The energy balance in the Ramdas layer

On calm clear nights, air at a height of a few decimetres above bare soil can be cooler than the surface by several degrees in what we shall call the Ramdas layer (Ramdas and Atmanathan, 1932). The authors have recently offered a logical explanation for such a lifted temperature minimum, together with a detailed numerical model. In this paper, we provide physical insight into the phenomenon by a detailed discussion of the energy budget in four typical cases, including one with a lifted minimum. It is shown that the net cooling rate near ground is the small difference between two dominant terms, representing respectively radiative upflux from the ground and from the air layers just above ground. The delicate energy balance that leads to the lifted minimum is upset by turbulent transport, by surface emissivity approaching unity, or by high ground cooling rates. The rapid variation of the flux emissivity of humid air is shown to dominate radiative transport near the ground.

Novel correlations in two dimensions: Two-body problem

We discuss a many-body Hamiltonian with two- and three-body interactions in two dimensions introduced recently by Murthy, Bhaduri and Sen. Apart from an analysis of some exact solutions in the many-body system, we analyse in detail the two-body problem which is completely solvable. We show that the solution of the two-body problem reduces to solving a known differential equation due to Heun. We show that the two-body spectrum becomes remarkably simple for large interaction strengths and the level structure resembles that of the Landau levels. We also clarify the 'ultraviolet' regularization which is needed to define an inverse-square potential properly and discuss its implications for our model.

Response, loads, and stability of interconnected rotor-body systems

A rotor-body system with blades interconnected through viscoelastic elements is analyzed for response, loads, and stability in propulsive trim in ground contact and under forward-flight conditions, A conceptual model of a multibladed rotor with rigid flap and lag motions, and the fuselage with rigid pitch and roll motions is considered, Although the interconnecting elements are placed in the in-plane direction, considerable coupling between the flap-lag motions of the blades can occur in certain ranges of interblade element stiffness, Interblade coupling can yield significant changes in the response, loads, and stability that are dependent on the interblade element and rotor-body parameters, Ground resonance stability investigations show that by tuning the interblade element stiffness, the ground resonance instability problem can be reduced or eliminated, The interblade elements with damping and stiffness provide an effective method to overcome the problems of ground and air resonance.

Triply-periodic balance surfaces

The list of possible G-H symmetries for triply-periodic balance surfaces, given by Koch and Fischer, is studied with a view to finding new types. It is found that balance surfaces exist for all the cases that were labelled as undecided in the work of Koch and Fischer. For some of these, new minimal surfaces have been found, with the aid of Brakke's 'Surface Evolver'. (C) 1997 Elsevier Science B.V.

A differential geometric method for kinematic analysis of two- and three-degree-of-freedom rigid body motions

In this paper, we present a novel differential geometric characterization of two- and three-degree-of-freedom rigid body kinematics, using a metric defined on dual vectors. The instantaneous angular and linear velocities of a rigid body are expressed as a dual velocity vector, and dual inner product is defined on this dual vector, resulting in a positive semi-definite and symmetric dual matrix. We show that the maximum and minimum magnitude of the dual velocity vector, for a unit speed motion, can be obtained as eigenvalues of this dual matrix. Furthermore, we show that the tip of the dual velocity vector lies on a dual ellipse for a two-degree-of-freedom motion and on a dual ellipsoid for a three-degree-of-freedom motion. In this manner, the velocity distribution of a rigid body can be studied algebraically in terms of the eigenvalues of a dual matrix or geometrically with the dual ellipse and ellipsoid. The second-order properties of the two- and three-degree-of-freedom motions of a rigid body are also obtained from the derivatives of the elements of the dual matrix. This results in a definition of the geodesic motion of a rigid body. The theoretical results are illustrated with the help of a spatial 2R and a parallel three-degree-of-freedom manipulator.

Lubricity of an oil in water emulsion in metal cutting: The effect of hydrophilic/lypophilic balance of emulsifiers

A steel disc is cut using a single point tool. The coefficient of friction of the nascent cut surface is measured by a spherical steel pin situated in close proximity of the point of cutting. The tool, disc and the friction pin are immersed in an oil in water emulsion bath during the experiment. The purpose of the experiments conducted here is to record the effect of hydrophilic/lypophilic balance (HLB) of the emulsifier on the lubricity experienced in the cutting operation. The more lypophilic emulsifiers were found to give greater lubricity than what is recorded when the emulsifier is more hydrophilic. XPS and FTIR spectroscopy are used to explore the tribofilm generated on the nascent cut surface to indicate a possible rationale for the effect. (C) 2011 Elsevier B.V. All rights reserved.

Fully Comprehensive Geometrically Non-Linear Dynamic Analysis of Multi-Body Beam Systems with Elastic Couplings

This paper is concerned with the dynamic analysis of flexible,non-linear multi-body beam systems. The focus is on problems where the strains within each elastic body (beam) remain small. Based on geometrically non-linear elasticity theory, the non-linear 3-D beam problem splits into either a linear or non-linear 2-D analysis of the beam cross-section and a non-linear 1-D analysis along the beam reference line. The splitting of the three-dimensional beam problem into two- and one-dimensional parts, called dimensional reduction,results in a tremendous savings of computational effort relative to the cost of three-dimensional finite element analysis,the only alternative for realistic beams. The analysis of beam-like structures made of laminated composite materials requires a much more complicated methodology. Hence, the analysis procedure based on Variational Asymptotic Method (VAM), a tool to carry out the dimensional reduction, is used here.The analysis methodology can be viewed as a 3-step procedure. First, the sectional properties of beams made of composite materials are determined either based on an asymptotic procedure that involves a 2-D finite element nonlinear analysis of the beam cross-section to capture trapeze effect or using strip-like beam analysis, starting from Classical Laminated Shell Theory (CLST). Second, the dynamic response of non-linear, flexible multi-body beam systems is simulated within the framework of energy-preserving and energy-decaying time integration schemes that provide unconditional stability for non-linear beam systems. Finally,local 3-D responses in the beams are recovered, based on the 1-D responses predicted in the second step. Numerical examples are presented and results from this analysis are compared with those available in the literature.

Thermal Weight Functions and Stress Intensity Factors for Bonded Dissimilar Media Using Body Analogy

In this study, an analytical method is presented for the computation of thermal weight functions in two dimensional bi-material elastic bodies containing a crack at the interface and subjected to thermal loads using body analogy method. The thermal weight functions are derived for two problems of infinite bonded dissimilar media, one with a semi-infinite crack and the other with a finite crack along the interface. The derived thermal weight functions are shown to reduce to the already known expressions of thermal weight functions available in the literature for the respective homogeneous elastic body. Using these thermal weight functions, the stress intensity factors are computed for the above interface crack problems when subjected to an instantaneous heat source.