A four-variable model for the pattern-forming mechanism in Hydra

A generalized Gierer-Meinhardt model has been used to account for the transplantation experiments in Hydra. In this model, a cross inhibition between the two organizing centres (namely, head and foot) are assumed to be the only mode of interaction in setting up a stable morphogen distribution for the pattern formation in Hydra.

Dynamics of dense sheared granular flows. Part II. The relative velocity distributions

The distribution of relative velocities between colliding particles in shear flows of inelastic spheres is analysed in the Volume fraction range 0.4-0.64. Particle interactions are considered to be due to instantaneous binary collisions, and the collision model has a normal coefficient of restitution e(n) (negative of the ratio of the post- and pre-collisional relative velocities of the particles along the line joining the centres) and a tangential coefficient of restitution e(t) (negative of the ratio of post- and pre-collisional velocities perpendicular to line joining the centres). The distribution or pre-collisional normal relative velocities (along the line Joining the centres of the particles) is Found to be an exponential distribution for particles with low normal coefficient of restitution in the range 0.6-0.7. This is in contrast to the Gaussian distribution for the normal relative velocity in all elastic fluid in the absence of shear. A composite distribution function, which consists of an exponential and a Gaussian component, is proposed to span the range of inelasticities considered here. In the case of roughd particles, the relative velocity tangential to the surfaces at contact is also evaluated, and it is found to be close to a Gaussian distribution even for highly inelastic particles.Empirical relations are formulated for the relative velocity distribution. These are used to calculate the collisional contributions to the pressure, shear stress and the energy dissipation rate in a shear flow. The results of the calculation were round to be in quantitative agreement with simulation results, even for low coefficients of restitution for which the predictions obtained using the Enskog approximation are in error by an order of magnitude. The results are also applied to the flow down an inclined plane, to predict the angle of repose and the variation of the volume fraction with angle of inclination. These results are also found to be in quantitative agreement with previous simulations.

Design of single variable controllers for ammonia reactors

Abstract is not available.

Inelastic Postbuckling of Columns of Variable Flexural Rigidity

Effects of large deformation and inelasticity are considered in formulating the behavior of columns of variable cross section subjected to an axial compressive load. Simple, approximate methods are used to obtain numerical results. The combined effect of the nonlinearities is shown to be of a hardening type for small column deflections

A simple method of estimating the detonation velocity from chemical composition of organic explosives

A simple yet fairly accurate method of calculating the ideal detonation velocity of an organic explosive from a knowledge of the chemical composition alone is proposed. The method is based on the concept that the energetics of a stoichiometrically balanced fuel-oxidizer system is a function of the total oxidizing or reducing valences of the composition. A combination of the valences in the form of Image , where R and P are, respectively, the reducing and oxidizing valences and MW is the molecular weight, has been found to be linearly related to the detonation velocity of the expolosive. The predicting capacity of the method has been found to be superior to other methods in the literature.

Hydration numbers of some metal acetates, monochloroacetates and trichloroacetates in solution from ultrasonic velocity and conpressibility measurements

Ultrasonic velocities in aqueous solutions of some metal acetates, monochloroacelates and trichloroacetates, and the respective acids have been measured at 1 MHz frequency using the pulse technique. The ultrsonic velocity, adiabatic compressibility and apperent molal compressibility were measured as a function of concentration. The apparent molal compressibility values at infinite dilution were calculated and used to determine the hydration numbers.

Velocity ratio in the analysis of linear dynamical systems

The transfer matrix method is known to be well suited for a complete analysis of a lumped as well as distributed element, one-dimensional, linear dynamical system with a marked chain topology. However, general subroutines of the type available for classical matrix methods are not available in the current literature on transfer matrix methods. In the present article, general expressions for various aspects of analysis-viz., natural frequency equation, modal vectors, forced response and filter performance—have been evaluated in terms of a single parameter, referred to as velocity ratio. Subprograms have been developed for use with the transfer matrix method for the evaluation of velocity ratio and related parameters. It is shown that a given system, branched or straight-through, can be completely analysed in terms of these basic subprograms, on a stored program digital computer. It is observed that the transfer matrix method with the velocity ratio approach has certain advantages over the existing general matrix methods in the analysis of one-dimensional systems.

Non-linear bending of beams of variable cross-section

For the non-linear bending of cantilever beams of variable cross-section, the effect of large deformations, but with linear elasticity, is considered. The governing integral equation is solved by a numerical iterative procedure. Results for some typical cases are obtained and compared with some of those available in the literature.

Planar pursuit-evasion with variable speeds, part 1, extremal trajectory maps

Pursuit evasion in a plane is formulated with both players allowed to vary their speeds between fixed limits. A suitable choice of real-space coordinates confers open-loop optimality on the game. The solution in the small is described in terms of the individual players'' extremal trajectory maps (ETM). Each map is independent of role, adversary, and capture radius. An ETM depicts the actual real-space trajectories. A template method of generating constant control arcs is described. Examples of ETM for an aircraft flying at a constant altitude with fixed and varying speeds are presented.

Planar pursuit-evasion with variable speeds, part 2, barrier sections

An iterative method of constructing sections of the game surfaces from the players'' extremal trajectory maps is discussed. Barrier sections are presented for aircraft pursuit-evasion at constant altitude, with one aircraft flying at sustained speed and the other varying its speed.

Unsteady laminar boundary layers in a compressible stagnation flow

The unsteady laminar compressible boundary-layer flow in the immediate vicinity of a two-dimensional stagnation point due to an incident stream whose velocity varies arbitrarily with time is considered. The governing partial differential equations, involving both time and the independent similarity variable, are transformed into new co-ordinates with finite ranges by means of a transformation which maps an infinite interval into a finite one. The resulting equations are solved by converting them into a matrix equation through the application of implicit finite-difference formulae. Computations have been carried out for two particular unsteady free-stream velocity distributions: (1) a constantly accelerating stream and (2) a fluctuating stream. The results show that in the former case both the skin-friction and the heat-transfer parameter increase steadily with time after a certain instant, while in the latter they oscillate thus responding to the fluctuations in the free-stream velocity.

Zero-crossings in turbulent signals

A primary motivation for this work arises from the contradictory results obtained in some recent measurements of the zero-crossing frequency of turbulent fluctuations in shear flows. A systematic study of the various factors involved in zero-crossing measurements shows that the dynamic range of the signal, the discriminator characteristics, filter frequency and noise contamination have a strong bearing on the results obtained. These effects are analysed, and explicit corrections for noise contamination have been worked out. New measurements of the zero-crossing frequency N0 have been made for the longitudinal velocity fluctuation in boundary layers and a wake, for wall shear stress in a channel, and for temperature derivatives in a heated boundary layer. All these measurements show that a zero-crossing microscale, defined as Λ = (2πN0)−1, is always nearly equal to the well-known Taylor microscale λ (in time). These measurements, as well as a brief analysis, show that even strong departures from Gaussianity do not necessarily yield values appreciably different from unity for the ratio Λ/λ. Further, the variation of N0/N0 max across the boundary layer is found to correlate with the familiar wall and outer coordinates; the outer scaling for N0 max is totally inappropriate, and the inner scaling shows only a weak Reynolds-number dependence. It is also found that the distribution of the interval between successive zero-crossings can be approximated by a combination of a lognormal and an exponential, or (if the shortest intervals are ignored) even of two exponentials, one of which characterizes crossings whose duration is of the order of the wall-variable timescale ν/U2*, while the other characterizes crossings whose duration is of the order of the large-eddy timescale δ/U[infty infinity]. The significance of these results is discussed, and it is particularly argued that the pulse frequency of Rao, Narasimha & Badri Narayanan (1971) is appreciably less than the zero-crossing rate.

Velocity Distribution in Smooth Rectangular Open Channels-Closure

Abstract is not available.

A thymine-related mutation system in immunoglobulin variable regions

Abstract is not available.