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1.
2.
This paper is concerned with the Cauchy problem on the Boltzmann equation without angular cutoff assumption for hard potential in the whole space. When the initial data is a small perturbation of a global Maxwellian, the global existence of solution to this problem is proved in unweighted Sobolev spaces with . But if we want to obtain the optimal temporal decay estimates, we need to add the velocity weight function, in this case the global existence and the optimal temporal decay estimate of the Boltzmann equation are all established. Meanwhile, we further gain a more accurate energy estimate, which can guarantee the validity of the assumption in Chen et al. (0000). 相似文献
3.
《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2021,38(5):1337-1371
In this paper we consider minimizers of the functional where is a bounded open set and where are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets have finite perimeter and that their free boundary is composed of a regular part, which is locally the graph of a -regular function, and a singular part, which is empty if , discrete if and of Hausdorff dimension at most if , for some . 相似文献
4.
We investigate the possibility of phantom crossing in the dark energy sector and the solution for the Hubble tension between early and late universe observations. We use robust combinations of different cosmological observations, namely the Cosmic Microwave Background (CMB), local measurement of Hubble constant (), Baryon Acoustic Oscillation (BAO) and SnIa for this purpose. For a combination of CMB+BAO data that is related to early universe physics, phantom crossing in the dark energy sector was confirmed at a 95% confidence level and we obtained the constraint km/s/Mpc at a 68% confidence level, which is in perfect agreement with the local measurement by Riess et al. We show that constraints from different combinations of data are consistent with each other and all of them are consistent with phantom crossing in the dark energy sector. For the combination of all data considered, we obtained the constraint km/s/Mpc at a 68% confidence level and the phantom crossing happening at the scale factor at a 68% confidence level. 相似文献
5.
Corinne Rondeau-Mouro Mireille Cambert Laurent Blondel Yves Diascorn Léo Mbaya Nor Nadiah Binti Ahmad Nazari Sarah Helary Tiphaine Lucas 《Magnetic resonance in chemistry : MRC》2022,60(7):678-691
A temperature control unit was implemented to vary the temperature of samples studied on a commercial Mobile Universal Surface Explorer nuclear magnetic resonance (MOUSE-NMR) apparatus. The device was miniaturized to fit the maximum MOUSE sampling depth (25 mm). It was constituted by a sample holder sandwiched between two heat exchangers placed below and above the sample. Air was chosen as the fluid to control the temperature at the bottom of the sample, at the interface between the NMR probe and the sample holder, in order to gain space. The upper surface of the sample was regulated by the circulation of water inside a second heat exchanger placed above the sample holder. The feasibility of using such a device was demonstrated first on pure water and then on several samples of bread dough with different water contents. For this, T1 relaxation times were measured at various temperatures and depths and were then compared with those acquired with a conventional compact closed-magnet spectrometer. Discussion of results was based on biochemical transformations in bread dough (starch gelatinization and gluten heat denaturation). It was demonstrated that, within a certain water level range, and because of the low magnetic field strength of the MOUSE, a linear relationship could be established between T1 relaxation times and the local temperature in the dough sample. 相似文献
6.
In this work, a continuum model is presented for size and orientation dependent thermal buckling and post-buckling of anisotropic nanoplates considering surface and bulk residual stresses. The model with von-Karman nonlinear strains and material cubic anisotropy of single crystals contains two parameters that reflect the orientation effects. Using Ritz method, closed form solutions are given for buckling temperature and post-buckling deflections. Regarding self-instability states of nanoplates and their recovering at higher temperatures, an experiment is discussed based on low pressurized membranes to verify the predictions. For simply supported nanoplates, the size effects are lowest when they are aligned in [100] direction. When the edges get clamped, the orientation dependence is ignorable and the behavior becomes symmetric about [510] axis. The surface residual stress makes drastic increase in buckling temperature of thinner nanoplates for which a minimum thickness is pointed to stay far from material softening at higher temperatures. Deflection of [100]-oriented buckled nanoplates is higher than [110] ones but this reverses at higher temperatures. The results for long nanoplates show that the buckling mode numbers are changed by orientation which is verified by FEM. 相似文献
7.
Dr. Antonio M. Rodríguez Dr. Pilar Prieto Prof. Antonio de la Hoz Prof. Ángel Díaz-Ortiz D. Raúl Martín Prof. José I. García 《ChemistryOpen》2015,4(3):308-317
The aim of this work was to determine the parameters that have decisive roles in microwave-assisted reactions and to develop a model, using computational chemistry, to predict a priori the type of reactions that can be improved under microwaves. For this purpose, a computational study was carried out on a variety of reactions, which have been reported to be improved under microwave irradiation. This comprises six types of reactions. The outcomes obtained in this study indicate that the most influential parameters are activation energy, enthalpy, and the polarity of all the species that participate. In addition to this, in most cases, slower reacting systems observe a much greater improvement under microwave irradiation. Furthermore, for these reactions, the presence of a polar component in the reaction (solvent, reagent, susceptor, etc.) is necessary for strong coupling with the electromagnetic radiation. We also quantified that an activation energy of 20–30 kcal mol−1 and a polarity (μ) between 7–20 D of the species involved in the process is required to obtain significant improvements under microwave irradiation. 相似文献
8.
We report optical and nonlinear optical properties of CuS quantum dots and nanoparticles prepared through a nontoxic, green, one-pot synthesis method. The presence of surface states and defects in the quantum dots are evident from the luminescent behavior and enhanced nonlinear optical properties measured using the open aperture Z-scan, employing 5 ns laser pulses at 532 nm. The quantum dots exhibit large effective third order nonlinear optical coefficients with a relatively lower optical limiting threshold of 2.3 J cm−2, and the optical nonlinearity arises largely from absorption saturation and excited state absorption. Results suggest that these materials are potential candidates for designing efficient optical limiters with applications in laser safety devices. 相似文献
9.
We present the fabrication of core-shell-satellite Au@SiO2-Pt nanostructures and demonstrate that LSPR excitation of the core Au nanoparticle can induce plasmon coupling effect to initiate photocatalytic hydrogen generation from decomposition of formic acid. Further studies suggest that the plasmon coupling effect induces a strong local electric field between the Au core and Pt nanoparticles on the SiO2 shell, which enables creation of hot electrons on the non-plasmonic-active Pt nanoparticles to participate hydrogen evolution reaction on the Pt surface. In addition, small SiO2 shell thickness is required in order to obtain a strong plamon coupling effect and achieve efficient photocatalytic activities for hydrogen generation. 相似文献
10.
This minireview describes the strategies for synthesis of fiuorinated surfactants potentially nonbioaccumulable.Various strategies have been focused on(Ⅰ) reducing the length of the perfluorocarbon chain,(Ⅱ) introducing hetero atoms into the fluorocarbon chain,(Ⅲ) introducing branch(herein and after branch means the fluoro-carbon chain section is not straight).In most cases,the surface tensions versus the surfactant concentrations have been assessed.These above strategies led to various highly fiuorinated(perfluorinated or not perfluorinated) surfactants whose chemical changes enabled to obtain novel alternatives to perfluorooctanoic acid(PFOA) and perfluorooctane sulphonate(PFOS). 相似文献