Electron energy distributions and transport coefficients in N2 in E times B fields

Using the concept of energy-dependent effective field intensity, electron transport coefficients in nitrogen have been determined in E times B fields (E = electric field intensity, B = magnetic flux density) by the numerical solution of the Boltzmann transport equation for the energy distribution of electrons. It has been observed that as the value of B/p (p = gas pressure) is increased from zero, the perpendicular drift velocity increased linearly at first, reaches a maximum value, and then decreases with increasing B/p. In general, the electron mean energy is found to be a function of Eavet/p( Eavet = averaged effective electric field intensity) only, but the other transport coefficients, such as transverse drift velocity, perpendicular drift velocity, and the Townsend ionization coefficient, are functions of both E/p and B/p.

Velocity-Space Contours of Collision Integrals

Based on the recently found closed-form expressions of the Boltzmann collision integrals in a rigid-sphere gas for multi-Maxwellian distributions, a few typical sets of contour surfaces of the integrals in the space of molecular velocities are presented. These show graphically the tendency toward equilibrium under the influence of collisions. A brief preliminary comparison with Monte Carlo results is also given.

Dynamics of prolate spheroidal mass distributions with varying eccentricity

In this paper we calculate the potential for a prolate spheroidal distribution as in a dark matter halo with a radially varying eccentricity. This is obtained by summing up the shell-by-shell contributions of isodensity surfaces, which are taken to be concentric and with a common polar axis and with an axis ratio that varies with radius. Interestingly, the constancy of potential inside a shell is shown to be a good approximation even when the isodensity contours are dissimilar spheroids, as long as the radial variation in eccentricity is small as seen in realistic systems. We consider three cases where the isodensity contours are more prolate at large radii, or are less prolate or have a constant eccentricity. Other relevant physical quantities like the rotation velocity, the net orbital and vertical frequency due to the halo and an exponential disc of finite thickness embedded in it are obtained. We apply this to the kinematical origin of Galactic warp, and show that a prolate-shaped halo is not conducive to making long-lived warps - contrary to what has been proposed in the literature. The results for a prolate mass distribution with a variable axis ratio obtained are general, and can be applied to other astrophysical systems, such as prolate bars, for a more realistic treatment.

Dynamics of a dilute sheared inelastic fluid. I. Hydrodynamic modes and velocity correlation functions

The hydrodynamic modes and the velocity autocorrelation functions for a dilute sheared inelastic fluid are analyzed using an expansion in the parameter epsilon=(1-e)(1/2), where e is the coefficient of restitution. It is shown that the hydrodynamic modes for a sheared inelastic fluid are very different from those for an elastic fluid in the long-wave limit, since energy is not a conserved variable when the wavelength of perturbations is larger than the ``conduction length.'' In an inelastic fluid under shear, there are three coupled modes, the mass and the momenta in the plane of shear, which have a decay rate proportional to k(2/3) in the limit k -> 0, if the wave vector has a component along the flow direction. When the wave vector is aligned along the gradient-vorticity plane, we find that the scaling of the growth rate is similar to that for an elastic fluid. The Fourier transforms of the velocity autocorrelation functions are calculated for a steady shear flow correct to leading order in an expansion in epsilon. The time dependence of the autocorrelation function in the long-time limit is obtained by estimating the integral of the Fourier transform over wave number space. It is found that the autocorrelation functions for the velocity in the flow and gradient directions decay proportional to t(-5/2) in two dimensions and t(-15/4) in three dimensions. In the vorticity direction, the decay of the autocorrelation function is proportional to t(-3) in two dimensions and t(-7/2) in three dimensions.

Fluctuations in protein synthesis from a single RNA template: Stochastic kinetics of ribosomes

Proteins are polymerized by cyclic machines called ribosomes, which use their messenger RNA (mRNA) track also as the corresponding template, and the process is called translation. We explore, in depth and detail, the stochastic nature of the translation. We compute various distributions associated with the translation process; one of them-namely, the dwell time distribution-has been measured in recent single-ribosome experiments. The form of the distribution, which fits best with our simulation data, is consistent with that extracted from the experimental data. For our computations, we use a model that captures both the mechanochemistry of each individual ribosome and their steric interactions. We also demonstrate the effects of the sequence inhomogeneities of real genes on the fluctuations and noise in translation. Finally, inspired by recent advances in the experimental techniques of manipulating single ribosomes, we make theoretical predictions on the force-velocity relation for individual ribosomes. In principle, all our predictions can be tested by carrying out in vitro experiments.

Fast decay of the velocity autocorrelation function in dense shear flow of inelastic hard spheres

We find in complementary experiments and event-driven simulations of sheared inelastic hard spheres that the velocity autocorrelation function psi(t) decays much faster than t(-3/2) obtained for a fluid of elastic spheres at equilibrium. Particle displacements are measured in experiments inside a gravity-driven flow sheared by a rough wall. The average packing fraction obtained in the experiments is 0.59, and the packing fraction in the simulations is varied between 0.5 and 0.59. The motion is observed to be diffusive over long times except in experiments where there is layering of particles parallel to boundaries, and diffusion is inhibited between layers. Regardless, a rapid decay of psi(t) is observed, indicating that this is a feature of the sheared dissipative fluid, and is independent of the details of the relative particle arrangements. An important implication of our study is that the non-analytic contribution to the shear stress may not be present in a sheared inelastic fluid, leading to a wider range of applicability of kinetic theory approaches to dense granular matter.

On the relationship between finger width, velocity, and fluxes in thermohaline convection

Double-diffusive finger convection occurs in many natural processes.The theories for double-diffusive phenomena that exist at present consider systems with linear stratification in temperature and salinity. The double-diffusive systems with step change in salinity and temperature are, however, not amenable to simple stability analysis. Hence factors that control the width of the finger, velocity, and fluxes in systems that have step change in temperature and salinity have not been understood so far. In this paper we provide new physical insight regarding factors that influence finger convection in two-layer double-diffusive system through two-dimensional numerical simulations. Simulations have been carried out for density stability ratios (R-rho) from 1.5 to 10. For each density stability ratio, the thermal Rayleigh number (Ra-T) has been systematically varied from 7x10(3) to 7x10(8). Results from these simulations show how finger width, velocity, and flux ratios in finger convection are interrelated and the influence of governing parameters such as density stability ratio and the thermal Rayleigh number. The width of the incipient fingers at the time of onset of instability has been shown to vary as Ra-T-1/3. Velocity in the finger varies as Ra(T)1/3/R-rho. Results from simulation agree with the scale analysis presented in the paper. Our results demonstrate that wide fingers have lower velocities and flux ratios compared to those in narrow fingers. This result contradicts present notions about the relation between finger width and flux ratio. A counterflow heat-exchanger analogy is used in understanding the dependence of flux ratio on finger width and velocity.

Turbulent mixed convection in a shallow enclosure with a series of heat generating components

Turbulent mixed convection flow and heat transfer in a shallow enclosure with and without partitions and with a series of block-like heat generating components is studied numerically for a range of Reynolds and Grashof numbers with a time-dependent formulation. The flow and temperature distributions are taken to be two-dimensional. Regions with the same velocity and temperature distributions can be identified assuming repeated placement of the blocks and fluid entry and exit openings at regular distances, neglecting the end wall effects. One half of such module is chosen as the computational domain taking into account the symmetry about the vertical centreline. The mixed convection inlet velocity is treated as the sum of forced and natural convection components, with the individual components delineated based on pressure drop across the enclosure. The Reynolds number is based on forced convection velocity. Turbulence computations are performed using the standard k– model and the Launder–Sharma low-Reynolds number k– model. The results show that higher Reynolds numbers tend to create a recirculation region of increasing strength in the core region and that the effect of buoyancy becomes insignificant beyond a Reynolds number of typically 5×105. The Euler number in turbulent flows is higher by about 30 per cent than that in the laminar regime. The dimensionless inlet velocity in pure natural convection varies as Gr1/3. Results are also presented for a number of quantities of interest such as the flow and temperature distributions, Nusselt number, pressure drop and the maximum dimensionless temperature in the block, along with correlations.

On optimum stratification with proportional allocation for a class of pareto distributions

Cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0001.gif rule [Singh (1975)] has been suggested in the literature for finding approximately optimum strata boundaries for proportional allocation, when the stratification is done on the study variable. This paper shows that for the class of density functions arising from the Wang and Aggarwal (1984) representation of the Lorenz Curve (or DBV curves in case of inventory theory), the cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0002.gif rule in place of giving approximately optimum strata boundaries, yields exactly optimum boundaries. It is also shown that the conjecture of Mahalanobis (1952) “. . .an optimum or nearly optimum solutions will be obtained when the expected contribution of each stratum to the total aggregate value of Y is made equal for all strata” yields exactly optimum strata boundaries for the case considered in the paper.

Long Wavelength Peristaltic Transport of Non-Newton Fluids

Solutions are obtained for the stream function and the pressure field for the flow of non-Newtonian fluids in a tube by long peristaltic waves of arbitrary shape. The axial velocity profiles and stress distributions on the wall are discussed for particular waves of some practical interest. The effect of non- Newtonian character of the fluid is examined.

Practical Algorithms For Mean Velocity Estimation In Pulse Doppler Weather Radars Using A Small Number Of Samples

Doppler weather radars with fast scanning rates must estimate spectral moments based on a small number of echo samples. This paper concerns the estimation of mean Doppler velocity in a coherent radar using a short complex time series. Specific results are presented based on 16 samples. A wide range of signal-to-noise ratios are considered, and attention is given to ease of implementation. It is shown that FFT estimators fare poorly in low SNR and/or high spectrum-width situations. Several variants of a vector pulse-pair processor are postulated and an algorithm is developed for the resolution of phase angle ambiguity. This processor is found to be better than conventional processors at very low SNR values. A feasible approximation to the maximum entropy estimator is derived as well as a technique utilizing the maximization of the periodogram. It is found that a vector pulse-pair processor operating with four lags for clear air observation and a single lag (pulse-pair mode) for storm observation may be a good way to estimate Doppler velocities over the entire gamut of weather phenomena.

Transitional intermittency in boundary layers subjected to pressure gradient

Results are reported from an extensive series of experiments on boundary layers in which the location of pressure gradient and transition onset could be varied almost independently, by judicious use of tunnel wall liners and transition-fixing devices. The experiments show that the transition zone is sensitive to the pressure gradient especially near onset, and can be significantly asymmetric; no universal similarity appears valid in general. Observed intermittency distributions cannot be explained on the basis of the hypothesis, often made, that the spot propagates at speeds proportional to the local free-stream velocity but is otherwise unaffected by the pressure gradient.

Bed Shear from Velocity Profiles: A New Approach

A new binary law of velocity distribution has been developed to describe the velocity profile for the entire flow region. The law is a combination of logarithmic law, valid in the wall (inner) region, and parabolic law, valid in the core (outer) region of the flow. The validity of the law has been established based on earlier data on flat plates, rough and smooth pipes and experimental data obtained from rigid-walled open channels with plane sand beds. A procedure of estimating bed shear stress from the proposed law of velocity distribution using the measured velocity profile has been evolved. Bed shear estimates made according to this procedure are in agreement with the values obtained from uniform flow analysis in the case of open channel flow over a sediment bed. The proposed method of estimating the bed shear stress from the observed velocity profiles is found to be particularly useful in cases where it is difficult to determine precisely the true bed level, such as in the case of flow over sediment beds.

The effects of sliding velocity and sliding time on nanocrystalline tribolayer development and properties in copper

The growth of the nanocrystalline tribolayer produced in oxygen free high conductivity copper after sliding against 440C stainless steel was studied. Tests were conducted on a pin-on-disk tribometer at sliding velocities of 0.05 and 1.0 m/s and sliding times of 0.1 to 10,000 s. Subsurface deformation and the growth of the tribolayer as a function of time were studied with the use of transmission electron microscopy and ion induced secondary electron microscopy. A continuous nanocrystalline tribolayer was produced after as little as 10 s of sliding at both sliding velocities. The tribolayer produced by sliding at 0.05 m/s continued to grow at sliding times up to 10,000 s and developed texture. Dynamic recrystallization of the tribolayer at a sliding velocity of 1.0 m/s inhibited the growth of a continuous anocrystalline tribolayer.