A preconditioned Lanczos method for space-fractional reaction-diffusion equations on two-dimensional unstructured meshes

We consider a two-dimensional space-fractional reaction diffusion equation with a fractional Laplacian operator and homogeneous Neumann boundary conditions. The finite volume method is used with the matrix transfer technique of Ilić et al. (2006) to discretise in space, yielding a system of equations that requires the action of a matrix function to solve at each timestep. Rather than form this matrix function explicitly, we use Krylov subspace techniques to approximate the action of this matrix function. Specifically, we apply the Lanczos method, after a suitable transformation of the problem to recover symmetry. To improve the convergence of this method, we utilise a preconditioner that deflates the smallest eigenvalues from the spectrum. We demonstrate the efficiency of our approach for a fractional Fisher’s equation on the unit disk.

A vibrational spectroscopic study of philipsbornite PbAl3(AsO4)2(OH)5⋅H2O-molecular structural implications and relationship to the crandallite subgroup arsenates

The presence of arsenic in the environment is a hazard. The accumulation of arsenate by a range of cations in the formation of minerals provides a mechanism for the remediation of arsenate contamination. The formation of the crandallite group of minerals provides a mechanism for arsenate accumulation. Among the crandallite minerals are philipsbornite, arsenocrandallite and arsenogoyazite. Raman spectroscopy complimented with infrared spectroscopy has enabled aspects of the structure of philipsbornite to be studied. The Raman spectrum of philipsbornite displays an intense band at around 840 cm−1 attributed to the overlap of the symmetric and antisymmetric stretching modes. Raman bands observed at 325, 336, 347, 357, 376 and 399 cm−1 are assigned to the ν2 (AsO4)3− symmetric bending vibration (E) and to the ν4 bending vibration (F2). The observation of multiple bending modes supports the concept of a reduction in symmetry of the arsenate anion in philipsbornite. Evidence for phosphate in the mineral is provided. By using an empirical formula, hydrogen bond distances for the OH units in philipsbornite of 2.8648 Å, 2.7864 Å, 2.6896 Å cm−1 and 2.6220 were calculated.

A vibrational spectroscopic study of the phosphate mineral zanazziite - Ca2(MgFe2+)(MgFe2+Al)4Be4(PO4)6⋅6(H2O)

Zanazziite is the magnesium member of a complex beryllium calcium phosphate mineral group named roscherite. The studied samples were collected from the Ponte do Piauí mine, located in Itinga, Minas Gerais. The mineral was studied by electron microprobe, Raman and infrared spectroscopy. The chemical formula can be expressed as Ca2.00(Mg3.15,Fe0.78,Mn0.16,Zn0.01,Al0.26,Ca0.14)Be4.00(PO4)6.09(OH)4.00⋅5.69(H2O) and shows an intermediate member of the zanazziite–greinfeinstenite series, with predominance of zanazziite member. The molecular structure of the mineral zanazziite has been determined using a combination of Raman and infrared spectroscopy. A very intense Raman band at 970 cm−1 is assigned to the phosphate symmetric stretching mode whilst the Raman bands at 1007, 1047, 1064 and 1096 cm−1 are attributed to the phosphate antisymmetric stretching mode. The infrared spectrum is broad and the antisymmetric stretching bands are prominent. Raman bands at 559, 568, 589 cm−1 are assigned to the ν4 out of plane bending modes of the PO4 and HPO4 units. The observation of multiple bands supports the concept that the symmetry of the phosphate unit in the zanazziite structure is reduced in symmetry. Raman bands at 3437 and 3447 cm−1 are attributed to the OH stretching vibrations; Raman bands at 3098 and 3256 are attributed to water stretching vibrations. The width and complexity of the infrared spectral profile in contrast to the well resolved Raman spectra, proves that the pegmatitic phosphates are better studied with Raman spectroscopy.

Multipurpose identity-based signcryption : a Swiss army knife for identity-based cryptography

Identity-Based (IB) cryptography is a rapidly emerging approach to public-key cryptography that does not require principals to pre-compute key pairs and obtain certificates for their public keys— instead, public keys can be arbitrary identifiers such as email addresses, while private keys are derived at any time by a trusted private key generator upon request by the designated principals. Despite the flurry of recent results on IB encryption and signature, some questions regarding the security and efficiency of practicing IB encryption (IBE) and signature (IBS) as a joint IB signature/encryption (IBSE) scheme with a common set of parameters and keys, remain unanswered. We first propose a stringent security model for IBSE schemes. We require the usual strong security properties of: (for confidentiality) indistinguishability against adaptive chosen-ciphertext attacks, and (for nonrepudiation) existential unforgeability against chosen-message insider attacks. In addition, to ensure as strong as possible ciphertext armoring, we also ask (for anonymity) that authorship not be transmitted in the clear, and (for unlinkability) that it remain unverifiable by anyone except (for authentication) by the legitimate recipient alone. We then present an efficient IBSE construction, based on bilinear pairings, that satisfies all these security requirements, and yet is as compact as pairing-based IBE and IBS in isolation. Our scheme is secure, compact, fast and practical, offers detachable signatures, and supports multirecipient encryption with signature sharing for maximum scalability.

SEM-EDX, Raman and infrared spectroscopic characterization of the phosphate mineral frondelite (Mn2+)(Fe3+)4(PO4)3(OH)5

We have analyzed a frondelite mineral sample from the Cigana mine, located in the municipality of Conselheiro Pena, a well-known pegmatite in Brazil. In the Cigana pegmatite, secondary phosphates, namely eosphorite, fairfieldite, fluorapatite, frondelite, gormanite, hureaulite, lithiophilite, reddingite and vivianite are common minerals in miarolitic cavities and in massive blocks after triphylite. The chemical formula was determined as (Mn0.68, Fe0.32)(Fe3+)3,72(PO4)3.17(OH)4.99. The structure of the mineral was assessed using vibrational spectroscopy. Bands attributed to the stretching and bending modes of PO4 3- and HOPO3 3- units were identified. The observation of multiple bands supports the concept of symmetry reduction of the phosphate anion in the frondelite structure. Sharp Raman and infrared bands at 3581 cm−1 is assigned to the OH stretching vibration. Broad Raman bands at 3063, 3529 and 3365 cm−1 are attributed to water stretching vibrational modes.

Infrared and Raman spectroscopic characterisation of the sulphate mineral creedite – Ca3Al2SO4(F,OH)·2H2O – and in comparison with the alums

The mineral creedite is a fluorinated hydroxy hydrated sulphate of aluminium and calcium of formula Ca3Al2SO4(F,OH)·2H2O. The mineral has been studied by a combination of electron probe analysis to determine the molecular formula of the mineral and the structure assessed by vibrational spectroscopy. The spectroscopy of creedite may be compared with that of the alums. The Raman spectrum of creedite is characterised by an intense sharp band at 986 cm−1 assigned to the View the MathML source ν1 (Ag) symmetric stretching mode. Multiple bands of creedite in the antisymmetric stretching region support the concept of a reduction in symmetry of the sulphate anion. Multiple bands are also observed in the bending region with the three bands at 601, 629 and 663 cm−1 assigned to the View the MathML source ν4 (Ag) bending modes. The observation of multiple bands at 440, 457 and 483 cm−1 attributed to the View the MathML source ν2 (Bg) bending modes supports the concept that the symmetry of the sulphate is reduced by coordination to the water bonded to the Al3+ in the creedite structure. The splitting of the ν2, ν3 and ν4 modes is attributed to the reduction of symmetry of the SO4 and it is proposed that the sulphate coordinates to water in the hydrated aluminium in bidentate chelation.

Conserved and variable features of gag structure and arrangement in immature retrovirus particles

The assembly of retroviruses is driven by oligomerization of the Gag polyprotein. We have used cryo-electron tomography together with subtomogram averaging to describe the three-dimensional structure of in vitro-assembled Gag particles from human immunodeficiency virus, Mason-Pfizer monkey virus, and Rous sarcoma virus. These represent three different retroviral genera: the lentiviruses, betaretroviruses and alpharetroviruses. Comparison of the three structures reveals the features of the supramolecular organization of Gag that are conserved between genera and therefore reflect general principles of Gag-Gag interactions and the features that are specific to certain genera. All three Gag proteins assemble to form approximately spherical hexameric lattices with irregular defects. In all three genera, the N-terminal domain of CA is arranged in hexameric rings around large holes. Where the rings meet, 2-fold densities, assigned to the C-terminal domain of CA, extend between adjacent rings, and link together at the 6-fold symmetry axis with a density, which extends toward the center of the particle into the nucleic acid layer. Although this general arrangement is conserved, differences can be seen throughout the CA and spacer peptide regions. These differences can be related to sequence differences among the genera. We conclude that the arrangement of the structural domains of CA is well conserved across genera, whereas the relationship between CA, the spacer peptide region, and the nucleic acid is more specific to each genus.

Comparison between analytical and 3D finite element solutions for borehole stresses in anisotropic elastic rock

We present a rigorous validation of the analytical Amadei solution for the stress concentration around an arbitrarily orientated borehole in general anisotropic elastic media. First, we revisit the theoretical framework of the Amadei solution and present analytical insights that show that the solution does indeed contain all special cases of symmetry, contrary to previous understanding, provided that the reduced strain coefficients b11 and b55 are not equal. It is shown from theoretical considerations and published experimental data that the b11 and b55 are not equal for realistic rocks. Second, we develop a 3D finite element elastic model within a hybrid analytical–numerical workflow that circumvents the need to rebuild and remesh the model for every borehole and material orientation. Third, we show that the borehole stresses computed from the numerical model and the analytical solution match almost perfectly for different borehole orientations (vertical, deviated and horizontal) and for several cases involving isotropic, transverse isotropic and orthorhombic symmetries. It is concluded that the analytical Amadei solution is valid with no restriction on the borehole orientation or the symmetry of the elastic anisotropy.

2-[(3,3-Dimethylindolin-2-ylidene)methyl]-4-[(3,3-dimethyl-3H-indol-1-ium-2-yl)methylidene]-3-oxocyclobut-1-en-1-olate chloroform disolvate

In the title squaraine dye solvate, C26H24N2O2·2CHCl3, the dye molecule is essentially planar, except for the methyl groups, having a maximum deviation over the 26-membered delocalized bond system of 0.060 (2) Å. It possesses crystallographic twofold rotational symmetry with the indole ring systems adopting a syn conformation. The molecular structure features intramolecular N-HO hydrogen bonds enclosing conjoint S7 ring motifs about one of the dioxocyclobutene O atoms, while the two chloroform solvent molecules are linked to the second O atom through C-HO hydrogen bonds.

Do RNA viruses require genome cyclisation for replication?

Complementary sequences at the 5′ and 3′ ends of the dengue virus RNA genome are essential for viral replication, and are believed to cyclise the genome through long-range base pairing in cis. Although consistent with evidence in the literature, this view neglects possible biologically active multimeric forms that are equally consistent with the data. Here, we propose alternative multimeric structures, and suggest that multigenome noncovalent concatemers are more likely to exist under cellular conditions than single cyclised monomers. Concatemers provide a plausible mechanism for the dengue virus to overcome the single-stranded (+)-sense RNA virus dilemma, and can potentially assist genome transport from the virus-induced vesicles into the cytosol.

Raman spectroscopic study of the mineral qingheiite Na2(Mn2+,Mg,Fe2+)2(Al,Fe3+)(PO4)3, a pegmatite phosphate mineral from Santa Ana pegmatite, Argentina

The pegmatite mineral qingheiite Na2(Mn2+,Mg,Fe2+)2(Al,Fe3+)(PO4)3 has been studied by a combination of SEM and EMP, Raman and infrared spectroscopy. The studied sample was collected from the Santa Ana pegmatite, Argentina. The mineral occurs as a primary mineral in lithium bearing pegmatite, in association with beausite and lithiophilite. The Raman spectrum is characterized by a very sharp intense Raman band at 980 cm�1 assigned to the PO3�4 symmetric stretching mode. Multiple Raman bands are observed in the PO3�4 antisymmetric stretching region, providing evidence for the existence of more than one phosphate unit in the structure of qingheiite and evidence for the reduction in symmetry of the phosphate units. This concept is affirmed by the number of bands in the m4 and m2 bending regions. No intensity was observed in the OH stretching region in the Raman spectrum but significant intensity is found in the infrared spectrum. Infrared bands are observed at 2917, 3195, 3414 and 3498 cm�1 are assigned to water stretching vibrations. It is suggested that some water is coordinating the metal cations in the structure of qingheiite.

The molecular structure of the phosphate mineral senegalite Al2(PO4)(OH)3⋅3H2O – A vibrational spectroscopic study

We have studied the mineral senagalite, a hydrated hydroxy phosphate of aluminium with formula Al2(PO4)(OH)3⋅3H2O using a combination of electron microscopy and vibrational spectroscopy. Senegalite crystal aggregates shows tabular to prismatic habitus and orthorhombic form. The Raman spectrum is dominated by an intense band at 1029 cm−1 assigned to the PO43- ν1 symmetric stretching mode. Intense Raman bands are found at 1071 and 1154 cm−1 with bands of lesser intensity at 1110, 1179 and 1206 cm−1 and are attributed to the PO43- ν3 antisymmetric stretching vibrations. The infrared spectrum shows complexity with a series overlapping bands. A comparison is made with spectra of other aluminium containing phosphate minerals such as augelite and turquoise. Multiple bands are observed for the phosphate bending modes giving support for the reduction of symmetry of the phosphate anion. Vibrational spectroscopy offers a means for the assessment of the structure of senagalite.

Fast formulas for computing cryptographic pairings

The most powerful known primitive in public-key cryptography is undoubtedly elliptic curve pairings. Upon their introduction just over ten years ago the computation of pairings was far too slow for them to be considered a practical option. This resulted in a vast amount of research from many mathematicians and computer scientists around the globe aiming to improve this computation speed. From the use of modern results in algebraic and arithmetic geometry to the application of foundational number theory that dates back to the days of Gauss and Euler, cryptographic pairings have since experienced a great deal of improvement. As a result, what was an extremely expensive computation that took several minutes is now a high-speed operation that takes less than a millisecond. This thesis presents a range of optimisations to the state-of-the-art in cryptographic pairing computation. Both through extending prior techniques, and introducing several novel ideas of our own, our work has contributed to recordbreaking pairing implementations.

Vibrational spectroscopic characterization of the phosphate mineral kulanite Ba(Fe2+,Mn2+,Mg)2(Al,Fe3+)2(PO4)3(OH)3

The mineral kulanite BaFe2Al2(PO4)3(OH)3, a barium iron aluminum phosphate, has been studied by using a combination of electron microscopy and vibrational spectroscopy. Scanning electron microscopy with EDX shows the mineral is homogenous with no other phases present. The Raman spectrum is dominated by an intense band at 1022 cm−1 assigned to the PO43-ν1 symmetric stretching mode. Low intensity Raman bands at 1076, 1110, 1146, 1182 cm−1 are attributed to the PO43-ν3 antisymmetric stretching vibrations. The infrared spectrum shows a complex spectral profile with overlapping bands. Multiple phosphate bending vibrations supports the concept of a reduction in symmetry of the phosphate anion. Raman spectrum at 3211, 3513 and 3533 cm−1 are assigned to the stretching vibrations of the OH units. Vibrational spectroscopy enables aspects on the molecular structure of kulanite to be assessed.

Molecular dynamics simulation of structural characteristics in metal cluster deposition on surfaces

The deposition of small metal clusters (Cu, Au and Al) on f.c.c. metals (Cu, Au and Ni) has been studied by molecular dynamics simulation using Finnis–Sinclair (FS) potential. The impact energy varied from 0.01 to 10 eV/atom. First, the deposition of single cluster was simulated. We observed that, even at much lower energy, a small cluster with (Ih) icosahedral symmetry was reconstructed to match the substrate structure (f.c.c.) after deposition. Next, clusters were modeled to drop, one after the other, on the surface. The nanostructure was found by soft landing of Au clusters on Cu with increasing coverage, where interfacial energy dominates. While at relatively higher deposition energy (a few eV), the ordered f.c.c.-like structure was observed in the first adlayer of the film formed by Al clusters depositing on Ni substrate. This characteristic is mainly attributive to the ballistic collision. Our results indicate that the surface morphology synthesized by cluster deposition could be controlled by experimental parameters, which will be helpful for controlled design of nanostructure.