New stress and velocity fields for highly frictional granular materials

The idealised theory for the quasi-static flow of granular materials which satisfy the Coulomb-Mohr hypothesis is considered. This theory arises in the limit that the angle of internal friction approaches $\pi/2$, and accordingly these materials may be referred to as being `highly frictional'. In this limit, the stress field for both two-dimensional and axially symmetric flows may be formulated in terms of a single nonlinear second order partial differential equation for the stress angle. To obtain an accompanying velocity field, a flow rule must be employed. Assuming the non-dilatant double-shearing flow rule, a further partial differential equation may be derived in each case, this time for the streamfunction. Using Lie symmetry methods, a complete set of group-invariant solutions is derived for both systems, and through this process new exact solutions are constructed. Only a limited number of exact solutions for gravity driven granular flows are known, so these results are potentially important in many practical applications. The problem of mass flow through a two-dimensional wedge hopper is examined as an illustration.

Free surface problems for static Coulomb-Mohr granular solids

This paper is concerned with some plane strain and axially symmetric free surface problems which arise in the study of static granular solids that satisfy the Coulomb-Mohr yield condition. Such problems are inherently nonlinear, and hence difficult to attack analytically. Given a Coulomb friction condition holds on a solid boundary, it is shown that the angle a free surface is allowed to attach to the boundary is dependent only on the angle of wall friction, assuming the stresses are all continuous at the attachment point, and assuming also that the coefficient of cohesion is nonzero. As a model problem, the formation of stable cohesive arches in hoppers is considered. This undesirable phenomena is an obstacle to flow, and occurs when the hopper outlet is too small. Typically, engineers are concerned with predicting the critical outlet size for a given hopper and granular solid, so that for hoppers with outlets larger than this critical value, arching cannot occur. This is a topic of considerable practical interest, with most accepted engineering methods being conservative in nature. Here, the governing equations in two limiting cases (small cohesion and high angle of internal friction) are considered directly. No information on the critical outlet size is found; however solutions for the shape of the free boundary (the arch) are presented, for both plane and axially symmetric geometries.

Perturbation solutions for flow through symmetrical hoppers with inserts and asymmetrical wedge hoppers

Under certain circumstances, an industrial hopper which operates under the "funnel-flow" regime can be converted to the "mass-flow" regime with the addition of a flow-corrective insert. This paper is concerned with calculating granular flow patterns near the outlet of hoppers that incorporate a particular type of insert, the cone-in-cone insert. The flow is considered to be quasi-static, and governed by the Coulomb-Mohr yield condition together with the non-dilatant double-shearing theory. In two dimensions, the hoppers are wedge-shaped, and as such the formulation for the wedge-in-wedge hopper also includes the case of asymmetrical hoppers. A perturbation approach, valid for high angles of internal friction, is used for both two-dimensional and axially symmetric flows, with analytic results possible for both leading order and correction terms. This perturbation scheme is compared with numerical solutions to the governing equations, and is shown to work very well for angles of internal friction in excess of 45 degree.

A Raman spectroscopic study of the antimony mineral klebelsbergite Sb4O4(OH)2(SO4)

Many minerals based upon antimonite and antimonate anions remain to be studied. Most of the bands occur in the low wavenumber region, making infrared spectroscopy difficult to use. This problem can be overcome by using Raman spectroscopy. Raman spectra of the mineral klebelsbergite Sb4O4(OH)2(SO4) were studied, and related to the structure of the mineral. Raman bands observed at 971 cm-1 and a series of overlapping bands are observed at 1029, 1074, 1089, 1139 and 1142 cm-1 are assigned to the SO42- ν1 symmetric and ν3 antisymmetric stretching modes. Two Raman bands are observed at 662 and 723 cm-1 and assigned to the SbO ν3 antisymmetric and ν1 symmetric stretching modes. The intense Raman bands at 581, 604 and 611 cm-1 are assigned to the ν4 SO42- bending modes. Two overlapping bands at 481 and 489 cm-1 are assigned to the ν2 SO42- bending mode. Low intensity bands at 410, 435 and 446 cm-1 may be attributed to OSbO bending modes. The Raman band at 3435 cm-1 is attributed to the OH stretching vibration of the OH units. Multiple Raman bands for both SO42- and SbO stretching vibrations support the concept of the non-equivalence of these units in the klebelsbergite structure. It is proposed that two sulphate anions are distorted to different extents in the klebelsbergite structure.

Infrared and infrared emission spectroscopy of nesquehonite Mg(OH)(HCO3)•2H2O : implications for the formula of nesquehonite

The mineral nesquehonite Mg(OH)(HCO3)•2H2O has been analysed by a combination of infrared (IR) and infrared emission spectroscopy (IES). Both techniques show OH vibrations, both stretching and deformation modes. IES proves the OH units are stable up to 450°C. The strong IR band at 934 cm-1 is evidence for MgOH deformation modes supporting the concept of HCO3- units in the molecular structure. Infrared bands at 1027, 1052 and 1098 cm-1 are attributed to the symmetric stretching modes of HCO3- and CO32- units. Infrared bands at 1419, 1439, 1511, and 1528 cm-1 are assigned to the antisymmetric stretching modes of CO32- and HCO3- units. IES supported by thermoanalytical results defines the thermal stability of nesquehonite IES defines the changes in the molecular structure of nesquehonite with temperature. The results of IR and IES supports the concept that the formula of nesquehonite is better defined as Mg(OH)(HCO3)•2H2O.

A Raman and infrared spectroscopic study of the mineral delvauxite CaFe3+4(PO4,SO4)2(OH)8•4-6H2O- a ‘colloidal’ mineral

The mineral delvauxite CaFe3+4(PO4,SO4)2(OH)8•4-6H2O has been characterised by Raman spectroscopy and infrared spectroscopy. The mineral is associated with the minerals diadochite and destinezite. Delvauxite appears to vary in crystallinity from amorphous to semi-crystalline. The mineral is often X-ray non-diffracting. The minerals are found in soils and may be described as ‘colloidal’ minerals. Vibrational spectroscopy enables determination of the molecular structure of delvauxite. Bands are assigned to phosphate and sulphate stretching and bending modes. Two symmetric stretching modes for both the phosphate and sulphate symmetric stretching modes support the concept of non-equivalent phosphate and sulphate units in the mineral structure. Multiple water bending and stretching modes imply that non-equivalent water molecules in the structure exist with different hydrogen bond strengths.

Sequential nonlinear manifold learning

The computation of compact and meaningful representations of high dimensional sensor data has recently been addressed through the development of Nonlinear Dimensional Reduction (NLDR) algorithms. The numerical implementation of spectral NLDR techniques typically leads to a symmetric eigenvalue problem that is solved by traditional batch eigensolution algorithms. The application of such algorithms in real-time systems necessitates the development of sequential algorithms that perform feature extraction online. This paper presents an efficient online NLDR scheme, Sequential-Isomap, based on incremental singular value decomposition (SVD) and the Isomap method. Example simulations demonstrate the validity and significant potential of this technique in real-time applications such as autonomous systems.

Raman spectroscopy of selected borate minerals of the pinakiolite group

The Raman spectra of a series of related minerals of the pinakiolite group of minerals have been collected and the spectra related to the mineral structure. These minerals are based upon an isolated BO33- ion. The site symmetry is reduced from D3h to C1. Intense Raman bands are observed for the minerals takeuchiite, pinakiolite, fredrikssonite and azoproite at 1084, 1086, 1086 and 1086 cm-1. These bands are assigned to the ν1 BO33- symmetric stretching mode. Low intensity Raman bands are observed for the minerals at 1345, 1748; 1435, 1748; 1435, 1750; 1436, 1749 cm-1. One probable assignment is to ν3 BO33- antisymmetric stretching mode. Intense Raman bands of takeuchiite, pinakiolite, fredrikssonite and azoproite at 712 cm-1 attributed to the ν2 out-of-plane bending mode. Importantly, through the comparison of the Raman spectra, the molecular structure of borate minerals with ill-defined structures can be obtained.

Overview of mesenchymal stem cells

Stem cells are unprogrammed cells which possess plasticity and self renewal capability. The term of stem cell was first used to describe cells committed to give rise to germline cells, and to describe proposed progenitor cells of the blood system [1]. A unique feature of stem cell is to remain quiescent in vivo in an uncommitted state. They serve as reservoir or natural support system to replenish cells lost due to disease, injury or aging. When triggered by appropriate signals these cells divide and may become specialized, committed cells; however being able to control this differentiation process still remains one of the biggest challenge in stem cell research [2]. The cell division of stem cells is a distinct aspect of their biology, since this division may be either symmetric or asymmetric. Symmetric division takes place when the stem cells divides and forms two new daughter cells. Asymmetric division is thought to take place only under certain conditions where stem cells divides and gives rise to a daughter cell which remains primitive and does not proliferate, and one committed progenitor cell, which heads down a path of differentiation. Asymmetric division of stem cells helps reparative process, and also ensures that the stem cells pool does not decrease, whereas symmetric division is responsible for stem cells undergoing self renewal and proliferation. The factors which prompt the stem cells to undergo asymmetric division are, however, not well understood, but it is clear that the delicate balance between the self renewal and differentiation is what maintains tissue homeostasis.

A Raman spectroscopic study of M2+M3+ sulfate minerals, römerite Fe2+Fe23+ (SO4)4· 14H2O and botryogen Mg2+Fe3+ (SO4)2(OH)·7H2O

The mixed valency (M2+M3+) sulphate minerals, römerite Fe2+Fe23+(SO4)4•14H2O and botryogen Mg2+Fe3+(SO4)2(OH).7H2O have been studied by Raman spectroscopy. The Raman spectra of the two types of crystals proved very similar but not identical. The observation of two symmetric stretching modes confirmed the presence of the two non-equivalent sulphate units in the römerite structure. The observation of multiple bands in the antisymmetric stretching region and in the bending regions proves the symmetry of the sulphate anion is significantly reduced in the römerite structure. The number of Raman bands related to the (SO4)2- symmetric and antisymmetric vibrations support the X-ray single crystal structure conclusion that two symmetrically distinct S6+ are present in the structure of botryogen. Römerite is a mineral of environmental significance as it is commonly found in tailings and dumps.

Modulation of depth-dependent properties in tissue-engineered cartilage with a semi-permeable membrane and perfusion : a continuum model of matrix metabolism and transport

The functional properties of cartilaginous tissues are determined predominantly by the content, distribution, and organization of proteoglycan and collagen in the extracellular matrix. Extracellular matrix accumulates in tissue-engineered cartilage constructs by metabolism and transport of matrix molecules, processes that are modulated by physical and chemical factors. Constructs incubated under free-swelling conditions with freely permeable or highly permeable membranes exhibit symmetric surface regions of soft tissue. The variation in tissue properties with depth from the surfaces suggests the hypothesis that the transport processes mediated by the boundary conditions govern the distribution of proteoglycan in such constructs. A continuum model (DiMicco and Sah in Transport Porus Med 50:57-73, 2003) was extended to test the effects of membrane permeability and perfusion on proteoglycan accumulation in tissue-engineered cartilage. The concentrations of soluble, bound, and degraded proteoglycan were analyzed as functions of time, space, and non-dimensional parameters for several experimental configurations. The results of the model suggest that the boundary condition at the membrane surface and the rate of perfusion, described by non-dimensional parameters, are important determinants of the pattern of proteoglycan accumulation. With perfusion, the proteoglycan profile is skewed, and decreases or increases in magnitude depending on the level of flow-based stimulation. Utilization of a semi-permeable membrane with or without unidirectional flow may lead to tissues with depth-increasing proteoglycan content, resembling native articular cartilage.

Single crystal Raman spectroscopy of brandholzite Mg[Sb(OH)6]2•6H2O and bottinoite Ni[Sb(OH)6]2•6H2O and the polycrystalline Raman spectrum of mopungite Na[Sb(OH)6]

The single crystal Raman spectra of minerals brandholzite and bottinoite, formula M[Sb(OH)6]2•6H2O, where M is Mg+2 and Ni+2 respectively, and the non-aligned Raman spectrum of mopungite, formula Na[Sb(OH)6], are presented for the first time. The mixed metal minerals comprise of alternating layers of [Sb(OH)6]-1 octahedra and mixed [M(H2O)6]+2 / [Sb(OH)6]-1 octahedra. Mopungite comprises hydrogen bonded layers of [Sb(OH)6]-1 octahedra linked within the layer by Na+ ions. The spectra of the three minerals were dominated by the Sb-O symmetric stretch of the [Sb(OH)6]-1 octahedron, which occurs at approximately 620 cm-1. The Raman spectrum of mopungite showed many similarities to spectra of the di-octahedral minerals informing the view that the Sb octahedra gave rise to most of the Raman bands observed, particularly below 1200 cm-1. Assignments have been proposed based on the spectral comparison between the minerals, prior literature and density field theory calculations of the vibrational spectra of the free [Sb(OH)6]-1 and [M(H2O)6]+2 octahedra by a model chemistry of B3LYP/6-31G(d) and lanl2dz for the Sb atom. The single crystal data spectra showed good mode separation, allowing the majority of the bands to be assigned a symmetry species of A or E.

Raman spectroscopy of newberyite Mg(PO3OH)•3H2O – a cave mineral

Newberyite Mg(PO3OH)•3H2O is a mineral found in caves such as from Moorba cave, Jurien Bay, Western Australia, the Skipton Lava tubes (SW of Ballarat, Victoria, Australia) and in the Petrogale Cave (Madura , Eucla, Western Australia). Because these minerals contain oxyanions, hydroxyl units and water, the minerals lend themselves to spectroscopic analysis. Raman spectroscopy can investigate the complex paragenetic relationships existing between a number of ‘cave’ minerals. The intense sharp band at 982 cm-1 is assigned to the PO43- ν1 symmetric stretching mode. Low intensity Raman bands at 1152, 1263 and 1277 cm-1 are assigned to the PO43- ν3 antisymmetric stretching vibrations. Raman bands at 497 and 552 cm-1 are attributed to the PO43- ν4 bending modes. An intense Raman band for newberyite at 398 cm-1 with a shoulder band at 413 cm-1 is assigned to the PO43- ν2 bending modes. The values for the OH stretching vibrations provide hydrogen bond distances of 2.728Å (3267 cm-1), 2.781Å (3374cm-1), 2.868Å (3479 cm-1), and 2.918Å (3515 cm-1). Such hydrogen bond distances are typical of secondary minerals. Estimates of the hydrogen-bond distances have been made from the position of the OH stretching vibrations and show a wide range in both strong and weak bonds.

A vibrational spectroscopic study of the mixed anion mineral sanjuanite Al2(PO4)(SO4)(OH)•9H2O

The mineral sanjuanite Al2(PO4)(SO4)(OH)•9H2O has been characterised by Raman spectroscopy complimented by infrared spectroscopy. The mineral is characterised by an intense Raman band at 984 cm-1, assigned to the (PO4)3- ν1 symmetric stretching mode. A shoulder band at 1037 cm-1 is attributed to the (SO4)2- ν1 symmetric stretching mode. Two Raman bands observed at 1102 and 1148 cm-1 are assigned to (PO4)3- and (SO4)2- ν3 antisymmetric stretching modes. Multiple bands provide evidence for the reduction in symmetry of both anions. This concept is supported by the multiple sulphate and phosphate bending modes. Raman spectroscopy shows that there are more than one non-equivalent water molecules in the sanjuanite structure. There is evidence that structural disorder exists, shown by the complex set of overlapping bands in the Raman and infrared spectra. At least two types of water are identified with different hydrogen bond strengths. The involvement of water in the sanjuanite structure is essential for the mineral stability.

Raman spectroscopic study of the minerals diadochite and destinezite Fe3+2(PO4,SO4)2(OH)•6H2O – implications for soil science

The two minerals diadochite and destinezite of formula Fe2(PO4,SO4)2(OH)•6H2O have been characterised by Raman spectroscopy and complimented with infrared spectroscopy. These two minerals are both found in soils and are identical except for their morphology. Diadochite is amorphous whereas destinezite is highly crystalline. The spectra of diadochite are broad and ill-defined, whereas the spectra of destinezite are intense and well defined. Bands are assigned to phosphate and sulphate stretching and bending modes. Two symmetric stretching modes for both the phosphate and sulphate symmetric stretching modes support the concept of non-equivalent phosphate and sulphate units in the mineral structure. Multiple water bending and stretching modes imply that non-equivalent water molecules in the structure exist with different hydrogen bond strengths.