scholarly journals On Hill's operator with a matrix potential

2008 ◽  
Vol 281 (9) ◽  
pp. 1341-1350 ◽  
Author(s):  
O. A. Veliev
Keyword(s):  
Matrix Potential ◽  
Hill’S Operator

scholarly journals Stability of the Non-abelian X-ray Transform in Dimension $$\ge 3$$

2021 ◽  
Author(s):  
Jan Bohr
Keyword(s):  
Stability Estimate ◽  
Scattering Data ◽  
Regularity Conditions ◽  
Uniform Bounds ◽  
Ray Transform ◽  
Shallow Layer ◽  
Matrix Potential ◽  
Novel Method ◽  
Statistical Consistency ◽  
Appl Math

AbstractNon-abelian X-ray tomography seeks to recover a matrix potential $$\Phi :M\rightarrow {\mathbb {C}}^{m\times m}$$ Φ : M → C m × m in a domain M from measurements of its so-called scattering data $$C_\Phi $$ C Φ at $$\partial M$$ ∂ M . For $$\dim M\ge 3$$ dim M ≥ 3 (and under appropriate convexity and regularity conditions), injectivity of the forward map $$\Phi \mapsto C_\Phi $$ Φ ↦ C Φ 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 $$\dim M =2$$ 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 $$\partial M$$ ∂ 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.

scholarly journals Dirac electrons in the presence of a matrix potential barrier: application to graphene and topological insulators

2016 ◽  
Vol 28 (11) ◽  
pp. 115501 ◽  
Author(s):  
Mikhail Erementchouk ◽  
Pinaki Mazumder ◽  
M A Khan ◽  
Michael N Leuenberger
Keyword(s):  
Potential Barrier ◽  
Topological Insulators ◽  
Matrix Potential

S-Nitrosoglutathione incorporated in poly(ethylene glycol) matrix: potential use for topical nitric oxide delivery

Nitric Oxide ◽  
2004 ◽  
Vol 11 (3) ◽  
pp. 263-272 ◽  
Author(s):  
Amedea Barozzi Seabra ◽  
Gabriela Freitas Pereira de Souza ◽  
Lilian Lúcia da Rocha ◽  
Marcos Nogueira Eberlin ◽  
Marcelo Ganzarolli de Oliveira
Keyword(s):  
Nitric Oxide ◽  
Ethylene Glycol ◽  
Poly Ethylene Glycol ◽  
Matrix Potential ◽  
Poly Ethylene ◽  
Nitric Oxide Delivery ◽  
Potential Use

scholarly journals Higher-order Darboux transformations for two-dimensional Dirac systems with diagonal matrix potential

2021 ◽  
Vol 2090 (1) ◽  
pp. 012038
Author(s):  
A Schulze-Halberg
Keyword(s):  
Dirac Equation ◽  
Explicit Form ◽  
Higher Order ◽  
Diagonal Matrix ◽  
Two Dimensional ◽  
Darboux Transformations ◽  
Dirac Systems ◽  
Matrix Potential ◽  
De Vries ◽  
The Matrix

Abstract We construct the explicit form of higher-order Darboux transformations for the two-dimensional Dirac equation with diagonal matrix potential. The matrix potential entries can depend arbitrarily on the two variables. Our construction is based on results for coupled Korteweg-de Vries equations [27].

Role of soil microstructure on the emission of N2O in intact small soil columns

2021 ◽  
Author(s):  
Patricia Ortega-Ramirez ◽  
Valérie Pot ◽  
Patricia Laville ◽  
Steffen Schlüter ◽  
Dalila Hadjar ◽  
...  
Keyword(s):  
Geodesic Distance ◽  
Soil Column ◽  
Volume Effect ◽  
Radial Dependence ◽  
Soil Columns ◽  
Soil Matrix ◽  
Large Variability ◽  
Soil Microstructure ◽  
Matrix Potential

<p>N<sub>2</sub>O emission in soils is a consequence of the activity of nitrifying and denitrifying microorganisms and potentially abiotic processes. However, the <span>large</span> microscale variability of the soil characteristics that influence these processes and in particular the location of anoxic microsites, limits prediction efforts. Better understanding of denitrification activity on microscopic scales is required to improve predictions of N<sub>2</sub>O emissions.</p><p>This study explored the role of soil microstructure on N<sub>2</sub>O emission. To fulfill this objective we sampled 24 soil columns (5 cm diameter, 6 cm height) in the surface layer of a same plot in a cultivated soil (Luvisol, La Cage, Versailles, France). The soil samples were saturated with a solution of ammonium nitrate (NH<sub>4</sub>NO<sub>3</sub>), and equilibrated at a matrix potential of -32 cm (pF 1.5). The emitted fluxes of N<sub>2</sub>O were measured during 7 days. At the end of the experiment, the soil columns were scanned in a X-ray micro tomograph, at the University of Poitiers. A 32 µm voxel resolution was achieved for the 3D reconstructed images.</p><p>In order to reduce noise and segment the 3D images, the same protocol was implemented for all columns. The reduction of noise consisted of passing a non-local mean filter, a non-sharp mask and a radial correction. Such combination of steps succeeded in removing both ring artifacts and the radial dependence of the voxel values. Due to the variety of material densities in the soil, a local segmentation based on the watershed method was implemented to classify the soil <span>constituents</span> in four <span>classes (based on its density value)</span>: air, water and organic matter (OM), soil matrix and minerals. This method is good for detecting thin pores and avoids missclassification of voxels undergoing partial volume effect, which can lead to false organic coatings around macropores.</p><p>The soil columns exhibited a large variability of accumulated N<sub>2</sub>O after 7 days (from 107 to 1940 <span>µgN kg</span><sup><span>-1</span></sup><span> d.w. soil</span>). The size of OM clusters varied between a couple and up to t<span>housands</span> of voxels. No correlation was found between the emission of N<sub>2</sub>O and the porosity, nor between the N<sub>2</sub>O emission and the connectivity of the air phase. Based on the <span>premise</span> that the less accessible is the oxygen to the OM, the bigger should be the N<sub>2</sub>O emission of the soil column, we proposed and computed a microscopic spatial descriptor, I<sub>gd</sub>, based on the notion of the geodesic distance between <span>clusters</span> of OM and air for each soil column 3D image. We expect to find a correlation between I<sub>gd</sub> and the <span>N</span><sub><span>2</span></sub><span>O emission.</span></p>

Inverse problem for one-dimensional wave equation with matrix potential

2019 ◽  
Vol 27 (2) ◽  
pp. 217-223 ◽  
Author(s):  
Ammar Khanfer ◽  
Alexander Bukhgeim
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Uniqueness Theorem ◽  
Cauchy Data ◽  
Global Uniqueness ◽  
One Dimensional ◽  
Matrix Potential ◽  
The Matrix ◽  
Real Matrices ◽  
Dimensional Wave

AbstractWe prove a global uniqueness theorem of reconstruction of a matrix-potential {a(x,t)} of one-dimensional wave equation {\square u+au=0}, {x>0,t>0}, {\square=\partial_{t}^{2}-\partial_{x}^{2}} with zero Cauchy data for {t=0} and given Cauchy data for {x=0}, {u(0,t)=0}, {u_{x}(0,t)=g(t)}. Here {u,a,f}, and g are {n\times n} smooth real matrices, {\det(f(0))\neq 0}, and the matrix {\partial_{t}a} is known.

scholarly journals Numerical Modelling of Stress/Strain Field Arising in Diamond-Impregnated Cobalt

2014 ◽  
Vol 59 (2) ◽  
pp. 443-446 ◽  
Author(s):  
J. Borowiecka-Jamrozek ◽  
J. Lachowski
Keyword(s):  
Strain Field ◽  
Diamond Crystal ◽  
Metallic Matrix ◽  
Stress And Strain ◽  
Stress Strain ◽  
Strain Fields ◽  
Matrix Potential ◽  
The Matrix ◽  
Saw Blade ◽  
Diamond Retention

Abstract The paper presents results of computer simulations of the stress/strain field built up in a cobalt matrix diamond impregnated saw blade segment during its fabrication and after loading the protruding diamond with an external force. The main objective of this work was to create better understanding of the factors affecting retention of diamond particles in a metallic matrix of saw blade segments, which are produced by means of the powder metallurgy technology. The effective use of diamond impregnated tools strongly depends on mechanical and tribological properties of the matrix, which has to hold the diamond grits firmly. The diamond retention capability of the matrix is affected in a complex manner by chemical or mechanical interactions between the diamond crystal and the matrix during the segment manufacture. Due to the difference between the thermal expansion coefficients of the diamond and metallic matrix, a complex stress/strain field is generated in the matrix surrounding each diamond crystal. It is assumed that the matrix potential for diamond retention can be associated with the amount of the elastic and plastic deformation energy and the size of the deformation zone occurring in the matrix around diamonds. The stress and strain fields generated in the matrix were calculated using the Abaqus software. It was found that the stress and strain fields generated during segment fabrication change to a large extent as the diamond crystal emerges from the cobalt matrix to reach its working height of protrusion.

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