A note on the damping and oscillations of a fluid drop moving in another fluid

The oscillations of a drop moving in another fluid medium have been studied at low values of Reynolds number and Weber number by taking into consideration the shape of the drop and the viscosities of the two phases in addition to the interfacial tension. The deformation of the drop modifies the Lamb's expression for frequency by including a correction term while the viscous effects split the frequency into a pair of frequencies—one lower and the other higher than Lamb's. The lower frequency mode has ample experimental support while the higher frequency mode has also been observed. The two modes almost merge with Lamb's frequency for the asymptotic cases of a drop in free space or a bubble in a dense viscous fluid but the splitting becomes large when the two fluids have similar properties. Instead of oscillations, aperiodic damping modes are found to occur in drops with sizes smaller than a critical size ($\sim\hat{\rho}\hat{\nu}^2/T $). With the help of these calculations, many of the available experimental results are analyzed and discussed.

A Note on the Genericity of Simultaneous Stabilizability and Pole Assignability

n this paper we study the genericity of simultaneous stabilizability, simultaneous strong stabilizability, and simultaneous pole assignability, in linear multivariable systems. The main results of the paper had been previously established by Ghosh and Byrnes using state-space methods. In contrast, the proofs in the present paper are based on input-output arguments, and are much simpler to follow, especially in the case of simultaneous and simultaneous strong stabilizability. Moreover, the input-output methods used here suggest computationally reliable algorithms for solving these two types of problems. In addition to the main results, we also prove some lemmas on generic greatest common divisors which are of independent interest.

Experimental and Analytical Investigations of the actions taking place in a Synchronous machine during the starting period when the starting Is effected by means of alternating current

The literature on the subject of the present investigation is somewhat meagre. A rotary converter or synchronous motor no! provided with any special starting devices forms, when started from the alternating current side, a type of induction motor whoso Htator is provided with a polyphase winding, and whoso rotor has a single-phase (or single magnetic axis) winding.

Note on the Similarity Solutions of Unsteady Jets in Rotating Fluids

The structure of time dependent jets in rotating fluids using similarity transformations is studied theoretically for which exact solutions are discussed. Approximate solution using a modified yon Mises transformation is also explored.

A note on acyclic edge coloring of complete bipartite graphs

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic (2-colored) cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a'(G). Let Delta = Delta(G) denote the maximum degree of a vertex in a graph G. A complete bipartite graph with n vertices on each side is denoted by K-n,K-n. Alon, McDiarmid and Reed observed that a'(K-p-1,K-p-1) = p for every prime p. In this paper we prove that a'(K-p,K-p) <= p + 2 = Delta + 2 when p is prime. Basavaraju, Chandran and Kummini proved that a'(K-n,K-n) >= n + 2 = Delta + 2 when n is odd, which combined with our result implies that a'(K-p,K-p) = p + 2 = Delta + 2 when p is an odd prime. Moreover we show that if we remove any edge from K-p,K-p, the resulting graph is acyclically Delta + 1 = p + 1-edge-colorable. (C) 2009 Elsevier B.V. All rights reserved.

Note On The Stability Of Parallel Magnetic-Fields - Comment

It is shown that the conclusions arrived at regarding the instability of an incompressible fluid cylinder in the presence of the magnetic field and the streaming velocity in a recent communication easily follow from the study of propagation characteristics of Alfvén surface waves along cylindrical plasma columns made earlier.

A note on the existence of Alfvén surface waves

The Alfvén surface waves can arise due to the discontinuity in the Alfvén speed across the interface along which these waves propagate. This note studies the relationship between v A1 and v A2 which is required for the existence of Alfvén surface waves in low-beta.

Note on the one-parameter scaling theory of localisation

The necessary and sufficient condition for the existence of the one-parameter scale function, the /Munction, is obtained exactly. The analysis reveals certain inconsistency inherent in the scaling theory, and tends to support Motts’ idea of minimum metallic conductivity.

Note on the one-parameter scaling theory of localisation

The necessary and sufficient condition for the existence of the one-parameter scale function, the /Munction, is obtained exactly. The analysis reveals certain inconsistency inherent in the scaling theory, and tends to support Motts’ idea of minimum metallic conductivity.

A Note on the Determination of Plastic Limit of Fine-Grained Soils

Plastic limit of fine-grained soils is conventionally determined in the laboratory by the soil thread rolling method. Many adverse comments have been recorded in the geotechnical engineering literature on the method about its reproducibility and operator dependency. The presen experimental study, which is based on a well-planned and meticulously executed experimental program, critically evaluates the effect of size of the rolled soil thread on the plastic limit of fine-grained soil and the operator dependency of the results. The results have shown that if the plastic limit tests are performed by a trained operator, then consistent results can be obtained and that the effect of size of the rolled soil thread on plastic limit is negligibly small.

A Note on Southwood's Instability Criterion

It is shown that Southwood's instability criterion for the onset of the Kelvin-Helmholtz instability at the magnetopause can be directly obtained from the marginal instability condition for the pure Alfven surface waves propagating along the interface between two incompressible media in the limit when the wave propagation direction is nearly perpendicular to the direction of the largest magnetic field. The phase velocity of the surface waves first excited at the onset of the instability depends on the angle between the interplanetary magnetic field and flow velocity in the solar wind in front of the bow shock.

A note on mass transfer in turbulent wall jets

THE PROCESS of mass transfer from saturated porous surfaces virtual origin ; exposed to turbulent air streams finds many practical applitransverse coordinate; cations. In many cases, the air stream will be in the form of a height of nozzle above flat plate--radial wall jet; wall jet over the porous surface. The aerodynamics of both plane and radial wall jets have been investigated in detail and a vast amount of literature is available on the subject [l-3].

A note on the existence of Alfven surface waves

The Alfven surface waves can arise due to the discontinuity in the Alfven speed across the interface along which these waves propagate. This note studies the relationship between v A1 and v A2 which is required for the existence of Alfven surface waves in low-beta plasma.