Search results for "Modulus"
showing 10 items of 491 documents
Mechanical and optical properties of as-grown and thermally annealed titanium dioxide from titanium tetrachloride and water by atomic layer deposition
2021
Funding Information: This work was carried out within the MECHALD project funded by Business Finland (Tekes) and is linked to the Finnish Centers of Excellence in Atomic Layer Deposition (ref. 251220) and Nuclear and Accelerator Based Physics (refs. 213503 and 251353) of the Academy of Finland. Funding Information: This work was carried out within the MECHALD project funded by Business Finland (Tekes) and is linked to the Finnish Centers of Excellence in Atomic Layer Deposition (ref. 251220 ) and Nuclear and Accelerator Based Physics (refs. 213503 and 251353 ) of the Academy of Finland. Publisher Copyright: © 2021 The use of thin-films made by atomic layer deposition (ALD) is increasing in …
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.
On the regularity of very weak solutions for linear elliptic equations in divergence form
2020
AbstractIn this paper we consider a linear elliptic equation in divergence form $$\begin{aligned} \sum _{i,j}D_j(a_{ij}(x)D_i u )=0 \quad \hbox {in } \Omega . \end{aligned}$$ ∑ i , j D j ( a ij ( x ) D i u ) = 0 in Ω . Assuming the coefficients $$a_{ij}$$ a ij in $$W^{1,n}(\Omega )$$ W 1 , n ( Ω ) with a modulus of continuity satisfying a certain Dini-type continuity condition, we prove that any very weak solution $$u\in L^{n'}_\mathrm{loc}(\Omega )$$ u ∈ L loc n ′ ( Ω ) of (0.1) is actually a weak solution in $$W^{1,2}_\mathrm{loc}(\Omega )$$ W loc 1 , 2 ( Ω ) .
Weighted Hardy Spaces of Quasiconformal Mappings
2019
We establish a weighted version of the $H^p$-theory of quasiconformal mappings.
Mappings of L p -integrable distortion: regularity of the inverse
2016
Let X be an open set in R n and suppose that f : X → R n is a Sobolev homeomorphism. We study the regularity of f −1 under the L p -integrability assumption on the distortion function Kf . First, if X is the unit ball and p > n−1, then the optimal local modulus of continuity of f −1 is attained by a radially symmetric mapping. We show that this is not the case when p 6 n − 1 and n > 3, and answer a question raised by S. Hencl and P. Koskela. Second, we obtain the optimal integrability results for |Df −1 | in terms of the L p -integrability assumptions of Kf . peerReviewed
Mappings of Lp-integrable distortion: regularity of the inverse
2016
Let be an open set in ℝn and suppose that is a Sobolev homeomorphism. We study the regularity of f–1 under the Lp-integrability assumption on the distortion function Kf. First, if is the unit ball and p > n – 1, then the optimal local modulus of continuity of f–1 is attained by a radially symmetric mapping. We show that this is not the case when p ⩽ n – 1 and n ⩾ 3, and answer a question raised by S. Hencl and P. Koskela. Second, we obtain the optimal integrability results for ∣Df–1∣ in terms of the Lp-integrability assumptions of Kf.
Regularity and modulus of continuity of space-filling curves
2019
We study critical regularity assumptions on space-filling curves that possess certain modulus of continuity. The bounds we obtain are essentially sharp, as demonstrated by an example. peerReviewed
Local mechanical properties by Atomic Force Microscopy nanoindentations
2008
The analysis of mechanical properties on a nanometer scale is a useful tool for combining information concerning texture organization obtained by microscopy with the properties of individual components- Moreover, this technique promotes the understanding of the hierarchical arrangement in complex natural materials as well in the case of simpler morphologies arising from industrial processes. Atomic Force Microscopy, AFM, can bridge morphological information, obtained with outstanding resolution, to local mechanical properties. When performing an AFM nanoindentation, the rough force curve, i.e., the plot of the voltage output from the photodiode vs. the voltage applied to the piezo-scanner, …
Effect of the extensional flow on the properties of oriented nanocomposite films for twist wrapping
2011
In this study, we examined the mechanical behavior of nanocomposite films based on polyethylene (PE) and pristine PE films. The films were prepared by film blowing and were then cold-drawn at low temperature. The experimental results show that cold drawing significantly enhanced the orientation; with increasing draw ratio (DR), the elastic modulus and tensile strength of the PE films strongly increased, particularly in the presence of the organoclay. To obtain polymeric films suitable for twist wrapping, the films must be sufficiently stiff so that no shrinkage or elastic recovery occur during or after twisting. The elongation at break and the yield strain sharply decreased with orientation…
Alteration-Induced Volcano Instability at La Soufrière de Guadeloupe (Eastern Caribbean)
2021
International audience; Volcanoes are unstable structures that deform laterally and frequently experience mass wasting events. Hydrothermal alteration is often invoked as a mechanism that contributes significantly to volcano instability. We present a study that combines laboratory experiments, geophysical data, and large-scale numerical modeling to better understand the influence of alteration on volcano stability, using La Soufrière de Guadeloupe (Eastern Caribbean) as a case study. Laboratory experiments on variably altered (advanced argillic alteration) blocks show that uniaxial compressive strength, Young's modulus, and cohesion decrease as a function of increasing alteration, but that …