Novel numerical methods for time-space fractional reaction diffusion equations in two dimensions

We consider time-space fractional reaction diffusion equations in two dimensions. This equation is obtained from the standard reaction diffusion equation by replacing the first order time derivative with the Caputo fractional derivative, and the second order space derivatives with the fractional Laplacian. Using the matrix transfer technique proposed by Ilic, Liu, Turner and Anh [Fract. Calc. Appl. Anal., 9:333--349, 2006] and the numerical solution strategy used by Yang, Turner, Liu, and Ilic [SIAM J. Scientific Computing, 33:1159--1180, 2011], the solution of the time-space fractional reaction diffusion equations in two dimensions can be written in terms of a matrix function vector product $f(A)b$ at each time step, where $A$ is an approximate matrix representation of the standard Laplacian. We use the finite volume method over unstructured triangular meshes to generate the matrix $A$, which is therefore non-symmetric. However, the standard Lanczos method for approximating $f(A)b$ requires that $A$ is symmetric. We propose a simple and novel transformation in which the standard Lanczos method is still applicable to find $f(A)b$, despite the loss of symmetry. Numerical results are presented to verify the accuracy and efficiency of our newly proposed numerical solution strategy.

Ocular characteristics in myopic anisometropia

PURPOSE: To investigate the interocular symmetry of ocular optical, biometric and biomechanical characteristics between the more and less ametropic eyes of myopic anisometropes. METHODS: Thirty-four young, healthy myopic anisometropic adults (≥ 1 D spherical equivalent difference between eyes) without amblyopia or strabismus were recruited. A range of biometric and optical parameters were measured in the more and less ametropic eye of each subject including; axial length, ocular aberrations, intraocular pressure and corneal topography, thickness and biomechanics. Morphology of the anterior eye in primary and downward gaze was examined using custom software analysis of high resolution digital images. Ocular sighting dominance was assessed using the hole-in-the-card test. RESULTS: Mean absolute spherical equivalent anisometropia was 1.74 ± 0.74 D. There was a strong correlation between the degree of anisometropia and the interocular difference in axial length (r = 0.81, p < 0.001). The more and less ametropic fellow eyes displayed a high degree of interocular symmetry for the majority of biometric, biomechanical and optical parameters measured. When the level of anisometropia exceeded 1.75 D (n = 10), the more myopic eye was the dominant sighting eye in nine of these ten subjects. Subjects with greater levels of anisometropia (> 1.75 D) also showed high levels of correlation between the dominant and non-dominant eyes in their biometric, biomechanical and optical characteristics. CONCLUSIONS: Although significantly different in axial length, anisometropic eyes display a high degree of interocular symmetry for a range of anterior eye biometrics and optical parameters. For higher levels of anisometropia, the more myopic eye tends to be the dominant sighting eye.

Ethane-1,2-diaminium 4,4'-sulfonyldibenzoate

In the title compound 2(C2H10N2+) C14H8O6S2-, both the ethylenediaminium cations and the 4,4'-sulfonyldibenzoate dianions have crystallographic two-fold rotational symmetry and are interlinked by aminium N-H...O(carboxyl) hydrogen-bonding associations giving sheets which extend along (101) and are further linked down b forming a three-dimensional structure.

Ocular characteristics of anisometropia

Animal models of refractive error development have demonstrated that visual experience influences ocular growth. In a variety of species, axial anisometropia (i.e. a difference in the length of the two eyes) can be induced through unilateral occlusion, image degradation or optical manipulation. In humans, anisometropia may occur in isolation or in association with amblyopia, strabismus or unilateral pathology. Non-amblyopic myopic anisometropia represents an interesting anomaly of ocular growth, since the two eyes within one visual system have grown to different endpoints. These experiments have investigated a range of biometric, optical and mechanical properties of anisometropic eyes (with and without amblyopia) with the aim of improving our current understanding of asymmetric refractive error development. In the first experiment, the interocular symmetry in 34 non-amblyopic myopic anisometropes (31 Asian, 3 Caucasian) was examined during relaxed accommodation. A high degree of symmetry was observed between the fellow eyes for a range of optical, biometric and biomechanical measurements. When the magnitude of anisometropia exceeded 1.75 D, the more myopic eye was almost always the sighting dominant eye. Further analysis of the optical and biometric properties of the dominant and non-dominant eyes was conducted to determine any related factors but no significant interocular differences were observed with respect to best-corrected visual acuity, corneal or total ocular aberrations during relaxed accommodation. Given the high degree of symmetry observed between the fellow eyes during distance viewing in the first experiment and the strong association previously reported between near work and myopia development, the aim of the second experiment was to investigate the symmetry between the fellow eyes of the same 34 myopic anisometropes following a period of near work. Symmetrical changes in corneal and total ocular aberrations were observed following a short reading task (10 minutes, 2.5 D accommodation demand) which was attributed to the high degree of interocular symmetry for measures of anterior eye morphology, and corneal biomechanics. These changes were related to eyelid shape and position during downward gaze, but gave no clear indication of factors associated with near work that might cause asymmetric eye growth within an individual. Since the influence of near work on eye growth is likely to be most obvious during, rather than following near tasks, in the third experiment the interocular symmetry of the optical and biometric changes was examined during accommodation for 11 myopic anisometropes. The changes in anterior eye biometrics associated with accommodation were again similar between the eyes, resulting in symmetrical changes in the optical characteristics. However, the more myopic eyes exhibited slightly greater amounts of axial elongation during accommodation which may be related to the force exerted by the ciliary muscle. This small asymmetry in axial elongation we observed between the eyes may be due to interocular differences in posterior eye structure, given that the accommodative response was equal between eyes. Using ocular coherence tomography a reduced average choroidal thickness was observed in the more myopic eyes compared to the less myopic eyes of these subjects. The interocular difference in choroidal thickness was correlated with the magnitude of spherical equivalent and axial anisometropia. The symmetry in optics and biometrics between fellow eyes which have undergone significantly different visual development (i.e. anisometropic subjects with amblyopia) is also of interest with respect to refractive error development. In the final experiment the influence of altered visual experience upon corneal and ocular higher-order aberrations was investigated in 21 amblyopic subjects (8 refractive, 11 strabismic and 2 form deprivation). Significant differences in aberrations were observed between the fellow eyes, which varied according to the type of amblyopia. Refractive amblyopes displayed significantly higher levels of 4th order corneal aberrations (spherical aberration and secondary astigmatism) in the amblyopic eye compared to the fellow non-amblyopic eye. Strabismic amblyopes exhibited significantly higher levels of trefoil, a third order aberration, in the amblyopic eye for both corneal and total ocular aberrations. The results of this experiment suggest that asymmetric visual experience during development is associated with asymmetries in higher-order aberrations, proportional to the magnitude of anisometropia and dependent upon the amblyogenic factor. This suggests a direct link between the development of higher-order optical characteristics of the human eye and visual feedback. The results from these experiments have shown that a high degree of symmetry exists between the fellow eyes of non-amblyopic myopic anisometropes for a range of biomechanical, biometric and optical parameters for different levels of accommodation and following near work. While a single specific optical or biomechanical factor that is consistently associated with asymmetric refractive error development has not been identified, the findings from these studies suggest that further research into the association between ocular dominance, choroidal thickness and higher-order aberrations with anisometropia may improve our understanding of refractive error development.

Single crystal raman spectroscopy of natural finnemanite and comparison with the synthesised analogue

The single crystal Raman spectra of natural mineral finnemanite Pb5(AsO3)3Cl from the Långban locality, Filipstad district, Värmland province, Sweden are presented for the first time. It is a hexagonal mineral belonging to the ortho arsenite group, where the [AsO3]3- ion is isolated. The spectra of finnemanite are characterized by a strong band at 734 cm-1 overlying a shoulder at 726 cm-1, and broad overlapping bands in the lower wavenumber with the strongest band positioned at 174 cm-1. Band assignments were made based on band symmetry, experimental band positions from literature and DFT calculated Raman spectrum, and spectral comparison with other ortho arsenite minerals reinerite, cafarsite, and nealite and synthetic lead arsenite compounds Pb2(AsO2)3Cl, Pb2As2O5, and PbAs2O4 . The band at 734 cm-1 was assigned to υ1(AsO3), bands at 726 and 640 cm-1 assigned to υ3, 372 and 357 cm-1 to υ2, and 244, 239 and 207 cm-1 to υ4. The single crystal spectra of finnemanite showed good mode separation, allowing bands to be assigned a symmetry species of Ag, E1g, or E2g.

Single crystal raman spectroscopy of natural paulmooreite Pb2As2O5 and in comparison with the synthesised analogue

The single crystal Raman spectra of natural mineral paulmooreite Pb2As2O5 from the Långban locality, Filipstad district, Värmland province, Sweden are presented for the first time. It is a monoclinic mineral containing an isolated [As2O5]4-. Depolarised and single crystal spectra of the natural and synthetic sample compare favorably and are characterized by strong bands around 186 and 140 cm-1 and three medium bands at 800 – 700 cm-1. Band assignments were made based on band symmetry and spectral comparison between experimental band positions and those resulting from Hartree-Fock calculation of an isolated [As2O5]4- ion. Spectral comparison was also made with lead arsenites such as synthetic PbAs2O4 and Pb2(AsO2)3Cl and natural finnemanite in order to determine the contribution of the terminal and bridging O in paulmooreite. Bands at 760 – 733 cm-1 were assigned to terminal As-O vibrations, whereas stretches of the bridging O occur at 562 and 503 cm-1. The single crystal spectra showed good mode separation, allowing bands to be assigned a symmetry species of Ag or Bg.

Determination of stress-strain characteristics of railhead steel using image analysis

True stress-strain curve of railhead steel is required to investigate the behaviour of railhead under wheel loading through elasto-plastic Finite Element (FE) analysis. To reduce the rate of wear, the railhead material is hardened through annealing and quenching. The Australian standard rail sections are not fully hardened and hence suffer from non-uniform distribution of the material property; usage of average properties in the FE modelling can potentially induce error in the predicted plastic strains. Coupons obtained at varying depths of the railhead were, therefore, tested under axial tension and the strains were measured using strain gauges as well as an image analysis technique, known as the Particle Image Velocimetry (PIV). The head hardened steel exhibit existence of three distinct zones of yield strength; the yield strength as the ratio of the average yield strength provided in the standard (σyr=780MPa) and the corresponding depth as the ratio of the head hardened zone along the axis of symmetry are as follows: (1.17 σyr, 20%), (1.06 σyr, 20%- 80%) and (0.71 σyr, > 80%). The stress-strain curves exhibit limited plastic zone with fracture occurring at strain less than 0.1.

Raman spectroscopy of the multianion mineral gartrellite-PbCu(Fe3+,Cu)(AsO4)2(OH,H2O)2

The multianion mineral gartrellite PbCu(Fe3+,Cu)(AsO4)2(OH,H2O)2 has been studied by a combination of Raman and infrared spectroscopy. The vibrational spectra of two gartrellite samples from Durango and Ashburton Downs were compared. Gartrellite is one of the tsumcorite mineral group based upon arsenate and sulphate anions. Crystal symmetry is either triclinic in the case of an ordered occupation of two cationic sites, triclinic due to ordering of the H bonds in the case of species with 2 water molecules per formula unit, or monoclinic in the other cases. Characteristic Raman spectra of the minerals enable the assignment of the bands to specific vibrational modes. These spectra are related to the structure of gartrellite. The position of the hydroxyl and water stretching vibrations are related to the strength of the hydrogen bond formed between the OH unit and the AsO4 anion.

A vibrational spectroscopic study of the phosphate mineral Wardite NaAl3(PO4)2(OH)4•2(H2O)

Three wardite mineral samples from different origins have been analysed by vibrational spectroscopy. The mineral is unusual in that it belongs to a unique symmetry class, namely the tetragonal-trapezohedral group. The structure of wardite contains layers of corner-linked –OH bridged MO6 octahedra stacked along the tetragonal C-axis in a four-layer sequence and linked by PO4 groups. Consequentially not all phosphate units are identical. Thus, two intense Raman bands observed at 995 and 1051 cm-1 are assigned to the ν1 PO43- symmetric stretching mode. Intense Raman bands are observed at 605 and 618 cm-1 with shoulders at 578 and 589 cm-1 are assigned to the ν4 out of plane bending modes of the PO43-. The observation of multiple bands supports the concept of non-equivalent phosphate units in the structure. Sharp infrared bands are observed at 3544 and 3611 cm-1 are attributed to the OH stretching vibrations of the hydroxyl units. Vibrational spectroscopy enables subtle details of the molecular structure of wardite to be determined.

Poly[[diaquabis[mu-2-(4-fluorophenoxy)acetato-k2O1:O1']magnesium] 0.4-hydrate]

In the structure of the title compound, [Mg(H2O)2(C8H6FO3)2]n(0.4H2O)n, slightly distorted octahedral MgO6 complex units have crystallographic inversion symmetry, the coordination polyhedron comprising two trans-related water molecules and four carboxyl O-atom donors, two of which are bridging. Within the two-dimensional complex polymer which is parallel to (100), the coordinating water molecules form intermolecular O---H...O hydrogen-bonds with carboxylate and phenoxy O-atom acceptors, as well as with the partial-occupancy solvent water molecules.

Quality based frame selection for video face recognition

Quality based frame selection is a crucial task in video face recognition, to both improve the recognition rate and to reduce the computational cost. In this paper we present a framework that uses a variety of cues (face symmetry, sharpness, contrast, closeness of mouth, brightness and openness of the eye) to select the highest quality facial images available in a video sequence for recognition. Normalized feature scores are fused using a neural network and frames with high quality scores are used in a Local Gabor Binary Pattern Histogram Sequence based face recognition system. Experiments on the Honda/UCSD database shows that the proposed method selects the best quality face images in the video sequence, resulting in improved recognition performance.

Corneal changes following near work in myopic anisometropia

PURPOSE: To examine the symmetry of corneal changes following near work in the fellow eyes of non-amblyopic myopic anisometropes. METHODS: Thirty-four non-amblyopic myopic anisometropes (minimum 1 D spherical equivalent anisometropia) were recruited. Corneal topography was measured with the Medmont E300 Videokeratoscope before and after a controlled near task. Subjects were positioned to minimise head movements and read continuous text on a computer monitor for 10 minutes at an angle of 25 degrees downward gaze and an accommodation demand of 2.5 D. Measures of palpebral aperture morphology during primary and downward gaze were also obtained using digital photography and analysed with customised software. RESULTS: Significant changes in corneal topography were observed after ten minutes of reading. Localised superior regions of corneal topographical change (a hyperopic shift in corneal power) were typically exhibited in both eyes following the near task. The mean change in the corneal sphero-cylinder was +0.02/-0.11 x 113 and +0.02/-0.06 x 68 for the more and less myopic eyes respectively for a 6 mm corneal diameter. A significantly greater change in corneal astigmatism power vector J0 (a larger increase in against the rule astigmatism) was observed in the more myopic eyes (p < 0.01 for a 6 mm diameter). The more and less myopic eyes exhibited a high degree of interocular symmetry for measures of palpebral aperture morphology during both primary and downward gaze. Changes in corneal power vectors following reading were associated with eyelid position during downward gaze. CONCLUSIONS: Changes in corneal topography observed following a controlled reading task were highly symmetrical between the fellow eyes of myopic anisometropes due to the interocular symmetry of the palpebral aperture. However, the more myopic eye did exhibit a small but significantly greater magnitude of change in corneal astigmatism compared to the less myopic eye following reading. These findings may have implications for understanding the mechanism of development of non-amblyopic myopic anisometropia.

Corneal changes following near work in myopic anisometropia

Purpose: To examine the symmetry of corneal changes following near work in the fellow eyes of non-amblyopic myopic anisometropes. Methods: Thirty-four non-amblyopic, myopic anisometropes (minimum 1 D spherical equivalent anisometropia) had corneal topography measured before and after a controlled near work task. Subjects were positioned in a headrest to minimise head movements and read continuous text on a computer monitor for 10 minutes at an angle of 25 degrees downward gaze and an accommodation demand of 2.5 D. Measures of the morphology of the palpebral aperture during primary and downward gaze were also obtained. Results: The more and less myopic eyes exhibited a high degree of interocular symmetry for measures of palpebral aperture morphology during both primary and downward gaze. Following the near work task, fellow eyes also displayed a symmetrical change in superior corneal topography (hyperopic defocus) which correlated with the position of the upper eyelid during downward gaze. Greater changes in the spherical corneal power vector (M) following reading were associated with narrower palpebral aperture during downward gaze (p = 0.07 for more myopic and p = 0.03 for less myopic eyes). A significantly greater change in J0 (an increase in against the rule astigmatism) was observed in the more myopic eyes (-0.04 ± 0.04 D) compared to the less myopic eyes (-0.02 ± 0.06 D) over a 6 mm corneal diameter (p = 0.01). Conclusions: Changes in corneal topography following near work are highly symmetrical between the fellow eyes of myopic anisometropes due to the interocular symmetry of the palpebral aperture. However, the more myopic eye exhibits changes in corneal astigmatism of greater magnitude compared to the less myopic eye.

A comparison of calculated and experimental HRTEM images of twinned boron carbide

High resolution TEM images of boron carbide (B13C2) have been recorded and compared with images calculated using the multislice method as implemented by M. A. O'Keefe in the SHRLI programs. Images calculated for the [010] zone, using machine parameters for the JEOL 2000FX AEM operating at 200 keV, indicate that for the structure model of Will et al., the optimum defocus image can be interpreted such that white spots correspond to B12 icosahedra for thin specimens and to low density channels through the structure adjacent to the direct inter-icosahedral bonds for specimens of intermediate thickness (-40 > t > -100 nm). With this information, and from the symmetry observed in the TEM images, it is likely that the (101) twin plane passes through the center of icosahedron located at the origin. This model was tested using the method of periodic continuation. Resulting images compare favorably with experimental images, thus supporting the structural model. The introduction of a (101) twin plane through the origin creates distortions to the icosahedral linkages as well as to the intra-icosahedral bonding. This increases the inequivalence of adjacent icosahedral sites along the twin plane, and thereby increases the likelihood of bipolaron hopping.