Control system design using optimization techniques Final report

Optimization techniques for control of fuel valve systems for air breathing jet engines and 40-60 inlet control problem

Anomalous structure in the single particle spectrum of the fractional quantum Hall effect

The two-dimensional electron system (2DES) is a unique laboratory for the physics of interacting particles. Application of a large magnetic field produces massively degenerate quantum levels known as Landau levels. Within a Landau level the kinetic energy of the electrons is suppressed, and electron-electron interactions set the only energy scale. Coulomb interactions break the degeneracy of the Landau levels and can cause the electrons to order into complex ground states. In the high energy single particle spectrum of this system, we observe salient and unexpected structure that extends across a wide range of Landau level filling fractions. The structure appears only when the 2DES is cooled to very low temperature, indicating that it arises from delicate ground state correlations. We characterize this structure by its evolution with changing electron density and applied magnetic field. We present two possible models for understanding these observations. Some of the energies of the features agree qualitatively with what might be expected for composite Fermions, which have proven effective for interpreting other experiments in this regime. At the same time, a simple model with electrons localized on ordered lattice sites also generates structure similar to those observed in the experiment. Neither of these models alone is sufficient to explain the observations across the entire range of densities measured. The discovery of this unexpected prominent structure in the single particle spectrum of an otherwise thoroughly studied system suggests that there exist core features of the 2DES that have yet to be understood.Comment: 15 pages, 10 figure

Surface Production Fuels Deep Heterotrophic Respiration in Northern Peatlands

Multiple analyses of dissolved organic carbon (DOC) from pore waters were conducted to define the processes that govern carbon balance in peatlands: (1) source, reactivity, and transport of DOC with respect to vegetation, peat, and age of carbon substrate, (2) reactivity of DOC with respect to molecular size, and (3) lability to photoxidation of surficial DOC. We found that surface organic production fuels heterotrophic respiration at depth in advection-dominated peatlands, especially in fens. Fen DOC was Δ14Cenriched relative to the surrounding fen peat, and fen respiration products were similar to this enriched DOC indicating that DOC was the main microbial substrate. Bog DOC was more variable showing either enrichment in Δ14C at depth or Δ14C values that follow peat values. This variability in bogs is probably controlled by the relative importance of vertical transport of labile carbon substrates within the peat profile versus DOC production from bog peat. These results extended our set of observations to 10 years at one bog-fen pair and add two additional bog-fen pairs to our series of observations. Anaerobic incubations of peat, rinsed free of residual DOC, produced DOC and respiration products that were strikingly similar to the peat values in a bog and two fens. This result demonstrated conclusively that downward advection is the process responsible for the presence of modern DOC found at depth in the peat column. Fen DOC has lower C/N values and up to twice as much LMW (kDa) DOC as bogs due to differences in organic inputs and greater microbial processing. Fluorescence irradiation experiments showed that fen DOC is more photolabile than bog DOC

Effect of Oscillating Landau Bandwidth on the Integer Quantum Hall Effect in a Unidirectional Lateral Superlattice

We have measured activation gaps for odd-integer quantum Hall states in a unidirectional lateral superlattice (ULSL) -- a two-dimensional electron gas (2DEG) subjected to a unidirectional periodic modulation of the electrostatic potential. By comparing the activation gaps with those simultaneously measured in the adjacent section of the same 2DEG sample without modulation, we find that the gaps are reduced in the ULSL by an amount corresponding to the width acquired by the Landau levels through the introduction of the modulation. The decrement of the activation gap varies with the magnetic field following the variation of the Landau bandwidth due to the commensurability effect. Notably, the decrement vanishes at the flat band conditions.Comment: 7 pages, 6 figures, minor revisio

High Resolution Spectroscopy of Two-Dimensional Electron Systems

Spectroscopic methods involving the sudden injection or ejection of electrons in materials are a powerful probe of electronic structure and interactions. These techniques, such as photoemission and tunneling, yield measurements of the "single particle" density of states (SPDOS) spectrum of a system. The SPDOS is proportional to the probability of successfully injecting or ejecting an electron in these experiments. It is equal to the number of electronic states in the system able to accept an injected electron as a function of its energy and is among the most fundamental and directly calculable quantities in theories of highly interacting systems. However, the two-dimensional electron system (2DES), host to remarkable correlated electron states such as the fractional quantum Hall effect, has proven difficult to probe spectroscopically. Here we present an improved version of time domain capacitance spectroscopy (TDCS) that now allows us to measure the SPDOS of a 2DES with unprecedented fidelity and resolution. Using TDCS, we perform measurements of a cold 2DES, providing the first direct measurements of the single-particle exchange-enhanced spin gap and single particle lifetimes in the quantum Hall system, as well as the first observations of exchange splitting of Landau levels not at the Fermi surface. The measurements reveal the difficult to reach and beautiful structure present in this highly correlated system far from the Fermi surface.Comment: There are formatting and minor textual differences between this version and the published version in Nature (follow the DOI link below

HI, FRB, what's your z: The first FRB host galaxy redshift from radio observations

Identification and follow up observations of the host galaxies of fast radio bursts (FRBs) not only help us understand the environments in which the FRB progenitors reside, but also provide a unique way of probing the cosmological parameters using the dispersion measures of FRBs and distances to their origin. A fundamental requirement is an accurate distance measurement to the FRB host galaxy, but for some sources viewed through the Galactic plane, optical/NIR spectroscopic redshifts are extremely difficult to obtain due to dust extinction. Here we report the first radio-based spectroscopic redshift measurement for an FRB host galaxy, through detection of its neutral hydrogen (HI) 21-cm emission using MeerKAT observations. We obtain an HI-based redshift of z = 0.0357 for the host galaxy of FRB 20230718A, an apparently non-repeating FRB detected in the CRAFT survey and localized at a Galactic latitude of -0.367 deg. Our observations also reveal that the FRB host galaxy is interacting with a nearby companion, which is evident from the detection of an HI bridge connecting the two galaxies. A subsequent optical spectroscopic observation confirmed an FRB host galaxy redshift of 0.0359 +- 0.0004. This result demonstrates the value of HI to obtain redshifts of FRBs at low Galactic latitudes and redshifts. Such nearby FRBs whose dispersion measures are dominated by the Milky Way can be used to characterise these components and thus better calibrate the remaining cosmological contribution to dispersion for more distant FRBs that provide a strong lever arm to examine the Macquart relation between cosmological DM and redshift.Comment: 13 pages, 3 figures. Accepted to ApJ Letter

H i, FRB, What’s Your z: The First FRB Host Galaxy Redshift from Radio Observations

Identification and follow-up observations of the host galaxies of fast radio bursts (FRBs) not only help us understand the environments in which the FRB progenitors reside, but also provide a unique way of probing the cosmological parameters using the dispersion measures (DMs) of FRBs and distances to their origin. A fundamental requirement is an accurate distance measurement to the FRB host galaxy, but for some sources viewed through the Galactic plane, optical/near-infrared spectroscopic redshifts are extremely difficult to obtain due to dust extinction. Here we report the first radio-based spectroscopic redshift measurement for an FRB host galaxy, through detection of its neutral hydrogen (H i) 21 cm emission using MeerKAT observations. We obtain an H i-based redshift of z = 0.0357 ± 0.0001 for the host galaxy of FRB 20230718A, an apparently nonrepeating FRB detected in the Commensal Real-time ASKAP Fast Transients survey and localized at a Galactic latitude of -0.°367. Our observations also reveal that the FRB host galaxy is interacting with a nearby companion, which is evident from the detection of an H i bridge connecting the two galaxies. A subsequent optical spectroscopic observation confirmed an FRB host galaxy redshift of 0.0359 ± 0.0004. This result demonstrates the value of H i to obtain redshifts of FRBs at low Galactic latitudes and redshifts. Such nearby FRBs whose DMs are dominated by the Milky Way can be used to characterize these components and thus better calibrate the remaining cosmological contribution to dispersion for more distant FRBs that provide a strong lever arm to examine the Macquart relation between cosmological DM and redshift

Microscopic Polarization in Bilayer Graphene

Bilayer graphene has drawn significant attention due to the opening of a band gap in its low energy electronic spectrum, which offers a promising route to electronic applications. The gap can be either tunable through an external electric field or spontaneously formed through an interaction-induced symmetry breaking. Our scanning tunneling measurements reveal the microscopic nature of the bilayer gap to be very different from what is observed in previous macroscopic measurements or expected from current theoretical models. The potential difference between the layers, which is proportional to charge imbalance and determines the gap value, shows strong dependence on the disorder potential, varying spatially in both magnitude and sign on a microscopic level. Furthermore, the gap does not vanish at small charge densities. Additional interaction-induced effects are observed in a magnetic field with the opening of a subgap when the zero orbital Landau level is placed at the Fermi energy

The effect of oscillating Fermi energy on the line shape of the Shubnikov-de Haas oscillation in a two dimensional electron gas

The line shape of the Shubnikov-de Haas (SdH) oscillation has been analyzed in detail for a GaAs/AlGaAs two-dimensional electron gas. The line shape, or equivalently the behavior of the Fourier components, of the experimentally observed SdH oscillation is well reproduced by the sinusoidal density of states at the Fermi energy that oscillates with a magnetic field in a saw-tooth shape to keep the electron density constant. This suggests that the broadening of each Landau level by disorder is better described by a Gaussian than by a Lorentzian.Comment: 7 pages,6 figures, minor revision