The flipped longitudinal polarization sequence

By flipping the longitudinal magnetization with a chain of 180° pulses it is possible to effectively restore the effects of relaxation so that the same longitudinal magnetization is periodically recovered. The pulse sequence for achieving this, called Flipped LOngitudinal Polarization (FLOP), can be incorporated into any pulse sequence whenever it is desired to stop the attenuation in longitudinal magnetization caused by relaxation. We illustrate its use for fast, single-shot measurements of the longitudinal relaxation time and for three-dimensional T₁ mapping.     

Fast volumetric spatial-spectral MR imaging of hyperpolarized C-labeled compounds using multiple echo 3D bSSFP

Purpose

The goal of this work was to develop a fast 3D chemical shift imaging technique for the noninvasive measurement of hyperpolarized ¹³C-labeled substrates and metabolic products at low concentration.

Materials and Methods

Multiple echo 3D balanced steady state magnetic resonance imaging (ME-3DbSSFP) was performed in vitro on a syringe containing hyperpolarized [1,3,3-2H3; 1-¹³C]2-hydroxyethylpropionate (HEP) adjacent to a ¹³C-enriched acetate phantom, and in vivo on a rat before and after intravenous injection of hyperpolarized HEP at 1.5 T. Chemical shift images of the hyperpolarized HEP were derived from the multiple echo data by Fourier transformation along the echoes on a voxel by voxel basis for each slice of the 3D data set.

Results

ME-3DbSSFP imaging was able to provide chemical shift images of hyperpolarized HEP in vitro, and in a rat with isotropic 7-mm spatial resolution, 93 Hz spectral resolution and 16-s temporal resolution for a period greater than 45 s.

Conclusion

Multiple echo 3D bSSFP imaging can provide chemical shift images of hyperpolarized ¹³C-labeled compounds in vivo with relatively high spatial resolution and moderate spectral resolution. The increased signal-to-noise ratio of this 3D technique will enable the detection of hyperpolarized ¹³C-labeled metabolites at lower concentrations as compared to a 2D technique.     

Coupling p-multigrid to geometric multigrid for discontinuous Galerkin formulations of the convection–diffusion equation

An improved p-multigrid algorithm for discontinuous Galerkin (DG) discretizations of convection–diffusion problems is presented. The general p  -multigrid algorithm for DG discretizations involves a restriction from the p=1$p=1$ to p=0$p=0$ discontinuous polynomial solution spaces. This restriction is problematic and has limited the efficiency of the p  -multigrid method. For purely diffusive problems, Helenbrook and Atkins have demonstrated rapid convergence using a method that restricts from a discontinuous to continuous polynomial solution space at p=1$p=1$. It is shown that this method is not directly applicable to the convection–diffusion (CD) equation because it results in a central-difference discretization for the convective term. To remedy this, ideas from the streamwise upwind Petrov–Galerkin (SUPG) formulation are used to devise a transition from the discontinuous to continuous space at p=1$p=1$ that yields an upwind discretization. The results show that the new method converges rapidly for all Peclet numbers.     

Disorder-induced freezing of dynamical spin fluctuations in underdoped cuprate superconductors

We study the dynamical spin susceptibility of a correlated d-wave superconductor (dSC) in the presence of nonmagnetic disorder, using an unrestricted Hartree-Fock approach. This model provides a concrete realization of the notion that disorder slows down spin fluctuations, which eventually "freeze out." The evolution of disorder-induced spectral weight transfer agrees qualitatively with experimental observations on underdoped cuprate superconductors. For sufficiently large disorder concentrations, static spin density wave (SDW) order is created when droplets of magnetism nucleated by impurities overlap. We also study the disordered stripe state coexisting with a dSC and compare its magnetic fluctuation spectrum to that of the disorder-generated SDW phase.     

Integrating 3D images using laboratory‐based micro X‐ray computed tomography and confocal X‐ray fluorescence techniques

The application of non‐destructive imaging to characterizing samples has become more important as the costs of samples increase. Imaging a sample via X‐ray techniques is preferable when altering or even touching the sample affects its properties, or when the sample is fielded after characterization. Two laboratory‐based X‐ray techniques used at Los Alamos include micro X‐ray computed tomography (MXCT) and confocal micro X‐ray fluorescence (confocal MXRF). Both methods create a 3D rendering of the sample non‐destructively. MXCT produces a high‐resolution (sub‐µm voxel) rendering of the sample based upon X‐ray absorption; the resulting model is a function of density and does not contain any elemental information. Confocal MXRF produces an elementally specific 3D rendering of the sample, but at a lower (30 × 30 × 65 µm) resolution. By combining data from these two techniques, scientists provided a more comprehensive method of analysis. We will describe a MATLAB routine written to render each of these data sets individually and/or within the same coordinate system. This approach is shown in the analysis of two samples: an integrated circuit surface mounted resistor and a machined piece of polystyrene foam. The samples chosen provide an opportunity to compare and contrast the two X‐ray techniques, identify their weaknesses and show how they are used in a complementary fashion. Copyright © 2010 John Wiley & Sons, Ltd.     

Direct cryopreservation of winter buds of nine cultivars of blackcurrant (Ribes nigrum L)

Direct cryopreservation of overwintering, dormant buds has been applied to nine blackcurrant cultivars, using a 7 day dehydration period at c.-20° C before plunging directly into liquid nitrogen. The buds on shoots thawed from -20° C showed normal development simply by standing them in water and all the cultivars could be successfully recovered (> 58%) by grafting. None of the shoots thawed from liquid nitrogen showed any development after standing in water and all of the grafts failed. Shoots thawed from liquid nitrogen showed significant damage to xylem transport, and the cortical tissues necessary fro successful grafting showed significant loss of membrane semipermeability. However, buds excised from shoots immediately after thawing from liquid nitrogen were viable and could be recovered using in vitro culture. Survival ranged from 88 to 55%, depending upon cultivar.     

Closed Unstretchable Knotless Ribbons and the Wunderlich Functional

In 1962, Wunderlich published the article “On a developable Möbius band,” in which he attempted to determine the equilibrium shape of a free standing Möbius band. In line with Sadowsky’s pioneering works on Möbius bands of infinitesimal width, Wunderlich used an energy minimization principle, which asserts that the equilibrium shape of the Möbius band has the lowest bending energy among all possible shapes of the band. By using the developability of the band, Wunderlich reduced the bending energy from a surface integral to a line integral without assuming that the width of the band is small. Although Wunderlich did not completely succeed in determining the equilibrium shape of the Möbius band, his dimensionally reduced energy integral is arguably one of the most important developments in the field. In this work, we provide a rigorous justification of the validity of the Wunderlich integral and fully formulate the energy minimization problem associated with finding the equilibrium shapes of closed bands, including both orientable and nonorientable bands with arbitrary number of twists. This includes characterizing the function space of the energy functional, dealing with the isometry and local injectivity constraints, and deriving the Euler–Lagrange equations. Special attention is given to connecting edge conditions, regularity properties of the deformed bands, determination of the parameter space needed to ensure that the deformation is surjective, reduction in isometry constraints, and deriving matching conditions and jump conditions associated with the Euler–Lagrange equations.

     

A conjectural extension of Hecke’s converse theorem

By using specific subsequences of two different types of generalized Stern polynomials, we obtain several related classes of finite and infinite continued fractions involving a single term \(z^{t^j}\) in their partial numerators, where z is a complex variable and t is a positive integer. This approach is extended to other, sparser, subsequences of Stern polynomials, based on certain Lucas functions; this then leads to further infinite classes of continued fractions.     

A new look at a smart polling model

We analyze a Markovian smart polling model, which is a special case of the smart polling models studied in the work of Boon et al. (Queueing Syst 66:239–274, 2010), as well as a generalization of the gated M / M / 1 queue considered in Resing and Rietman (Stat Neerlandica 58:97–110, 2004). We first derive tractable expressions for the stationary distribution (when it exists) as well as the Laplace transforms of the transition functions of this polling model—while further assuming the system is empty at time zero—and we also present simple necessary and sufficient conditions for ergodicity of the smart polling model. Finally, we conclude the paper by briefly explaining how these techniques can be used to study other interesting variants of this smart polling model.