Search results for " Gradient"
showing 10 items of 575 documents
Slopes of Kantorovich potentials and existence of optimal transport maps in metric measure spaces
2014
We study optimal transportation with the quadratic cost function in geodesic metric spaces satisfying suitable non-branching assumptions. We introduce and study the notions of slope along curves and along geodesics and we apply the latter to prove suitable generalizations of Brenier's theorem of existence of optimal maps.
Tensorization of quasi-Hilbertian Sobolev spaces
2022
The tensorization problem for Sobolev spaces asks for a characterization of how the Sobolev space on a product metric measure space $X\times Y$ can be determined from its factors. We show that two natural descriptions of the Sobolev space from the literature coincide, $W^{1,2}(X\times Y)=J^{1,2}(X,Y)$, thus settling the tensorization problem for Sobolev spaces in the case $p=2$, when $X$ and $Y$ are infinitesimally quasi-Hilbertian, i.e. the Sobolev space $W^{1,2}$ admits an equivalent renorming by a Dirichlet form. This class includes in particular metric measure spaces $X,Y$ of finite Hausdorff dimension as well as infinitesimally Hilbertian spaces. More generally for $p\in (1,\infty)$ we…
Pointwise characterizations of Besov and Triebel–Lizorkin spaces and quasiconformal mappings
2011
Abstract In this paper, the authors characterize, in terms of pointwise inequalities, the classical Besov spaces B ˙ p , q s and Triebel–Lizorkin spaces F ˙ p , q s for all s ∈ ( 0 , 1 ) and p , q ∈ ( n / ( n + s ) , ∞ ] , both in R n and in the metric measure spaces enjoying the doubling and reverse doubling properties. Applying this characterization, the authors prove that quasiconformal mappings preserve F ˙ n / s , q s on R n for all s ∈ ( 0 , 1 ) and q ∈ ( n / ( n + s ) , ∞ ] . A metric measure space version of the above morphism property is also established.
Solution strategies for 1D elastic continuum with long-range interactions: Smooth and fractional decay
2010
Abstract An elastic continuum model with long-range forces is addressed in this study within the context of approximate analytical methods. Such a model stems from a mechanically-based approach to non-local theory where long-range central forces are introduced between non-adjacent volume elements. Specifically, long-range forces depend on the relative displacement, on the volume product between interacting elements and they are proportional to a proper, material-dependent, distance-decaying function. Smooth-decay functions lead to integro-differential governing equations whereas hypersingular, fractional-decay functions lead to a fractional differential governing equation of Marchaud type. …
Chronological records of metal deposition in sediments from the Strait of Sicily, central Mediterranean: assessing natural fluxes and anthropogenic a…
2010
Abstract Sediment box-cores were recovered from the Strait of Sicily along two onshore–offshore transects in water depths of 29–500 m. Samples were dated by 210 Pb and analysed for major and trace elements. Inspections of chronological profiles integrated with application of statistical algorithms to the geochemical dataset and supported by in situ hydrological observations were used to assess factors driving element distributions. Mineralogical and chemical variability of sediments offshore of the southwestern Sicily coast reflect the irregular sea floor morphology of the Adventure Bank. Anthropogenic inputs explain enrichments with respect to background values for Sb, As, Pb, and Hg, that…
Bi-layer PCL/PLA scaffold prepared by melt for interface tissue engineering
2017
The development of porous multilayer devices allow controlling chemical, physical and mechanical properties by tuning the properties of each single layer. For instance, this feature is of main concern for the production of porous devices designed to regenerate diseased zones at the interface of tissue presenting intrinsic anisotropic structures that gradually change from one tissue to another. In this context, synthetic biodegradable polymers commonly used biomedical applications include polylactic acid (PLA) and polycaprolactone (PCL). In this work, a novel bi-layered multiphasic scaffold (BLS) is presented. It is composed by a PLA-layer presenting pore size in the range of 90-110 μm while…
Model calculations of ion transport against its concentration gradient when the driving force is a pH difference across a charged membrane
1997
Model calculations of the steady-state ion transport against its external concentration gradient when the driving force of this transport is a pH difference across a charged membrane are presented. We have solved numerically the exact Nernst-Planck equations without any additional simplifying approximation, such as the Goldman constant field assumption within the membrane. The validity of this assumption for a broad range of pH values, and salt and membrane fixed charge concentrations was analyzed critically. The membrane characteristics studied are the ionic fluxes and the membrane potential. Special attention is paid to the physical mechanism which leads to the ion transport against the c…
Solidification microstructure during selective laser melting of Ni based superalloy: experiment and mesoscopic modelling
2019
International audience; A set of single track laser melting experiments was performed in a selective laser melting (SLM). The tracks were done on an Inconel 718 plate with various laser scan velocities at a constant laser power of 150 W. The geometries of the molten pool (MP), as well as the solidified dendrite structures, i.e., primary and secondary dendrite arm spacing (PDAS and SDAS), in the cross sections of the molten path were characterized to evaluate the effect of the laser scan velocity during SLM. Moreover, the local solidification thermal conditions (cooling rate R*, tip growth velocity V* and temperature gradient G*) at the MP bottom were deduced from the SDAS and the geometries…
A comparison of HONO budgets for two measurement heights at a field station within the boreal forest in Finland
2015
Atmospheric concentrations of nitrous acid (HONO), one of the major precursors of the hydroxyl radical (OH) in the troposphere, significantly exceed the values predicted by the assumption of a photostationary state (PSS) during daytime. Therefore, additional sources of HONO were intensively investigated in the last decades. This study presents budget calculations of HONO based on simultaneous measurements of all relevant species, including HONO and OH at two different measurement heights, i.e. 1 m above the ground and about 2 to 3 m above the canopy (24 m above the ground), conducted in a boreal forest environment. We observed mean HONO concentrations of about 6.5 × 108 molecules cm−3 (26 p…
Comparison between the energy performance of a ground coupled water to water heat pump system and an air to water heat pump system for heating and co…
2008
Abstract The investigation presented in this article was aimed at demonstrating the technical and economical feasibility of using ground source heat pump systems in mixed climate applications, where cooling requirements are dominant. We show an experimental comparison between a ground coupled heat pump system and a conventional air to water heat pump system, focussing at the heating and cooling energy performance. A direct comparison could be made as both systems are linked, in parallel, to the same building with exactly the same loads and climatic conditions. For a whole climatic season the results obtained show that the geothermal system saves, in terms of primary energy consumption, a 43…