Local similarity in organic crystals and the non-uniqueness of X-ray powder patterns

Two new concepts for molecular solids, 'local similarity' and 'boundary-preserving isometry', are defined mathematically and a theorem which relates these concepts is formulated. 'Locally similar' solids possess an identical short-range structure and a 'boundary-preserving isometry' is a new mathematical operation on a finite region of a solid that transforms mathematically a given solid to a locally similar one. It is shown further that the existence of such a 'boundary-preserving isometry' in a given solid has infinitely many 'locally similar' solids as a consequence. Chemical implications, referring to the similarity of X-ray powder patterns and patent registration, are discussed as well. These theoretical concepts, which are first introduced in a schematic manner, are proved to exist in nature by the elucidation of the crystal structure of some diketopyrrolopyrrole (DPP) derivatives with surprisingly similar powder patterns. Although the available powder patterns were not indexable, the underlying crystals could be elucidated by using the new technique of ab initio prediction of possible polymorphs and a subsequent Rietveld refinement. Further ab initio packing calculations on other molecules reveal that 'local crystal similarity' is not restricted to DPP derivatives and should also be exhibited by other molecules such as quinacridones. The 'boundary-preserving isometry' is presented as a predictive tool for crystal engineering purposes and attempts to detect it in crystals of the Cambridge Structural Database (CSD) are reported.

An analysis of collective damage for short fatigue cracks based on equilibrium of crack numerical density

Collective damage of short fatigue cracks was analyzed in the light of equilibrium of crack numerical density. With the estimation of crack growth rate and crack nucleation rate, the solution of the equilibrium equation was studied to reveal the distinct feature of saturation distribution for crack numerical density. The critical time that characterized the transition of short and long-crack regimes was estimated, in which the influences of grain size and grain-boundary obstacle effect were investigated. Furthermore, the total number of cracks and the first order of damage moment were discussed.

Analysis of steric mass-action model for protein adsorption equilibrium onto porous anion-exchange adsorbent

The ion-exchange equilibrium of bovine serum albumin (BSA) to an anion exchanger, DEAE Spherodex M, has been studied by batch adsorption experiments at pH values ranging from 5.26 to 7.6 and ionic strengths from 10 to 117.1 mmol/l. Using the unadjustable adsorption equilibrium parameters obtained from batch experiments, the applicability of the steric mass-action (SMA) model was analyzed for describing protein ion-exchange equilibrium in different buffer systems. The parametric sensitivity analysis was performed by perturbing each of the model parameters, while holding the rest constant. The simulation results showed that, at high salt concentrations or low pHs close to the isoelectric point of the protein, the precision of the model prediction decreased. Parametric sensitivity analysis showed that the characteristic charge and protein steric factor had the largest effects on ion-exchange equilibrium, while the effect of equilibrium constant was about 70%-95% smaller than those of characteristic charge and steric factor under all conditions investigated. The SMA model with the relationship between the adjusted characteristic charge and the salt concentration can well predict the protein adsorption isotherms in a wide pH range from 5.84 to 7.6. It is considered that the SMA model could be further improved by taking into account the effect of salt concentration on the intermolecular interactions of proteins. (c) 2006 Elsevier Ltd. All rights reserved.

Elasticity, stability, and ideal strength of beta-SiC in plane-wave-based ab initio calculations

On the basis of the pseudopotential plane-wave method and the local-density-functional theory, this paper studies energetics, stress-strain relation, stability, and ideal strength of beta-SiC under various loading modes, where uniform uniaxial extension and tension and biaxial proportional extension are considered along directions [001] and [111]. The lattice constant, elastic constants, and moduli of equilibrium state are calculated and the results agree well with the experimental data. As the four SI-C bonds along directions [111], [(1) over bar 11], [11(1) over bar] and [111] are not the same under the loading along [111], internal relaxation and the corresponding internal displacements must be considered. We find that, at the beginning of loading, the effect of internal displacement through the shuffle and glide plane diminishes the difference among the four Si-C bonds lengths, but will increase the difference at the subsequent loading, which will result in a crack nucleated on the {111} shuffle plane and a subsequently cleavage fracture. Thus the corresponding theoretical strength is 50.8 GPa, which agrees well with the recent experiment value, 53.4 GPa. However, with the loading along [001], internal relaxation is not important for tetragonal symmetry. Elastic constants during the uniaxial tension along [001] are calculated. Based on the stability analysis with stiffness coefficients, we find that the spinodal and Born instabilities are triggered almost at the same strain, which agrees with the previous molecular-dynamics simulation. During biaxial proportional extension, stress and strength vary proportionally with the biaxial loading ratio at the same longitudinal strain.

A Study of Composite Beam with Shape Memory Alloy Arbitrarily Embedded under Thermal and Mechanical Loadings

The constitutive relations and kinematic assumptions on the composite beam with shape memory alloy (SMA) arbitrarily embedded are discussed and the results related to the different kinematic assumptions are compared. As the approach of mechanics of materials is to study the composite beam with the SMA layer embedded, the kinematic assumption is vital. In this paper, we systematically study the kinematic assumptions influence on the composite beam deflection and vibration characteristics. Based on the different kinematic assumptions, the equations of equilibrium/motion are different. Here three widely used kinematic assumptions are presented and the equations of equilibrium/motion are derived accordingly. As the three kinematic assumptions change from the simple to the complex one, the governing equations evolve from the linear to the nonlinear ones. For the nonlinear equations of equilibrium, the numerical solution is obtained by using Galerkin discretization method and Newton-Rhapson iteration method. The analysis on the numerical difficulty of using Galerkin method on the post-buckling analysis is presented. For the post-buckling analysis, finite element method is applied to avoid the difficulty due to the singularity occurred in Galerkin method. The natural frequencies of the composite beam with the nonlinear governing equation, which are obtained by directly linearizing the equations and locally linearizing the equations around each equilibrium, are compared. The influences of the SMA layer thickness and the shift from neutral axis on the deflection, buckling and post-buckling are also investigated. This paper presents a very general way to treat thermo-mechanical properties of the composite beam with SMA arbitrarily embedded. The governing equations for each kinematic assumption consist of a third order and a fourth order differential equation with a total of seven boundary conditions. Some previous studies on the SMA layer either ignore the thermal constraint effect or implicitly assume that the SMA is symmetrically embedded. The composite beam with the SMA layer asymmetrically embedded is studied here, in which symmetric embedding is a special case. Based on the different kinematic assumptions, the results are different depending on the deflection magnitude because of the nonlinear hardening effect due to the (large) deflection. And this difference is systematically compared for both the deflection and the natural frequencies. For simple kinematic assumption, the governing equations are linear and analytical solution is available. But as the deflection increases to the large magnitude, the simple kinematic assumption does not really reflect the structural deflection and the complex one must be used. During the systematic comparison of computational results due to the different kinematic assumptions, the application range of the simple kinematic assumption is also evaluated. Besides the equilibrium study of the composite laminate with SMA embedded, the buckling, post-buckling, free and forced vibrations of the composite beam with the different configurations are also studied and compared.

Mandibular morphometric variation among Chinese cercopithecoids and the unique structure of the snub-nosed monkey (Rhinopithecus) mandible

In order to understand how mandibular structure differs among the Chinese cercopithecoids (Rhinopithecus, Trachypithecus and Macaca), particularly the uniqueness of the snub-nosed monkeys (Rhinopithecus), we analysed ten mandibular measurements by principal components analysis (PCA), and examined scaling patterns. The results provided by the PCA illustrated differences due to size among the cercopithecoids and the relationship between colobines (Trachypithecus and Rhinopithecus) and cercopithecines, in which macaques (Macaca) are included. Allometric analysis indicated that, biomechanically, there is not a marked difference between macaques and leaf-eating monkeys. This may be associated with the fact that both share some similar ecology and niches in south and southwest China. The snub-nosed monkeys exhibit a significantly more robust mandible, evident in the symphysis, corpus, condyle, and masticatory momentum arm. This supports the hypothesis, based on the study of dental structure, that Rhinopithecus is a unique group in Asian Old World monkeys (OWMs) and has developed some unique characteristics in order to adapt to the tough food available in the severe cold climate of the Plateaux of Qinghai-Tibet, Yun-Gui and Qingling in China.

Isothermal Crystallization Behavior of Poly(L-lactic acid)/Organo-Montmorillonite Nanocomposites

The isothermal crystallization behavior of poly(L-lactic acid)/organo-montmorillonite nanocomposites (PLLA/OMMT) with different content of OMMT, using a kind of twice-functionalized organoclay (TFC), prepared by melt intercalation process has been investigated by optical depolarizer. In isothermal crystallization from melt, the induction periods (t(i)) and half times for overall PLLA crystallization (100 degrees C <= T-c <= 120 degrees C) were affected by the temperature and the content of TFC in nanocomposites. The kinetic of isothermal crystallization of PLLA/TFC nanocomposites was studied by Avrami theory. Also, polarized optical photomicrographs supplied a direct way to know the role of TFC in PLLA isothermal crystallization process. Wide angle X-ray diffraction (WAXD) patterns showed the nanostructure of PLLA/TFC material, and the PLLA crystalline integrality was changed as the presence of TFC. Adding TFC led to the decrease of equilibrium melting point of nanocomposites, indicating that the layered structure of clay restricted the full formation of crystalline structure of polymer.

Single molecule dynamics and statistical fluctuations of gene regulatory networks: A repressilator

The authors developed a time dependent method to study the single molecule dynamics of a simple gene regulatory network: a repressilator with three genes mutually repressing each other. They quantitatively characterize the time evolution dynamics of the repressilator. Furthermore, they study purely dynamical issues such as statistical fluctuations and noise evolution. They illustrated some important features of the biological network such as monostability, spirals, and limit cycle oscillation. Explicit time dependent Fano factors which describe noise evolution and show statistical fluctuations out of equilibrium can be significant and far from the Poisson distribution. They explore the phase space and the interrelationships among fluctuations, order, amplitude, and period of oscillations of the repressilators. The authors found that repressilators follow ordered limit cycle orbits and are more likely to appear in the lower fluctuating regions. The amplitude of the repressilators increases as the suppressing of the genes decreases and production of proteins increases. The oscillation period of the repressilators decreases as the suppressing of the genes decreases and production of proteins increases.

Extraction mechanism of La3+ from hydrochloric acid solution using Cyanex 302

The solvent extraction of La3+ from hydrochloric acid solutions was investigated using his (2, 4, 4-trimethylpentyl) monothiophosphinic acid (Cyanex 302, HL) as an extractant. The effect of equilibrium of aqueous acidity on extraction of La3+ using Cyanex 302 In different diluents was discussed. The effects of extractant concentration and chloride ion on the extraction reaction were also studied. Stoichiometry of the extraction reactions and the nature of metal complexes formed were determined using slope analysis technique and IR measurement.

Selective separation of yttrium by CA-100 in the presence of a complexing agent

The selective separation of Y from yttrium solution containing small heavy rare earth (HRE) impurities (Ho, Er, Tm, Yb, Lu) by liquid-liquid extraction using CA-100 in the presence of a water-soluble complexing agent of ethylenediaminetetraacetic acid (EDTA) was experimentally studied at 298K. Experiments were carried Out in two feeds, Feed-I: [RE](f) = 4.94 x 10(-3) M, Y = 98.5%, HRE (Ho, Er, Tm, Yb, Lu) = 1.5%; Feed-II: [RE](f) = 4.94 x 10(-3) M, Y = 99.9%, HRE (Ho, Er, Tm, Yb, Lu) = 0.1%, as a function of equilibrium pH (pH(eq)), the concentration ratio of [EDTA]:[HRE impurities]. It was shown that the extraction of HRE in the presence of EDTA was suppressed when compared to that of Y because of the masking effect, while the selective extraction of Y was enhanced and the separation factors increased to maximum at appropriate condition for Feed-I: Y/Ho = 1.53, Y/Er = 3.09, Y/Tm = 5.61, Y/Yb = 12.04, Y/Lu = 27.51 at pH 4.37 and [EDTA]:[HRE impurities] = 4: 1, for Feed-II: Y/Ho = 1.32, Y/Er = 1.91, Y/Tm = 2.00, Y/Yb = 3.05, Y/Lu = 3.33 at pH 4.42 and [EDTA]: [HRE impurities] = 8:1. The separation and purification of Y by this method was discussed.

Electrochemical identification of intermediate forms of urea denaturation of horse heart cytochrome c

The electrochemical identification of the urea denaturation of horse heart cytochrome c in bulk solution at the 4,4'-dithiodipyridine-modified gold electrode is reported. The results are similar to the three-step transitions of equilibrium studies (Myer et al., Biochemistry, 19 (1980) 199) of urea denaturation of cytochrome c in bulk solution. This method permits a clear resolution of which of the three steps of urea denaturation is electrochemically related. In addition, by analysing the effects of urea on the structural forms of cytochrome c and on the solution properties, as well as the cyclic voltammetric responses of the protein, the individual forms of the urea denaturation of cytochrome c can be understood. The results reflect the superposition of protein denaturation on the electrode surface and in solution.

SOLVENT-EXTRACTION OF SC(III), ZR(IV), TH(IV), FE(III), AND LU(III) WITH THIOSUBSTITUTED ORGANOPHOSPHINIC ACID EXTRACTANTS

The solvent extraction of Sc(III), Zr(IV), Th(IV), Fe(III) and Lu(III) with Cyanex 302 (bis(2,4,4-trimethylpentyl)monothiophosphinic acid) and Cyanex 301 ( bis(2,4,4-trimethylpentyl) dithiophosphinic acid) in n-hexane from acidic aqueous solutions has been investigated systematically. The effect of equilibrium aqueous acidity on the extraction with these reagents was studied. The separation of Th(IV), Fe(III) and Lu(III) from Sc(III), or the separation of other metals from Lu(III) with Cyanex 302, can be achieved by controlling the aqueous acidity. However, Cyanex 301 exhibited a poor selectivity for the above metals, except for Lu(III). The extraction of these metals with Cyanex 272, Cyanex 302 and Cyanex 301 has been compared. The stripping percentages of Sc(III) for Cyanex 302 and Cyanex 301 in a single stage are near 78% and 75% with 3.5 mol/L and 5.8 mol/L sulphuric acid solutions, respectively. The effects of extractant concentration and temperature on the extraction of Sc(III) were investigated. The stoichiometry of the extraction of Sc(III) with Cyanex 302 was determined. The role of different components of Cyanex 302 in the extraction of Sc(III) was discussed.

Periodical mixing of MORB magmas near East Pacific Rise 13N: evidence from modeling and zoned plagioclase phenocrysts

Thirty-six basalt samples from near East Pacific Rise 13N are analyzed for major and trace elements. Different types of zoned plagioclase phenocrysts in basalts are also backscatter imaged, and major element profiles scanned and analyzed for microprobe. Basalts dredged from a restricted area have evolved to different extents (MgO=9.38wt%-6.76wt%). High MgO basalts are modeled for crystallization to MgO of about 7wt%, and resulted in the Ni contents (28 ppm) that are generally lower than that in observed basalts (> 60 ppm). It suggests that low MgO basalts may have experienced more intensive magma mixing. High MgO (9.38wt%) basalt is modeled for self-"mixing-crystallization", and the high Ni contents in low MgO basalts can be generated in small scale and periodical self-mixing of new magma (high MgO). "Mixing-crystallization" processes that low MgO magmas experienced accord with recent 226Ra/230Th disequilibria studies for magma residence time, in which low MgO magmas have experienced more circles of "mixing-crystallization" in relatively longer residence time. Magma mixing is not homogeneous in magma chamber, however, low MgO magmas are closer to stable composition produced by periodical "mixing-crystallization", which is also an important reason for magma diversity in East Pacific Rise. Zoned plagioclase phenocrysts can be divided into two types: with and without high An# cores, both of which have multiple reversed An# zones, suggesting periodical mixing of their host magmas. Cores of zoned plagioclase in low MgO (7.45wt%) basalt differ significantly with their mantle in An#, but are similar in An# with microlite cores (products of equilibrium crystallization) in high MgO (9.38wt%) basalt, which further shows that plagioclase phenocryst cores in low MgO basalts may have formed in their parental magmas before entering into the magma chamber.

Potential refugium on the Qinghai-Tibet Plateau revealed by the chloroplast DNA phylogeography of the alpine species Metagentiana striata (Gentianaceae)

Metagentiana striata is an alpine annual herbaceous plant endemic to the east of the Qinghai-Tibet (Q-T) Plateau and adjacent areas. The phylogeography of M. striata was studied by sequencing the chloroplast DNA (cpDNA) trnS-trnG intergenic spacer. Ten haplotypes were identified from an investigation of 232 individuals of M. striata from 14 populations covering the entire geographical range of this species. The level of differentiation amongst populations was very high (G(ST) = 0.746; N-ST = 0.774) and a significant phylogeographical structure was observed (P < 0.05). An analysis of molecular variance found a high variation amongst populations (76%), with F-ST = 0.762 (highly significant, P < 0.001), indicating that little gene flow occurred amongst the different regions; this was explained by the isolation of populations by high mountains along the Q-T Plateau and adjacent areas (N-m = 0.156). Only one ancestral haplotype (A) was common and widespread throughout the distributional range of M. striata. The populations of the Hengduan Mountains region of the south-eastern Q-T Plateau showed high diversity and uniqueness of haplotypes. It is suggested that this region was the potential refugium of M. striata during the Quaternary glaciation, and that interglacial and postglacial range expansion occurred from this refugium. This scenario was in good agreement with the results of nested clade analysis, which inferred that the current spatial distribution of cpDNA haplotypes and populations resulted from range expansion, together with past allopatric fragmentation events. (c) 2008 The Linnean Society of London.