Experimental investigation of cowl shape and location on inlet characteristics at hypersonic Mach number

An experimental study is presented to show the effect of the cowl location and shape on the shock interaction phenomena in the inlet region for a 2D, planar scramjet inlet model. Investigations include schlieren visualization around the cowl region and heat transfer rate measurement inside the inlet chamber.Both regular and Mach reflections are observed when the forebody ramp shock reflects from the cowl plate. Mach stem heights of 3.3 mm and 4.1 mm are measured in 18.5 mm and 22.7 mm high inlet chambers respecively. Increased heat transfer rate is measured at the same location of chamber for cowls of longer lenghs is indicating additional mass flow recovery by the inlet.

Nature of dependence of spin-orbit splittings on atomic number

It has been shown that Dirac equation employing a constant value of the screening constant Z0 does not explain the variation of spin-orbit splittings of 2p and 3p levels with atomic number Z. A model which takes into account the variation of Z0 withZ is shown to satisfactorily predict the dependence of spinorbit splittings onZ.

Vertex-Fused Metallaborane Clusters: Synthesis, Characterization and Electronic Structure of [(eta(5)-C5Me5Mo)(3)MoB9H18]

The reaction of the [(eta(5)-C5Me5)MoCl4] complex with [LiBH4 - TH F] in toluene at - 70 degrees C, followed by pyrolysis at 110 degrees C, afforded dark brown [(eta(5)-C5Me5Mo)(3)MoB9H18], 2, in parallel with the known [(eta(5)-C5Me5Mo)(2)B5H9], 1. Compound 2 has been characterized in solution by H-1, B-11, and C-13 NMR spectroscopy and elemental analysis, and the structural types were unequivocally established by crystallographic studies. The title compound represents a novel class of vertex-fused clusters in which a Mo atom has been fused in a perpendicular fashion between two molybdaborane clusters. Electronic structure calculations employing density functional theory yield geometries in agreement with the structure determinations, and on grounds of density functional theory calculations, we have analyzed the bonding patterns in the structure,

A note on the Hadwiger number of circular arc graphs

The intention of this note is to motivate the researchers to study Hadwiger's conjecture for circular arc graphs. Let η(G) denote the largest clique minor of a graph G, and let χ(G) denote its chromatic number. Hadwiger's conjecture states that η(G)greater-or-equal, slantedχ(G) and is one of the most important and difficult open problems in graph theory. From the point of view of researchers who are sceptical of the validity of the conjecture, it is interesting to study the conjecture for graph classes where η(G) is guaranteed not to grow too fast with respect to χ(G), since such classes of graphs are indeed a reasonable place to look for possible counterexamples. We show that in any circular arc graph G, η(G)less-than-or-equals, slant2χ(G)−1, and there is a family with equality. So, it makes sense to study Hadwiger's conjecture for this family.

Measurement of shock stand-off distance on a 120 degrees blunt cone model at hypersonic Mach number in Argon

The flow around a 120 degrees blunt cone model with a base radius of 60mm has been visualised at Mach 14.8 and 9.1 using argon as the test gas, at the newly established high speed schlieren facility in the IISc hypersonic shock tunnel HST2. The experimental shock stand off distance around the blunt cone is compared with that obtained using a commercial CFD package. The computed values of shock stand off distance of the blunt cone is found to agree reasonably well with the experimental data.

Long-lived giant number fluctuations in a swarming granular nematic

Coherently moving flocks of birds, beasts, or bacteria are examples of living matter with spontaneous orientational order. How do these systems differ from thermal equilibrium systems with such liquid crystalline order? Working with a fluidized monolayer of macroscopic rods in the nematic liquid crystalline phase, we find giant number fluctuations consistent with a standard deviation growing linearly with the mean, in contrast to any situation where the central limit theorem applies. These fluctuations are long-lived, decaying only as a logarithmic function of time. This shows that flocking, coherent motion, and large-scale inhomogeneity can appear in a system in which particles do not communicate except by contact.

Hadwiger Number and the Cartesian Product of Graphs

The Hadwiger number eta(G) of a graph G is the largest integer n for which the complete graph K-n on n vertices is a minor of G. Hadwiger conjectured that for every graph G, eta(G) >= chi(G), where chi(G) is the chromatic number of G. In this paper, we study the Hadwiger number of the Cartesian product G square H of graphs. As the main result of this paper, we prove that eta(G(1) square G(2)) >= h root 1 (1 - o(1)) for any two graphs G(1) and G(2) with eta(G(1)) = h and eta(G(2)) = l. We show that the above lower bound is asymptotically best possible when h >= l. This asymptotically settles a question of Z. Miller (1978). As consequences of our main result, we show the following: 1. Let G be a connected graph. Let G = G(1) square G(2) square ... square G(k) be the ( unique) prime factorization of G. Then G satisfies Hadwiger's conjecture if k >= 2 log log chi(G) + c', where c' is a constant. This improves the 2 log chi(G) + 3 bound in [2] 2. Let G(1) and G(2) be two graphs such that chi(G1) >= chi(G2) >= clog(1.5)(chi(G(1))), where c is a constant. Then G1 square G2 satisfies Hadwiger's conjecture. 3. Hadwiger's conjecture is true for G(d) (Cartesian product of G taken d times) for every graph G and every d >= 2. This settles a question by Chandran and Sivadasan [2]. ( They had shown that the Hadiwger's conjecture is true for G(d) if d >= 3).

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.

Flow of a maxwell liquid fluid between two rotating coaxial cones having the same vertex

We consider the secondary flows arising in the motion of a Maxwell fluid between two rotating coaxial cones having the same vertex. We find that in any meridian plane passing through the common axis of the cones, the flow field is divided into two regions. Such a division of flow field was first reported by Bhatnagar and Rathna.

A cost effective pipelined divider for double precision floating point number

he growth of high-performance application in computer graphics, signal processing and scientific computing is a key driver for high performance, fixed latency; pipelined floating point dividers. Solutions available in the literature use large lookup table for double precision floating point operations.In this paper, we propose a cost effective, fixed latency pipelined divider using modified Taylor-series expansion for double precision floating point operations. We reduce chip area by using a smaller lookup table. We show that the latency of the proposed divider is 49.4 times the latency of a full-adder. The proposed divider reduces chip area by about 81% than the pipelined divider in [9] which is based on modified Taylor-series.

An Estimator Algorithm For Learning Automata With Changing Number Of Actions

In many problems of decision making under uncertainty the system has to acquire knowledge of its environment and learn the optimal decision through its experience. Such problems may also involve the system having to arrive at the globally optimal decision, when at each instant only a subset of the entire set of possible alternatives is available. These problems can be successfully modelled and analysed by learning automata. In this paper an estimator learning algorithm, which maintains estimates of the reward characteristics of the random environment, is presented for an automaton with changing number of actions. A learning automaton using the new scheme is shown to be e-optimal. The simulation results demonstrate the fast convergence properties of the new algorithm. The results of this study can be extended to the design of other types of estimator algorithms with good convergence properties.

Design of crosspoint-irredundant PLAs using minimal number of control inputs

The problem of determining a minimal number of control inputs for converting a programmable logic array (PLA) with undetectable faults to crosspoint-irredundant PLA for testing has been formulated as a nonstandard set covering problem. By representing subsets of sets as cubes, this problem has been reformulated as familiar problems. It is noted that this result has significance because a crosspoint-irredundant PLA can be converted to a completely testable PLA in a straightforward fashion, thus achieving very good fault coverage and easy testability.