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1.
Fabrizio Colombo Samuele Mongodi Marco Peloso Stefano Pinton 《Mathematical Methods in the Applied Sciences》2019,42(5):1662-1686
Let e?, for ? = 1,2,3, be orthogonal unit vectors in and let be a bounded open set with smooth boundary ?Ω. Denoting by a point in Ω, the heat equation, for nonhomogeneous materials, is obtained replacing the Fourier law, given by the following: into the conservation of energy law, here a, b, are given functions. With the S‐spectrum approach to fractional diffusion processes we determine, in a suitable way, the fractional powers of T. Then, roughly speaking, we replace the fractional powers of T into the conservation of energy law to obtain the fractional evolution equation. This method is important for nonhomogeneous materials where the Fourier law is not simply the negative gradient. In this paper, we determine under which conditions on the coefficients a, b, the fractional powers of T exist in the sense of the S‐spectrum approach. More in general, this theory allows to compute the fractional powers of vector operators that arise in different fields of science and technology. This paper is devoted to researchers working in fractional diffusion and fractional evolution problems, partial differential equations, and noncommutative operator theory. 相似文献
2.
Chevillard L Roux SG Lévêque E Mordant N Pinton JF Arnéodo A 《Physical review letters》2005,95(6):064501
We analyze the statistics of turbulent velocity fluctuations in the time domain. Three cases are computed numerically and compared: (i) the time traces of Lagrangian fluid particles in a (3D) turbulent flow (referred to as the dynamic case); (ii) the time evolution of tracers advected by a frozen turbulent field (the static case); (iii) the evolution in time of the velocity recorded at a fixed location in an evolving Eulerian velocity field, as it would be measured by a local probe (referred to as the virtual probe case). We observe that the static case and the virtual probe cases share many properties with Eulerian velocity statistics. The dynamic (Lagrangian) case is clearly different; it bears the signature of the global dynamics of the flow. 相似文献
3.
Chevillard L Roux SG Levêque E Mordant N Pinton JF Arneodo A 《Physical review letters》2003,91(21):214502
We use the multifractal formalism to describe the effects of dissipation on Lagrangian velocity statistics in turbulent flows. We analyze high Reynolds number experiments and direct numerical simulation data. We show that this approach reproduces the shape evolution of velocity increment probability density functions from Gaussian to stretched exponentials as the time lag decreases from integral to dissipative time scales. A quantitative understanding of the departure from scaling exhibited by the magnitude cumulants, early in the inertial range, is obtained with a free parameter function D(h) which plays the role of the singularity spectrum in the asymptotic limit of infinite Reynolds number. We observe that numerical and experimental data are accurately described by a unique quadratic D(h) spectrum which is found to extend from h(min) approximately 0.18 to h(max) approximately 1. 相似文献
4.
Roberto Terzano Matthias Alfeld Koen Janssens Bart Vekemans Tom Schoonjans Laszlo Vincze Nicola Tomasi Roberto Pinton Stefano Cesco 《Analytical and bioanalytical chemistry》2013,405(10):3341-3350
Iron (Fe) is an essential element for plant growth and development; hence determining Fe distribution and concentration inside plant organs at the microscopic level is of great relevance to better understand its metabolism and bioavailability through the food chain. Among the available microanalytical techniques, synchrotron μ-XRF methods can provide a powerful and versatile array of analytical tools to study Fe distribution within plant samples. In the last years, the implementation of new algorithms and detection technologies has opened the way to more accurate (semi)quantitative analyses of complex matrices like plant materials. In this paper, for the first time the distribution of Fe within tomato roots has been imaged and quantified by means of confocal μ-XRF and exploiting a recently developed fundamental parameter-based algorithm. With this approach, Fe concentrations ranging from few hundreds of ppb to several hundreds of ppm can be determined at the microscopic level without cutting sections. Furthermore, Fe (semi)quantitative distribution maps were obtained for the first time by using two opposing detectors to collect simultaneously the XRF radiation emerging from both sides of an intact cucumber leaf. Figure
Elemental distribution maps within intact tomato roots as determined by confocal micro X‐ray fluorescence 相似文献
5.
We describe along the guidelines of Kohn (Quantitative Estimates for Global Regularity. Analysis and Geometry in Several Complex Variables, pp. 97–128. Trend Math. Birkhäuser, Boston, 1999), the constant ${\mathcal {E}}_s$ which is needed to control the commutator of a totally real vector field $T_{{\mathcal {E}}}$ with $\bar{\partial }^*$ in order to have $H^s$ a-priori estimates for the Bergman projection $B_k, k\ge q-1$ , on a smooth $q$ -convex domain $D\subset \subset {\mathbb {C}}^{n}$ . This statement, not explicit in Kohn (Quantitative Estimates for Global Regularity. Analysis and Geometry in Several Complex Variables, pp. 97–128. Trend Math. Birkhäuser, Boston, 1999), yields regularity of $B_k$ in specific Sobolev degree $s$ . Next, we refine the pseudodifferential calculus at the boundary in order to relate, for a defining function $r$ of $D$ , the operators $(T^+)^{-\frac{\delta }{2}}$ and $(-r)^{\frac{\delta }{2}}$ . We are thus able to extend to general degree $k\ge 0$ of $B_k$ , the conclusion of (Quantitative Estimates for Global Regularity. Analysis and Geometry in Several Complex Variables, pp. 97–128. Trend Math. Birkhäuser, Boston, 1999) which only holds for $q=1$ and $k=0$ : if for the Diederich–Fornaess index $\delta $ of $D$ , we have $(1-\delta )^{\frac{1}{2}}\le {\mathcal {E}}_s$ , then $B_k$ is $H^s$ -regular. 相似文献
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7.
Using a new experimental technique, based on the scattering of ultrasounds, we perform a direct measurement of particle velocities, in a fully turbulent flow. This allows us to approach intermittency in turbulence from a dynamical point of view and to analyze the Lagrangian velocity fluctuations in the framework of random walks. We find experimentally that the elementary steps in the walk have random uncorrelated directions but a magnitude that is extremely long range correlated in time. Theoretically, a Langevin equation is proposed and shown to account for the observed one- and two-point statistics. This approach connects intermittency to the dynamics of the flow. 相似文献
8.
Monchaux R Berhanu M Bourgoin M Moulin M Odier P Pinton JF Volk R Fauve S Mordant N Pétrélis F Chiffaudel A Daviaud F Dubrulle B Gasquet C Marié L Ravelet F 《Physical review letters》2007,98(4):044502
We report the observation of dynamo action in the von Kármán sodium experiment, i.e., the generation of a magnetic field by a strongly turbulent swirling flow of liquid sodium. Both mean and fluctuating parts of the field are studied. The dynamo threshold corresponds to a magnetic Reynolds number R(m) approximately 30. A mean magnetic field of the order of 40 G is observed 30% above threshold at the flow lateral boundary. The rms fluctuations are larger than the corresponding mean value for two of the components. The scaling of the mean square magnetic field is compared to a prediction previously made for high Reynolds number flows. 相似文献
9.
N. Lyotard W. L. Shew L. Bocquet J.-F. Pinton 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,60(4):469-476
We make time resolved velocity measurements of steel
spheres in free fall through liquid using a continuous ultrasound
technique. We explore two different ways to induce large changes in
drag on the spheres: 1) a small quantity of viscoelastic polymer
added to water and 2) altering the surface of the sphere. Low
concentration polymer solutions and/or a pattern of grooves in the
sphere surface induce an early drag crisis, which may reduce drag by
more than 50% compared to smooth spheres in pure water. On
the other hand, random surface roughness and/or high concentration
polymer solutions reduce drag progressively and suppress the drag
crisis. We also present a qualititative argument which ties the
drag reduction observed in low concentration polymer solutions to
the Weissenberg number and normal stress difference. 相似文献
10.
Sperança A Godoi B Pinton S Back DF Menezes PH Zeni G 《The Journal of organic chemistry》2011,76(16):6789-6797
A series of 4-Se-(Te, S)-isochromenones and 3-substituted isochromenones were synthesized in good yields via FeCl(3)-mediated cyclization of alkynylaryl esters with different diorganyl dichalcogenides. This methodology was carried out at room temperature, using inexpensive and environmentally friendly iron salts as metallic source and under air atmosphere. The reaction showed to be tolerant to a range of substituents bonded into the aromatic ring of the diorganyl dichalcogenides as well as to alkyl groups directly bonded to the chalcogen atom. Alternatively, the cyclization reaction of 2-alkynylaryl esters with FeCl(3), in the absence of diorganyl dichalcogenide, gave the isochromenones without the chalcogen moiety in the structure. This approach proved to be highly regioselective, providing only six-membered ring products, once the possible five-membered products were not observed in any experiments. 相似文献