bond activation. Similarly the addition of AlMe3 led to a three order of magnitude rate increase. Addition of AlMe₃ at -80 °C led to the formation of an intermediate which was identified by NOESY correlations as a system in which the AlMe3 is coordinated to the ether moiety of the backbone. The rates and activation parameters of aryl oxygen bond activation in the presence of AlMe3 were investigated.

The last two chapters involve the study of metalla-macrocycles as ligands. Chapter 5 details the synthesis of a variety of glyoxime backbones and diphenol precursors and their metallation with aluminum. The coordination chemistry of iron on the aluminum scaffolds was investigated. Varying the electronics of the aluminum macrocycle was found to affect the observed electrochemistry of the iron center.

Chapter 6 extends the studies of chapter 5 to cobalt complexes. The synthesis of cobalt dialuminum glyoxime metal complexes is described. The electrochemistry of the cobalt complexes was investigated. The electrochemistry was compared to the observed electrochemistry of a zinc analog to identify the redox activity of the ligand. In the presence of acid the cobalt complexes were found to electrochemically reduce protons to dihydrogen. The electronics of the ancillary aluminum ligands were found to affect the potential of proton reduction in the cobalt complexes. These potentials were compared to other diglyoximate complexes.

Micromechanical damage and fracture in elastomeric polymers

This thesis aims at a simple one-parameter macroscopic model of distributed damage and fracture of polymers that is amenable to a straightforward and efficient numerical implementation. The failure model is motivated by post-mortem fractographic observations of void nucleation, growth and coalescence in polyurea stretched to failure, and accounts for the specific fracture energy per unit area attendant to rupture of the material.

Furthermore, it is shown that the macroscopic model can be rigorously derived, in the sense of optimal scaling, from a micromechanical model of chain elasticity and failure regularized by means of fractional strain-gradient elasticity. Optimal scaling laws that supply a link between the single parameter of the macroscopic model, namely the critical energy-release rate of the material, and micromechanical parameters pertaining to the elasticity and strength of the polymer chains, and to the strain-gradient elasticity regularization, are derived. Based on optimal scaling laws, it is shown how the critical energy-release rate of specific materials can be determined from test data. In addition, the scope and fidelity of the model is demonstrated by means of an example of application, namely Taylor-impact experiments of polyurea rods. Hereby, optimal transportation meshfree approximation schemes using maximum-entropy interpolation functions are employed.

Finally, a different crazing model using full derivatives of the deformation gradient and a core cut-off is presented, along with a numerical non-local regularization model. The numerical model takes into account higher-order deformation gradients in a finite element framework. It is shown how the introduction of non-locality into the model stabilizes the effect of strain localization to small volumes in materials undergoing softening. From an investigation of craze formation in the limit of large deformations, convergence studies verifying scaling properties of both local- and non-local energy contributions are presented.

Isotope shift studies in the rare earths and lead

Isotope shifts of K_α1 x-ray transitions were measured for the Neodymium isotopes Nd 142, 143, 144, 145, 146, 148 and 150, the Samarium isotopes Sm 147, 148, 149, 150, 152 and 154, the Gadolinium isotopes Gd 154, 155, 156, 157, 158 and 160, the Dysprosium isotopes Dy 162 and 164, the Erbium isotopes Er 166, 168 and 170, the Hafnium isotopes Hf 178 and 180 and the Lead isotopes Pb 204, 206, 207 and 208. A curved crystal Cauchois spectrometer was used. The analysis of the measurement furnished the variation of the mean square charge radius of the nucleus, δ˂r²˃, for 23 isotope pairs. The experimental results were compared with theoretical values from nuclear models. Combining the x-ray shifts and the optical shifts in Nd and Sm yielded the optical mass shifts. An anomaly was observed in the odd-even shifts when the optical and the x-ray shifts were plotted against each other.