Search results for " Applied"

Atomic layer deposition of AlN from AlCl3 using NH3 and Ar/NH3 plasma

2018

The atomic layer deposition (ALD) of AlN from AlCl3 was investigated using a thermal process with NH3 and a plasma-enhanced (PE)ALD process with Ar/NH3 plasma. The growth was limited in the thermal process by the low reactivity of NH3, and impractically long pulses were required to reach saturation. Despite the plasma activation, the growth per cycle in the PEALD process was lower than that in the thermal process (0.4A ° vs 0.7A ° ). However, the plasma process resulted in a lower concentration of impurities in the films compared to the thermal process. Both the thermal and plasma processes yielded crystalline films; however, the degree of crystallinity was higher in the plasma process. The…

Mittaus- ja laskentamenetelmä dokumentinhallinnan työvälineenä opettajan työssä

2016

Opettajan työ on viestimistä osana sitä organisaatiota, missä hän työskentelee. Organisaatioiden viestintä muodostuu niiden sisällä sovittujen periaatteiden mukaan. Ulkopuolelta tulevat vaikutteet muokkaavat myös viestintää, mutta jo-kainen organisaatio rakentaa oman kielensä, jolla se viestii sisäisesti ja toisten or-ganisaatioiden kanssa. Tämän viestinnän yhteydessä syntyy tunnistettavia vies-tintäkategorioita, joita kutsutaan genreiksi eli lajityypeiksi. Liittämällä lajityyp-peihin niihin kuuluva sosiaalinen konteksti sitoutuvat lajityypit organisaation toimintaa. Analysoimalla organisaation viestintään kuuluvia lajityyppejä voi-daan tutkia organisaation prosesseja, näissä prosesseissa l…

Biharmonic obstacle problem: guaranteed and computable error bounds for approximate solutions

2020

The paper is concerned with a free boundary problem generated by the biharmonic operator and an obstacle. The main goal is to deduce a fully guaranteed upper bound of the difference between the exact minimizer u and any function (approximation) from the corresponding energy class (which consists of the functions in $H^2$ satisfying the prescribed boundary conditions and the restrictions stipulated by the obstacle). For this purpose we use the duality method of the calculus of variations and general type error identities earlier derived for a wide class of convex variational problems. By this method, we define a combined primal--dual measure of error. It contains four terms of different natu…

Equivalence of viscosity and weak solutions for the normalized $p(x)$-Laplacian

2018

We show that viscosity solutions to the normalized $p(x)$-Laplace equation coincide with distributional weak solutions to the strong $p(x)$-Laplace equation when $p$ is Lipschitz and $\inf p>1$. This yields $C^{1,\alpha}$ regularity for the viscosity solutions of the normalized $p(x)$-Laplace equation. As an additional application, we prove a Rad\'o-type removability theorem.

Fixed Angle Inverse Scattering for Almost Symmetric or Controlled Perturbations

2020

We consider the fixed angle inverse scattering problem and show that a compactly supported potential is uniquely determined by its scattering amplitude for two opposite fixed angles. We also show that almost symmetric or horizontally controlled potentials are uniquely determined by their fixed angle scattering data. This is done by establishing an equivalence between the frequency domain and the time domain formulations of the problem, and by solving the time domain problem by extending the methods of [RS19] which adapts the ideas introduced in [BK81] and [IY01] on the use of Carleman estimates for inverse problems.

Limiting Carleman weights and conformally transversally anisotropic manifolds

2020

We analyze the structure of the set of limiting Carleman weights in all conformally flat manifolds, 3 3 -manifolds, and 4 4 -manifolds. In particular we give a new proof of the classification of Euclidean limiting Carleman weights, and show that there are only three basic such weights up to the action of the conformal group. In dimension three we show that if the manifold is not conformally flat, there could be one or two limiting Carleman weights. We also characterize the metrics that have more than one limiting Carleman weight. In dimension four we obtain a complete spectrum of examples according to the structure of the Weyl tensor. In particular, we construct unimodular Lie groups whose …

An evolutionary Haar-Rado type theorem

2021

AbstractIn this paper, we study variational solutions to parabolic equations of the type $$\partial _t u - \mathrm {div}_x (D_\xi f(Du)) + D_ug(x,u) = 0$$ ∂ t u - div x ( D ξ f ( D u ) ) + D u g ( x , u ) = 0 , where u attains time-independent boundary values $$u_0$$ u 0 on the parabolic boundary and f, g fulfill convexity assumptions. We establish a Haar-Rado type theorem: If the boundary values $$u_0$$ u 0 admit a modulus of continuity $$\omega $$ ω and the estimate $$|u(x,t)-u_0(\gamma )| \le \omega (|x-\gamma |)$$ | u ( x , t ) - u 0 ( γ ) | ≤ ω ( | x - γ | ) holds, then u admits the same modulus of continuity in the spatial variable.

Gradient walks and $p$-harmonic functions

2017

The fractional Calderón problem: Low regularity and stability

2017

The Calder\'on problem for the fractional Schr\"odinger equation was introduced in the work \cite{GSU}, which gave a global uniqueness result also in the partial data case. This article improves this result in two ways. First, we prove a quantitative uniqueness result showing that this inverse problem enjoys logarithmic stability under suitable a priori bounds. Second, we show that the results are valid for potentials in scale-invariant $L^p$ or negative order Sobolev spaces. A key point is a quantitative approximation property for solutions of fractional equations, obtained by combining a careful propagation of smallness analysis for the Caffarelli-Silvestre extension and a duality argumen…

A sharp stability estimate for tensor tomography in non-positive curvature

2021

Funder: University of Cambridge