Search results for "46"
showing 10 items of 1176 documents
Design and Implementation of Density Sensor for Liquids Using Fiber Bragg Grating Sensor
2022
In this paper, an optical fiber sensor based density sensor is proposed and demonstrated experimentally. The sensor is formed by fiber Bragg grating (FBG) sensor. The proposed sensor design is very simple and versatile for density measurements of liquids. The FBG strain sensor has one end mounted to a 3D printed rigid support, and the other end connected to a 3D manufactured clamp in this sensor design. A metal ball is suspended from this clamp by a non-stretchable cord. When it is completely immersed in liquid, the liquid buoyancy force acts on it. As a result, the strain in FBG varies depending on the force applied to the ball. This results in a wavelength shift in the FBG sensor. The pro…
High Quality Factor Silicon Membrane Metasurface for Intensity-Based Refractive Index Sensing
2021
We propose a new sensing device based on all-optical nano-objects placed in a suspended periodic array. We demonstrate that the intensity-based sensing mechanism can measure environment refractive index change of the order of 1.8×10−6, which is close to record efficiencies in plasmonic devices.
An epitaxial hexagonal tungsten bronze as precursor for WO3 nanorods on mica.
2008
International audience; Tungsten oxide nanorods are grown at atmospheric pressure and low temperature (360 1C), by sublimation of WO3 and condensation on mica substrates. The nanorods are characterized by atomic force microscopy, high-resolution electron microscopy, energy-dispersive X-ray spectroscopy and high energy electron diffraction. The experimental results evidence the formation of a hexagonal tungsten bronze at the nanorod–substrate interface. The epitaxial relationships of the nanorods on mica are determined and the role of epitaxial orientation of the interfacial bronze in the nanorod growth and morphology are discussed.
Isolation of a perfectly linear uranium(II) metallocene
2020
Reduction of the uranium(III) metallocene [(eta(5)-(C5Pr5)-Pr-i)(2)UI] (1) with potassium graphite produces the "second-generation" uranocene [(eta(5)-(C5Pr5)-Pr-i)(2)U] (2), which contains uranium in the formal divalent oxidation state. The geometry of 2 is that of a perfectly linear bis(cyclopentadienyl) sandwich complex, with the ground-state valence electron configuration of uranium(II) revealed by electronic spectroscopy and density functional theory to be 5f(3) 6d(1). Appreciable covalent contributions to the metal-ligand bonds were determined from a computational study of 2, including participation from the uranium 5f and 6d orbitals. Whereas three unpaired electrons in 2 occupy orbi…
Higher integrability and stability of (p,q)-quasiminimizers
2023
Using purely variational methods, we prove local and global higher integrability results for upper gradients of quasiminimizers of a $(p,q)$-Dirichlet integral with fixed boundary data, assuming it belongs to a slightly better Newtonian space. We also obtain a stability property with respect to the varying exponents $p$ and $q$. The setting is a doubling metric measure space supporting a Poincar\'e inequality.
Volume growth, capacity estimates, p-parabolicity and sharp integrability properties of p-harmonic Green functions
2023
In a complete metric space equipped with a doubling measure supporting a $p$-Poincar\'e inequality, we prove sharp growth and integrability results for $p$-harmonic Green functions and their minimal $p$-weak upper gradients. We show that these properties are determined by the growth of the underlying measure near the singularity. Corresponding results are obtained also for more general $p$-harmonic functions with poles, as well as for singular solutions of elliptic differential equations in divergence form on weighted $\mathbf{R}^n$ and on manifolds. The proofs are based on a new general capacity estimate for annuli, which implies precise pointwise estimates for $p$-harmonic Green functions…
Loomis-Whitney inequalities in Heisenberg groups
2021
This note concerns Loomis-Whitney inequalities in Heisenberg groups $\mathbb{H}^n$: $$|K| \lesssim \prod_{j=1}^{2n}|\pi_j(K)|^{\frac{n+1}{n(2n+1)}}, \qquad K \subset \mathbb{H}^n.$$ Here $\pi_{j}$, $j=1,\ldots,2n$, are the vertical Heisenberg projections to the hyperplanes $\{x_j=0\}$, respectively, and $|\cdot|$ refers to a natural Haar measure on either $\mathbb{H}^n$, or one of the hyperplanes. The Loomis-Whitney inequality in the first Heisenberg group $\mathbb{H}^1$ is a direct consequence of known $L^p$ improving properties of the standard Radon transform in $\mathbb{R}^2$. In this note, we show how the Loomis-Whitney inequalities in higher dimensional Heisenberg groups can be deduced…
X-ray Tomography of One-forms with Partial Data
2021
If the integrals of a one-form over all lines meeting a small open set vanish and the form is closed in this set, then the one-form is exact in the whole Euclidean space. We obtain a unique continuation result for the normal operator of the X-ray transform of one-forms, and this leads to one of our two proofs of the partial data result. Our proofs apply to compactly supported covector-valued distributions.
On Radon Transforms on Tori
2014
We show injectivity of the X-ray transform and the $d$-plane Radon transform for distributions on the $n$-torus, lowering the regularity assumption in the recent work by Abouelaz and Rouvi\`ere. We also show solenoidal injectivity of the X-ray transform on the $n$-torus for tensor fields of any order, allowing the tensors to have distribution valued coefficients. These imply new injectivity results for the periodic broken ray transform on cubes of any dimension.
Approximation by mappings with singular Hessian minors
2018
Let $\Omega\subset\mathbb R^n$ be a Lipschitz domain. Given $1\leq p<k\leq n$ and any $u\in W^{2,p}(\Omega)$ belonging to the little H\"older class $c^{1,\alpha}$, we construct a sequence $u_j$ in the same space with $\operatorname{rank}D^2u_j<k$ almost everywhere such that $u_j\to u$ in $C^{1,\alpha}$ and weakly in $W^{2,p}$. This result is in strong contrast with known regularity behavior of functions in $W^{2,p}$, $p\geq k$, satisfying the same rank inequality.