5,493 research outputs found
An induction theorem and nonlinear regularity models
A general nonlinear regularity model for a set-valued mapping , where and are metric spaces, is considered
using special iteration procedures, going back to Banach, Schauder, Lusternik
and Graves. Namely, we revise the induction theorem from Khanh, J. Math. Anal.
Appl., 118 (1986) and employ it to obtain basic estimates for studying
regularity/openness properties. We also show that it can serve as a
substitution of the Ekeland variational principle when establishing other
regularity criteria. Then, we apply the induction theorem and the mentioned
estimates to establish criteria for both global and local versions of
regularity/openness properties for our model and demonstrate how the
definitions and criteria translate into the conventional setting of a
set-valued mapping .Comment: 28 page
Accelerating Dynamical Density Response Code on Summit and Its Application for Computing the Density Response Function of Vanadium Sesquioxide
This thesis details the process of porting the Eguiluz group dynamical density response computational platform to the hybrid CPU+GPU environment at the Summit supercomputer at Oak Ridge National Laboratory (ORNL) Leadership Computing Center. The baseline CPU-only version is a Gordon Bell-winning platform within the formally-exact time-dependent density functional theory (TD-DFT) framework using the linearly augmented plane wave (LAPW) basis set. The code is accelerated using a combination of the OpenACC programming model and GPU libraries -- namely, the Matrix Algebra for GPU and Multicore Architectures (MAGMA) library -- as well as exploiting the sparsity pattern of the matrices involved in the matrix-matrix multiplication. Benchmarks show a 12.3x speedup compared to the CPU-only version. This performance boost should accelerate discovery in material and condensed matter physics through computational means. After the hybrid CPU+GPU code has been sufficiently optimized, it is used to study the dynamical density response function of vanadium sesquioxide, and the results are compared with spectroscopic data from non-resonant inelastic X-ray scattering {NIXS} experiments
Magnetocaloric effect in nano- and polycrystalline manganite
samples were prepared in nano- and polycrystalline
forms by sol-gel and solid state reaction methods, respectively, and
structurally characterized by synchrotron X-ray diffraction. The magnetic
properties determined by ac susceptibility and dc magnetization measurements
are discussed. The magnetocaloric effect in this nanocrystalline manganite is
spread over a broader temperature interval than in the polycrystalline case.
The relative cooling power of the poly- and nanocrystalline manganites is used
to evaluate a possible application for magnetic cooling below room temperature.Comment: 6 pages, 5 (double) figures, 1 table, 16 references; submitted to
Appl. Phys.
Some results of the Lipschitz constant of 1-Field on
We study the relations between the Lipschitz constant of -field and the
Lipschitz constant of the gradient canonically associated with this -field.
Moreover, we produce two explicit formulas that make up Minimal Lipschitz
extensions for -field. As consequence of the previous results, for the
problem of minimal extension by continuous functions from to
, we also produce analogous explicit formulas to those of
Bauschke and Wang. Finally, we show that Wells's extensions of -field are
absolutely minimal Lipschitz extension when the domain of -field to expand
is finite. We provide a counter-example showing that this result is false in
general.Comment: E.L.G. and T.V.P. are partially supported by the ANR (Agence
Nationale de la Recherche) through HJnet projet ANR-12-BS01-0008-0
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