The magnetic moment of the 344 keV level of Gd

The magnetic moment of the 344 keV level of ¹⁵²Gd was determined from measurements of the rotations of the angular correlations of γ-γ cascades involving this level in the magnetic hyperfine field of Gd metal. The value found for gτ is (2.43±0.22)·10⁻¹¹ sec.. Taking τ = (7.6±1.3)·10⁻¹¹ sec, a value of 0.32±0.06 was derived for the gyromagnetic ratio of this level.     

Networks of polynomial pieces with application to the analysis of point clouds and images

We consider Hölder smoothness classes of surfaces for which we construct piecewise polynomial approximation networks, which are graphs with polynomial pieces as nodes and edges between polynomial pieces that are in ‘good continuation’ of each other. Little known to the community, a similar construction was used by Kolmogorov and Tikhomirov in their proof of their celebrated entropy results for Hölder classes.We show how to use such networks in the context of detecting geometric objects buried in noise to approximate the scan statistic, yielding an optimization problem akin to the Traveling Salesman. In the same context, we describe an alternative approach based on computing the longest path in the network after appropriate thresholding.For the special case of curves, we also formalize the notion of ‘good continuation’ between beamlets in any dimension, obtaining more economical piecewise linear approximation networks for curves.We include some numerical experiments illustrating the use of the beamlet network in characterizing the filamentarity content of 3D data sets, and show that even a rudimentary notion of good continuity may bring substantial improvement.     

Enhancement of the superconducting transition temperature of La2-xSrxCuO4 bilayers: role of pairing and phase stiffness

The superconducting transition temperature T(c) of bilayers comprising underdoped La(2-x)Sr(x)CuO(4) films capped by a thin heavily overdoped metallic La(1.65)Sr(0.35)CuO(4) layer, is found to increase with respect to T(c) of the bare underdoped films. The highest T(c) is achieved for x=0.12, close to the "anomalous" 1/8 doping level, and exceeds that of the optimally doped bare film. Our data suggest that the enhanced superconductivity is confined to the interface between the layers. We attribute the effect to a combination of the high pairing scale in the underdoped layer with an enhanced phase stiffness induced by the overdoped film.     

Hydrodynamic boundary conditions and dynamic forces between bubbles and surfaces

Dynamic forces between a 50 microm radius bubble driven towards and from a mica plate using an atomic force microscope in electrolyte and in surfactant exhibit different hydrodynamic boundary conditions at the bubble surface. In added surfactant, the forces are consistent with the no-slip boundary condition at the mica and bubble surfaces. With no surfactant, a new boundary condition that accounts for the transport of trace surface impurities explains variations of dynamic forces at different speeds and provides a direct connection between dynamic forces and surface transport effects at the air-water interface.     

Variational multiple-tensor fitting of fiber-ambiguous diffusion-weighted magnetic resonance imaging voxels

Partial volume effects are often experienced in diffusion-weighted MRI of biologic tissue. This is when the signal attenuation reflects a mixture of diffusion processes, originating from different tissue compartments, residing in the same voxel. Decomposing the mixture requires elaborated models that account for multiple compartments, yet the fitting problem for those models is usually ill posed. We suggest a novel approach for stabilizing the fitting problem of the multiple-tensors model by a variational framework that adds biologically oriented assumption of neighborhood alignments. The framework is designed to address fiber ambiguity caused by a number of neuronal fiber compartments residing in the same voxel. The method requires diffusion data acquired by common, clinically feasible MRI sequences, and is able to derive familiar tensor quantities for each compartment. Neighborhood alignment is performed by adding piece-wise smooth regularization constraints to an energy function. Minimization with the gradient descent method produces a set of diffusion-reaction partial differential equations that describe a tensor-preserving flow towards a best approximation of the data while maintaining the constraints. We analyze fiber compartment separation capabilities on a synthetic model of crossing fibers and on brain areas known to have crossing fibers. We compare the results with diffusion tensor imaging analysis and discuss applications for the framework.     

Flat corannulene: when a transition state becomes a stable molecule

Flat corannulene has been considered so far only as a transition state of the bowl-to-bowl inversion process. This study was driven by the prediction that substituents with strong steric repulsion could destabilize the bowl-shaped conformation of this molecule to such an extent that the highly unstable planar geometry would become an isolable molecule. To examine the substituents'' effect on the corannulene bowl depth, optimized structures for the highly-congested decakis(t-butylsulfido)corannulene were calculated. The computations, performed with both the M06-2X/def2-TZVP and the B3LYP/def2-TZVP methods (the latter with and without Grimme''s D3 dispersion correction), predict that this molecule can achieve two minimum structures: a flat carbon framework and a bowl-shaped structure, which are very close in energy. This rather unusual compound was easily synthesized from decachlorocorannulene under mild reaction conditions, and X-ray crystallographic studies gave similar results to the theoretical predictions. This compound crystallized in two different polymorphs, one exhibiting a completely flat corannulene core and the other having a bowl-shaped conformation.

The first flat metal-free corannulene derivative was predicted by computations and achieved by synthesis.     

Maximum of the Characteristic Polynomial for a Random Permutation Matrix

Let P_N be a uniform random N × N permutation matrix and let χ_N(z) = det(zI_N − P_N) denote its characteristic polynomial. We prove a law of large numbers for the maximum modulus of χ_N on the unit circle, specifically, with probability tending to 1 as N → ∞ , for a numerical constant x₀ ≈ 0.652 . The main idea of the proof is to uncover a logarithmic correlation structure for the distribution of (the logarithm of) χ_N , viewed as a random field on the circle, and to adapt a well-known second-moment argument for the maximum of the branching random walk. Unlike the well-studied CUE field in which P_N is replaced with a Haar unitary, the distribution of χ_N(e^2πit) is sensitive to Diophantine properties of the point t . To deal with this we borrow tools from the Hardy-Littlewood circle method. © 2020 Wiley Periodicals LLC     

Geometry and Temperature Chaos in Mixed Spherical Spin Glasses at Low Temperature: The Perturbative Regime

We study the Gibbs measure of mixed spherical p -spin glass models at low temperature, in (part of) the 1-RSB regime, including, in particular, models close to pure in an appropriate sense. We show that the Gibbs measure concentrates on spherical bands around deep critical points of the (extended) Hamiltonian restricted to the sphere of radius , where is the rightmost point in the support of the overlap distribution. We also show that the relevant critical points are pairwise orthogonal for two different low temperatures. This allows us to explain why temperature chaos occurs for those models, in contrast to the pure spherical models. © 2019 Wiley Periodicals, Inc.