Linearization Errors in Discrete Goal-Oriented Error Estimation

Goal-oriented error estimation provides the ability to approximate the discretization error in a chosen functional quantity of interest. Adaptive mesh methods provide the ability to control this discretization error to obtain accurate quantity of interest approximations while still remaining computationally feasible. Traditional discrete goal-oriented error estimates incur linearization errors in their derivation. In this paper, we investigate the role of linearization errors in adaptive goal-oriented error simulations. In particular, we develop a novel two-level goal-oriented error estimate that is free of linearization errors. Additionally, we highlight how linearization errors can facilitate the verification of the adjoint solution used in goal-oriented error estimation. We then verify the newly proposed error estimate by applying it to a model nonlinear problem for several quantities of interest and further highlight its asymptotic effectiveness as mesh sizes are reduced. In an adaptive mesh context, we then compare the newly proposed estimate to a more traditional two-level goal-oriented error estimate. We highlight that accounting for linearization errors in the error estimate can improve its effectiveness in certain situations and demonstrate that localizing linearization errors can lead to more optimal adapted meshes

Voltage-Controlled Optics of a Quantum Dot

We show how the optical properties of a single semiconductor quantum dot can be controlled with a small dc voltage applied to a gate electrode. We find that the transmission spectrum of the neutral exciton exhibits two narrow lines with $\sim 2$ $\mu$eV linewidth. The splitting into two linearly polarized components arises through an exchange interaction within the exciton. The exchange interaction can be turned off by choosing a gate voltage where the dot is occupied with an additional electron. Saturation spectroscopy demonstrates that the neutral exciton behaves as a two-level system. Our experiments show that the remaining problem for manipulating excitonic quantum states in this system is spectral fluctuation on a $\mu$eV energy scale.Comment: 4 pages, 4 figures; content as publishe

Bayesian Optimal Experimental Design for Constitutive Model Calibration

Computational simulation is increasingly relied upon for high-consequence engineering decisions, and a foundational element to solid mechanics simulations, such as finite element analysis (FEA), is a credible constitutive or material model. Calibration of these complex models is an essential step; however, the selection, calibration and validation of material models is often a discrete, multi-stage process that is decoupled from material characterization activities, which means the data collected does not always align with the data that is needed. To address this issue, an integrated workflow for delivering an enhanced characterization and calibration procedure (Interlaced Characterization and Calibration (ICC)) is introduced. This framework leverages Bayesian optimal experimental design (BOED) to select the optimal load path for a cruciform specimen in order to collect the most informative data for model calibration. The critical first piece of algorithm development is to demonstrate the active experimental design for a fast model with simulated data. For this demonstration, a material point simulator that models a plane stress elastoplastic material subject to bi-axial loading was chosen. The ICC framework is demonstrated on two exemplar problems in which BOED is used to determine which load step to take, e.g., in which direction to increment the strain, at each iteration of the characterization and calibration cycle. Calibration results from data obtained by adaptively selecting the load path within the ICC algorithm are compared to results from data generated under two naive static load paths that were chosen a priori based on human intuition. In these exemplar problems, data generated in an adaptive setting resulted in calibrated model parameters with reduced measures of uncertainty compared to the static settings.Comment: 39 pages, 13 figure

The Potential of the Diphosphorus Complex [Cp2W2(CO)4(ƞ2-P2)] as an Organometallic Connecter in Supramolecular Chemistry

For the first time, the tetrahedral diphosphorus complex [Cp2W2(CO)(4)(mu,eta(2):eta(2)-P-2)] (Cp = C5H5) (3) is used as a connecter in supramolecular chemistry. The treatment of 3 with Cu-I halides leads to the formation of the new one-dimensional (1D) linear polymers [Cu(mu-X){Cp2W2(CO)(4)(mu,eta(2):eta(2):eta(1):eta(1)-P-2)}](n) {X = Cl (4), Br (5), I (6)}. The coordination polymers (CPs) 4-6 are almost insoluble in organic solvents, thus, their P-31 MAS-NMR spectra were recorded and found to be remarkably influenced by their solid-state structures. Additionally, we demonstrate that by reacting the Cp-substituted diphosphorus complex [Cp ' W-2(2)(CO)(4)(mu,eta(2):eta(2)-P-2)] {Cp ' = C5H4{C(CH3)(3)}} (7) with CuBr, the unprecedented soluble 1D CP [Cu(mu-Br){Cp ' W-2(2)(CO)(4)(mu,eta(2):eta(2):eta(1):eta(1)-P-2)}](n) (8) is obtained. Furthermore, the reactions of 3 with the Ag-I salts Ag[CF3SO3] and Ag[PF6] result in the formation of the oligomeric dicationic species [Ag-2{Cp2W2(CO)(4)(mu,eta(2):eta(2):eta(2)-P-2)}(2) {Cp2W2(CO)(4)(mu,eta(2):eta(2):eta(1):eta(1)-P-2)}(2)][X '](2) {X ' = [CF3SO3](-) (9), [PF6](-) (10)}

Optical detection of single electron spin resonance in a quantum dot

We demonstrate optically detected spin resonance of a single electron confined to a self-assembled quantum dot. The dot is rendered dark by resonant optical pumping of the spin with a coherent laser. Contrast is restored by applying a radio frequency (rf) magnetic field at the spin resonance. The scheme is sensitive even to rf fields of just a few micro-T. In one case, the spin resonance behaves exactly as a driven 3-level quantum system (a lambda-system) with weak damping. In another, the dot exhibits remarkably strong (67% signal recovery) and narrow (0.34 MHz) spin resonances with fluctuating resonant positions, evidence of unusual dynamic processes of non-Markovian character.Comment: 4 pages, 5 figure

The Prevalence and Clinical Implications of Comorbid Back Pain in Shoulder Instability: A Multicenter Orthopaedic Outcomes Network (MOON) Shoulder Instability Cohort Study.

Background:Understanding predictors of pain is critical, as recent literature shows that comorbid back pain is an independent risk factor for worse functional and patient-reported outcomes (PROs) as well as increased opioid dependence after total joint arthroplasty. Purpose/Hypothesis:The purpose of this study was to evaluate whether comorbid back pain would be predictive of pain or self-reported instability symptoms at the time of stabilization surgery. We hypothesized that comorbid back pain will correlate with increased pain at the time of surgery as well as with worse scores on shoulder-related PRO measures. Study Design:Cross-sectional study; Level of evidence, 3. Methods:As part of the Multicenter Orthopaedic Outcomes Network (MOON) Shoulder Instability cohort, patients consented to participate in pre- and intraoperative data collection. Demographic characteristics, injury history, preoperative PRO scores, and radiologic and intraoperative findings were recorded for patients undergoing surgical shoulder stabilization. Patients were also asked, whether they had any back pain. Results:The study cohort consisted of 1001 patients (81% male; mean age, 24.1 years). Patients with comorbid back pain (158 patients; 15.8%) were significantly older (28.1 vs 23.4 years; P < .001) and were more likely to be female (25.3% vs 17.4%; P = .02) but did not differ in terms of either preoperative imaging or intraoperative findings. Patients with self-reported back pain had significantly worse preoperative pain and shoulder-related PRO scores (American Shoulder and Elbow Surgeons score, Western Ontario Shoulder Instability Index) (P < .001), more frequent depression (22.2% vs 8.3%; P < .001), poorer mental health status (worse scores for the RAND 36-Item Health Survey Mental Component Score, Iowa Quick Screen, and Personality Assessment Screener) (P < .01), and worse preoperative expectations (P < .01). Conclusion:Despite having similar physical findings, patients with comorbid back pain had more severe preoperative pain and self-reported symptoms of instability as well as more frequent depression and lower mental health scores. The combination of disproportionate shoulder pain, comorbid back pain and mental health conditions, and inferior preoperative expectations may affect not only the patient's preoperative state but also postoperative pain control and/or postoperative outcomes

Network protocol scalability via a topological Kadanoff transformation

A natural hierarchical framework for network topology abstraction is presented based on an analogy with the Kadanoff transformation and renormalisation group in theoretical physics. Some properties of the renormalisation group bear similarities to the scalability properties of network routing protocols (interactions). Central to our abstraction are two intimately connected and complementary path diversity units: simple cycles, and cycle adjacencies. A recursive network abstraction procedure is presented, together with an associated generic recursive routing protocol family that offers many desirable features.Comment: 4 pages, 5 figures, PhysComNet 2008 workshop submissio

Electro-elastic tuning of single particles in individual self-assembled quantum dots

We investigate the effect of uniaxial stress on InGaAs quantum dots in a charge tunable device. Using Coulomb blockade and photoluminescence, we observe that significant tuning of single particle energies (~ -0.5 meV/MPa) leads to variable tuning of exciton energies (+18 to -0.9 micro-eV/MPa) under tensile stress. Modest tuning of the permanent dipole, Coulomb interaction and fine-structure splitting energies is also measured. We exploit the variable exciton response to tune multiple quantum dots on the same chip into resonance.Comment: 16 pages, 4 figures, 1 table. Final versio

Students Studying Students and Reasoning about Reasoning: A Qualitative Analysis

In this work, a faculty member takes a journey along with students as they enhance their understanding of how people solve mathematical problems through a mainly qualitative statistical project. Student authors of this paper registered for a problem solving seminar led by the faculty author, and then created and analyzed self-built assessment tools to explore problem solving techniques. Here we share our findings and recommendations, which we hope will inspire others to explore novel pedagogical techniques in the teaching of mathematical problem solving. We incorporate into our presentation ur voices, reflecting on how we and others solve problems