Lower bounds on Ricci flow invariant curvatures and geometric applications

We consider Ricci flow invariant cones C in the space of curvature operators lying between the cones ``nonnegative Ricci curvature'' and ``nonnegative curvature operator''. Assuming some mild control on the scalar curvature of the Ricci flow, we show that if a solution to the Ricci flow has its curvature operator which satisfies R + epsilon I is an element of C at the initial time, then it satisfies R + epsilon I is an element of C on some time interval depending only on the scalar curvature control. This allows us to link Gromov-Hausdorff convergence and Ricci flow convergence when the limit is smooth and R + I is an element of C along the sequence of initial conditions. Another application is a stability result for manifolds whose curvature operator is almost in C. Finally, we study the case where C is contained in the cone of operators whose sectional curvature is nonnegative. This allows us to weaken the assumptions of the previously mentioned applications. In particular, we construct a Ricci flow for a class of (not too) singular Alexandrov spaces.

NUMERICAL STUDIES OF DYNAMO ACTION IN A TURBULENT SHEAR FLOW. I.

We perform numerical experiments to study the shear dynamo problem where we look for the growth of a large-scale magnetic field due to non-helical stirring at small scales in a background linear shear flow in previously unexplored parameter regimes. We demonstrate the large-scale dynamo action in the limit where the fluid Reynolds number (Re) is below unity while the magnetic Reynolds number (Rm) is above unity; the exponential growth rate scales linearly with shear, which is consistent with earlier numerical works. The limit of low Re is particularly interesting, as seeing the dynamo action in this limit would provide enough motivation for further theoretical investigations, which may focus attention on this analytically more tractable limit of Re < 1 compared to the more formidable limit of Re > 1. We also perform simulations in the regimes where (i) both (Re, Rm) < 1, and (ii) Re > 1 and Rm < 1, and compute all of the components of the turbulent transport coefficients (alpha(ij) and alpha(ij)) using the test-field method. A reasonably good agreement is observed between our results and the results of earlier analytical works in similar parameter regimes.

Imaging Flow Cytometry With Femtosecond Laser-Micromachined Glass Microfluidic Channels

Microfluidic/optofluidic microscopy is a versatile modality for imaging and analyzing properties of cells/particles while they are in flow. In this paper, we demonstrate the integration of fused silica microfluidics fabricated using femtosecond laser machining into optofluidic imaging systems. By using glass for the sample stage of our microscope, we have exploited its superior optical quality for imaging and bio-compatibility. By integrating these glass microfluidic devices into a custom-built bright field microscope, we have been able to image red blood cells in flow with high-throughputs and good fidelity. In addition, we also demonstrate imaging as well as detection of fluorescent beads with these microfluidic devices.

NON-COERCIVE RICCI FLOW INVARIANT CURVATURE CONES

This note is a study of nonnegativity conditions on curvature preserved by the Ricci flow. We focus on a specific class of curvature conditions which we call non-coercive: These are the conditions for which nonnegative curvature and vanishing scalar curvature does not imply flatness. We show, in dimensions greater than 4, that if a Ricci flow invariant nonnegativity condition is satisfied by all Einstein curvature operators with nonnegative scalar curvature, then this condition is just the nonnegativity of scalar curvature. As a corollary, we obtain that a Ricci flow invariant curvature condition, which is stronger than a nonnegative scalar curvature, cannot be strictly satisfied by curvature operators (other than multiples of the identity) of compact Einstein symmetric spaces. We also investigate conditions which are satisfied by all conformally flat manifolds with nonnegative scalar curvature.

Surface motions and intraplate continental deformation in Alaska driven by mantle flow

The degree to which the lithosphere and mantle are coupled and contribute to surface deformation beneath continental regions remains a fundamental question in the field of geodynamics. Here we use a new approach with a surface deformation field constrained by GPS, geologic, and seismicity data, together with a lithospheric geodynamic model, to solve for tractions inferred to be generated by mantle convection that (1) drive extension within interior Alaska generating southward directed surface motions toward the southern convergent plate boundary, (2) result in accommodation of the relative motions between the Pacific and North America in a comparatively small zone near the plate boundary, and (3) generate the observed convergence within the North American plate interior in the Mackenzie mountains in northwestern Canada. The evidence for deeper mantle influence on surface deformation beneath a continental region suggests that this mechanism may be an important contributing driver to continental plate assemblage and breakup.

Experimental studies on the flow through soft tubes and channels

Experiments conducted in channels/tubes with height/diameter less than 1 mm with soft walls made of polymer gels show that the transition Reynolds number could be significantly lower than the corresponding value of 1200 for a rigid channel or 2100 for a rigid tube. Experiments conducted with very viscous fluids show that there could be an instability even at zero Reynolds number provided the surface is sufficiently soft. Linear stability studies show that the transition Reynolds number is linearly proportional to the wall shear modulus in the low Reynolds number limit, and it increases as the 1/2 and 3/4 power of the shear modulus for the `inviscid' and `wall mode' instabilities at high Reynolds number. While the inviscid instability is similar to that in the flow in a rigid channel, the mechanisms of the viscous and wall mode instabilities are qualitatively different. These involve the transfer of energy from the mean flow to the fluctuations due to the shear work done at the interface. The experimental results for the viscous instability mechanism are in quantitative agreement with theoretical predictions. At high Reynolds number, the instability mechanism has characteristics similar to the wall mode instability. The experimental transition Reynolds number is smaller, by a factor of about 10, than the theoretical prediction for the parabolic flow through rigid tubes and channels. However, if the modification in the tube shape due to the pressure gradient, and the consequent modification in the velocity profile and pressure gradient, are incorporated, there is quantitative agreement between theoretical predictions and experimental results. The transition has important practical consequences, since there is a significant enhancement of mixing after transition.

Taming Control Divergence in GPUs through Control Flow Linearization

Branch divergence is a very commonly occurring performance problem in GPGPU in which the execution of diverging branches is serialized to execute only one control flow path at a time. Existing hardware mechanism to reconverge threads using a stack causes duplicate execution of code for unstructured control flow graphs. Also the stack mechanism cannot effectively utilize the available parallelism among diverging branches. Further, the amount of nested divergence allowed is also limited by depth of the branch divergence stack. In this paper we propose a simple and elegant transformation to handle all of the above mentioned problems. The transformation converts an unstructured CFG to a structured CFG without duplicating user code. It incurs only a linear increase in the number of basic blocks and also the number of instructions. Our solution linearizes the CFG using a predicate variable. This mechanism reconverges the divergent threads as early as possible. It also reduces the depth of the reconvergence stack. The available parallelism in nested branches can be effectively extracted by scheduling the basic blocks to reduce the effect of stalls due to memory accesses. It can also increase execution efficiency of nested loops with different trip counts for different threads. We implemented the proposed transformation at PTX level using the Ocelot compiler infrastructure. We evaluated the technique using various benchmarks to show that it can be effective in handling the performance problem due to divergence in unstructured CFGs.

Stability of Poiseuille flow in a fluid overlying an anisotropic and inhomogeneous porous layer

We present the linear stability analysis of horizontal Poiseuille flow in a fluid overlying a porous medium with anisotropic and inhomogeneous permeability. The generalized Darcy model is used to describe the flow in the porous medium with the Beavers-Joseph condition at the interface of the two layers and the eigenvalue problem is solved numerically. The effect of major system parameters on the stability characteristics is addressed in detail. It is shown that the anisotropic and inhomogeneous modulation of the permeability of the underlying porous layer provides an effective means for passive control of the flow stability.

Field-Portable Microfluidics-Based Imaging Flow Cytometer

Clinical microscopy is a versatile and robust tool used for the diagnosis of a plethora of diseases. However, due to various reasons, it remains inaccessible in resource limited settings. In this paper, we present an automated and cost-effective alternative to microscopy for use in clinical diagnostics. With the use of custom optics and microfluidics, we demonstrate a field-portable imaging flow cytometry system. Using the presented system, we have been able to image 586 cells per second. We demonstrate the clinical relevance of the proposed system by differentiating between suspensions of healthy and sphered RBCs based on high-throughput morphometric analysis. The instrument presented here is a major advancement in the domain of field portable diagnostics as it enables fast and robust quantitative diagnostic testing at the point-of-care.

Deformability Measurement of Single-Cells at High-Throughput With Imaging Flow Cytometry

Disease conditions like malaria, sickle cell anemia, diabetes mellitus, cancer, etc., are known to significantly alter the deformability of certain types of cells (red blood cells, white blood cells, circulating tumor cells, etc.). To determine the cellular deformability, techniques like micropipette aspiration, atomic force microscopy, optical tweezers, quantitative phase imaging have been developed. Many of these techniques have an advantage of determining the single cell deformability with ultrahigh precision. However, the suitability of these techniques for the realization of a deformability based diagnostic tool is questionable as they are expensive and extremely slow to operate on a huge population of cells. In this paper, we propose a technique for high-throughput (800 cells/s) determination of cellular deformability on a single cell basis. This technique involves capturing the image(s) of cells in flow that have undergone deformation under the influence of shear gradient generated by the fluid flowing through the microfluidic channels. Deformability indices of these cells can be computed by performing morphological operations on these images. We demonstrate the applicability of this technique for examining the deformability index on healthy, diabetic, and sphered red blood cells. We believe that this technique has a strong role to play in the realization of a potential tool that uses deformability as one of the important criteria in disease diagnosis.

Investigation of schemes for incorporating generator Q limits in the fast decoupled load flow method

Fast Decoupled Load Flow (FDLF) is a very popular and widely used power flow analysis method because of its simplicity and efficiency. Even though the basic FDLF algorithm is well investigated, the same is not true in the case of additional schemes/modifications required to obtain adjusted load flow solutions using the FDLF method. Handling generator Q limits is one such important feature needed in any practical load flow method. This paper presents a comprehensive investigation of two classes of schemes intended to handle this aspect i.e. the bus type switching scheme and the sensitivity scheme. We propose two new sensitivity based schemes and assess their performance in comparison with the existing schemes. In addition, a new scheme to avoid the possibility of anomalous solutions encountered while using the conventional schemes is also proposed and evaluated. Results from extensive simulation studies are provided to highlight the strengths and weaknesses of these existing and proposed schemes, especially from the point of view of reliability.

Atmospheric pressure plasma chemical vapor deposition reactor for 100 mm wafers, optimized for minimum contamination at low gas flow rates

Gas discharge plasmas used for thinfilm deposition by plasma-enhanced chemical vapor deposition (PECVD) must be devoid of contaminants, like dust or active species which disturb the intended chemical reaction. In atmospheric pressure plasma systems employing an inert gas, the main source of such contamination is the residual air inside the system. To enable the construction of an atmospheric pressure plasma (APP) system with minimal contamination, we have carried out fluid dynamic simulation of the APP chamber into which an inert gas is injected at different mass flow rates. On the basis of the simulation results, we have designed and built a simple, scaled APP system, which is capable of holding a 100 mm substrate wafer, so that the presence of air (contamination) in the APP chamber is minimized with as low a flow rate of argon as possible. This is examined systematically by examining optical emission from the plasma as a function of inert gas flow rate. It is found that optical emission from the plasma shows the presence of atmospheric air, if the inlet argon flow rate is lowered below 300 sccm. That there is minimal contamination of the APP reactor built here, was verified by conducting an atmospheric pressure PECVD process under acetylene flow, combined with argon flow at 100 sccm and 500 sccm. The deposition of a polymer coating is confirmed by infrared spectroscopy. X-ray photoelectron spectroscopy shows that the polymer coating contains only 5% of oxygen, which is comparable to the oxygen content in polymer deposits obtained in low-pressure PECVD systems. (C) 2015 AIP Publishing LLC.

EXPERIMENTAL INVESTIGATION OF UNSTEADY FLOW IN A TRANSONIC UNI-STAGE AXIAL COMPRESSOR

Detailed steady and unsteady experimental measurements and analysis were performed on a Single stage Transonic Axial Compressor with asymmetric rotor tip clearance for studying the compressor stall phenomena. The installed compressor had asymmetric tip clearance around the rotor casing varying from about 0.65mm to 1.25mm. A calibrated 5-hole aerodynamic probe was traversed radially at exit of rotor and showed the characteristics of increased flow angle at lower mass flow rates for all the speeds. Mach number distribution and boundary layer effects were also clearly captured. Unsteady measurements for velocity were carried out to study the stall cell behavior using a single component calibrated hotwire probe oriented in axial and tangential directions for choke/free flow and near stall conditions. The hotwire probe was traversed radially across the annulus at inlet to the compressor and showed that the velocity fluctuations were dissimilar when probe was aligned axial and tangential to the flow. Averaged velocities across the annulus showed the reduction in velocity as stall was approached. Axial mean flow velocity decreased across the annulus for all the speeds investigated. Tangential velocity at free flow condition was higher at the tip region due to larger radius. At stall condition, the tangential velocity showed decreased velocities at the tip and slightly increased velocities at the hub section indicating that the flow has breakdown at the tip region of the blade and fluid is accelerated below the blockage zone. The averaged turbulent intensity in axial and tangential flow directions increased from free flow to stall condition for all compressor rated speeds. Fast Fourier Transform (FFT) of the raw signals at stall flow condition showed stall cell and its corresponding frequency of occurrence. The stalling frequency of about half of rotational speed of the rotor along with large tip clearance suggests that modal type stall inception was occurring.

TURBULENCE-TRANSPORT-CHEMISTRY INTERACTION IN STATISTICALLY PLANAR PREMIXED FLAMES AND IGNITION KERNELS IN NEAR ISOTROPIC TURBULENCE

Turbulence-transport-chemistry interaction plays a crucial role on the flame surface geometry, local and global reactionrates, and therefore, on the propagation and extinction characteristics of intensely turbulent, premixed flames encountered in LPP gas-turbine combustors. The aim of the present work is to understand these interaction effects on the flame surface annihilation and extinction of lean premixed flames, interacting with near isotropic turbulence. As an example case, lean premixed H-2-air mixture is considered so as to enable inclusion of detailed chemistry effects in Direct Numerical Simulations (DNS). The work is carried out in two phases namely, statistically planar flames and ignition kernel, both interacting with near isotropic turbulence, using the recently proposed Flame Particle Tracking (FPT) technique. Flame particles are surface points residing and commoving with an iso-scalar surface within a premixed flame. Tracking flame particles allows us to study the evolution of propagating surface locations uniquely identified with time. In this work, using DNS and FPT we study the flame speed, reaction rate and transport histories of such flame particles residing on iso-scalar surfaces. An analytical expression for the local displacement flame speed (SO is derived, and the contribution of transport and chemistry on the displacement flame speed is identified. An examination of the results of the planar case leads to a conclusion that the cause of variation in S-d may be attributed to the effects of turbulent transport and heat release rate. In the second phase of this work, the sustenance of an ignition kernel is examined in light of the S-curve. A newly proposed Damkohler number accounting for local turbulent transport and reaction rates is found to explain either the sustenance or otherwise propagation of flame kernels in near isotropic turbulence.

QUANTITATIVE OH PLANAR LASER INDUCED FLUORESCENCE DIAGNOSTICS OF SYNGAS AND METHANE COMBUSTION IN A CAVITY COMBUSTOR

The current work reports quantitative OH species concentration in the cavity of a trapped vortex combustor (TVC) in the context of mixing and flame stabilization studies using both syngas and methane fuels. Planar laser induced fluorescence (PLIF) measurements of OH radical obtained using a Nd: YAG pumped dye laser are quantified using a flat flame McKenna burner. The momentum flux ratio (MFR), defined as the ratio of the cavity fuel jet momentum to that of the guide vane air stream, is observed to be a key governing parameter. At high MFRs similar to 4.5, the flame front is observed to form at the interface of the fuel jet and the air jet stream. This is substantiated by velocity vector field measurements. For syngas, as the MFR is lowered to similar to 0.3, the fuel-air mixing increases and a flame front is formed at the bottom and downstream edge of the cavity where a stratified charge is present. This trend is observed for different velocities at similar equivalence ratios. In case of methane combustion in the cavity, where the MFRs employed are extremely low at similar to 0.01, a different mechanism is observed. A fuel-rich mixture is now observed at the center of the cavity and this mixture undergoes combustion. On further increase of the cavity equivalence ratio, the rich mixture exceeds the flammability limit and forms a thin reaction zone at the interface with air stream. As a consequence, a shear layer flame at the top of the cavity interface with the mainstream is also observed. The equivalence ratio in the cavity also determines the combustion characteristics in the case of fuel-air mixtures that are formed as a result of the mixing. Overall, flame stabilization mechanisms have been proposed, which account for the wide range of MFRs and premixing in the mainstream as well.