Surfaces of Bounded Mean Curvature In Riemannian Manifolds

Consider a sequence of closed, orientable surfaces of fixed genus g in a Riemannian manifold M with uniform upper bounds on the norm of mean curvature and area. We show that on passing to a subsequence, we can choose parametrisations of the surfaces by inclusion maps from a fixed surface of the same genus so that the distance functions corresponding to the pullback metrics converge to a pseudo-metric and the inclusion maps converge to a Lipschitz map. We show further that the limiting pseudo-metric has fractal dimension two. As a corollary, we obtain a purely geometric result. Namely, we show that bounds on the mean curvature, area and genus of a surface F subset of M, together with bounds on the geometry of M, give an upper bound on the diameter of F. Our proof is modelled on Gromov's compactness theorem for J-holomorphic curves.

Turbulence measurements in an ‘equilibrium’ axisymmetric wall jet Journal

This paper reports measurements of turbulent quantities in an axisymmetric wall jet subjected to an adverse pressure gradient in a conical diffuser, in such a way that a suitably defined pressure-gradient parameter is everywhere small. Self-similarity is observed in the mean velocity profile, as well as the profiles of many turbulent quantities at sufficiently large distances from the injection slot. Autocorrelation measurements indicate that, in the region of turbulent production, the time scale of ν fluctuations is very much smaller than the time scale of u fluctuations. Based on the data on these time scales, a possible model is proposed for the Reynolds stress. One-dimensional energy spectra are obtained for the u, v and w components at several points in the wall jet. It is found that self-similarity is exhibited by the one-dimensional wavenumber spectrum of $\overline{q^2}(=\overline{u^2}+\overline{v^2}+\overline{w^2})$, if the half-width of the wall jet and the local mean velocity are used for forming the non-dimensional wavenumber. Both the autocorrelation curves and the spectra indicate the existence of periodicity in the flow. The rate of dissipation of turbulent energy is estimated from the $\overline{q^2}$ spectra, using a slightly modified version of a previously suggested method.

Influence of matrix characteristics on fracture toughness of high volume fraction Al2O3/Al–AlN composites

The role of matrix microstructure on the fracture of Al-alloy composites with 60 vol% alumina particulates was studied. The matrix composition and microstructure were systematically varied by changing the infiltration temperature and heat treatment. Characterization was carried out by a combination of metallography, hardness measurements, and fracture studies conducted on compact tension specimens to study the fracture toughness and crack growth in the composites. The composites showed a rise in crack resistance with crack extension (R curves) due to bridges of intact matrix ligaments formed in the crack wake. The steady-state or plateau toughness reached upon stable crack growth was observed to be more sensitive to the process temperature rather than to the heat treatment. Fracture in the composites was predominantly by particle fracture, extensive deformation, and void nucleation in the matrix. Void nucleation occurred in the matrix in the as-solutionized and peak-aged conditions and preferentially near the interface in the underaged and overaged conditions. Micromechanical models based on crack bridging by intact ductile ligaments were modified by a plastic constraint factor from estimates of the plastic zone formed under indentations, and are shown to be adequate in predicting the steady-state toughness of the composite.

A dynamical instability due to fluid–wall coupling lowers the transition Reynolds number in the flow through a flexible tube

A flow-induced instability in a tube with flexible walls is studied experimentally. Tubes of diameter 0.8 and 1.2 mm are cast in polydimethylsiloxane (PDMS) polymer gels, and the catalyst concentration in these gels is varied to obtain shear modulus in the range 17–550 kPa. A pressure drop between the inlet and outlet of the tube is used to drive fluid flow, and the friction factor $f$ is measured as a function of the Reynolds number $Re$. From these measurements, it is found that the laminar flow becomes unstable, and there is a transition to a more complicated flow profile, for Reynolds numbers as low as 500 for the softest gels used here. The nature of the $f$–$Re$ curves is also qualitatively different from that in the flow past rigid tubes; in contrast to the discontinuous increase in the friction factor at transition in a rigid tube, it is found that there is a continuous increase in the friction factor from the laminar value of $16\ensuremath{/} Re$ in a flexible tube. The onset of transition is also detected by a dye-stream method, where a stream of dye is injected into the centre of the tube. It is found that there is a continuous increase of the amplitude of perturbations at the onset of transition in a flexible tube, in contrast to the abrupt disruption of the dye stream at transition in a rigid tube. There are oscillations in the wall of the tube at the onset of transition, which is detected from the laser scattering off the walls of the tube. This indicates that the coupling between the fluid stresses and the elastic stresses in the wall results in an instability of the laminar flow.

Effect of Post-Metallization Hydrogen Annealing on C-V Characteristic of Zirconia Grown Using Atomic Layer Deposition

Substantial amount of fixed charge present in most of the alternative gate dielectrics gives rise to large shifts in the flat-band voltage (VFB) and charge trapping and de-trapping causes hysterectic changes on voltage cycling. Both phenomena affect stable and reliable transistor operation. In this paper we have studied for the first time the effect of post-metallization hydrogen annealing on the C-V curve of MOS capacitors employing zirconia, one of the most promising gate dielectric. Samples were annealed in hydrogen ambient for up to 30 minutes at different temperatures ranging from room temperature to 400°C. C-V measurements were done after annealing at each temperature and the hysteresis width was calculated from the C-V curves. A minimum hysteresis width of ∼35 mV was observed on annealing the sample at 200°C confirming the excellent suitability of this dielectric

Structural, optical and nanomechanical properties of (1 1 1) oriented nanocrystalline ZnTe thin films

Structural, optical and nanomechanical properties of nanocrystalline Zinc Telluride (ZnTe) films of thickness upto 10 microns deposited at room temperature on borosilicate glass substrates are reported. X-ray diffraction patterns reveal that the films were preferentially oriented along the (1 1 1) direction. The maximum refractive index of the films was 2.74 at a wavelength of 2000 nm. The optical band gap showed strong thickness dependence. The average film hardness and Young's modulus obtained from load-displacement curves and analyzed by Oliver-Pharr method were 4 and 70 GPa respectively. Hardness of (1 1 1) oriented ZnTe thin films exhibited almost 5 times higher value than bulk. The studies show clearly that the hardness increases with decreasing indentation size, for indents between 30 and 300 nm in depth indicating the existence of indentation size effect. The coefficient of friction for these films as obtained from the nanoscratch test was ~0.4.

Structural, optical and nanomechanical properties of (1 1 1) oriented nanocrystalline ZnTe thin films

Structural, optical and nanomechanical properties of nanocrystalline Zinc Telluride (ZnTe) films of thickness upto 10 microns deposited at room temperature on borosilicate glass substrates are reported. X-ray diffraction patterns reveal that the films were preferentially oriented along the (1 1 1) direction. The maximum refractive index of the films was 2.74 at a wavelength of 2000 nm. The optical band gap showed strong thickness dependence. The average film hardness and Young's modulus obtained from load-displacement curves and analyzed by Oliver-Pharr method were 4 and 70 GPa respectively. Hardness of (1 1 1) oriented ZnTe thin films exhibited almost 5 times higher value than bulk. The studies show clearly that the hardness increases with decreasing indentation size, for indents between 30 and 300 nm in depth indicating the existence of indentation size effect. The coefficient of friction for these films as obtained from the nanoscratch test was ~0.4.

Optical and Electronic Properties of Conjugated Polymer -Nanocluster Semiconductor Hybrid Systems

Conjugated polymers are intensively pursued as candidate materials for emission and detection devices with the optical range of interest determined by the chemical structure. On the other hand the optical range for emission and detection can also be tuned by size selection in semiconductor nanoclusters. The mechanisms for charge generation and separation upon optical excitation, and light emission are different for these systems. Hybrid systems based on these different class of materials reveal interesting electronic and optical properties and add further insight into the individual characteristics of the different components. Multilayer structures and blends of these materials on different substrates were prepared for absorption, photocurrent (Iph), photoluminescence (PL) and electroluminscence (EL) studies. Polymers chosen were derivatives of polythiophene (PT) and polyparaphenylenevinylene (PPV) along with nanoclusters of cadmium sulphide of average size 4.4 nm (CdS-44). The photocurrent spectral response in these systems followed the absorption response around the band edges for each of the components and revealed additional features, which depended on bias voltage, thickness of the layers and interfacial effects. The current-voltage curves showed multi-component features with emission varying for different regimes of voltage. The emission spectral response revealed additive features and is discussed in terms of excitonic mechanisms.

Effect of screening of intermicellar interactions on the linear and nonlinear rheology of a viscoelastic gel

We report our studies of the linear and nonlinear rheology of aqueous solutions of the surfactant cetyl trimethylammonium tosylate (CTAT) with varying amounts of sodium chloride (NaCl). The CTAT concentration is fixed at 42 mM, and the salt concentration is varied between 0 and 120 mM. On increasing the salt (NaCl) concentration, we see three distinct regimes in the zero-shear viscosity and the high-frequency plateau modulus data. In regime 1, the zero-shear viscosity shows a weak increase with salt concentration due to enhanced micellar growth. The decrease in the zero-shear viscosities with salt concentration in regimes II and III can be explained in terms of intermicellar branching. The most intriguing feature of our data, however, is the anomalous behavior of the high-frequency plateau modulus in regime II (0.12 less than or equal to [NaCl]/[CTAT] less than or equal to 1.42). In this regime, the plateau modulus increases with an increase in NaCl concentration. This is highly interesting, since the correlation length of concentration fluctuations and hence the plateau modulus G(0) are not expected to change appreciably in the semidilute regime. We propose to explain the changes in regime II in terms of a possible unbinding of the organic counterions (tosylate) from the CTA(+) surfaces on the addition of NaCl. In the nonlinear flow curves of the samples with high salt content, significant deviations from the predictions of the Giesekus model for entangled micelles are observed.

Thermal cycling of Mg-MMCs

Creep resistant Mg alloy QE22 reinforced with maftec(R), saffil(R) or supertec(R) short fibres is cycled between room temperature and 308degreesC at different ramp rates in the longitudinal and transverse directions. From the careful analysis of the strain vs. temperature thermal cycling curves true material behaviour and artifacts from the dilatometer are deciphered. From this analysis true coefficient of thermal expansion and relaxation processes are deduced. Hysteresis at higher temperatures is attributed to the relaxation process, whereas hysteresis at low temperatures giving a tilt-ground shape to the thermal cycling curves is again an artifact due to the instrument. The change in ramp rate highlights this effect. Finally, the effect of thermal cycling on microstructure is examined.

Theoretical determination of HI vertical scale heights in the dwarf galaxies DDO 154, Ho II, IC 2574 and NGC 2366

In this paper, we model dwarf galaxies as a two-component system of gravitationally coupled stars and atomic hydrogen gas in the external force field of a pseudo-isothermal dark matter halo, and numerically obtain the radial distribution of HI vertical scale heights. This is done for a group of four dwarf galaxies (DDO 154, Ho II, IC 2574 and NGC 2366) for which most necessary input parameters are available from observations. The formulation of the equations takes into account the rising rotation curves generally observed in dwarf galaxies. The inclusion of self-gravity of the gas into the model at par with that of the stars results in scale heights that are smaller than what was obtained by previous authors. This is important as the gas scale height is often used for deriving other physical quantities. The inclusion of gas self-gravity is particularly relevant in the case of dwarf galaxies where the gas cannot be considered a minor perturbation to the mass distribution of the stars. We find that three out of four galaxies studied show a flaring of their HI discs with increasing radius, by a factor of a few within several disc scale lengths. The fourth galaxy has a thick HI disc throughout. This flaring arises as a result of the gas velocity dispersion remaining constant or decreasing only slightly while the disc mass distribution declines exponentially as a function of radius.

Interacting magnetic sublattices and ferrimagnetism in Sr-doped DyMnO3

We present the magnetic properties of polycrystalline Dy1−xSrxMnO3 (0.1 ≤ x ≤ 0.4) with an orthorhombic (o) crystal structure. The parent compound, o-DyMnO3, undergoes an incommensurate antiferromagnetic ordering of the Mn spins at 39 K, followed by a spiral order at 18 K. A further antiferromagnetic transition at 5 K marks an ordering of the Dy-sublattice. Doping of divalent Sr ions results in diverse magnetization phenomena. The zero-field cooled (ZFC) and field cooled (FC) magnetization curves display the presence of strongly interacting magnetic sublattices. For x = 0.1 and 0.2, a bifurcation between the ZFC and FC magnetization sets in at around 30 and 32 K, respectively. The ZFC magnetization peaks at about 5 K, indicating antiferromagnetic Dy-couplings similar to the case of o-DyMnO3. For x = 0.3, clear signatures of ferrimagnetism and strong anisotropy are found, including negative magnetization. The compound with x = 0.4 behaves as a spin glass, similar to Dy0.5Sr0.5MnO3.

Numerical modeling of the contaminant Transport through stratified soil

The transport processes of the dissolved chemicals in stratified or layered soils have been studied for several decades. In case of the solute transport through stratified layers, interface condition plays an important role in determining appropriate transport parameters. First‐ type and third‐ type interface conditions are generally used in the literature. A first‐type interface condition will result in a continuous concentration profile across the interface at the expense of solute mass balance. On the other hand, a discontinuity in concentration develops when a third‐ type interface condition is used. To overcome this problem, a combined first‐ and third‐ type condition at the interface has been widely employed which yields second‐ type condition. This results in a similar break‐through curve irrespective of the layering order, which is non‐physical. In this work, an interface condition is proposed which satisfies the mass balance implicitly and brings the distinction between the breakthrough curves for different layering sequence corroborating with the experimental observations. This is in disagreement with the earlier work by H. M. Selim and co‐workers but, well agreement with the hypothetical result by Bosma and van der Zee; and Van der Zee.

Time dependent deformations in concrete: A multi-scale approach

Estimation of creep and shrinkage are critical in order to compute loss of prestress with time in order to compute leak tightness and assess safety margins available in containment structures of nuclear power plants. Short-term creep and shrinkage experiments have been conducted using in-house test facilities developed specifically for the present research program on 35 and 45 MPa normal concrete and 25 MPa heavy density concrete. The extensive experimental program for creep, has cylinders subject to sustained levels of load typically for several days duration (till negligible strain increase with time is observed in the creep specimen), to provide the total creep strain versus time curves for the two normal density concrete grades and one heavy density concrete grade at different load levels, different ages at loading, and at different relative humidity’s. Shrinkage studies on prism specimen for concrete of the same mix grades are also being studied. In the first instance, creep and shrinkage prediction models reported in the literature has been used to predict the creep and shrinkage levels in subsequent experimental data with acceptable accuracy. While macro-scale short experiments and analytical model development to estimate time dependent deformation under sustained loads over long term, accounting for the composite rheology through the influence of parameters such as the characteristic strength, age of concrete at loading, relative humidity, temperature, mix proportion (cement: fine aggregate: coarse aggregate: water) and volume to surface ratio and the associated uncertainties in these variables form one part of the study, it is widely believed that strength, early age rheology, creep and shrinkage are affected by the material properties at the nano-scale that are not well established. In order to understand and improve cement and concrete properties, investigation of the nanostructure of the composite and how it relates to the local mechanical properties is being undertaken. While results of creep and shrinkage obtained at macro-scale and their predictions through rheological modeling are satisfactory, the nano and micro indenting experimental and analytical studies are presently underway. Computational mechanics based models for creep and shrinkage in concrete must necessarily account for numerous parameters that impact their short and long term response. A Kelvin type model with several elements representing the influence of various factors that impact the behaviour is under development. The immediate short term deformation (elastic response), effects of relative humidity and temperature, volume to surface ratio, water cement ratio and aggregate cement ratio, load levels and age of concrete at loading are parameters accounted for in this model. Inputs to this model, such as the pore structure and mechanical properties at micro/nano scale have been taken from scanning electron microscopy and micro/nano-indenting of the sample specimen.

Modified lattice model for mode-I fracture analysis of notched plain concrete beam using probabilistic approach

A modified lattice model using finite element method has been developed to study the mode-I fracture analysis of heterogeneous materials like concrete. In this model, the truss members always join at points where aggregates are located which are modeled as plane stress triangular elements. The truss members are given the properties of cement mortar matrix randomly, so as to represent the randomness of strength in concrete. It is widely accepted that the fracture of concrete structures should not be based on strength criterion alone, but should be coupled with energy criterion. Here, by incorporating the strain softening through a parameter ‘α’, the energy concept is introduced. The softening branch of load-displacement curves was successfully obtained. From the sensitivity study, it was observed that the maximum load of a beam is most sensitive to the tensile strength of mortar. It is seen that by varying the values of properties of mortar according to a normal random distribution, better results can be obtained for load-displacement diagram.