Segregation by thermal diffusion in moderately dense granular mixtures

A theory based on a solution of the inelastic Enskog equation that goes beyond the weak dissipation limit is used to determine the thermal diffusion factor of a binary granular mixture under gravity. The Enskog equation that aims to describe moderate densities neglects velocity correlations but retains spatial correlations arising from volume exclusion effects. As expected, the thermal diffusion factor provides a segregation criterion that shows the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE) by varying the parameters of the system (masses, sizes, composition, density and coefficients of restitution). The form of the phase diagrams for the BNE/RBNE transition is illustrated in detail in the tracer limit case, showing that the phase diagrams depend sensitively on the value of gravity relative to the thermal gradient. Two specific situations are considered: i) absence of gravity, and ii) homogeneous temperature. In the latter case, after some approximations, our results are consistent with previous theoretical results derived from the Enskog equation. Our results also indicate that the influence of dissipation on thermal diffusion is more important in the absence of gravity than in the opposite limit. The present analysis, which is based on a preliminary short report of the author (Phys. Rev. E 78, 020301(R) (2008)), extends previous theoretical results derived in the dilute limit case.     

Maximum entropy principle and power-law tailed distributions

In ordinary statistical mechanics the Boltzmann-Shannon entropy is related to the Maxwell-Bolzmann distribution p_i by means of a twofold link. The first link is differential and is offered by the Jaynes Maximum Entropy Principle. Indeed, the Maxwell-Boltzmann distribution is obtained by maximizing the Boltzmann-Shannon entropy under proper constraints. The second link is algebraic and imposes that both the entropy and the distribution must be expressed in terms of the same function in direct and inverse form. Indeed, the Maxwell-Boltzmann distribution p_i is expressed in terms of the exponential function, while the Boltzmann-Shannon entropy is defined as the mean value of -ln (p_i). In generalized statistical mechanics the second link is customarily relaxed. Of course, the generalized exponential function defining the probability distribution function after inversion, produces a generalized logarithm Λ(p_i). But, in general, the mean value of -Λ(p_i) is not the entropy of the system. Here we reconsider the question first posed in [Phys. Rev. E 66, 056125 (2002) and 72, 036108 (2005)], if and how is it possible to select generalized statistical theories in which the above mentioned twofold link between entropy and the distribution function continues to hold, such as in the case of ordinary statistical mechanics. Within this scenario, apart from the standard logarithmic-exponential functions that define ordinary statistical mechanics, there emerge other new couples of direct-inverse functions, i.e. generalized logarithms Λ(x) and generalized exponentials Λ^-1(x), defining coherent and self-consistent generalized statistical theories. Interestingly, all these theories preserve the main features of ordinary statistical mechanics, and predict distribution functions presenting power-law tails. Furthermore, the obtained generalized entropies are both thermodynamically and Lesche stable.     

Cooling kinetics of a granular gas of viscoelastic particles

The evolution of a granular gas of viscoelastic particles in the homogeneous cooling state is studied. The velocity distribution function of granular particles and the time dependence of the mean kinetic energy of particles (granular temperature) are found. The noticeable deviation of the distribution function from the Maxwell distribution and its non-monotonous evolution are established. The perturbation theory with respect to the small dispersion parameter is elaborated and the analytical expressions for the asymptotic time dependence of the velocity distribution function and the granular gas temperature are derived.     

Superfluid phases of the three-species fermion gas

We discuss the zero temperature phase diagram of a dilute gas with three fermionic species. We make use of solvable limits to conjecture the behavior of the system in the “unitary” regions. The physics of the Thomas-Efimov effect plays a role in these considerations. We find a rich phase diagram with superfluid, gapless superfluid and inhomogeneous phases with different symmetry breaking patterns. We then discuss one particular possible experimental implementation in a system of ⁶Li atoms and the possible phases arising in this system as an external magnetic field is varied across three overlapping Feshbach resonances. We also suggest how to experimentally distinguish the different phases.     

Approximation of the Dymond-Rigby-Smith potential function using the Lennard-Jones form

Due to the mathematical similarities between the Dymond-Rigby-Smith (DRS) function with the conventional Lennard-Jones (LJ) functions, modification to the LJ indices is made herein in order to approximate the DRS energy curve. It is herein shown that the LJ(9-6) potential approximates well the DRS curve for interatomic distance shorter than the equilibrium distance. For interatomic distance longer than the equilibrium distance, a pair of LJ indices, based on the equal mean stretching energy, was found to give very good agreement with the DRS curve. Modification to the conventional LJ functions for describing the DRS energy, rather than the replacement of the LJ potentials with DRF function, allows numerous computational chemistry softwares to quantify the DRS energy with minimal hard-coding of their algorithms.     

Fluorination of alumino-silicate minerals: The example of lepidolite

The effect of fluorination on silicate and alumino-silicate minerals has been investigated, in particular on the lepidolite [K(Li,Al)₃ [Si₃AlO₁₀] (F,OH)₂] of the mica-type. The fluorination techniques included direct F₂-gas and cold radio-frequency-plasma involving c-C₄F₈ or O₂/CF₄ mixtures. The modifications of the surface properties have been followed mostly by XPS. Depending of the fluorination route used, either a reactive etching process involving M-F bonding occurs (direct F₂-gas; O₂-CF₄ rf-plasma), or a carbon fluoride deposition takes place (c-C₄F₈ rf-plasma).     

重量法制备氮中微量氧气体标准物质

介绍重量法制备氮中微量氧气体标准物质的实验方法和结果.考察了环境空气对微量氧配制过程中引入误差的影响,对称量法制备气体标准物质不确定度进行了评定并对不确定度进行了验证,验证结果吻合在l%之内;氧含量在0～10 μmoL/mol范围内重量法制备的气体标准物质的不确定度小于1%,并且取得了国际的等效性.     

Comparison of different pairing fluctuation approaches to BCS-BEC crossover

The subject of BCS-Bose-Einstein condensation (BEC) crossover is particularly exciting because of its realization in ultracold atomic Fermi gases and its possible relevance to high temperature superconductors. In this paper we review the body of theoretical work on this subject, which represents a natural extension of the seminal papers by Leggett and by Nozières and Schmitt-Rink (NSR). The former addressed only the ground state, now known as the “BCS-Leggett” wave-function, and the key contributions of the latter pertain to calculations of the superfluid transition temperature T_c. These two papers have given rise to two main and, importantly, distinct, theoretical schools in the BCS-BEC crossover literature. The first of these extends the BCS-Leggett ground state to finite temperature and the second extends the NSR scheme away from T_c both in the superfluid and normal phases. It is now rather widely accepted that these extensions of NSR produce a different ground state than that first introduced by Leggett. This observation provides a central motivation for the present paper which seeks to clarify the distinctions in the two approaches. Our analysis shows how the NSR-based approach views the bosonic contributions more completely but treats the fermions as “quasi-free”. By contrast, the BCS-Leggett based approach treats the fermionic contributions more completely but treats the bosons as “quasi-free”. In a related fashion, the NSR-based schemes approach the crossover between BCS and BEC by starting from the BEC limit and the BCS-Leggett based scheme approaches this crossover by starting from the BCS limit. Ultimately, one would like to combine these two schemes. There are, however, many difficult problems to surmount in any attempt to bridge the gap in the two theory classes. In this paper we review the strengths and weaknesses of both approaches. The flexibility of the BCS-Leggett based approach and its ease of handling make it widely used in T=0 applications, although the NSR-based schemes tend to be widely used at . To reach a full understanding, it is important in the future to invest effort in investigating in more detail the T=0 aspects of NSR-based theory and at the same time the T≠0 aspects of BCS-Leggett theory.     

Quantum simulation of the Hubbard model with ultracold fermions in optical lattices

Ultracold atomic gases provide a fantastic platform to implement quantum simulators and investigate a variety of models initially introduced in condensed matter physics or other areas. One of the most promising applications of quantum simulation is the study of strongly correlated Fermi gases, for which exact theoretical results are not always possible with state-of-the-art approaches. Here, we review recent progress of the quantum simulation of the emblematic Fermi–Hubbard model with ultracold atoms. After introducing the Fermi–Hubbard model in the context of condensed matter, its implementation in ultracold atom systems, and its phase diagram, we review landmark experimental achievements, from the early observation of the onset of quantum degeneracy and superfluidity to the demonstration of the Mott insulator regime and the emergence of long-range anti-ferromagnetic order. We conclude by discussing future challenges, including the possible observation of high-$T_{\mathrm{c}}$ superconductivity, transport properties, and the interplay of strong correlations and disorder or topology.     

星载高光谱成像光谱仪狭缝函数测试方法的研究

为了满足大气微量成分高精度测量需求,需要能准确描述星载高光谱大气微量成份探测仪的仪器狭缝函数。针对高光谱大气微量成份探测仪视场大、波段宽、空间分辨率和光谱分辨率高等特点,研制了狭缝函数测量仪。介绍了狭缝函数测量仪的工作原理及基本结构,并利用狭缝函数测量仪可同时实现高分辨率、宽谱段测量的特点,通过搭建定标装置,对高光谱大气微量成份探测仪进行全视场的狭缝函数测试,得出了仪器狭缝函数的数学表达式,给出仪器狭缝函数的特性分布,并对结果进行分析。测试结果表明：高光谱大气微量成份探测仪全视场光谱分辨率在0.423～0.597 nm之间,其狭缝函数特性曲线近似满足高斯分布规律。由于星载大视场成像光谱仪存在光谱弯曲现象,从而导致边缘视场分辨能力略低于中心视场分辨能力。狭缝函数测量仪是基于中阶梯衍射光栅设计,可同时输出多条高分辨率谱线,且分布均匀,不仅可以测量高光谱成像光谱仪的仪器狭缝函数,也可对星载高光谱仪器光谱定标,为后续研究提供了参考依据和方法。