Dynamics of dense sheared granular flows. Part 1. Structure and diffusion

Shear flows of inelastic spheres in three dimensions in the Volume fraction range 0.4-0.64 are analysed using event-driven simulations.Particle interactions are considered to be due to instantaneous binary collisions, and the collision model has a normal coefficient of restitution e(n) (negative of the ratio of the post- and pre-collisional relative velocities of the particles along the line joining the centres) and a tangential coefficient of restitution e(t) (negative of the ratio of post- and pre-collisional velocities perpendicular to the line Joining the centres). Here, we have considered both e(t) = +1 and e(t) = e(n) (rough particles) and e(t) =-1 (smooth particles), and the normal coefficient of restitution e(n) was varied in the range 0.6-0.98. Care was taken to avoid inelastic collapse and ensure there are no particle overlaps during the simulation. First, we studied the ordering in the system by examining the icosahedral order parameter Q(6) in three dimensions and the planar order parameter q(6) in the plane perpendicular to the gradient direction. It was found that for shear flows of sufficiently large size, the system Continues to be in the random state, with Q(6) and q(6) close to 0, even for volume fractions between phi = 0.5 and phi = 0.6; in contrast, for a system of elastic particles in the absence of shear, the system orders (crystallizes) at phi = 0.49. This indicates that the shear flow prevents ordering in a system of sufficiently large size. In a shear flow of inelastic particles, the strain rate and the temperature are related through the energy balance equation, and all time scales can be non-dimensionalized by the inverse of the strain rate. Therefore, the dynamics of the system are determined only by the volume fraction and the coefficients of restitution. The variation of the collision frequency with volume fraction and coefficient of estitution was examined. It was found, by plotting the inverse of the collision frequency as a function of volume fraction, that the collision frequency at constant strain rate diverges at a volume fraction phi(ad) (volume fraction for arrested dynamics) which is lower than the random close-packing Volume fraction 0.64 in the absence of shear. The volume fraction phi(ad) decreases as the coefficient of restitution is decreased from e(n) = 1; phi(ad) has a minimum of about 0.585 for coefficient of restitution e(n) in the range 0.6-0.8 for rough particles and is slightly larger for smooth particles. It is found that the dissipation rate and all components of the stress diverge proportional to the collision frequency in the close-packing limit. The qualitative behaviour of the increase in the stress and dissipation rate are well Captured by results derived from kinetic theory, but the quantitative agreement is lacking even if the collision frequency obtained from simulations is used to calculate the pair correlation function used In the theory.

Dynamics of dense sheared granular flows. Part II. The relative velocity distributions

The distribution of relative velocities between colliding particles in shear flows of inelastic spheres is analysed in the Volume fraction range 0.4-0.64. Particle interactions are considered to be due to instantaneous binary collisions, and the collision model has a normal coefficient of restitution e(n) (negative of the ratio of the post- and pre-collisional relative velocities of the particles along the line joining the centres) and a tangential coefficient of restitution e(t) (negative of the ratio of post- and pre-collisional velocities perpendicular to line joining the centres). The distribution or pre-collisional normal relative velocities (along the line Joining the centres of the particles) is Found to be an exponential distribution for particles with low normal coefficient of restitution in the range 0.6-0.7. This is in contrast to the Gaussian distribution for the normal relative velocity in all elastic fluid in the absence of shear. A composite distribution function, which consists of an exponential and a Gaussian component, is proposed to span the range of inelasticities considered here. In the case of roughd particles, the relative velocity tangential to the surfaces at contact is also evaluated, and it is found to be close to a Gaussian distribution even for highly inelastic particles.Empirical relations are formulated for the relative velocity distribution. These are used to calculate the collisional contributions to the pressure, shear stress and the energy dissipation rate in a shear flow. The results of the calculation were round to be in quantitative agreement with simulation results, even for low coefficients of restitution for which the predictions obtained using the Enskog approximation are in error by an order of magnitude. The results are also applied to the flow down an inclined plane, to predict the angle of repose and the variation of the volume fraction with angle of inclination. These results are also found to be in quantitative agreement with previous simulations.

Adsopption isotherms-A critique

The possibility or the impossibility of separating the particle and the electrode interactions is discussed in a wider context of the effects due to any two interaction potentials on the equation of state. The involved nature of the pressure dependence on two individually definable forces is illustrated through the Percus Yevick results for the adhesive hard spheres. An alternative form of the adsorption isotherm is given to bring home the intimate relationship between the actual equation of state and the free energy of adsorption. Thermodynamic consequences of congruence with respect to E (or q) as reflected through the linear plots of q (or E) vs. θ are well known. Mathematical consequences of simultaneous congruence have been pointed out recently. In this paper, the physical nature of congruence hypothesis is revealed. In passing "the pseudo-congruence" is also discussed. It is emphasised that the problem is no less ambiguous with regard to modelling the particle/particle interaction. The ad hoc nature of our dependence of the available equations of state is emphasised through a discussion on the HFL theory. Finally, a heuristic method for modelling ΔG mathematically-incorporating its behaviour at saturation coverages-is advanced. The more interesting aspects of this approach, which generalises almost all isotherms hitherto known, are sketched.

Post-liquefaction undrained monotonic behaviour of sands: experiments and DEM simulations

This paper presents the results of a series of servo-controlled cyclic triaxial tests and numerical simulations using the three- dimensional discrete element method (DEM) on post-liquefaction undrained monotonic strength of granular materials. In a first test series,undrained monotonic tests were carried out after dissipating the excess pore water pressure developed during liquefaction. The influence of different parameters such as amplitude of axial strain,relative density and confining pressure prior to liquefaction on the post-liquefaction undrained response have been investigated.The results obtained highlight an insignificant influence of amplitude of axial strain, confining pressure and a significant influence of relative density on the post-liquefaction undrained monotonic stress-strain response.In the second series, undrained monotonic tests were carried out on similar triaxial samples without dissipating the excess pore water pressure developed during liquefaction. The results highlight that the amplitude of axial strain prior to liquefaction has a significant influence on the post-liquefaction undrained monotonic response.In addition,DEM simulations have been carried out on an assembly of spheres to simulate post-liquefaction behaviour.The simulations were very similar to the experiments with an objective to understand the behaviour of monotonic strength of liquefied samples from the grain scale. The numerical simulations using DEM have captured qualitatively all the features of the post-liquefaction undrained monotonic response in a manner similar to that of the experiments.In addition,a detailed study on the evolution of micromechanical parameters such as the average coordination number and induced anisotropic coefficients has been reported during the post-liquefaction undrained monotonic loading.

Phenotypic and Functional Characterization of Human Mammary Stem/Progenitor Cells in Long Term Culture

Background: Cancer stem cells exhibit close resemblance to normal stem cells in phenotype as well as function. Hence, studying normal stem cell behavior is important in understanding cancer pathogenesis. It has recently been shown that human breast stem cells can be enriched in suspension cultures as mammospheres. However, little is known about the behavior of these cells in long-term cultures. Since extensive self-renewal potential is the hallmark of stem cells, we undertook a detailed phenotypic and functional characterization of human mammospheres over long-term passages. Methodology: Single cell suspensions derived from human breast `organoids' were seeded in ultra low attachment plates in serum free media. Resulting primary mammospheres after a week (termed T1 mammospheres) were subjected to passaging every 7th day leading to the generation of T2, T3, and T4 mammospheres. Principal Findings: We show that primary mammospheres contain a distinct side-population (SP) that displays a CD24(low)/CD44(low) phenotype, but fails to generate mammospheres. Instead, the mammosphere-initiating potential rests within the CD44(high)/CD24(low) cells, in keeping with the phenotype of breast cancer-initiating cells. In serial sphere formation assays we find that even though primary (T1) mammospheres show telomerase activity and fourth passage T4 spheres contain label-retaining cells, they fail to initiate new mammospheres beyond T5. With increasing passages, mammospheres showed an increase in smaller sized spheres, reduction in proliferation potential and sphere forming efficiency, and increased differentiation towards the myoepithelial lineage. Significantly, staining for senescence-associated beta-galactosidase activity revealed a dramatic increase in the number of senescent cells with passage, which might in part explain the inability to continuously generate mammospheres in culture. Conclusions: Thus, the self-renewal potential of human breast stem cells is exhausted within five in vitro passages of mammospheres, suggesting the need for further improvisation in culture conditions for their long-term maintenance.

Modelling heterogeneity of concrete using 2D lattice network for concrete fracture and comparison with AE study

In this paper, numerical modelling of fracture in concrete using two-dimensional lattice model is presented and also a few issues related to lattice modelling technique applicable to concrete fracture are reviewed. A comparison is made with acoustic emission (AE) events with the number of fractured elements. To implement the heterogeneity of the plain concrete, two methods namely, by generating grain structure of the concrete using Fuller's distribution and the concrete material properties are randomly distributed following Gaussian distribution are used. In the first method, the modelling of the concrete at meso level is carried out following the existing methods available in literature. The shape of the aggregates present in the concrete are assumed as perfect spheres and shape of the same in two-dimensional lattice network is circular. A three-point bend (TPB) specimen is tested in the experiment under crack mouth opening displacement (CMOD) control at a rate of 0.0004 mm/sec and the fracture process in the same TPB specimen is modelled using regular triangular 2D lattice network. Load versus crack mouth opening isplacement (CMOD) plots thus obtained by using both the methods are compared with experimental results. It was observed that the number of fractured elements increases near the peak load and beyond the peak load. That is once the crack starts to propagate. AE hits also increase rapidly beyond the peak load. It is compulsory here to mention that although the lattice modelling of concrete fracture used in this present study is very similar to those already available in literature, the present work brings out certain finer details which are not available explicitly in the earlier works.

Processing of Mycobacterium tuberculosis bacilli by human monocytes for CD4+ alphabeta and gammadelta T cells: role of particulate antigen.

Mycobacterium tuberculosis readily activates both CD4+ and Vdelta2+ gammadelta T cells. Despite similarity in function, these T-cell subsets differ in the antigens they recognize and the manners in which these antigens are presented by M. tuberculosis-infected monocytes. We investigated mechanisms of antigen processing of M. tuberculosis antigens to human CD4 and gammadelta T cells by monocytes. Initial uptake of M. tuberculosis bacilli and subsequent processing were required for efficient presentation not only to CD4 T cells but also to Vdelta2+ gammadelta T cells. For gammadelta T cells, recognition of M. tuberculosis-infected monocytes was dependent on Vdelta2+ T-cell-receptor expression. Recognition of M. tuberculosis antigens by CD4+ T cells was restricted by the class II major histocompatibility complex molecule HLA-DR. Processing of M. tuberculosis bacilli for Vdelta2+ gammadelta T cells was inhibitable by Brefeldin A, whereas processing of soluble mycobacterial antigens for gammadelta T cells was not sensitive to Brefeldin A. Processing of M. tuberculosis bacilli for CD4+ T cells was unaffected by Brefeldin A. Lysosomotropic agents such as chloroquine and ammonium chloride did not affect the processing of M. tuberculosis bacilli for CD4+ and gammadelta T cells. In contrast, both inhibitors blocked processing of soluble mycobacterial antigens for CD4+ T cells. Chloroquine and ammonium chloride insensitivity of processing of M. tuberculosis bacilli was not dependent on the viability of the bacteria, since processing of both formaldehyde-fixed dead bacteria and mycobacterial antigens covalently coupled to latex beads was chloroquine insensitive. Thus, the manner in which mycobacterial antigens were taken up by monocytes (particulate versus soluble) influenced the antigen processing pathway for CD4+ and gammadelta T cells.

High lithium storage in micrometre sized mesoporous spherical self-assembly of anatase titania nanospheres and carbon

Composite of anatase titania (TiO2) nanospheres and carbon grown and self-assembled into micron-sized mesoporous spheres via a solvothermal synthesis route are discussed here in the context of rechargeable lithium-ion battery. The morphology and carbon content and hence the electrochemical performance are observed to be significantly influenced by the synthesis parameters. Synthesis conditions resulting in a mesoporous arrangement of an optimized amount carbon and TiO2 exhibited the best lithium battery performance. The first discharge cycle capacity of carbon-titania mesoporous spheres (solvothermal reaction at 150 degrees C at 6 h, calcination at 500 degrees C under air, BET surface area 80 m(2)g(-1)) was 334 mAhg(-1) (approximately 1 Li) at current rate of 0.066 Ag-1. High storage capacity and good cyclability is attributed to the nanostructuring of TiO2 (mesoporosity) as well as due to formation of a percolation network of carbon around the TiO2 nanoparticles. The micron-sized mesoporous spheres of carbon-titania composite nanoparticles also show good rate cyclability in the range (0.066-6.67) Ag-1.

Spherical means with centers on a hyperplane in even dimensions

Given a real-valued function on R-n we study the problem of recovering the function from its spherical means over spheres centered on a hyperplane. An old paper of Bukhgeim and Kardakov derived an inversion formula for the odd n case with great simplicity and economy. We apply their method to derive an inversion formula for the even n case. A feature of our inversion formula, for the even n case, is that it does not require the Fourier transform of the mean values or the use of the Hilbert transform, unlike the previously known inversion formulas for the even n case. Along the way, we extend the isometry identity of Bukhgeim and Kardakov for odd n, for solutions of the wave equation, to the even n case.

Uniqueness of Walkup's 9-vertex 3-dimensional Klein bottle

Via a computer search, Altshuler and Steinberg found that there are 1296+1 combinatorial 3-manifolds on nine vertices, of which only one is non-sphere. This exceptional 3-manifold View the MathML source triangulates the twisted S2-bundle over S1. It was first constructed by Walkup. In this paper, we present a computer-free proof of the uniqueness of this non-sphere combinatorial 3-manifold. As opposed to the computer-generated proof, ours does not require wading through all the 9-vertex 3-spheres. As a preliminary result, we also show that any 9-vertex combinatorial 3-manifold is equivalent by proper bistellar moves to a 9-vertex neighbourly 3-manifold.

Drag interaction effects in linear sphere-assemblies

Free-fall terminal velocities of single spheres and of single-row assemblies containing up to six spheres, with line of centres of spheres perpendicular to the direction of motion, have been determined in the particle Reynolds numbers range 0.2-4, and interaction effects obtained in the case of assemblies relative to drag on single isolated spheres, are discussed. The observed decrease in the drag on a sphere of an assembly is explained on the basis of theoretical considerations governing flow phenomena in such systems.

Slow rotation of a sphere in a non-Newtonian fluid with or without suction or injection

The flow generated by the rotation of a sphere in an infinitely extending fluid has recently been studied by Goldshtik. The corresponding problem for non-Newtonian Reiner-Rivlin fluids has been studied by Datta. Bhatnagar and Rajeswari have studied the secondary flow between two concentric spheres rotating about an axis in the non-Newtonian fluids. This last investigation was further generalised by Rajeswari to include the effects of small radial suction or injection. In Part A of the present investigation, we have studied the secondary flow generated by the slow rotation of a single sphere in non-Newtonian fluid obeying the Rivlin-Ericksen constitutive equation. In Part B, the effects of small suction or injection have been studied which is applied in an arbitrary direction at the surface of the sphere. In the absence of suction or injection, the secondary flow for small values of the visco-elastic parameter is similar to that of Newtonian fluids with inclusion of inertia terms in the Oseen approximation. If this parameter exceeds Kc = 18R/219, whereR is the Reynolds number, the breaking of the flow field takes place into two domains, in one of which the stream lines form closed loops. For still higher values of this parameter, the complete reversal of the sense of the flow takes place. When suction or injection is included, the breaking of the flow persists under certain condition investigated in this paper. When this condition is broken, the breaking of the flow is obliterated.

Effect of natural ventilation on the boundary layer separation and near-wake vortex shedding characteristics of a sphere

Experiments were conducted in water and wind tunnels on spheres in the Reynolds number range 6 x 10(3) to 6.5 x 10(5) to study the effect of natural ventilation on the boundary layer separation and near-wake Vortex shedding characteristics. In the subcritical range of Re (<2 x 10(5)), ventilation caused a marginal downstream shift in the location of laminar boundary layer separation; there was only a small change in the vortex shedding frequency. In the supercritical range (Re > 4 x 10(5)), ventilation caused a downstream shift in the mean locations of boundary layer separation and reattachment; these lines showed significant axisymmetry in the presence of venting. No distinct vortex shedding frequency was found. Instead, a dramatic reduction occurred in the wake unsteadiness at all frequencies. The reduction of wake unsteadiness is consistent with the reduction in total drag already reported. Based on the present results and those reported earlier, the effects of natural ventilation on the flow past a sphere can be categorized in two broad regimes, viz., weak and strong interaction regimes. In the weak interaction regime (subcritical Re), the broad features of the basic sphere are largely unaltered despite the large addition of mass in the near wake. Strong interaction is promoted by the closer proximity of the inner and outer shear layers at supercritical Re. This results in a modified and steady near-wake flow, characterized by reduced unsteadiness and small drag.

Transient Momentum and Enthalpy Transfer in Packed Beds at High Reynolds Numbers

An experimental study for transient temperature response and pressure drop in a randomly packed bed at high Reynolds numbers is presented.The packed bed is used as a compact heat exchanger along with a solid-propellant gas generator, to generate room-temperature gases for use in control actuation, air bottle pressurization, etc. Packed beds of lengths 200 and 300 mm were characterized for packing-sphere-based Reynolds numbers ranging from 0.8 x 10(4) to 8.5 x 10(4).The solid packing used in the bed consisted of phi 9.5 mm steel spheres. The bed-to-particle diameter ratio was with the average packed-bed porosity around 0.43. The inlet flow temperature was unsteady and a mesh of spheres was used at either end to eliminate flow entrance and exit effects. Gas temperature and pressure were measured at the entry, exit,and at three axial locations along centerline in the packed beds. The solid packing temperature was measured at three axial locations in the packed bed. A correlation based on the ratio of pressure drop and inlet-flow momentum (Euler number) exhibited an asymptotically decreasing trend with increasing Reynolds number. Axial conduction across the packed bed was found to he negligible in the investigated Reynolds number range. The enthalpy absorption rate to solid packing from hot gases is plotted as a function of a nondimensional time constant for different Reynolds numbers. A longer packed bed had high enthalpy absorption rate at Reynolds number similar to 10(4), which decreased at Reynolds number similar to 10(5). The enthalpy absorption plots can be used for estimating enthalpy drop across packed bed with different material, but for a geometrically similar packing.

Splittings of free groups, normal forms and partitions of ends

Splittings of a free group correspond to embedded spheres in the 3-manifold M = # (k) S (2) x S (1). These can be represented in a normal form due to Hatcher. In this paper, we determine the normal form in terms of crossings of partitions of ends corresponding to normal spheres, using a graph of trees representation for normal forms. In particular, we give a constructive proof of a criterion determining when a conjugacy class in pi (2)(M) can be represented by an embedded sphere.