Physics and Astronomy

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This is the collection for the University of Waterloo's Department of Physics and Astronomy.

Research outputs are organized by type (eg. Master Thesis, Article, Conference Paper).

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Now showing 1 - 20 of 803

The electrostatic potential in a finite ionic crystal
(University of Waterloo, 1972-11-01) Redlack, Austin
This thesis is written in two parts. In Part One, we develop a new method for evaluating three dimensional lattice summations and apply it to the evaluation of the electrostatic potential of a finite ionic crystal. We then compare our expression with those obtained using infinite crystals. Some of the effects which are not obtainable using an infinite crystal are: i. the electrostatic potential depends on the shape of the sample when a dipole or quadrupole moment is present, and 2. the electrostatic potential at the surface of a crystal changes rapidly near the surface. In Part Two, we use the method developed in Part One to evaluate the electrostatic potential in a deformed crystal and use the resulting expression to define the macroscopic electric field and the electric displacement field. For the case of uniform fields, the expressions for these fields reduce to those in common use.
Electric-field-dependent variable-range hopping conductance in quasi-two-dimensional systems: Application to PrBa2Cu3O7-y-based superconductor–normal-metal–superconductor junctions
(American Physical Society, 1996-03) Singh, M.; Thompson, Russell B.; Dumas, O.
We have calculated the hopping conductivity of quasi-two-dimensional systems by using the variable-range hopping conduction mechanism in the presence of an electric field. We considered that the localized states are randomly distributed both in energy and space coordinates. Localized carriers hop from one state to another in both coordinates. We also considered that at a particular temperature the localized carriers are distributed according to the Fermi distribution function both below and above the Fermi level. The expression of the conductivity for the constant density of states was calculated. After some approximations, the expression of the conductivity was shown to reduce to expressions found in the literature. We also compared our theory with experimental results of PrBa2Cu3O7-y based S/N/S junctions. Good agreement between theory and experiment was found.
Electric-field-dependent variable-range hopping conduction in PrBa2Cu307-y
(Taylor & Francis, 1997-02) Thompson, Russell B.; Singh, M.
The variable-range hopping conductivities of quasi-two-dimensional systems in electric fields were calculated for the cases of both constant and energy-dependent densities of states. The localized states were considered to be randomly distributed in space and energy coordinates, and the carriers were considered to be distributed according to the Fermi distribution. Approximations yielded analytic results valid for most temperatures and electric fields and included localized states both above and below the Fermi level. We hypothesized that the localized states of PrBa2Cu3O7-y (PBCO) are distributed in the CuO planes, making that compound behave as a quasi-two- dimensional material. We compared our theory with experiments of PBCO-based junctions and found good agreement between theory and experiment.
Magnetoconductance due to variable-range hopping in quasi-two-dimensional systems: Application to PrBa2Cu3O7-delta
(American Physical Society, 1998-01) Thompson, Russell B.; Singh, M.
In this paper, we have developed a theory of magnetoconductance (magnetoresistance) due to variable-range hopping for quasi-two-dimensional systems. We have included the effect of electric fields on the calculation of the magnetoconductance. The effects of scattering and electron-electron interactions have also been included in our theory. We found analytical expressions for the conductivity for both the scattering and nonscattering cases, and obtained electric- and magnetic-field-dependent power laws in certain approximations. We found that the electric and magnetic-field dependences of the magnetoconductance had different power laws for the scattering and nonscattering cases. We tried to explain the van Ancum et al. magnetoconductance experiments of PrBa2Cu3O7-delta (PBCO) thin films by using our theory. A good agreement between theory and experiment was found if we included the effect of scattering. In the above PBCO films, it was found that the approximate value of the concentration of localized states lies between 10^11 and 10^12 cm^-2.
Small-polaron variable-range hopping in quasi-two-dimensional materials: application to PrBa2Cu3-xGax07-y
(Taylor & Francis, 1999-01) Thompson, Russell B.; Singh, M.
We have developed a theory for variable-rangehopping (VRH) due to small polarons in quasi-two-dimensionalsystems at high temperatures.We included the effects of temperature, electric fields, magnetic fields and scattering in the derivation of the conductivity. We found that the conductivity for quasi-two- dimensional systems depends on these factors differently from three- dimensional systems. We applied the theory to explain the resistivity data of PrBa2Cu3p,Ga,07-l, at high temperatures ( T > 150K). To explain the low- temperature data ( T < 150K), we used the pure electron VRH mechanisms. Good agreement between theory and experiment was found.
A Quasilocal Hamiltonian for Gravity with Classical and Quantum Applications
(University of Waterloo, 2000) Booth, Ivan S. N.
I modify the quasilocal energy formalism of Brown and York into a purely Hamiltonian form. As part of the reformulation, I remove their restriction that the time evolution of the boundary of the spacetime be orthogonal to the leaves of the time foliation. Thus the new formulation allows an arbitrary evolution of the boundary which physically corresponds to allowing general motions of the set of observers making up that boundary. I calculate the rate of change of the quasilocal energy in such situations, show how it transforms with respect to boosts of the boundaries, and use the Lanczos-Israel thin shell formalism to reformulate it from an operational point of view. These steps are performed both for pure gravity and gravity with attendant matter fields. I then apply the formalism to characterize naked black holes and study their properties, investigate gravitational tidal heating, and combine it with the path integral formulation of quantum gravity to analyze the creation of pairs of charged and rotating black holes. I show that one must use complex instantons to study this process though the probabilities of creation remain real and consistent with the view that the entropy of a black hole is the logarithm of the number of its quantum states.
Predicting the Mesophases of Copolymer-Nanoparticle Composites
(American Association for the Advancement of Science, 2001) Thompson, Russell B.; Ginzburg, Valeriy V.; Matsen, Mark W.; Balazs, Anna C.
The interactions between mesophase-forming copolymers and nanoscopic par- ticles can lead to highly organized hybrid materials. The morphology of such composites depends not only on the characteristics of the copolymers, but also on the features of the nanoparticles. To explore this vast parameter space and predict the mesophases of the hybrids, we have developed a mean field theory for mixtures of soft, flexible chains and hard spheres. Applied to diblock- nanoparticle mixtures, the theory predicts ordered phases where particles and diblocks self-assemble into spatially periodic structures. The method can be applied to other copolymer-particle mixtures and can be used to design novel composite architectures.
Effect of Nanoscopic Particles on the Mesophase Structure of Diblock Copolymers
(American Chemical Society, 2002) Lee, Jae Youn; Thompson, Russell B.; Jasnow, David; Balazs, Anna C.
Introduction. The fabrication of novel biomimetic photonic and electronic materials requires the manipulation of both organic and inorganic materials at the nanometer length scale. One possible means of achieving this level of control is to add inorganic nanoparticles to a melt of diblock copolymers. The microphase separation of the copolymers into nanoscopic, ordered domains could be harnessed to “template” the organization of the particles into nanoplanes, -wires, or -spheres within the polymer matrix. However, as we show below, the particles are not passive and can affect the overall morphology of the mixture. We also show that this effect is sufficiently robust that it can be found in both the strong and intermediate segregation limits of the diblock melts (i.e., both low and intermediate temperatures).
Block Copolymer-Directed Assembly of Nanoparticles: Forming Mesoscopically Ordered Hybrid Materials
(American Chemical Society, 2002) Thompson, Russell B.; Ginzburg, Valeriy V.; Matsen, Mark W.; Balazs, Anna C.
Mixtures of diblock copolymers and nanoscopic spherical particles can yield well-ordered hybrid materials, which can be used for separation processes, catalysis, and optoelectronic applications. Predicting the morphologies of these systems is difficult because the final structures depend not only on the characteristics of the copolymer but also on the features of the particles. Combining self-consistent field and density functional theories, we develop a model that allows us to determine the equilibrium or metastable phases of diblock copolymer/spherical nanoparticle composites, without making a priori assumptions about the structure of the system. Using this model, we illustrate various examples where mixtures of diblocks and nanoparticles self-assemble into mesoscopically ordered phases. The model can be generalized to other types of copolymers and particles and can be modified to include homopolymers or solvent molecules. Thus, the technique constitutes a useful tool for determining the structures of a large class of nanocomposites.
Modelling Quantum Well Lasers
(University of Waterloo, 2002) Weetman, Philip
In this thesis, two methods to model quantum well lasers will be examined. The first model is based on well-known techniques to determine some of the spectral and dynamical properties of the laser. For the spectral properties, an expression for TE and TM modal amplitude gain is derived. For the dynamical properties, the rate equations are shown. The spectral and dynamical properties can be examined separately for specific operating characteristics or used in conjunction with each other for a complete description of the laser. Examples will be shown to demonstrate some of the analysis and results that can be obtained. The second model used is based on Wigner functions and the quantum Boltzmann equation. It is derived from general non-equilibrium Greens functions with the application of the Kadanoff-Baym ansatz. This model is less phenomenological than the previous model and does not require the separation of physical processes such as the former spectral and dynamical properties. It therefore has improved predictive power for the performance of novel laser designs. To the Author's knowledge, this is the first time such a model has been formulated. The quantum Boltzmann equations will be derived and some calculations will be performed for a simplified system in order to illustrate some calculation techniques as well as results that can be obtained.
Entropically Driven Formation of Hierarchically Ordered Nanocomposites
(American Physical Society, 2002) Lee, Jae Youn; Thompson, Russell B.; Jasnow, David; Balazs, Anna C.
Using theoretical models, we undertake the first investigation into the rich behavior that emerges when binary particle mixtures are blended with microphase-separating copolymers. We isolate an example of coupled self-assembly in such materials, where the system undergoes a nanoscale ordering of the particles along with a phase transformation in the copolymer matrix. Furthermore, the self- assembly is driven by entropic effects involving all the different components. The results reveal that entropy can be exploited to create highly ordered nanocomposites with potentially unique electronic and photonic properties.
Self-assembly of a binary mixture of particles and diblock copolymers
(Royal Society of Chemistry, 2003) Lee, Jae Youn; Thompson, Russell B.; Jasnow, David; Balazs, Anna C.
Using theoretical models, we undertake the first investigation into the synergy and rich phase behavior that emerges when binary particle mixtures are blended with microphase- separating copolymers. We isolate an example of spontaneous hierarchical self-assembly in such hybrid materials, where the system exhibits both nanoscopic ordering of the particles and macroscopic phase transformation in the copolymer matrix. Furthermore, the self- assembly is driven by entropic effects involving all the different components. The results reveal that entropy can be exploited to create highly ordered nanocomposites with potentially unique electronic and photonic properties.
HIGH RESOLUTION MICROWAVE SPECTROSCOPY OF ULTRA COLD RYDBERG ATOMS AS A PROBE OF ELECTRIC AND MAGNETIC FIELDS
(University of Waterloo, 2003) Bohlouli-Zanjani, Parisa
In highly excited Rydberg atoms, the excited electron is in a large, loosely bound orbit. Hence, in contrast with the ground states, the Rydberg states are very sensitive to external electric field and can be ionized in rather weak fields. The low ionization threshold of Rydberg states results in effective state-specific detection by the selective field ionization technique. In this thesis, high-resolution spectroscopy of Rydberg states of Rubidium using millimeter wave transitions and selective field ionization has been used as a probe of external electric and magnetic fields. Laser cooling and trapping techniques in a magneto-optical trap (MOT) are employed to have a high density and narrow velocity distribution for the atomic sample. In this work the magnetic field inhomogeneity inherent in a MOT is minimized and the stray electric field present at the trap region is compensated in order to have resolved spectra. The Stark line broadening of the spectra obtained in this work may be used to determine the electric field distribution in an expanding ultra-cold neutral plasma.
Physics in Higher-Dimensional Manifolds
(University of Waterloo, 2003) Seahra, Sanjeev
In this thesis, we study various aspects of physics in higher-dimensional manifolds involving a single extra dimension. After giving some historical perspective on the motivation for studying higher-dimensional theories of physics, we describe classical tests for a non-compact extra dimension utilizing test particles and pointlike gyroscopes. We then turn our attention to the problem of embedding any given n-dimensional spacetime within an (n+1)-dimensional manifold, paying special attention to how any structure from the extra dimension modifies the standard n-dimensional Einstein equations. Using results derived from this investigation and the formalism derived for test particles and gyroscopes, we systematically introduce three specific higher-dimensional models and classify their properties; including the Space-Time-Matter and two types of braneworld models. The remainder of the thesis concentrates on specific higher-dimensional cosmological models drawn from the above mentioned scenarios; including an analysis of the embedding of Friedmann-Lemaitre-Robertson-Walker submanifolds in 5-dimensional Minkowski and topological Schwarzschild spaces, and an investigation of the dynamics of a d-brane that takes the form of a thin shell encircling a (d+2)-dimensional topological black hole in anti-deSitter space. The latter is derived from a finite-dimensional action principle, which allows us to consider the canonical quantization of the model and the solutions of the resulting Wheeler-DeWitt equation.
Characterisation and Optimization of Ultrashort Laser Pulses
(University of Waterloo, 2003) Macpherson, James
The ultrafast optical regime is defined, as it applies to laser pulses, along with a brief introduction to pulse generation and characterisation technologies. A more extensive description of our particular amplified pulse generation and SPIDER characterisation systems follows. Data verifying the correct operation of the characterisation system is presented and interpreted. Our laser system is then characterised in two different configurations. In each case, the data describing the system is presented and analyzed. Conclusions are made regarding the performance of both the characterisation and laser systems, along with suggested improvements for each.
Self-Assembly of Amphiphilic Nanoparticle-Coil “Tadpole” Macromolecules
(American Chemical Society, 2004) Lee, Jae Youn; Balazs, Anna C.; Thompson, Russell B.; Hill, Randall M.
There has been considerable fascination with the self-assembling behavior of amphiphilic chainlike molecules that range from short-chain surfactants to high molecular weight block copolymers. The self-assembly of simple amphiphiles into membranes may have played an important role in the origin of life. The self-organization of amphiphiles with more complex architectures can lead to a stunning variety of complex morphologies. In the case of short-chain surfactants, the equilibrium morphology of the self-assembled sys- tem depends on geometric factors, such as the ratio of the “head” to “tail” sizes. Here, the headgroups are small molecules and the tails are coillike. In the case of block copolymers, the structure of the melt depends on the relative composition of the chains, the degree of polymerization, and the incompatibility between the different blocks.
Electrostatics of the Binding and Bending of Lipid Bilayers: Charge-Correlation Forces and Preferred Curvatures
(University of Waterloo, 2004) Li, Yang
Lipid bilayers are key components of biomembranes; they are self-assembled two-dimensional structures, primarily serving as barriers to the leakage of cell's contents. Lipid bilayers are typically charged in aqueous solution and may electrostatically interact with each other and with their environment. In this work, we investigate electrostatics of charged lipid bilayers with the main focus on the binding and bending of the bilayers. We first present a theoretical approach to charge-correlation attractions between like-charged lipid bilayers with neutralizing counterions assumed to be localized to the bilayer surface. In particular, we study the effect of nonzero ionic sizes on the attraction by treating the bilayer charges (both backbone charges and localized counterions) as forming a two-dimensional ionic fluid of hard spheres of the same diameter D. Using a two-dimensional Debye-Hückel approach to this system, we examine how ion sizes influence the attraction. We find that the attraction gets stronger as surface charge densities or counterion valency increase, consistent with long-standing observations. Our results also indicate non-trivial dependence of the attraction on separations h: The attraction is enhanced by ion sizes for h ranges of physical interest, while it crosses over to the known D-independent universal behavior as h → ∞; it remains finite as h → 0, as expected for a system of finite-sized ions. We also study the preferred curvature of an asymmetrically charged bilayer, in which the inner leaflet is negatively charged, while the outer one is neutral. In particular, we calculate the relaxed area difference Δ A₀ and the spontaneous curvature C₀ of the bilayer. We find Δ A₀ and C₀ are determined by the balance of a few distinct contributions: net charge repulsions, charge correlations, and the entropy associated with counterion release from the bilayer. The entropic effect is dominant for weakly charged surfaces in the presence of monovalent counterions only and tends to expand the inner leaflet, leading to negative Δ A₀ and C₀. In the presence of even a small concentration of divalent counterions, however, charge correlations counterbalance the entropic effect and shrink the inner leaflet, leading to positive Δ A₀ and C₀. We outline biological implications of our results.
Self-Assembly of Amphiphilic Nanoparticle-Coil “Tadpole” Macromolecules
(American Chemical Society, 2004) Lee, Jae Youn; Balazs, Anna C.; Thompson, Russell B.; Hill, Randall M.
None.
Improved convergence in block copolymer self-consistent field theory by Anderson mixing
(American Institute of Physics, 2004) Thompson, Russell B.; Rasmussen, Kim O.; Lookman, Turab
A modification to real space polymeric self-consistent field theory algorithms that greatly improves the convergence properties is presented. The method is based on Anderson mixing (D. G. Anderson, J. Assoc. Comput. Mach. 12, 547 1965), and each iteration computed takes negligibly longer to perform than with other methods, but the number of iterations required to reach a high accuracy solution is greatly reduced. No a priori knowledge of possible phases is required to apply this method. We apply our approach to a standard diblock copolymer melt, and demonstrate iteration reductions of more than a factor of 5 in some cases.
Origins of Elastic Properties in Ordered Block Copolymer/Nanoparticle Composites
(American Chemical Society, 2004) Thompson, Russell B.; Rasmussen, Kim O.; Lookman, Turab
We predict a diblock copolymer melt in the lamellar phase with added spherical nanoparticles that have an affinity for one block to have a lower tensile modulus than a pure diblock copolymer system. This weakening is due to the swelling of the lamellar domain by nanoparticles and the displacement of polymer by elastically inert fillers. Despite the overall decrease in the tensile modulus of a polydomain sample, the shear modulus for a single domain is unaffected by fillers.

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