A high-order scheme for solving wave propagation problems via the direct construction of an approximate time-evolution operator

ArticleThis is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Numerical Analysis following peer review. The version of record IMA J Numer Anal (2015) is available online at http://imajna.oxfordjournals.org/content/early/2015/06/16/imanum.drv021The manuscript presents a technique for efficiently solving the classical wave equation, the shallow water equations, and, more generally, equations of the form ∂u/∂t=Lu∂u/∂t=Lu, where LL is a skew-Hermitian differential operator. The idea is to explicitly construct an approximation to the time-evolution operator exp(τL)exp⁡(τL) for a relatively large time-step ττ. Recently developed techniques for approximating oscillatory scalar functions by rational functions, and accelerated algorithms for computing functions of discretized differential operators are exploited. Principal advantages of the proposed method include: stability even for large time-steps, the possibility to parallelize in time over many characteristic wavelengths and large speed-ups over existing methods in situations where simulation over long times are required. Numerical examples involving the 2D rotating shallow water equations and the 2D wave equation in an inhomogenous medium are presented, and the method is compared to the 4th order Runge–Kutta (RK4) method and to the use of Chebyshev polynomials. The new method achieved high accuracy over long-time intervals, and with speeds that are orders of magnitude faster than both RK4 and the use of Chebyshev polynomials

High-resolution DCE-MRI of the pituitary gland using radial k-space acquisition with compressed sensing reconstruction

BACKGROUND AND PURPOSE: The pituitary gland is located outside of the blood-brain barrier. Dynamic T1 weighted contrast enhanced sequence is considered to be the gold standard to evaluate this region. However, it does not allow assessment of intrinsic permeability properties of the gland. Our aim was to demonstrate the utility of radial volumetric interpolated brain examination with the golden-angle radial sparse parallel technique to evaluate permeability characteristics of the individual components (anterior and posterior gland and the median eminence) of the pituitary gland and areas of differential enhancement and to optimize the study acquisition time. MATERIALS AND METHODS: A retrospective study was performed in 52 patients (group 1, 25 patients with normal pituitary glands; and group 2, 27 patients with a known diagnosis of microadenoma). Radial volumetric interpolated brain examination sequences with goldenangle radial sparse parallel technique were evaluated with an ROI-based method to obtain signal-time curves and permeability measures of individual normal structures within the pituitary gland and areas of differential enhancement. Statistical analyses were performed to assess differences in the permeability parameters of these individual regions and optimize the study acquisition time. RESULTS: Signal-time curves from the posterior pituitary gland and median eminence demonstrated a faster wash-in and time of maximum enhancement with a lower peak of enhancement compared with the anterior pituitary gland (P .005). Time-optimization analysis demonstrated that 120 seconds is ideal for dynamic pituitary gland evaluation. In the absence of a clinical history, differences in the signal-time curves allow easy distinction between a simple cyst and a microadenoma. CONCLUSIONS: This retrospective study confirms the ability of the golden-angle radial sparse parallel technique to evaluate the permeability characteristics of the pituitary gland and establishes 120 seconds as the ideal acquisition time for dynamic pituitary gland imaging

Calculations of polarizabilities and hyperpolarizabilities for the Be+^+ ion

The polarizabilities and hyperpolarizabilities of the Be$^+$ ion in the $2^2S$ state and the $2^2P$ state are determined. Calculations are performed using two independent methods: i) variationally determined wave functions using Hylleraas basis set expansions and ii) single electron calculations utilizing a frozen-core Hamiltonian. The first few parameters in the long-range interaction potential between a Be$^+$ ion and a H, He, or Li atom, and the leading parameters of the effective potential for the high-$L$ Rydberg states of beryllium were also computed. All the values reported are the results of calculations close to convergence. Comparisons are made with published results where available.Comment: 18 pp; added details to Sec. I

The Integrity and Yield of Genomic DNA Isolated from Whole Blood Following Long-Term Storage at -30°C.

Long-term storage of whole blood can affect the integrity of DNA if it is not done under optimal conditions. The aim of this study was to determine whether long-term storage (2-19 years) of whole blood samples at -30°C had a negative effect on the quality or quantity of genomic DNA that could be recovered at extraction. Genomic DNA was isolated from 2758 whole blood samples collected in 4 mL EDTA vacutainers from 1997 to 2012. DNA was extracted using the Qiagen® FlexiGene® DNA kit. The average storage duration at -30°C was 12 years. The quality and quantity of the isolated DNA were assessed using spectrophotometry (NanoDrop™), a fluorometric assay for double-stranded DNA (Qubit™), and agarose gel electrophoresis. The mean DNA yield per sample was found to be 114 μg from whole blood volumes that ranged from 0.5 to 4 mL. The mean A260/280 ratio and median A260/280 ratios were both 1.8. No correlation was found between the duration of storage and the total yield or the quality of DNA extracted. These data suggest that high-quality DNA can be extracted from whole blood samples that are stored at -30°C for up to 19 years

Long-range interactions of metastable helium atoms

Polarizabilities, dispersion coefficients, and long-range atom-surface interaction potentials are calculated for the n=2 triplet and singlet states of helium using highly accurate, variationally determined, wave functions.Comment: RevTeX, epsf, 4 fig

Exact Casimir-Polder potential between a particle and an ideal metal cylindrical shell and the proximity force approximation

We derive the exact Casimir-Polder potential for a polarizable microparticle inside an ideal metal cylindrical shell using the Green function method. The exact Casimir-Polder potential for a particle outside a shell, obtained recently by using the Hamiltonian approach, is rederived and confirmed. The exact quantum field theoretical result is compared with that obtained using the proximity force approximation and a very good agreement is demonstrated at separations below 0.1$R$, where $R$ is the radius of the cylinder. The developed methods are applicable in the theory of topological defects.Comment: 8 pages, 4 figures, Accepted for publication in Eur. Phys. J.

Borrelia burgdorferi EbfC defines a newly-identified, widespread family of bacterial DNA-binding proteins

The Lyme disease spirochete, Borrelia burgdorferi, encodes a novel type of DNA-binding protein named EbfC. Orthologs of EbfC are encoded by a wide range of bacterial species, so characterization of the borrelial protein has implications that span the eubacterial kingdom. The present work defines the DNA sequence required for high-affinity binding by EbfC to be the 4 bp broken palindrome GTnAC, where ‘n’ can be any nucleotide. Two high-affinity EbfC-binding sites are located immediately 5′ of B. burgdorferi erp transcriptional promoters, and binding of EbfC was found to alter the conformation of erp promoter DNA. Consensus EbfC-binding sites are abundantly distributed throughout the B. burgdorferi genome, occurring approximately once every 1 kb. These and other features of EbfC suggest that this small protein and its orthologs may represent a distinctive type of bacterial nucleoid-associated protein. EbfC was shown to bind DNA as a homodimer, and site-directed mutagenesis studies indicated that EbfC and its orthologs appear to bind DNA via a novel α-helical ‘tweezer’-like structure