Resonator-induced dissipation of transverse nuclear-spin signals in cold nanoscale samples

The back action of typical macroscopic resonators used for detecting nuclear magnetic resonance can cause a reversible decay of the signal, known as radiation damping. A mechanical resonator that is strongly coupled to a microscopic sample can in addition induce an irreversible dissipation of the nuclear-spin signal, distinct from radiation damping. We provide a theoretical description of resonator-induced transverse relaxation that is valid for samples of a few nuclear spins in the low-temperature regime, where quantum fluctuations play a significant role in the relaxation process, as well as for larger samples and at higher temperatures. Transverse relaxation during free evolution and during spin locking are analyzed, and simulations of relaxation in example systems are presented. In the case where an isolated spin 1/2 interacts with the resonator, transverse relaxation is exponential during free evolution, and the time constant for the relaxation is T_2=2/R_h, where R_h is the rate constant governing the exchange of quanta between the resonator and the spin. For a system of multiple spins, the time scale of transverse relaxation during free evolution depends on the spin Hamiltonian, which can modify the relaxation process through the following effects: (1) changes in the structure of the spin-spin correlations present in the energy eigenstates, which affect the rates at which these states emit and absorb energy, (2) frequency shifts that modify emission and absorption rates within a degenerate manifold by splitting the energy degeneracy and thus suppressing the development of resonator-induced correlations within the manifold, and (3) frequency shifts that introduce a difference between the oscillation frequencies of single-quantum coherences ρ_(ab) and ρ_(cd) and average to zero the transfers between them. This averaging guarantees that the spin transitions responsible for the coupling between ρ_(ab) and ρ_(cd) cause irreversible loss of order rather than a reversible interconversion of the coherences. In systems of a few spins, transverse relaxation is accelerated by a dipolar Hamiltonian that is either the dominant term in the internal spin Hamiltonian or a weak perturbation to the chemical-shift Hamiltonian. A pure chemical-shift Hamiltonian yields exponential relaxation with T_2=2/R_h in the case where the Larmor frequencies of the spins are distinct and sufficiently widely spaced. During spin locking with a nutation frequency fast enough to average the evolution under the internal spin Hamiltonian but not the interactions occurring during the correlation time of the resonator, relaxation of the spin-locked component is exponential with time constant T_(1ρ)=2/R_h

Polarization of nuclear spins by a cold nanoscale resonator

A cold nanoscale resonator coupled to a system of nuclear spins can induce spin relaxation. In the low-temperature limit where spin-lattice interactions are “frozen out,” spontaneous emission by nuclear spins into a resonant mechanical mode can become the dominant mechanism for cooling the spins to thermal equilibrium with their environment. We provide a theoretical framework for the study of resonator-induced cooling of nuclear spins in this low-temperature regime. Relaxation equations are derived from first principles, in the limit where energy donated by the spins to the resonator is quickly dissipated into the cold bath that damps it. A physical interpretation of the processes contributing to spin polarization is given. For a system of spins that have identical couplings to the resonator, the interaction Hamiltonian conserves spin angular momentum, and the resonator cannot relax the spins to thermal equilibrium unless this symmetry is broken by the spin Hamiltonian. The mechanism by which such a spin system becomes “trapped” away from thermal equilibrium can be visualized using a semiclassical model, which shows how an indirect spin-spin interaction arises from the coupling of multiple spins to one resonator. The internal spin Hamiltonian can affect the polarization process in two ways: (1) By modifying the structure of the spin-spin correlations in the energy eigenstates, and (2) by splitting the degeneracy within a manifold of energy eigenstates, so that zero-frequency off-diagonal terms in the density matrix are converted to oscillating coherences. Shifting the frequencies of these coherences sufficiently far from zero suppresses the development of resonator-induced correlations within the manifold during polarization from a totally disordered state. Modification of the spin-spin correlations by means of either mechanism affects the strength of the fluctuating spin dipole that drives the resonator. In the case where product states can be chosen as energy eigenstates, spontaneous emission from eigenstate populations into the resonant mode can be interpreted as independent emission by individual spins, and the spins relax exponentially to thermal equilibrium if the development of resonator-induced correlations is suppressed. When the spin Hamiltonian includes a significant contribution from the homonuclear dipolar coupling, the energy eigenstates entail a correlation specific to the coupling network. Simulations of dipole-dipole coupled systems of up to five spins suggest that these systems contain weakly emitting eigenstates that can trap a fraction of the population for time periods ≫100/R_0, where R_0 is the rate constant for resonator-enhanced spontaneous emission by a single spin 1/2. Much of the polarization, however, relaxes with rates comparable to R_0. A distribution of characteristic high-field chemical shifts tends to increase the relaxation rates of weakly emitting states, enabling transitions to states that can quickly relax to thermal equilibrium. The theoretical framework presented in this paper is illustrated with discussions of spin polarization in the contexts of force-detected nuclear-magnetic-resonance spectroscopy and magnetic-resonance force microscopy

Botany

Botany is situated on the northern shores of Botany Bay in the south-eastern suburbs of Sydney, 10 kilometres south of Sydney's central business district. The presence of water, whether fresh or salt, is so inextricably bound to the history of Botany that the two are almost synonymous.In modern terms, the area is also strongly associated with various industries, aeroplanes, major arterial roads and seaports. For these reasons it is often regarded as the 'gateway' to Sydney, yet it is also much maligned and often overlooked, as people quickly pass through on their way to other destinations around the country or across the world. Still it is steeped in history of national significance with a large record of 'firsts' to its credit

Nanoscale Torsional Resonator for Polarization and Spectroscopy of Nuclear Spins

We propose a torsional resonator that couples to the transverse spin dipole of an attached sample. The absence of relative motion eliminates a source of friction that would otherwise hinder nanoscale implementation. Enhanced spontaneous emission induced by the resonator relaxes the longitudinal spin dipole at a rate of ~1  s^(-1) in the low-temperature limit. With signal averaging, single-proton magnetic resonance spectroscopy appears feasible at ~10  mK and a high magnetic field, while single-shot sensitivity is practical for samples with at least tens of protons in a volume of ~5  nm^3

Urban dwelling environments : Istanbul, Turkey

Thesis. 1976. M.ArchAS--Massachusetts Institute of Technology. Dept. of Architecture.Microfiche copy available in Archives and Rotch.Bibliography: p. 106.by Mark Horne Butler and Nedret Tayyibe Butler.M.ArchA

Marked expansion of exocrine and endocrine pancreas with incretin therapy in humans with increased exocrine pancreas dysplasia and the potential for glucagon-producing neuroendocrine tumors.

Controversy exists regarding the potential regenerative influences of incretin therapy on pancreatic β-cells versus possible adverse pancreatic proliferative effects. Examination of pancreata from age-matched organ donors with type 2 diabetes mellitus (DM) treated by incretin therapy (n = 8) or other therapy (n = 12) and nondiabetic control subjects (n = 14) reveals an ∼40% increased pancreatic mass in DM treated with incretin therapy, with both increased exocrine cell proliferation (P < 0.0001) and dysplasia (increased pancreatic intraepithelial neoplasia, P < 0.01). Pancreata in DM treated with incretin therapy were notable for α-cell hyperplasia and glucagon-expressing microadenomas (3 of 8) and a neuroendocrine tumor. β-Cell mass was reduced by ∼60% in those with DM, yet a sixfold increase was observed in incretin-treated subjects, although DM persisted. Endocrine cells costaining for insulin and glucagon were increased in DM compared with non-DM control subjects (P < 0.05) and markedly further increased by incretin therapy (P < 0.05). In conclusion, incretin therapy in humans resulted in a marked expansion of the exocrine and endocrine pancreatic compartments, the former being accompanied by increased proliferation and dysplasia and the latter by α-cell hyperplasia with the potential for evolution into neuroendocrine tumors

Computational Investigation of an Improved Cowl Concept for Hypersonic Propulsive Nozzles

The effects of placing a gas generator into the cowl of a hypersonic nozzle/afterbody were investigated computationally. Gas generator mass flow and deflection angle effects were analyzed for two nozzle/cowl geometries; an experimentally validated nozzle/cowl configuration evaluated at off-design conditions and a generic hypersonic propulsive nozzle evaluated at more realistic on design conditions. A combination of Van Leer flux-vector splitting and Roe flux-difference splitting finite volume computational algorithms were used to solve the unsteady two-dimensional Navier-Stokes equations based on planar, laminar flow, perfect gas equation of state assumptions. For the low speed off-design cases analyzed, gas generator effects on nozzle wall pressure recovery were similar to geometric cowl extension and deflection effects. Nozzle wall pressure recovery increased with increased mass flow. Gas generator deflections towards the nozzle wall provided dramatic improvements in pressure recovery and only small penalties were paid for deflections away from the wall. As the combustor exit pressure and trajectory Mach number increased, the nozzle flow became increasingly dominated by large initial expansions which minimized the overall effects of the gas generator and tended to push the gas generator effects on nozzle wall pressure recovery further downstream

THE EFFECTS OF EMBEDDING FORMATIVE ASSESSMENT MEASURES IN A PROBLEM--BASED LEARNING MATHEMATICS CURRICULUM FOR MIDDLE SCHOOL STUDENTS

Student performance in the area of mathematics is a topic of national concern in the United States, with several reports documenting the need for effective instruction to boost student achievement. However, what type of math instruction will most effectively raise student achievement for students with disabilities (SWD) remains a matter of debate. Problem-based learning (PBL) is a promising methodology for engaging and motivating students’ learning while increasing their math skills. Enhanced Anchored Instruction (EAI) is a form of problem-based learning, rooted in a constructivist framework, which guides students through complex problems through video anchors and context rich environments that has been shown to significantly improve math performance of SWD. Assessing student performance during PBL units is often difficult. Formative assessments supplement curriculum by allowing teachers to gather information and assess student learning during the course of instruction. However, despite the rise in formative assessment use, the effects of formative assessment in PBL curricula are rarely addressed. This study examined the effect of embedding formative assessments in the EAI curriculum on academic outcomes in middle school math classrooms. Results showed that problem solving performance did not improve with the addition of formative assessment and gains on computation performance were mixed