Separation index of graphs and stacked 2-spheres

In 1987, Kalai proved that stacked spheres of dimension d >= 3 are characterised by the fact that they attain equality in Barnette's celebrated Lower Bound Theorem. This result does not extend to dimension d = 2. In this article, we give a characterisation of stacked 2-spheres using what we call the separation index. Namely, we show that the separation index of a triangulated 2-sphere is maximal if and only if it is stacked. In addition, we prove that, amongst all n-vertex triangulated 2-spheres, the separation index is minimised by some n-vertex flag sphere for n >= 6. Furthermore, we apply this characterisation of stacked 2-spheres to settle the outstanding 3-dimensional case of the Lutz-Sulanke-Swartz conjecture that ``tight-neighbourly triangulated manifolds are tight''. For dimension d >= 4, the conjecture has already been proved by Effenberger following a result of Novik and Swartz. (C) 2015 Elsevier Inc. All rights reserved.

Bearing capacity of circular footings over rock mass by using axisymmetric quasi lower bound finite element limit analysis

The ultimate bearing capacity of a circular footing, placed over rock mass, is evaluated by using the lower bound theorem of the limit analysis in conjunction with finite elements and nonlinear optimization. The generalized Hoek-Brown (HB) failure criterion, but by keeping a constant value of the exponent, alpha = 0.5, was used. The failure criterion was smoothened both in the meridian and pi planes. The nonlinear optimization was carried out by employing an interior point method based on the logarithmic barrier function. The results for the obtained bearing capacity were presented in a non-dimensional form for different values of GSI, m(i), sigma(ci)/(gamma b) and q/sigma(ci). Failure patterns were also examined for a few cases. For validating the results, computations were also performed for a strip footing as well. The results obtained from the analysis compare well with the data reported in literature. Since the equilibrium conditions are precisely satisfied only at the centroids of the elements, not everywhere in the domain, the obtained lower bound solution will be approximate not true. (C) 2015 Elsevier Ltd. All rights reserved.

Effect of Surface Energy Anisotropy on the Stability of Growth Fronts in Multiphase Alloys

Eutectic growth offers a variety of examples for pattern formation which are interesting both for theoreticians as well as experimentalists. One such example of patterns is ternary eutectic colonies which arise as a result of instabilities during growth of two solid phases. Here, in addition to the two major components being exchanged between the solid phases during eutectic growth, there is an impurity component which is rejected by both solid phases. During progress of solidification, there develops a boundary layer of the third impurity component ahead of the solidification front of the two solid phases. Similar to Mullins-Sekerka type instabilities, such a boundary layer tends to make the global solidification envelope unstable to morphological perturbations giving rise to two-phase cells. This phenomenon has been studied numerically in two dimensions for the conditions of directional solidification, by Plapp and Karma (Phys Rev E 66:061608, 2002) using phase-field simulations. While, in the work by Plapp and Karma (Phys Rev E 66:061608, 2002) all interfaces are isotropic, in our presentation, we extend the phase-field model by considering interfacial anisotropy in the solid-solid and solid-liquid interfaces and characterize the role of interfacial anisotropy on the stability of the growth front through phase-field simulations in two dimensions.

Necessary and sufficient conditions for optimality in constrained general sum stochastic games

In this paper we first derive a necessary and sufficient condition for a stationary strategy to be the Nash equilibrium of discounted constrained stochastic game under certain assumptions. In this process we also develop a nonlinear (non-convex) optimization problem for a discounted constrained stochastic game. We use the linear best response functions of every player and complementary slackness theorem for linear programs to derive both the optimization problem and the equivalent condition. We then extend this result to average reward constrained stochastic games. Finally, we present a heuristic algorithm motivated by our necessary and sufficient conditions for a discounted cost constrained stochastic game. We numerically observe the convergence of this algorithm to Nash equilibrium. (C) 2015 Elsevier B.V. All rights reserved.

Near-Optimal Detection Thresholds for Bayesian Spectrum Sensing Under Fading

This paper considers the problem of energy-based, Bayesian spectrum sensing in cognitive radios under various fading environments. Under the well-known central limit theorem based model for energy detection, we derive analytically tractable expressions for near-optimal detection thresholds that minimize the probability of error under lognormal, Nakagami-m, and Weibull fading. For the Suzuki fading case, a generalized gamma approximation is provided, which saves on the computation of an integral. In each case, the accuracy of the theoretical expressions as compared to the optimal thresholds are illustrated through simulations.

A note on tetrablock contractions

A commuting triple of operators (A, B, P) on a Hilbert space H is called a tetrablock contraction if the closure of the set E = {(a(11),a(22),detA) : A = GRAPHICS] with parallel to A parallel to <1} is a spectral set. In this paper, we construct a functional model and produce a set of complete unitary invariants for a pure tetrablock contraction. In this construction, the fundamental operators, which are the unique solutions of the operator equations A - B* P = DPX1DP and B - A* P = DPX2DP where X-1, X-2 is an element of B(D-P) play a pivotal role. As a result of the functional model, we show that every pure tetrablock isometry (A, B, P) on an abstract Hilbert space H is unitarily equivalent to the tetrablock contraction (MG1*+G2z, MG2*+G1z, M-z) on H-DP*(2). (D), where G(1) and G(2) are the fundamental operators of (A*, B*, P*). We prove a Beurling Lax Halmos type theorem for a triple of operators (MF1*+F2z, MF2*+F1z, M-z), where epsilon is a Hilbert space and F-1, F-2 is an element of B(epsilon). We also deal with a natural example of tetrablock contraction on a functions space to find out its fundamental operators.

Deviated linear cyclic pursuit

This paper analyses deviated linear cyclic pursuit in which an agent pursues its leader with an angle of deviation in both the continuous- and discrete-time domains, while admitting heterogeneous gains and deviations for the agents. Sufficient conditions for the stability of such systems, in both the domains, are presented in this paper along with the derivation of the reachable set, which is a set of points where the agents may converge asymptotically. The stability conditions are derived based on Gershgorin's theorem. Simulations validating the theoretical results presented in this paper are provided.

Behavior of Brick-Mortar Interfaces in FRP-Strengthened Masonry Assemblages under Normal Loading and Shear Loading

Determination of shear strength of brick-mortar bed joint is critical to overcome the sliding-shear or joint-shear failure in masonry. In the recent past, researchers have attempted to enhance the shear strength and deformation capacity of brick-mortar bed joints by gluing fiber-reinforced polymer (FRP) composite across the bed joint. FRP composites offer several advantages like high strength-to-weight ratio, and ease of application in terms of labor, time, and reduced curing period. Furthermore, FRP composites are desirable for strengthening old masonry buildings having heritage value because of its minimal interference with the existing architecture. A majority of earlier studies on shear strengthening of masonry available in the literature adopted masonry having the ratio of modulus of elasticity of masonry unit (Emu) to modulus of elasticity of mortar (Em) greater than one. Information related to shear behavior of FRP glued masonry composed of masonry units having Young's modulus lower than mortar is limited. Hence the present study is focused on characterizing the interfacial behavior of brick-mortar bed joint of masonry assemblages composed of solid burnt clay bricks and cement-sand mortar (E-mu/E-m ratio less than one), strengthened with FRP composites. Masonry triplets and prisms with bed joint inclined to loading axis (0 degrees, 30 degrees, 45 degrees, 60 degrees and 90 degrees) are employed in this study. Glass and carbon FRP composites composed of bidirectional FRP fabric with equal density in both directions are used for strengthening masonry. Masonry triplets are glued with glass and carbon FRP composites in two configurations: (1) both faces of the triplet specimens are fully glued with GFRP composites; and (2) both faces of the triplet specimens are glued with GFRP and CFRP composites in strip form. The performance of masonry assemblages strengthened with FRP composites is assessed in terms of gain in shear strength, shear displacement, and postpeak behavior for various configurations and types of FRP composites considered. A semianalytical model is proposed for the prediction of shear strength of masonry bed joints glued with FRP composites. A composite failure envelope consisting of a Coulomb friction model and a compression cap is obtained for unreinforced masonry and GFRP-strengthened masonry based on the test results of masonry triplets and masonry prisms with bed joints having various inclinations to the loading (C) 2015 American Society of Civil Engineers.

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.