The projection approach to the Fokker-Planck equation. I. Colored Gaussian noise

It is shown that the Fokker-Planck operator can be derived via a projection-perturbation approach, using the repartition of a more detailed operator into a perturbation ₁ and an unperturbed part ₀. The standard Fokker-Planck structure is recovered at the second order in ₁, whereas the perturbation terms of higher order are shown to provoke the breakdown of this structure. To get rid of these higher order terms, a key approximation, local linearization (LL), is made. In general, to evaluate at the second order in ₁ the exact expression of the diffusion coefficient which simulates the influence of a Gaussian noise with a finite correlation time, a resummation up to infinite order in must be carried out, leading to what other authors call the best Fokker-Planck approximation (BFPA). It is shown that, due to the role of terms of higher order in ₁, the BFPA leads to predictions on the equilibrium distributions that are reliable only up to the first order in t. The LL, on the contrary, in addition to making the influence of terms of higher order in ₁ vanish, results in a simple analytical expression for the term of second order that is formally coincident with the complete resummation over all the orders in t provided by the Fox theory. The corresponding diffusion coefficient in turn is shown to lead in the limiting case to exact results for the steady-state distributions. Therefore, over the whole range 0 the LL turns out to be an approximation much more accurate than the global linearization proposed by other authors for the same purpose of making the terms of higher order in ₁ vanish. In the short- region the LL leads to results virtually coincident with those of the BFPA. In the large- region the LL is a more accurate approximation than the BFPA itself. These theoretical arguments are supported by the results of both analog and digital simulation.     

Structural features of zinc hydroxyfluoride

Zinc hydroxyfluoride (ZnOHF), obtained by coprecipitation of a zinc salt in aqueous HF, exhibits a variable stoichiometry Zn(OH)_2−xF_x, where x is tuneable from 0.63 to 0.87 by controlling the pH of the solution. The structure was determined from Rietveld refinements using X-ray powder diffraction data. Crystallizing with the orthorhombic symmetry (SG : Pna2₁), the ZnOHF-type structure exhibits two different anionic sites. A bond valence analysis shows that fluorine exclusively occupies the anionic site that has shorter contacts to zinc. This site is split into two partially occupied sites, one corresponding to the position of a fluoride ion and the other to the position of a hydroxide ion. Bond valence calculations show that the split site model gives a more accurate picture of the local coordination of the anions on this site.     

(TiNi)_x(x=2~4)团簇结构和电子结构

从团簇角度对TiNi形状记忆合金进行了量子化学从头算研究。设计并优化了等原子比(TiNi)x(x=2~4)簇的多种可能几何结构,并对较稳定构型进行电子结构的分析。结果表明,等原子比的(TiNi)n团簇以TiNi成键为主要分子骨架,小团簇有较多能量接近的异构体,TiTi成键对能量降低有较大贡献。     

泡沫铅对VRLA电池负极活性物质结构及性能影响

0引言随着36V/42V汽车电源系统的提出,新一轮汽车用电池的竞争不断加剧。从目前情况看,铅酸电池由于具有成本低廉,使用可靠,原材料来源丰富,铅回收率可高达98%等优点,因此成为电动车电源最实际的选择之一[1]。但作为电动车用电池,需要克服其比能量低、充电接受能力差和负极硫酸盐化等缺点。为此各国科学家开展了大量的研究工作。最近报道用铸造多孔体作为敞口铅酸电池的集流体,它的比表面积为14cm2·cm-3,正极活性物质利用率上升到50%,远高于传统的铸造板栅[2]。在铅酸电池集流体研究领域里另一个重大进步,就是以R V C(R etic-ulated V i…     

一个新颖三维配位聚合物Pb(1，4-napdc)(DMF)的合成、结构及热稳定性研究

A novel 3D metal-organic coordination polymer Pb(1,4-napdc)(DMF) (1,4-napdc=naphthalene-1,4-dicarboxylate) was synthesized at room temperature using slow vapor diffusion method to grow single crystal that has been analyzed by X-ray diffraction. The crystal belongs to orthorhombic with space group P2₁2₁2₁. The unit cell parameters are as fellows: a=0.701 3(2) nm, b=1.407 6(3) nm, c=1.521 5(4) nm, V=1.501 8(6) nm³ and Z=4. In the crystal structure of Pb(1,4-napdc)(DMF), the square grids constructed with paddle-wheel units of Pb(Ⅱ) and 1,4-napdc links stack over each other to generate infinite 3D network, which has square apertures (1.158×1.158 nm²) along the crystallographic a-axis. The thermal stability of compound was investigated by differential scanning calorimetry and thermogravimetric analysis. CCDC: 293617.     

Structures and synthesis of framework Rb and Cs uranyl arsenates and their relationships with their phosphate analogues

Two hydrated uranyl arsenates, Cs₂(UO₂)[(UO₂)(AsO₄)]₄(H₂O)₂ (CsUAs) and Rb₂(UO₂)[(UO₂)(AsO₄)]₄(H₂O)_4.5 (RbUAs), were synthesized by hydrothermal methods. Intensity data were collected at room temperature using MoKα radiation and a CCD-based area detector. The crystal structure of RbUAs was solved by direct methods, whereas the structure model of the phosphate Cs₂(UO₂)[(UO₂)(PO₄)]₄(H₂O)₂ was used for CsUAs; both were refined by full-matrix least-squares techniques on the basis of F² to agreement indices (CsUAs, RbUAs) wR₂=0.061,0.041, for all data, and R₁=0.032,0.021, calculated for 5098, 4991 unique observed reflections (|F_o|>4σ_F), respectively. The compound CsUAs is orthorhombic, space group Cmc2₁, Z=4, a=15.157(2), b=14.079(2), c=13.439(2) Å, V=2867.9(1) Å³. RbUAs is monoclinic, space group C2/m, Z=4, a=13.4619(4), b=15.8463(5), c=14.0068(4) Å, β=92.311(1)°, V=2985.52(2) Å³. The structures consist of sheets of arsenate tetrahedra and uranyl pentagonal bipyramids, with composition [(UO₂)(AsO₄)]⁻, that are topologically identical to the uranyl silicate sheets in uranophane-beta. These sheets are connected by a uranyl pentagonal bipyramid in the interlayer that shares corners with two arsenate tetrahedra on each of two adjacent sheets and whose fifth equatorial vertex is an H₂O group, resulting in an open framework with alkali metal cations in the larger cavities of the structures. CsUAs is isostructural with its phosphate analogue, and has two Cs atoms and a H₂O group in its structural cavities. RbUAs is not isostructural with its phosphate analogue, although it has a homeotypic framework. Its structural cavities are occupied by three Rb atoms and four H₂O groups; one Rb position and three of the interstitial H₂O groups are half-occupied. The partial occupancies of these positions probably result from the accommodation of the larger As atoms (relative to P) in the framework and resultant larger cavities.     

Local and non-local sources of airborne particulate pollution at Beijing--The ratio of Mg/Al as an element tracer for estimating the contributions of mineral aerosols from outside Beijing

A new element tracer technique has firstly been established to estimate the contributions of mineral aerosols from both inside and outside Beijing. The ratio of Mg/Al in aerosol is a feasible element tracer to distinguish between the sources of inside and outside Beijing. Mineral aerosol, inorganic pollution aerosol mainly as sulfate and nitrate, and organic aerosol are the major components of airborne particulates in Beijing, of which mineral aerosol accounted for 32%―67% of total suspended particles (TSP), 10%―70% of fine particles (PM2.5), and as high as 74% and 90% of TSP and PM2.5, respectively, in dust storm. The sources from outside Beijing contributed 62% (38%―86%) of the total mineral aerosols in TSP, 69% (52%―90%) in PM10, and 76% (59%―93%) in PM2.5 in spring, and 69% (52%―83%), 79% (52%―93%), and 45% (7%―79%) in TSP, PM10, and PM2.5, respectively, in winter, while only ～20% in summer and autumn. The sources from outside Beijing contributed as high as 97% during dust storm and were the dominant source of airborne particulates in Beijing. The contributions from outside Beijing in spring and winter are higher than those in summer, indicating clearly that it was related to the various meteorological factors.     

Anion substitution effects on structure and magnetism in the chromium chalcogenide Cr5Te8—Part I: Cluster glass behavior in trigonal Cr(1+x)Q2 with basic cell (Q=Te, Se; Te:Se=7:1)

The effect of substitution of the anion Te by Se in non-stoichiometric Cr₅Te₈ has been investigated with respect to its crystal structure, magnetic properties, and electronic structure. The compounds Cr_(1+x)Q₂ (Q=Te, Se; Te:Se=7:1; (1+x)=1.234(6), 1.264(6), 1.300(7)) were synthesized at elevated temperatures followed by quenching the samples to room temperature. The crystal structures have been refined with X-ray powder diffraction data with the Rietveld method in the trigonal space group with lattice parameters a=3.8651(1)-3.8831(1) Å and c=5.9917(2)-6.0528(2) Å. The structure is related to the NiAs structure with full and deficient metal layers stacking alternatively along the c-axis. The irreversibility in the field-cooled/zero-field-cooled magnetization suggests that the substitution effects of one Te by one Se is strong enough to cause cluster-glass behavior, from ferromagnetic Cr₅Te₈ to cluster-glass Cr_(1+x)Q₂. Non-saturation magnetizations at 5.5 T and the magnetic relaxation results further support the existence of cluster-glass behavior. Accompanying SPR-KKR (spin-polarized relativistic Korringa-Kohn-Rostoker) band structure calculations strongly support the observation that the Cr(1) sites are preferentially occupied by Cr atoms and predict that these compounds are metallic. Results for the spin-resolved DOS and magnetic moments on each crystallographic sites are presented.     

Sampling and local models for multivariate image analysis

Local models are a very important concept for microscopic and macroscopic imaging. Different methods of sub-sampling a multivariate image are described both in general and for three examples. The need for sub-sampling and its influence on multivariate image analysis and visualization are studied. Examples from MRI (256 × 256), satellite imaging (7 × 512 × 512) and biofuel studies (6 × 512 × 512) are used to illustrate some of the principles involved.