SOME UNSTABLE CRITICAL METRICS FOR THE L-n/2-NORM OF THE CURVATURE TENSOR

We consider the Riemannian functional defined on the space of Riemannian metrics with unit volume on a closed smooth manifold M given by R-n/2(g) := integral(M) vertical bar R(g)vertical bar(n//2) dv(g) where R(g), dv(g) denote the Riemannian curvature and volume form corresponding to g. We show that there are locally symmetric spaces which are unstable critical points for this functional.

Effects of Microstructure and Loading on Fracture of Sn-3.8Ag-0.7Cu Joints on Cu Substrates with ENIG Surface Finish

When dropped, electronic packages often undergo failure by propagation of an interfacial crack in solder joints under a combination of tensile and shear loading. Hence, it is crucial to understand and predict the fracture behavior of solder joints under mixed-mode high-rate loading conditions. In this work, the effects of the loading conditions (strain rate and loading angle) and microstructure interfacial intermetallic compound (IMC) morphology and solder yield strength] on the mixed-mode fracture toughness of Sn-3.8 wt.%Ag-0.7 wt.%Cu solder joints sandwiched between two Cu substrates with electroless nickel immersion gold (ENIG) metallization have been studied, and compared with the fracture behavior of joints attached to bare Cu. Irrespective of the surface finish, the fracture toughness of the solder joints decreased monotonically with strain rate and mode-mixity, both resulting in increased fracture proportion through the interfacial IMC layer. Furthermore, the proportion of crack propagation through the interfacial IMC layer increased with increase in the thickness and the roughness of the interfacial IMC layer and the yield strength of the solder, resulting in a decrease in the fracture toughness of the joint. However, under most conditions, solder joints with ENIG finish showed higher resistance to fracture than joints attached directly to Cu substrates without ENIG metallization. Based on the experimental observations, a fracture mechanism map is constructed correlating the yield strength of the solder, the morphology and thickness of the interfacial IMC, and the fracture mechanisms as well as the fracture toughness values for different solder joints under mode I loading.

Streptococcus pneumoniae Genome Database (SPGDB): A database for strain specific comparative analysis of Streptococcus pneumoniae genes and proteins

Streptococcus pneumoniae causes pneumonia, septicemia and meningitis. S. pneumoniae is responsible for significant mortality both in children and in the elderly. In recent years, the whole genome sequencing of various S. pneumoniae strains have increased manifold and there is an urgent need to provide organism specific annotations to the scientific community. This prompted us to develop the Streptococcus pneumoniae Genome Database (SPGDB) to integrate and analyze the completely sequenced and available S. pneumoniae genome sequences. Further, links to several tools are provided to compare the pool of gene and protein sequences, and proteins structure across different strains of S. pneumoniae. SPGDB aids in the analysis of phenotypic variations as well as to perform extensive genomics and evolutionary studies with reference to S. pneumoniae. (C) 2014 Elsevier Inc. All rights reserved.

Performance Assessment of a Small Biogas-fuelled Power Generator Prototype

This study reports the development and performance evaluation of prototypes of biogas-fuelled stationary power generators in the range of 1 kW. Strategies to achieve high engine efficiency namely pulsed manifold injection, electronic throttle control and dual spark plugs, have been incorporated in the prototype. A complete closed-loop control of the engine operation to maintain a steady engine speed of 3000 rpm (+/- 5%) across the entire load range while maintaining an optimum fuel-air equivalence ratio is made possible by an electronic control unit (ECU) controlling the injection duration, ignition timing and throttle position. This study specifically focuses on the response of the generator to transient loads, and the overall efficiency obtained. The results obtained from testing the prototype have been found to be satisfactory and show that biogas power generators for low power applications can be made efficient (overall efficiency of 19% at electrical load of 640 W) using the strategies of biogas fuel injection.

Strongly minimal triangulations of (S (3) x S (1))(#3) and (S (3) x S (1))(#3)

A triangulated d-manifold K, satisfies the inequality for da parts per thousand yen3. The triangulated d-manifolds that meet the bound with equality are called tight neighbourly. In this paper, we present tight neighbourly triangulations of 4-manifolds on 15 vertices with as an automorphism group. One such example was constructed by Bagchi and Datta (Discrete Math. 311 (citeyearbd102011) 986-995). We show that there are exactly 12 such triangulations up to isomorphism, 10 of which are orientable.

GLOBAL REGISTRATION OF MULTIPLE POINT CLOUDS USING SEMIDEFINITE PROGRAMMING

Consider N points in R-d and M local coordinate systems that are related through unknown rigid transforms. For each point, we are given (possibly noisy) measurements of its local coordinates in some of the coordinate systems. Alternatively, for each coordinate system, we observe the coordinates of a subset of the points. The problem of estimating the global coordinates of the N points (up to a rigid transform) from such measurements comes up in distributed approaches to molecular conformation and sensor network localization, and also in computer vision and graphics. The least-squares formulation of this problem, although nonconvex, has a well-known closed-form solution when M = 2 (based on the singular value decomposition (SVD)). However, no closed-form solution is known for M >= 3. In this paper, we demonstrate how the least-squares formulation can be relaxed into a convex program, namely, a semidefinite program (SDP). By setting up connections between the uniqueness of this SDP and results from rigidity theory, we prove conditions for exact and stable recovery for the SDP relaxation. In particular, we prove that the SDP relaxation can guarantee recovery under more adversarial conditions compared to earlier proposed spectral relaxations, and we derive error bounds for the registration error incurred by the SDP relaxation. We also present results of numerical experiments on simulated data to confirm the theoretical findings. We empirically demonstrate that (a) unlike the spectral relaxation, the relaxation gap is mostly zero for the SDP (i.e., we are able to solve the original nonconvex least-squares problem) up to a certain noise threshold, and (b) the SDP performs significantly better than spectral and manifold-optimization methods, particularly at large noise levels.

Tight triangulations of closed 3-manifolds

A triangulation of a closed 2-manifold is tight with respect to a field of characteristic two if and only if it is neighbourly; and it is tight with respect to a field of odd characteristic if and only if it is neighbourly and orientable. No such characterization of tightness was previously known for higher dimensional manifolds. In this paper, we prove that a triangulation of a closed 3-manifold is tight with respect to a field of odd characteristic if and only if it is neighbourly, orientable and stacked. In consequence, the Kuhnel-Lutz conjecture is valid in dimension three for fields of odd characteristic. Next let F be a field of characteristic two. It is known that, in this case, any neighbourly and stacked triangulation of a closed 3-manifold is F-tight. For closed, triangulated 3-manifolds with at most 71 vertices or with first Betti number at most 188, we show that the converse is true. But the possibility of the existence of an F-tight, non-stacked triangulation on a larger number of vertices remains open. We prove the following upper bound theorem on such triangulations. If an F-tight triangulation of a closed 3-manifold has n vertices and first Betti number beta(1), then (n - 4) (617n - 3861) <= 15444 beta(1). Equality holds here if and only if all the vertex links of the triangulation are connected sums of boundary complexes of icosahedra. (C) 2015 Elsevier Ltd. All rights reserved.

Effect of current density on the microstructure and corrosion properties of plasma electrolytic oxidation (PEO) coatings on AM50 Mg alloy produced in an electrolyte containing clay additives

Plasma electrolytic oxidation coatings were produced on AM50 Mg alloy in alkaline phosphate based electrolyte with montmorillonite clay additives employing current densities of 30, 60, and 120 mA/cm(2). The effect of current density on the microstructure and corrosion properties of the coating was investigated. The clay additives got melted and reactively incorporated into the coating forming an amorphous phase, at all the current densities. However, the coating was predominantly amorphous only at 30 mA/cm(2) and with increasing current density, increasing fractions of crystalline phases were formed. Higher current densities resulted in increased thickness of the coating, but reduced the compactness of the coatings. Electrochemical impedance spectroscopy tests in 0.5 wt.% (0.08 M) and 3.5 wt.% (0.6 M) NaCl solution revealed that the coatings processed at 30 mA/cm(2) exhibited a relatively better initial corrosion resistance owing to its relatively defect-free barrier layer and compactness of the coating. However, the presence of amorphous phases in significant amounts and lack of MgO in the coating resulted in increased rate of dissolution of the coatings and degradation of corrosion resistance. Coatings produced at higher current densities exhibited initial inferior corrosion resistance due to a more defective barrier layer and increased porosity in pore band and outer porous layer. However, the increased amount of crystalline phases and an increased amount of MgO, which resisted dissolution, counterbalanced the negative effects of defective barrier and increased porosity resulting in a relatively lower rate of the degradation of the corrosion resistance. Thus, the corrosion resistance of all the coatings continuously decreased with time and became similar after prolonged immersion in NaCl solution. Increasing current density, therefore, did not prove to be beneficial for the improvement of the corrosion performance of the PEO coatings. (C) 2016 Elsevier B.V. All rights reserved.