Asymptotic scaling in the two-dimensional O(3) Nonlinear sigma model: a Monte Carlo study on parallel computers

We investigate the 2d O(3) model with the standard action by Monte Carlo simulation at couplings β up to 2.05. We measure the energy density, mass gap and susceptibility of the model, and gather high statistics on lattices of size L ≤ 1024 using the Floating Point Systems T-series vector hypercube and the Thinking Machines Corp.'s Connection Machine 2. Asymptotic scaling does not appear to set in for this action, even at β = 2.10, where the correlation length is 420. We observe a 20% difference between our estimate m/Λ^─_(Ms) = 3.52(6) at this β and the recent exact analytical result . We use the overrelaxation algorithm interleaved with Metropolis updates and show that decorrelation time scales with the correlation length and the number of overrelaxation steps per sweep. We determine its effective dynamical critical exponent to be z' = 1.079(10); thus critical slowing down is reduced significantly for this local algorithm that is vectorizable and parallelizable.

We also use the cluster Monte Carlo algorithms, which are non-local Monte Carlo update schemes which can greatly increase the efficiency of computer simulations of spin models. The major computational task in these algorithms is connected component labeling, to identify clusters of connected sites on a lattice. We have devised some new SIMD component labeling algorithms, and implemented them on the Connection Machine. We investigate their performance when applied to the cluster update of the two dimensional Ising spin model.

Finally we use a Monte Carlo Renormalization Group method to directly measure the couplings of block Hamiltonians at different blocking levels. For the usual averaging block transformation we confirm the renormalized trajectory (RT) observed by Okawa. For another improved probabilistic block transformation we find the RT, showing that it is much closer to the Standard Action. We then use this block transformation to obtain the discrete β-function of the model which we compare to the perturbative result. We do not see convergence, except when using a rescaled coupling β_E to effectively resum the series. For the latter case we see agreement for m/ Λ^─_(Ms) at , β = 2.14, 2.26, 2.38 and 2.50. To three loops m/Λ^─_(Ms) = 3.047(35) at β = 2.50, which is very close to the exact value m/ Λ^─_(Ms) = 2.943. Our last point at β = 2.62 disagrees with this estimate however.

Discovery of non-zero neutrino mixing angle θ_13 using Daya Bay antineutrino detectors

The Daya Bay Reactor Antineutrino Experiment observed the disappearance of reactor $\bar{\nu}_e$ from six $2.9~GW_{th}$ reactor cores in Daya Bay, China. The Experiment consists of six functionally identical $\bar{\nu}_e$ detectors, which detect $\bar{\nu}_e$ by inverse beta decay using a total of about 120 metric tons of Gd-loaded liquid scintillator as the target volume. These $\bar{\nu}_e$ detectors were installed in three underground experimental halls, two near halls and one far hall, under the mountains near Daya Bay, with overburdens of 250 m.w.e, 265 m.w.e and 860 m.w.e. and flux-weighted baselines of 470 m, 576 m and 1648 m. A total of 90179 $\bar{\nu}_e$ candidates were observed in the six detectors over a period of 55 days, 57549 at the Daya Bay near site, 22169 at the Ling Ao near site and 10461 at the far site. By performing a rate-only analysis, the value of $sin^2 2\theta_{13}$ was determined to be $0.092 \pm 0.017$.

Geochemistry and resonance ionization of platinum-group elements

Experimental studies were conducted with the goals of 1) determining the origin of Pt- group element (PGE) alloys and associated mineral assemblages in refractory inclusions from meteorites and 2) developing a new ultrasensitive method for the in situ chemical and isotopic analysis of PGE. A general review of the geochemistry and cosmochemistry of the PGE is given, and specific research contributions are presented within the context of this broad framework.

An important step toward understanding the cosmochemistry of the PGE is the determination of the origin of POE-rich metallic phases (most commonly εRu-Fe) that are found in Ca, AJ-rich refractory inclusions (CAI) in C3V meteorites. These metals occur along with γNi-Fe metals, Ni-Fe sulfides and Fe oxides in multiphase opaque assemblages. Laboratory experiments were used to show that the mineral assemblages and textures observed in opaque assemblages could be produced by sulfidation and oxidation of once homogeneous Ni-Fe-PGE metals. Phase equilibria, partitioning and diffusion kinetics were studied in the Ni-Fe-Ru system in order to quantify the conditions of opaque assemblage formation. Phase boundaries and tie lines in the Ni-Fe-Ru system were determined at 1273, 1073 and 873K using an experimental technique that allowed the investigation of a large portion of the Ni-Fe-Ru system with a single experiment at each temperature by establishing a concentration gradient within which local equilibrium between coexisting phases was maintained. A wide miscibility gap was found to be present at each temperature, separating a hexagonal close-packed εRu-Fe phase from a face-centered cubic γNi-Fe phase. Phase equilibria determined here for the Ni-Fe-Ru system, and phase equilibria from the literature for the Ni-Fe-S and Ni-Fe-O systems, were compared with analyses of minerals from opaque assemblages to estimate the temperature and chemical conditions of opaque assemblage formation. It was determined that opaque assemblages equilibrated at a temperature of ~770K, a sulfur fugacity 10 times higher than an equilibrium solar gas, and an oxygen fugacity 10⁶ times higher than an equilibrium solar gas.

Diffusion rates between -γNi-Fe and εRu-Fe metal play a critical role in determining the time (with respect to CAI petrogenesis) and duration of the opaque assemblage equilibration process. The diffusion coefficient for Ru in Ni (D^Ru_Ni) was determined as an analog for the Ni-Fe-Ru system by the thin-film diffusion method in the temperature range of 1073 to 1673K and is given by the expression:

D^Ru_Ni (cm² sec^-1) = 5.0(±0.7) x 10^-3 exp(-2.3(±0.1) x 10¹² erg mole^-1/RT) where R is the gas constant and T is the temperature in K. Based on the rates of dissolution and exsolution of metallic phases in the Ni-Fe-Ru system it is suggested that opaque assemblages equilibrated after the melting and crystallization of host CAI during a metamorphic event of ≥ 10³ years duration. It is inferred that opaque assemblages originated as immiscible metallic liquid droplets in the CAI silicate liquid. The bulk compositions of PGE in these precursor alloys reflects an early stage of condensation from the solar nebula and the partitioning of V between the precursor alloys and CAI silicate liquid reflects the reducing nebular conditions under which CAI were melted. The individual mineral phases now observed in opaque assemblages do not preserve an independent history prior to CAI melting and crystallization, but instead provide important information on the post-accretionary history of C3V meteorites and allow the quantification of the temperature, sulfur fugacity and oxygen fugacity of cooling planetary environments. This contrasts with previous models that called upon the formation of opaque assemblages by aggregation of phases that formed independently under highly variable conditions in the solar nebula prior to the crystallization of CAI.

Analytical studies were carried out on PGE-rich phases from meteorites and the products of synthetic experiments using traditional electron microprobe x-ray analytical techniques. The concentrations of PGE in common minerals from meteorites and terrestrial rocks are far below the ~100 ppm detection limit of the electron microprobe. This has limited the scope of analytical studies to the very few cases where PGE are unusually enriched. To study the distribution of PGE in common minerals will require an in situ analytical technique with much lower detection limits than any methods currently in use. To overcome this limitation, resonance ionization of sputtered atoms was investigated for use as an ultrasensitive in situ analytical technique for the analysis of PGE. The mass spectrometric analysis of Os and Re was investigated using a pulsed primary Ar⁺ ion beam to provide sputtered atoms for resonance ionization mass spectrometry. An ionization scheme for Os that utilizes three resonant energy levels (including an autoionizing energy level) was investigated and found to have superior sensitivity and selectivity compared to nonresonant and one and two energy level resonant ionization schemes. An elemental selectivity for Os over Re of ≥ 10³ was demonstrated. It was found that detuning the ionizing laser from the autoionizing energy level to an arbitrary region in the ionization continuum resulted in a five-fold decrease in signal intensity and a ten-fold decrease in elemental selectivity. Osmium concentrations in synthetic metals and iron meteorites were measured to demonstrate the analytical capabilities of the technique. A linear correlation between Os⁺ signal intensity and the known Os concentration was observed over a range of nearly 10⁴ in Os concentration with an accuracy of ~ ±10%, a millimum detection limit of 7 parts per billion atomic, and a useful yield of 1%. Resonance ionization of sputtered atoms samples the dominant neutral-fraction of sputtered atoms and utilizes multiphoton resonance ionization to achieve high sensitivity and to eliminate atomic and molecular interferences. Matrix effects should be small compared to secondary ion mass spectrometry because ionization occurs in the gas phase and is largely independent of the physical properties of the matrix material. Resonance ionization of sputtered atoms can be applied to in situ chemical analysis of most high ionization potential elements (including all of the PGE) in a wide range of natural and synthetic materials. The high useful yield and elemental selectivity of this method should eventually allow the in situ measurement of Os isotope ratios in some natural samples and in sample extracts enriched in PGE by fire assay fusion.

Phase equilibria and diffusion experiments have provided the basis for a reinterpretation of the origin of opaque assemblages in CAI and have yielded quantitative information on conditions in the primitive solar nebula and cooling planetary environments. Development of the method of resonance ionization of sputtered atoms for the analysis of Os has shown that this technique has wide applications in geochemistry and will for the first time allow in situ studies of the distribution of PGE at the low concentration levels at which they occur in common minerals.

Acceleration Sensing, Feedback Cooling, and Nonlinear Dynamics with Nanoscale Cavity-Optomechanical Devices

Light has long been used for the precise measurement of moving bodies, but the burgeoning field of optomechanics is concerned with the interaction of light and matter in a regime where the typically weak radiation pressure force of light is able to push back on the moving object. This field began with the realization in the late 1960's that the momentum imparted by a recoiling photon on a mirror would place fundamental limits on the smallest measurable displacement of that mirror. This coupling between the frequency of light and the motion of a mechanical object does much more than simply add noise, however. It has been used to cool objects to their quantum ground state, demonstrate electromagnetically-induced-transparency, and modify the damping and spring constant of the resonator. Amazingly, these radiation pressure effects have now been demonstrated in systems ranging 18 orders of magnitude in mass (kg to fg).

In this work we will focus on three diverse experiments in three different optomechanical devices which span the fields of inertial sensors, closed-loop feedback, and nonlinear dynamics. The mechanical elements presented cover 6 orders of magnitude in mass (ng to fg), but they all employ nano-scale photonic crystals to trap light and resonantly enhance the light-matter interaction. In the first experiment we take advantage of the sub-femtometer displacement resolution of our photonic crystals to demonstrate a sensitive chip-scale optical accelerometer with a kHz-frequency mechanical resonator. This sensor has a noise density of approximately 10 micro-g/rt-Hz over a useable bandwidth of approximately 20 kHz and we demonstrate at least 50 dB of linear dynamic sensor range. We also discuss methods to further improve performance of this device by a factor of 10.

In the second experiment, we used a closed-loop measurement and feedback system to damp and cool a room-temperature MHz-frequency mechanical oscillator from a phonon occupation of 6.5 million down to just 66. At the time of the experiment, this represented a world-record result for the laser cooling of a macroscopic mechanical element without the aid of cryogenic pre-cooling. Furthermore, this closed-loop damping yields a high-resolution force sensor with a practical bandwidth of 200 kHZ and the method has applications to other optomechanical sensors.

The final experiment contains results from a GHz-frequency mechanical resonator in a regime where the nonlinearity of the radiation-pressure interaction dominates the system dynamics. In this device we show self-oscillations of the mechanical element that are driven by multi-photon-phonon scattering. Control of the system allows us to initialize the mechanical oscillator into a stable high-amplitude attractor which would otherwise be inaccessible. To provide context, we begin this work by first presenting an intuitive overview of optomechanical systems and then providing an extended discussion of the principles underlying the design and fabrication of our optomechanical devices.

DNA-mediated oxidation of transcription factor p53

Transcription factor p53 is the most commonly altered gene in human cancer. As a redox-active protein in direct contact with DNA, p53 can directly sense oxidative stress through DNA-mediated charge transport. Electron hole transport occurs with a shallow distance dependence over long distances through the π-stacked DNA bases, leading to the oxidation and dissociation of DNA-bound p53. The extent of p53 dissociation depends upon the redox potential of the response element DNA in direct contact with each p53 monomer. The DNA sequence dependence of p53 oxidative dissociation was examined by electrophoretic mobility shift assays using radiolabeled oligonucleotides containing both synthetic and human p53 response elements with an appended anthraquinone photooxidant. Greater p53 dissociation is observed from DNA sequences containing low redox potential purine regions, particularly guanine triplets, within the p53 response element. Using denaturing polyacrylamide gel electrophoresis of irradiated anthraquinone-modified DNA, the DNA damage sites, which correspond to locations of preferred electron hole localization, were determined. The resulting DNA damage preferentially localizes to guanine doublets and triplets within the response element. Oxidative DNA damage is inhibited in the presence of p53, however, only at DNA sites within the response element, and therefore in direct contact with p53. From these data, predictions about the sensitivity of human p53-binding sites to oxidative stress, as well as possible biological implications, have been made. On the basis of our data, the guanine pattern within the purine region of each p53-binding site determines the response of p53 to DNA-mediated oxidation, yielding for some sequences the oxidative dissociation of p53 from a distance and thereby providing another potential role for DNA charge transport chemistry within the cell.

To determine whether the change in p53 response element occupancy observed in vitro also correlates in cellulo, chromatin immunoprecipition (ChIP) and quantitative PCR (qPCR) were used to directly quantify p53 binding to certain response elements in HCT116N cells. The HCT116N cells containing a wild type p53 were treated with the photooxidant [Rh(phi)2bpy]³⁺, Nutlin-3 to upregulate p53, and subsequently irradiated to induce oxidative genomic stress. To covalently tether p53 interacting with DNA, the cells were fixed with disuccinimidyl glutarate and formaldehyde. The nuclei of the harvested cells were isolated, sonicated, and immunoprecipitated using magnetic beads conjugated with a monoclonal p53 antibody. The purified immounoprecipiated DNA was then quantified via qPCR and genomic sequencing. Overall, the ChIP results were significantly varied over ten experimental trials, but one trend is observed overall: greater variation of p53 occupancy is observed in response elements from which oxidative dissociation would be expected, while significantly less change in p53 occupancy occurs for response elements from which oxidative dissociation would not be anticipated.

The chemical oxidation of transcription factor p53 via DNA CT was also investigated with respect to the protein at the amino acid level. Transcription factor p53 plays a critical role in the cellular response to stress stimuli, which may be modulated through the redox modulation of conserved cysteine residues within the DNA-binding domain. Residues within p53 that enable oxidative dissociation are herein investigated. Of the 8 mutants studied by electrophoretic mobility shift assay (EMSA), only the C275S mutation significantly decreased the protein affinity (KD) for the Gadd45 response element. EMSA assays of p53 oxidative dissociation promoted by photoexcitation of anthraquinone-tethered Gadd45 oligonucleotides were used to determine the influence of p53 mutations on oxidative dissociation; mutation to C275S severely attenuates oxidative dissociation while C277S substantially attenuates dissociation. Differential thiol labeling was used to determine the oxidation states of cysteine residues within p53 after DNA-mediated oxidation. Reduced cysteines were iodoacetamide labeled, while oxidized cysteines participating in disulfide bonds were ¹³C₂D₂-iodoacetamide labeled. Intensities of respective iodoacetamide-modified peptide fragments were analyzed using a QTRAP 6500 LC-MS/MS system, quantified with Skyline, and directly compared. A distinct shift in peptide labeling toward ¹³C₂D₂-iodoacetamide labeled cysteines is observed in oxidized samples as compared to the respective controls. All of the observable cysteine residues trend toward the heavy label under conditions of DNA CT, indicating the formation of multiple disulfide bonds potentially among the C124, C135, C141, C182, C275, and C277. Based on these data it is proposed that disulfide formation involving C275 is critical for inducing oxidative dissociation of p53 from DNA.

DNA-Mediated Charge Transport Devices for Protein Detection

Detection of biologically relevant targets, including small molecules, proteins, DNA, and RNA, is vital for fundamental research as well as clinical diagnostics. Sensors with biological elements provide a natural foundation for such devices because of the inherent recognition capabilities of biomolecules. Electrochemical DNA platforms are simple, sensitive, and do not require complex target labeling or expensive instrumentation. Sensitivity and specificity are added to DNA electrochemical platforms when the physical properties of DNA are harnessed. The inherent structure of DNA, with its stacked core of aromatic bases, enables DNA to act as a wire via DNA-mediated charge transport (DNA CT). DNA CT is not only robust over long molecular distances of at least 34 nm, but is also especially sensitive to anything that perturbs proper base stacking, including DNA mismatches, lesions, or DNA-binding proteins that distort the π-stack. Electrochemical sensors based on DNA CT have previously been used for single-nucleotide polymorphism detection, hybridization assays, and DNA-binding protein detection. Here, improvements to (i) the structure of DNA monolayers and (ii) the signal amplification with DNA CT platforms for improved sensitivity and detection are described.

First, improvements to the control over DNA monolayer formation are reported through the incorporation of copper-free click chemistry into DNA monolayer assembly. As opposed to conventional film formation involving the self-assembly of thiolated DNA, copper-free click chemistry enables DNA to be tethered to a pre-formed mixed alkylthiol monolayer. The total amount of DNA in the final film is directly related to the amount of azide in the underlying alkylthiol monolayer. DNA monolayers formed with this technique are significantly more homogeneous and lower density, with a larger amount of individual helices exposed to the analyte solution. With these improved monolayers, significantly more sensitive detection of the transcription factor TATA binding protein (TBP) is achieved.

Using low-density DNA monolayers, two-electrode DNA arrays were designed and fabricated to enable the placement of multiple DNA sequences onto a single underlying electrode. To pattern DNA onto the primary electrode surface of these arrays, a copper precatalyst for click chemistry was electrochemically activated at the secondary electrode. The location of the secondary electrode relative to the primary electrode enabled the patterning of up to four sequences of DNA onto a single electrode surface. As opposed to conventional electrochemical readout from the primary, DNA-modified electrode, a secondary microelectrode, coupled with electrocatalytic signal amplification, enables more sensitive detection with spatial resolution on the DNA array electrode surface. Using this two-electrode platform, arrays have been formed that facilitate differentiation between well-matched and mismatched sequences, detection of transcription factors, and sequence-selective DNA hybridization, all with the incorporation of internal controls.

For effective clinical detection, the two working electrode platform was multiplexed to contain two complementary arrays, each with fifteen electrodes. This platform, coupled with low density DNA monolayers and electrocatalysis with readout from a secondary electrode, enabled even more sensitive detection from especially small volumes (4 μL per well). This multiplexed platform has enabled the simultaneous detection of two transcription factors, TBP and CopG, with surface dissociation constants comparable to their solution dissociation constants.

With the sensitivity and selectivity obtained from the multiplexed, two working electrode array, an electrochemical signal-on assay for activity of the human methyltransferase DNMT1 was incorporated. DNMT1 is the most abundant human methyltransferase, and its aberrant methylation has been linked to the development of cancer. However, current methods to monitor methyltransferase activity are either ineffective with crude samples or are impractical to develop for clinical applications due to a reliance on radioactivity. Electrochemical detection of methyltransferase activity, in contrast, circumvents these issues. The signal-on detection assay translates methylation events into electrochemical signals via a methylation-specific restriction enzyme. Using the two working electrode platform combined with this assay, DNMT1 activity from tumor and healthy adjacent tissue lysate were evaluated. Our electrochemical measurements revealed significant differences in methyltransferase activity between tumor tissue and healthy adjacent tissue.

As differential activity was observed between colorectal tumor tissue and healthy adjacent tissue, ten tumor sets were subsequently analyzed for DNMT1 activity both electrochemically and by tritium incorporation. These results were compared to expression levels of DNMT1, measured by qPCR, and total DNMT1 protein content, measured by Western blot. The only trend detected was that hyperactivity was observed in the tumor samples as compared to the healthy adjacent tissue when measured electrochemically. These advances in DNA CT-based platforms have propelled this class of sensors from the purely academic realm into the realm of clinically relevant detection.

Optomechanical Inertial Sensors and Feedback Cooling

The optomechanical interaction is an extremely powerful tool with which to measure mechanical motion. The displacement resolution of chip-scale optomechanical systems has been measured on the order of 1⁄10th of a proton radius. So strong is this optomechanical interaction that it has recently been used to remove almost all thermal noise from a mechanical resonator and observe its quantum ground-state of motion starting from cryogenic temperatures.

In this work, chapter 1 describes the basic physics of the canonical optomechanical system, optical measurement techniques, and how the optomechanical interaction affects the coupled mechanical resonator. In chapter 2, we describe our techniques for realizing this canonical optomechanical system in a chip-scale form factor.

In chapter 3, we describe an experiment where we used radiation pressure feedback to cool a mesoscopic mechanical resonator near its quantum ground-state from room-temperature. We cooled the resonator from a room temperature phonon occupation of <n> = 6.5 million to an occupation of <n> = 66, which means the resonator is in its ground state approximately 2% of the time, while being coupled to a room-temperature thermal environment. At the time of this work, this is the closest a mesoscopic mechanical resonator has been to its ground-state of motion at room temperature, and this work begins to open the door to room-temperature quantum control of mechanical objects.

Chapter 4 begins with the realization that the displacement resolutions achieved by optomechanical systems can surpass those of conventional MEMS sensors by an order of magnitude or more. This provides the motivation to develop and calibrate an optomechanical accelerometer with a resolution of approximately 10 micro-g/rt-Hz over a bandwidth of approximately 30 kHz. In chapter 5, we improve upon the performance and practicality of this sensor by greatly increasing the test mass size, investigating and reducing low-frequency noise, and incorporating more robust optical coupling techniques and capacitive wavelength tuning. Finally, in chapter 6 we present our progress towards developing another optomechanical inertial sensor - a gyroscope.