X-ray Transform Research Articles

Investigation of the lithiation mechanism of tin phosphite SnHPO3 as anode for Lithium-ion batteries

Phosphite-based anodes are attracting increasing attention in energy storage, especially for lithium-ion technology, due to their distinctive structures and their good electrochemical performances. Herein, the lithiation mechanism of tin phosphite SnHPO3 as lithium anode was examined for the first time. SnHPO3 has been synthesized through a soft hydrothermal route. Its structure was characterized by X-ray diffraction, Fourier Transform Infrared spectroscopy and 31P Nuclear Magnetic Resonance spectroscopy techniques. The reaction mechanisms of lithiation-delithiation of SnHPO3 anode was conducted using operando X-ray diffraction, ex-situ X-ray and ex-situ Fourier Transform Infrared spectroscopy techniques at room temperature. Both in-situ and ex-situ measurements show that SnHPO3 undergoes a conversion mechanism. The lithiation-delithiation of tin phosphite took place in a complex redox reaction sequence, and the reversible electrochemical phenomenon exclusively occurs through the alloying of tin at a low potential. The lithiation of tin phosphite begins by partial degradation of its structure, signifying the start of the conversion process. Then, the phosphite matrix becomes amorphous. The reversible capacity of the system is governed by the lithium‑tin alloying de-alloying process, produced at low potential.

Sampling the X-ray Transform on Simple Surfaces

Sampling the X-ray Transform on Simple Surfaces

The X-Ray Transform on a Generic Family of Smooth Curves

The X-Ray Transform on a Generic Family of Smooth Curves

Single Pixel X-ray Transform and Related Inverse Problems

In this paper, we analyze the nonlinear single pixel X-ray transform $K$ and study the reconstruction of $f$ from the measurement $Kf$. Different from the well-known X-ray transform, the transform $K$ is a nonlinear operator and uses a single detector that integrates all rays in the space. We derive stability estimates and an inversion of the linearization at zero. We also consider the case where we integrate along geodesics of a Riemannian metric. Moreover, we conduct several numerical experiments to corroborate the theoretical results.

Boundary-Rigidity of Projective Metrics and the Geodesic X-Ray Transform

We prove that given a compact convex non-empty domain {mathcal {M}} in the plane, a function delta :partial mathcal Mtimes partial {mathcal {M}}rightarrow {mathbb {R}}_+ can be extended to a projective metric d on {mathcal {M}} if and only if delta (P,R)+delta (Q,S)-delta (P,S)-delta (Q,R)>0 for any convex quadrangle Box (PQRS) inscribed in partial {mathcal {M}}. Moreover, this extension is unique.

Local X-ray Transform on Asymptotically Hyperbolic Manifolds via Projective Compactification

We prove local injectivity near a boundary point for the geodesic X-ray transform for an asymptotically hyperbolic metric even mod $O(\rho^5)$ in dimensions three and higher.

Stability of the Non-abelian X-ray Transform in Dimension ge 3

Non-abelian X-ray tomography seeks to recover a matrix potential Phi :Mrightarrow {mathbb {C}}^{mtimes m} in a domain M from measurements of its so-called scattering data C_Phi at partial M. For dim Mge 3 (and under appropriate convexity and regularity conditions), injectivity of the forward map Phi mapsto C_Phi was established in (Paternain et al. in Am J Math 141(6):1707–1750, 2019). The present article extends this result by proving a Hölder-type stability estimate. As an application, a statistical consistency result for dim M =2 (Monard et al. in Commun Pure Appl Math, 2019) is generalised to higher dimensions. The injectivity proof in (Paternain et al. in Am J Math 141(6):1707–1750, 2019) relies on a novel method by Uhlmann and Vasy (Invent Math 205(1):83–120, 2016), which first establishes injectivity in a shallow layer below partial M and then globalises this by a layer stripping argument. The main technical contribution of this paper is a more quantitative version of these arguments, in particular, proving uniform bounds on layer depth and stability constants.

X-ray Transform in Asymptotically Conic Spaces

Abstract In this article, we study the properties of the geodesic X-ray transform for asymptotically Euclidean or conic Riemannian metrics and show injectivity under non-trapping and no conjugate point assumptions. We also define a notion of lens data for such metrics and study the associated inverse problem.

X-Ray Transform and Boundary Rigidity for Asymptotically Hyperbolic Manifolds

We consider the boundary rigidity problem for asymptotically hyperbolic manifolds. We show injectivity of the X-ray transform in several cases and consider the non-linear inverse problem which consists of recovering a metric from boundary measurements for the geodesic flow.

Admissible Complexes for the Projective X-ray Transform over a Finite Field

We consider the X-ray transform in a projective space over a finite field. It is well known (after Bolker) that this transform is injective. We formulate an analog of Gelfand’s admissibility problem for the Radon transform, which asks for a classification of all minimal sets of lines for which the restricted Radon transform is injective. The solution involves doubly ruled quadric surfaces.

Functional Relations, Sharp Mapping Properties, and Regularization of the X-Ray Transform on Disks of Constant Curvature

On simple geodesic disks of constant curvature, we derive new functional relations for the geodesic X-ray transform, involving a certain class of elliptic differential operators whose ellipticity d...

Effect of Gamma Irradiation on High Lead Borate Glass Doped with Tungsten Oxide

X-ray, Ultraviolet and Fourier Transform infrared spectral properties of tungsten ions doped in a host lead borate glass have a composition [60%PbO and 40%B2O3 weight%] was studied. Effect of gamma irradiation on the prepared glass samples was surveyed. Amorphization of the studied glass samples have been checked by X ray. Deep inspection for density, molar volume, UV and FTIR for base glass and tungsten oxide with different concentrations (0.15-2.28) weight% proved that the tungsten ions are pronounced as structural groups mostly in the hexavalent W6+. The constancy of optical absorption spectral curves reversed the shielding behavior for this combined glass towards successive gamma irradiation. Glasses containing high lead oxide content are extensively used for multi-applications including lead crystal glass and some special optical glasses, low-melting solder glasses and radiation protection windows and even in immobilization of radioactive nuclear wastes.

Numerical Inversion of Three-Dimensional Geodesic X-Ray Transform Arising from Travel Time Tomography

In this paper, we consider the inverse problem of determining an unknown function defined in three space dimensions from its geodesic X-ray transform. The standard X-ray transform is defined on the...

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We derive reconstruction formulas for a family of geodesic ray transforms with connection, defined on simple Riemannian surfaces. Such formulas provide injectivity of all such transforms in a neighborhood of constant curvature metrics and non-unitary connections with curvature close to zero. If certain Fredholm equations are injective in the absence of connection, then for any smooth enough connection multiplied by a complex parameter, the corresponding transform is injective for all values of that parameter outside a discrete set. Range characterizations are also provided.

The X-ray Transform on a General Family of Curves on Finsler Surfaces

For a compact oriented Finsler surface with smooth boundary, we consider the scalar and vector integral geometry problems over a general family of curves running between boundary points and parametrized by arc length. We impose a natural condition which results in the no conjugate points condition in the case when the curves in question are geodesic lines. Our main theorem generalizes Mukhometov’s theorem in several directions. We also consider these problems on a closed oriented Finsler surface. In this case the integral geometry problems make sense provided that sufficiently many curves in the family are periodic. To this end, we assume that the induced flow on the unit circle bundle of the surface is Anosov. Also, we study the cohomological equation of thermostats without conjugate points.

Optical and magnetic properties of ZnO/ZnFe2O4 nanocomposite

ZnO/ZnFe2O4 nanocomposite was prepared by a simple and low cost chemical precipitation method. The prepared composite was characterized by X-ray diffraction (XRD), energy-dispersive X-ray (EDX), Raman and Fourier Transform infrared spectroscopy (FTIR). The morphology of the prepared sample was studied by scanning electron microscopy (SEM). Photoluminescence (PL) emission of the sample has been investigated at different temperatures (10–300 K) in order to determine the effect of temperature on emission properties of the prepared composite. It was found that at low temperature, the samples show stronger emissions than those at room temperature. Magnetic properties of ZnO/ZnFe2O4 nanocomposite was discussed in temperature range of 5–300 K using VSM measurement. The effective anisotropy constant Keff, extracted from the magnetization vs. magnetic field, M(B), experimental curve obtained at 5 K and using the law of saturation magnetization, was found to be 2.3 × 106 erg/cm3. The high value of anisotropy constant is attributed to the existence of uncompensated surface spin in our sample as well as the magnetocrystalline contribution (which depends on the inversion degree in ZnFe2O4). By using of a modified Langevin equation, the contribution of the surface spins was quantitatively calculated in different temperature higher than TB. It was found that as the temperature increases from 100 K to 300 K, the surface spins contribution in the total magnetization increases from 44% to 68%.

Biosynthesis of gold nanoparticles using Capsicum annuum var. grossum pulp extract and its catalytic activity

Biological synthesis approach has been regarded as a green, eco-friendly and cost effective method for nanoparticles preparation without any toxic solvents and hazardous bi-products during the process. This present study reported a facile and rapid biosynthesis method for gold nanoparticles (GNPs) from Capsicum annuum var. grossum pulp extract in a single-pot process. The aqueous pulp extract was used as biotic reducing agent for gold nanoparticle growing. Various shapes (triangle, hexagonal, and quasi-spherical shapes) were observed within range of 6–37nm. The UV–Vis spectra showed surface plasmon resonance (SPR) peak for the formed GNPs at 560nm after 10min incubation at room temperature. The possible influences of extract amount, gold ion concentration, incubation time, reaction temperature and solution pH were evaluated to obtain the optimized synthesis conditions. The effects of the experimental factors on NPs synthesis process were also discussed. The produced gold nanoparticles were characterized by transform electron microscopy (TEM), X-ray diffraction (XRD), energy dispersive X-ray (EDS) and Fourier Transform infrared spectroscopy (FTIR). The results demonstrated that the as-obtained GNPs were well dispersed and stable with good catalytic activity. Biomolecules in the aqueous extract were responsible for the capping and stabilization of GNPs.

Inversion of the Attenuated Geodesic X-Ray Transform over Functions and Vector Fields on Simple Surfaces

We derive explicit reconstruction formulas for the attenuated geodesic X-ray transform over functions and, in the case of nonvanishing attenuation, vector fields, on a class of simple Riemannian surfaces with boundary. These formulas partly rely on new explicit approaches to construct continuous right-inverses for backprojection operators (and, in turn, holomorphic integrating factors), which were previously unavailable in a systematic form. The reconstruction of functions is presented in two ways, the latter being motivated by numerical considerations and successfully implemented in the last section of the paper (before the appendix). Constructing the aforementioned right-inverses requires that certain Fredholm equations, first appearing in [L. Pestov and G. Uhlmann, Int. Math. Res. Not., 2004 (2004), pp. 4331--4347], be invertible. Whether this last condition reduces the applicability of the overall approach to a strict subset of simple surfaces remains open at present.

The X-Ray Transform for Connections in Negative Curvature

We consider integral geometry inverse problems for unitary connections and skew-Hermitian Higgs fields on manifolds with negative sectional curvature. The results apply to manifolds in any dimension, with or without boundary, and also in the presence of trapped geodesics. In the boundary case, we show injectivity of the attenuated ray transform on tensor fields with values in a Hermitian bundle (i.e. vector valued case). We also show that a connection and Higgs field on a Hermitian bundle are determined up to gauge by the knowledge of the parallel transport between boundary points along all possible geodesics. The main tools are an energy identity, the Pestov identity with a unitary connection, which is presented in a general form, and a precise analysis of the singularities of solutions of transport equations when there are trapped geodesics. In the case of closed manifolds, we obtain similar results modulo the obstruction given by twisted conformal Killing tensors, and we also study this obstruction.

Tracking and erosion resistance performance investigation on nano-sized SiO<sub>2</sub> filled silicone rubber for outdoor insulation applications

This paper discusses the tracking and erosion resistance characteristics of nano-sized SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> filled virgin and aged silicon rubber (SiR) materials under AC voltage with ammonium chloride as a contaminant as per IEC-60587 test procedures. The characteristic variations in the tracking time, weight loss and eroded depth of nano-sized SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> filled virgin and aged SIR specimens are analysed in order to evaluate the relative erosion and tracking resistance of the composites. Statistical variation of the tracking time is evaluated by Weibull analysis. The Thermo Gravimetry-Derivative Thermo Gravimetric (TG-DTG) studies are performed to understand the thermal properties of the nano-sized SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> filled SIR materials with different percentage weights (% wt) of filler. The obtained result shows that the thermal performances of nano-filled virgin and aged SIR specimens are improved when the %wt of filler is increased. The Scanning Electron Microscope (SEM) with Energy Dispersive X-ray (EDAX) and Fourier Transform Infra-Red spectroscopy (FTIR) are used to investigate the physical and chemical properties of the virgin and aged SIR composites. It is observed that the tracking and erosion resistance is improved when nano-filler concentration is increased in both the virgin and aged SIR composites. Also thermal aging slightly reduces the tracking and erosion resistance of the nano-filled SIR composites.