Efficient Resolution of Anisotropic Structures

We highlight some recent new delevelopments concerning the sparse representation of possibly high-dimensional functions exhibiting strong anisotropic features and low regularity in isotropic Sobolev or Besov scales. Specifically, we focus on the solution of transport equations which exhibit propagation of singularities where, additionally, high-dimensionality enters when the convection field, and hence the solutions, depend on parameters varying over some compact set. Important constituents of our approach are directionally adaptive discretization concepts motivated by compactly supported shearlet systems, and well-conditioned stable variational formulations that support trial spaces with anisotropic refinements with arbitrary directionalities. We prove that they provide tight error-residual relations which are used to contrive rigorously founded adaptive refinement schemes which converge in $L_2$. Moreover, in the context of parameter dependent problems we discuss two approaches serving different purposes and working under different regularity assumptions. For frequent query problems, making essential use of the novel well-conditioned variational formulations, a new Reduced Basis Method is outlined which exhibits a certain rate-optimal performance for indefinite, unsymmetric or singularly perturbed problems. For the radiative transfer problem with scattering a sparse tensor method is presented which mitigates or even overcomes the curse of dimensionality under suitable (so far still isotropic) regularity assumptions. Numerical examples for both methods illustrate the theoretical findings

Tensor completion in hierarchical tensor representations

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the reconstruction of tensors of low multi-linear rank in recently introduced hierarchical tensor formats from a small number of measurements. Hierarchical tensors are a flexible generalization of the well-known Tucker representation, which have the advantage that the number of degrees of freedom of a low rank tensor does not scale exponentially with the order of the tensor. While corresponding tensor decompositions can be computed efficiently via successive applications of (matrix) singular value decompositions, some important properties of the singular value decomposition do not extend from the matrix to the tensor case. This results in major computational and theoretical difficulties in designing and analyzing algorithms for low rank tensor recovery. For instance, a canonical analogue of the tensor nuclear norm is NP-hard to compute in general, which is in stark contrast to the matrix case. In this book chapter we consider versions of iterative hard thresholding schemes adapted to hierarchical tensor formats. A variant builds on methods from Riemannian optimization and uses a retraction mapping from the tangent space of the manifold of low rank tensors back to this manifold. We provide first partial convergence results based on a tensor version of the restricted isometry property (TRIP) of the measurement map. Moreover, an estimate of the number of measurements is provided that ensures the TRIP of a given tensor rank with high probability for Gaussian measurement maps.Comment: revised version, to be published in Compressed Sensing and Its Applications (edited by H. Boche, R. Calderbank, G. Kutyniok, J. Vybiral

De Sitter Cosmic Strings and Supersymmetry

We study massive spinor fields in the geometry of a straight cosmic string in a de Sitter background. We find a hidden N=2 supersymmetry in the fermionic solutions of the equations of motion. We connect the zero mode solutions to the heat-kernel regularized Witten index of the supersymmetric algebra.Comment: Version similar to the one accepted by General Relativity and Gravitatio

Time and Amplitude of Afterpulse Measured with a Large Size Photomultiplier Tube

We have studied the afterpulse of a hemispherical photomultiplier tube for an upcoming reactor neutrino experiment. The timing, the amplitude, and the rate of the afterpulse for a 10 inch photomultiplier tube were measured with a 400 MHz FADC up to 16 \ms time window after the initial signal generated by an LED light pulse. The time and amplitude correlation of the afterpulse shows several distinctive groups. We describe the dependencies of the afterpulse on the applied high voltage and the amplitude of the main light pulse. The present data could shed light upon the general mechanism of the afterpulse.Comment: 11 figure

Pyrimidin‐6‐yl trifluoroborate salts as versatile templates for heterocycle synthesis

We report a novel and general method to access a highly under‐studied privileged scaffold – pyrimidines bearing a trifluoroborate at C4, and highlight the broad utility of these intermediates in a rich array of downstream functionalization reactions. This chemistry is underpinned by the unique features of the trifluoroborate group; its robustness provides an opportunity to carry out chemoselective reactions at other positions on the pyrimidine while providing a pathway for elaboration at the C‐B bond when suitably activated

Cosmological evolution of interacting dark energy in Lorentz violation

The cosmological evolution of an interacting scalar field model in which the scalar field interacts with dark matter, radiation, and baryon via Lorentz violation is investigated. We propose a model of interaction through the effective coupling $\bar{\beta}$. Using dynamical system analysis, we study the linear dynamics of an interacting model and show that the dynamics of critical points are completely controlled by two parameters. Some results can be mentioned as follows. Firstly, the sequence of radiation, the dark matter, and the scalar field dark energy exist and baryons are sub dominant. Secondly, the model also allows the possibility of having a universe in the phantom phase with constant potential. Thirdly, the effective gravitational constant varies with respect to time through $\bar{\beta}$. In particular, we consider a simple case where $\bar{\beta}$ has a quadratic form and has a good agreement with the modified $\Lambda$CDM and quintessence models. Finally, we also calculate the first post--Newtonian parameters for our model.Comment: 14 pages, published versio

New mechanism to cross the phantom divide

Recently, type Ia supernovae data appear to support a dark energy whose equation of state $w$ crosses -1, which is a much more amazing problem than the acceleration of the universe. We show that it is possible for the equation of state to cross the phantom divide by a scalar field in the gravity with an additional inverse power-law term of Ricci scalar in the Lagrangian. The necessary and sufficient condition for a universe in which the dark energy can cross the phantom divide is obtained. Some analytical solutions with $w<-1$ or $w>-1$ are obtained. A minimal coupled scalar with different potentials, including quadratic, cubic, quantic, exponential and logarithmic potentials are investigated via numerical methods, respectively. All these potentials lead to the crossing behavior. We show that it is a robust result which is hardly dependent on the concrete form of the potential of the scalar.Comment: 11 pages, 5 figs, v3: several references added, to match the published versio

Apparatus for a Search for T-violating Muon Polarization in Stopped-Kaon Decays

The detector built at KEK to search for T-violating transverse muon polarization in K+ --> pi0 mu+ nu (Kmu3) decay of stopped kaons is described. Sensitivity to the transverse polarization component is obtained from reconstruction of the decay plane by tracking the mu+ through a toroidal spectrometer and detecting the pi0 in a segmented CsI(Tl) photon calorimeter. The muon polarization was obtained from the decay positron asymmetry of muons stopped in a polarimeter. The detector included features which minimized systematic errors while maintaining high acceptance.Comment: 56 pages, 30 figures, submitted to NI

Review of Well-to-Wheel lifecycle emissions of liquefied natural gas heavy goods vehicles

It has been suggested that using liquefied natural gas as a fuel source for heavy goods vehicles could provide a reduction in greenhouse gas emissions. Various studies have investigated different aspects of the lifecycle emissions of natural gas heavy goods vehicles throughout the past decade, however, there has been little comparative analysis across these studies. This review provides a comprehensive examination of the well-to-wheel lifecycle emissions of liquefied natural gas for heavy goods vehicles in comparison to diesel, the current standard. A systematic selection criteria based on relevance to the defined well-to-wheel system boundary of liquefied natural gas as a fuel source for heavy goods vehicles, including greenhouse gas emissions, were augmented by the authors knowledge of the field. The various data are categorised by engine technology and model year (pre- and post-2015), average speed of the duty cycle, and then statistically analysed to identify clear trends and correlations in the emissions produced. The two primary factors affecting the well-to-wheel greenhouse gas emissions of natural gas heavy hoods vehicles are: (i) natural gas engine fuel efficiency relative to diesel, and (ii) methane leakage across the supply chain. Methane leakage rates are a significant uncertainty and range from 0.3 to 20 % of throughput. With long-term perspective of efficiency penalty (10 %) in natural gas engines, the well-to-wheel greenhouse gas emissions reduction of natural gas fuelled trucks against diesel is up to 10 %, which appears insufficient toward net zero emissions by 2050. The use of biomethane further reduces the greenhouse gas emissions by 34–66 % depending on the engine technology. Controlling fugitive methane emissions in the fuel production and supply chain remains critical