A multidomain spectral collocation method for the Stokes problem

A multidomain spectral collocation scheme is proposed for the approximation of the two-dimensional Stokes problem. It is shown that the discrete velocity vector field is exactly divergence-free and we prove error estimates both for the velocity and the pressure

A spectral collocation approximation for the radial-infall of a compact object into a Schwarzschild black hole

The inhomogeneous Zerilli equation is solved in time-domain numerically with the Chebyshev spectral collocation method to investigate a radial-infall of the point particle towards a Schwarzschild black hole. Singular source terms due to the point particle appear in the equation in the form of the Dirac $\delta$-function and its derivative. For the approximation of singular source terms, we use the direct derivative projection method without any regularization. The gravitational waveforms are evaluated as a function of time. We compare the results of the spectral collocation method with those of the explicit second-order central-difference method. The numerical results show that the spectral collocation approximation with the direct projection method is accurate and converges rapidly when compared with the finite-difference method.Comment: Accepted for publication in International Journal of Modern Physics C (IJMPC

Aeroacoustic Study of a High-Fidelity Aircraft Model: Part 1- Steady Aerodynamic Measurements

In this paper, we present steady aerodynamic measurements for an 18% scale model of a Gulfstream air-craft. The high fidelity and highly-instrumented semi-span model was developed to perform detailed aeroacoustic studies of airframe noise associated with main landing gear/flap components and gear-flap interaction noise, as well as to evaluate novel noise reduction concepts. The aeroacoustic tests, being conducted in the NASA Langley Research Center 14- by 22-Foot Subsonic Tunnel, are split into two entries. The first entry, completed November 2010, was entirely devoted to the detailed mapping of the aerodynamic characteristics of the fabricated model. Flap deflections of 39?, 20?, and 0? with the main landing gear on and off were tested at Mach numbers of 0.16, 0.20, and 0.24. Additionally, for each flap deflection, the model was tested with the tunnel both in the closed-wall and open-wall (jet) modes. During this first entry, global forces (lift and drag) and extensive steady and unsteady surface pressure measurements were obtained. Preliminary analysis of the measured forces indicates that lift, drag, and stall characteristics compare favorably with Gulfstream?s high Reynolds number flight data. The favorable comparison between wind-tunnel and flight data allows the semi-span model to be used as a test bed for developing/evaluating airframe noise reduction concepts under a relevant environment. Moreover, initial comparison of the aerodynamic measurements obtained with the tunnel in the closed- and open-wall configurations shows similar aerodynamic behavior. This permits the acoustic and off-surface flow measurements, planned for the second entry, to be conducted with the tunnel in the open-jet mode

Discrete Structures (KSU)

This Grants Collection for Discrete Structures was created under a Round Eleven ALG Textbook Transformation Grant. Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process. Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials: Linked Syllabus Initial Proposal Final Reporthttps://oer.galileo.usg.edu/compsci-collections/1025/thumbnail.jp

A Study of Quantum Error Correction by Geometric Algebra and Liquid-State NMR Spectroscopy

Quantum error correcting codes enable the information contained in a quantum state to be protected from decoherence due to external perturbations. Applied to NMR, quantum coding does not alter normal relaxation, but rather converts the state of a ``data'' spin into multiple quantum coherences involving additional ancilla spins. These multiple quantum coherences relax at differing rates, thus permitting the original state of the data to be approximately reconstructed by mixing them together in an appropriate fashion. This paper describes the operation of a simple, three-bit quantum code in the product operator formalism, and uses geometric algebra methods to obtain the error-corrected decay curve in the presence of arbitrary correlations in the external random fields. These predictions are confirmed in both the totally correlated and uncorrelated cases by liquid-state NMR experiments on 13C-labeled alanine, using gradient-diffusion methods to implement these idealized decoherence models. Quantum error correction in weakly polarized systems requires that the ancilla spins be prepared in a pseudo-pure state relative to the data spin, which entails a loss of signal that exceeds any potential gain through error correction. Nevertheless, this study shows that quantum coding can be used to validate theoretical decoherence mechanisms, and to provide detailed information on correlations in the underlying NMR relaxation dynamics.Comment: 33 pages plus 6 figures, LaTeX article class with amsmath & graphicx package

Docking and molecular dynamics simulations of the ternary complex nisin2:lipid II

Lanthionine antibiotics are an important class of naturally-occurring antimicrobial peptides. The best-known, nisin, is a commercial food preservative. However, structural and mechanistic details on nisin/lipid II membrane complexes are currently lacking. Recently, we have developed empirical force-field parameters to model lantibiotics. Docking and molecular dynamics (MD) simulations have been used to study the nisin2:lipid II complex in bacterial membranes, which has been put forward as the building block of nisin/lipid II binary membrane pores. A Ile1Trp mutation of the N-terminus of nisin has been modelled and docked onto lipid II models; the computed binding affinity increased compared to wildtype. Wild-type nisin was also docked onto three different lipid II structures and a stable 2:1 nisin:lipid II complex formed. This complex was inserted into a membrane. Six independent MD simulations revealed key interactions in the complex, specifically the N terminal engagement of nisin with lipid II at the pyrophosphate and C-terminus of the pentapeptide chain. Nisin2 inserts into the membrane and we propose this is the first step in pore formation, mediated by the nisin N-terminus–lipid II pentapeptide hydrogen bond. The lipid II undecaprenyl chain adopted different conformations in the presence of nisin, which may also have implications for pore formation

Reparameterization of RNA χ Torsion Parameters for the AMBER Force Field and Comparison to NMR Spectra for Cytidine and Uridine

A reparameterization of the torsional parameters for the glycosidic dihedral angle, χ, for the AMBER99 force field in RNA nucleosides is used to provide a modified force field, AMBER99χ. Molecular dynamics simulations of cytidine, uridine, adenosine, and guanosine in aqueous solution using the AMBER99 and AMBER99χ force fields are compared with NMR results. For each nucleoside and force field, 10 individual molecular dynamics simulations of 30 ns each were run. For cytidine with AMBER99χ force field, each molecular dynamics simulation time was extended to 120 ns for convergence purposes. Nuclear magnetic resonance (NMR) spectroscopy, including one-dimensional (1D) 1H, steady-state 1D 1H nuclear Overhauser effect (NOE), and transient 1D 1H NOE, was used to determine the sugar puckering and preferred base orientation with respect to the ribose of cytidine and uridine. The AMBER99 force field overestimates the population of syn conformations of the base orientation and of C2′-endo sugar puckering of the pyrimidines, while the AMBER99χ force field’s predictions are more consistent with NMR results. Moreover, the AMBER99 force field prefers high anti conformations with glycosidic dihedral angles around 310° for the base orientation of purines. The AMBER99χ force field prefers anti conformations around 185°, which is more consistent with the quantum mechanical calculations and known 3D structures of folded ribonucleic acids (RNAs). Evidently, the AMBER99χ force field predicts the structural characteristics of ribonucleosides better than the AMBER99 force field and should improve structural and thermodynamic predictions of RNA structures