Mean first passage time approach to the problem of optimal barrier subdivision for Kramer's escape rate

We consider the effect of subdividing the potential barrier along the reaction coordinate on Kramer's escape rate for a model potential, Using the known supersymmetric potential approach, we show the existence of an optimal number of subdivisions that maximizes the rate, We cast the problem as a mean first passage time problem of a biased random walker and obtain equivalent results, We briefly summarize the results of our investigation on the increase in the escape rate by placing a blow-torch in the unstable part of one of the potential wells. (C) 1999 Elsevier Science B.V. All rights reserved.

Tensile flow behaviour of 2.25Cr-1Mo ferritic steel base metal and simulated heat affected zone structures of 2.25Cr-1Mo weld joint

Tensile tests in the temperature range 298 to 873 K have been performed on 2.25Cr-1Mo base metal and simulated heat affected zone (HAZ) structures of its weld joint, namely coarse grain bainite, fine grain bainite and intercritical structure. Tensile flow behaviour of all the microstructural conditions could be adequately described by the Hollomon equation (sigma = K-1 epsilon(n1)) at higher (> 623 K) temperatures. Deviation from the Hollomon equation was observed at low strains and lower (< 623 K) temperatures. The Ludwigson modification of Hollomon's equation, sigma = K-1 epsilon(n1) + exp (K-2 + n(2) epsilon), was found to describe the flow curve. In general, the flow parameters n(1), K-1, n(2) and K-2 were found to decrease with increase in temperature except in the intermediate temperature range (423 to 623 K). Peaks/plateaus were observed in their variation with temperature in the intermediate temperature range coinciding with the occurrence of serrated flow in the load-elongation curve. The n(1) Value increased and the K-1 value decreased with the type of microstructure in the order: coarse grain bainite, fine grain bainite, base metal and intercritical structure. The variation of nl with microstructure has been rationalized on the basis of mean free path (MFP) of dislocations which is directly related to the inter-particle spacing. Larger MFP of dislocations lead to higher strain hardening exponents n(1).

Mean and fluctuating pressure in boat-tail separated flows at transonic speeds

Experiments were carried out investigating the features of mean and unsteady surface pressure fluctuations in boat-tail separated flows relevant to launch vehicle configurations at transonic speeds. The tests were performed on a generic axisymmetric body in the Mach-number range of 0.7-1.2, and the important geometrical parameters, namely, the boat-tail angle and diameter ratio, were varied systematically. The measurements made included primarily the mean and unsteady surface-pressure fluctuations on nine different model configurations. Flow-visualization studies employing a surface oil flow, and schlieren techniques were carried out to infer features like boundary-layer separation, reattachment, and shock waves in the flow. The features of mean and fluctuating surface pressures are discussed in detail including aspects of similarity. It has been observed that, on a generic configuration employed in the present study, the maximum levels of surface-pressure fluctuations in the reattachment zone are appreciably lower than those found on launch vehicle configurations having a bulbous or hammerhead nose shape. A simple correlation is suggested for the maximum value of rms pressure fluctuations in the reattachment zone at different freestream Mach numbers.

Surfaces of Bounded Mean Curvature In Riemannian Manifolds

Consider a sequence of closed, orientable surfaces of fixed genus g in a Riemannian manifold M with uniform upper bounds on the norm of mean curvature and area. We show that on passing to a subsequence, we can choose parametrisations of the surfaces by inclusion maps from a fixed surface of the same genus so that the distance functions corresponding to the pullback metrics converge to a pseudo-metric and the inclusion maps converge to a Lipschitz map. We show further that the limiting pseudo-metric has fractal dimension two. As a corollary, we obtain a purely geometric result. Namely, we show that bounds on the mean curvature, area and genus of a surface F subset of M, together with bounds on the geometry of M, give an upper bound on the diameter of F. Our proof is modelled on Gromov's compactness theorem for J-holomorphic curves.

Toward a Mean Field Formulation of the Babcock-Leighton Type Solar Dynamo. I. α-Coefficient versus Durney's Double-Ring Approach

We develop a model of the solar dynamo in which, on the one hand, we follow the Babcock-Leighton approach to include surface processes, such as the production of poloidal field from the decay of active regions, and, on the other hand, we attempt to develop a mean field theory that can be studied in quantitative detail. One of the main challenges in developing such models is to treat the buoyant rise of the toroidal field and the production of poloidal field from it near the surface. A previous paper by Choudhuri, Schüssler, & Dikpati in 1995 did not incorporate buoyancy. We extend this model by two contrasting methods. In one method, we incorporate the generation of the poloidal field near the solar surface by Durney's procedure of double-ring eruption. In the second method, the poloidal field generation is treated by a positive α-effect concentrated near the solar surface coupled with an algorithm for handling buoyancy. The two methods are found to give qualitatively similar results.

Axially homogeneous, zero mean flow buoyancy-driven turbulence in a vertical pipe

We report an experimental study of a new type of turbulent flow that is driven purely by buoyancy. The flow is due to an unstable density difference, created using brine and water, across the ends of a long (length/diameter=9) vertical pipe. The Schmidt number Sc is 670, and the Rayleigh number (Ra) based on the density gradient and diameter is about 108. Under these conditions the convection is turbulent, and the time-averaged velocity at any point is ‘zero’. The Reynolds number based on the Taylor microscale, Reλ, is about 65. The pipe is long enough for there to be an axially homogeneous region, with a linear density gradient, about 6–7 diameters long in the midlength of the pipe. In the absence of a mean flow and, therefore, mean shear, turbulence is sustained just by buoyancy. The flow can be thus considered to be an axially homogeneous turbulent natural convection driven by a constant (unstable) density gradient. We characterize the flow using flow visualization and particle image velocimetry (PIV). Measurements show that the mean velocities and the Reynolds shear stresses are zero across the cross-section; the root mean squared (r.m.s.) of the vertical velocity is larger than those of the lateral velocities (by about one and half times at the pipe axis). We identify some features of the turbulent flow using velocity correlation maps and the probability density functions of velocities and velocity differences. The flow away from the wall, affected mainly by buoyancy, consists of vertically moving fluid masses continually colliding and interacting, while the flow near the wall appears similar to that in wall-bound shear-free turbulence. The turbulence is anisotropic, with the anisotropy increasing to large values as the wall is approached. A mixing length model with the diameter of the pipe as the length scale predicts well the scalings for velocity fluctuations and the flux. This model implies that the Nusselt number would scale as Ra1/2Sc1/2, and the Reynolds number would scale as Ra1/2Sc−1/2. The velocity and the flux measurements appear to be consistent with the Ra1/2 scaling, although it must be pointed out that the Rayleigh number range was less than 10. The Schmidt number was not varied to check the Sc scaling. The fluxes and the Reynolds numbers obtained in the present configuration are much higher compared to what would be obtained in Rayleigh–Bénard (R–B) convection for similar density differences.

Voltage and Temperature Scalable Standard Cell Leakage Models Based on Stacks for Statistical Leakage Characterization

With extensive use of dynamic voltage scaling (DVS) there is increasing need for voltage scalable models. Similarly, leakage being very sensitive to temperature motivates the need for a temperature scalable model as well. We characterize standard cell libraries for statistical leakage analysis based on models for transistor stacks. Modeling stacks has the advantage of using a single model across many gates there by reducing the number of models that need to be characterized. Our experiments on 15 different gates show that we needed only 23 models to predict the leakage across 126 input vector combinations. We investigate the use of neural networks for the combined PVT model, for the stacks, which can capture the effect of inter die, intra gate variations, supply voltage(0.6-1.2 V) and temperature (0 - 100degC) on leakage. Results show that neural network based stack models can predict the PDF of leakage current across supply voltage and temperature accurately with the average error in mean being less than 2% and that in standard deviation being less than 5% across a range of voltage, temperature.

Voltage and Temperature Scalable Gate Delay and Slew Models Including Intra-Gate Variations

We investigate the feasibility of developing a comprehensive gate delay and slew models which incorporates output load, input edge slew, supply voltage, temperature, global process variations and local process variations all in the same model. We find that the standard polynomial models cannot handle such a large heterogeneous set of input variables. We instead use neural networks, which are well known for their ability to approximate any arbitrary continuous function. Our initial experiments with a small subset of standard cell gates of an industrial 65 nm library show promising results with error in mean less than 1%, error in standard deviation less than 3% and maximum error less than 11% as compared to SPICE for models covering 0.9- 1.1 V of supply, -40degC to 125degC of temperature, load, slew and global and local process parameters. Enhancing the conventional libraries to be voltage and temperature scalable with similar accuracy requires on an average 4x more SPICE characterization runs.

Voltage and Temperature Scalable Gate Delay and Slew Models Including Intra-Gate Variations

We investigate the feasibility of developing a comprehensive gate delay and slew models which incorporates output load, input edge slew, supply voltage, temperature, global process variations and local process variations all in the same model. We find that the standard polynomial models cannot handle such a large heterogeneous set of input variables. We instead use neural networks, which are well known for their ability to approximate any arbitrary continuous function. Our initial experiments with a small subset of standard cell gates of an industrial 65 nm library show promising results with error in mean less than 1%, error in standard deviation less than 3% and maximum error less than 11% as compared to SPICE for models covering 0.9- 1.1 V of supply, -40degC to 125degC of temperature, load, slew and global and local process parameters. Enhancing the conventional libraries to be voltage and temperature scalable with similar accuracy requires on an average 4x more SPICE characterization runs.

Expediency of Penetration Ratio and Evaluation of Mean Throughput for Safety and Commercial Applications in VANETs

Vehicular ad hoc network (VANET) applications are principally categorized into safety and commercial applications. Efficient traffic management for routing an emergency vehicle is of paramount importance in safety applications of VANETs. In the first case, a typical example of a high dense urban scenario is considered to demonstrate the role of penetration ratio for achieving reduced travel time between source and destination points. The major requirement for testing these VANET applications is a realistic simulation approach which would justify the results prior to actual deployment. A Traffic Simulator coupled with a Network Simulator using a feedback loop feature is apt for realistic simulation of VANETs. Thus, in this paper, we develop the safety application using traffic control interface (TraCI), which couples SUMO (traffic simulator) and NS2 (network simulator). Likewise, the mean throughput is one of the necessary performance measures for commercial applications of VANETs. In the next case, commercial applications have been considered wherein the data is transferred amongst vehicles (V2V) and between roadside infrastructure and vehicles (I2V), for which the throughput is assessed.

Model for Predicting the Mean Drop Size in Effervescent Sprays

This paper is focused on the development of a model for predicting the mean drop size in effervescent sprays. A combinatorial approach is followed in this modeling scheme, which is based on energy and entropy principles. The model is implemented in cascade in order to take primary breakup (due to exploding gas bubbles) and secondary breakup (due to shearing action of surrounding medium) into account. The approach in this methodology is to obtain the most probable drop size distribution by maximizing the entropy while satisfying the constraints of mass and energy balance. The comparison of the model predictions with the past experimental data is presented for validation. A careful experimental study is conducted over a wide range of gas-to-liquid ratios, which shows a good agreement with the model predictions: It is observed that the model gives accurate results in bubbly and annular flow regimes. However, discrepancies are observed in the transitional slug flow regime of the atomizer.

Voltage and Temperature-Aware SSTA Using Neural Network Delay Model

With the emergence of voltage scaling as one of the most powerful power reduction techniques, it has been important to support voltage scalable statistical static timing analysis (SSTA) in deep submicrometer process nodes. In this paper, we propose a single delay model of logic gate using neural network which comprehensively captures process, voltage, and temperature variation along with input slew and output load. The number of simulation programs with integrated circuit emphasis (SPICE) required to create this model over a large voltage and temperature range is found to be modest and 4x less than that required for a conventional table-based approach with comparable accuracy. We show how the model can be used to derive sensitivities required for linear SSTA for an arbitrary voltage and temperature. Our experimentation on ISCAS 85 benchmarks across a voltage range of 0.9-1.1V shows that the average error in mean delay is less than 1.08% and average error in standard deviation is less than 2.85%. The errors in predicting the 99% and 1% probability point are 1.31% and 1%, respectively, with respect to SPICE. The two potential applications of voltage-aware SSTA have been presented, i.e., one for improving the accuracy of timing analysis by considering instance-specific voltage drops in power grids and the other for determining optimum supply voltage for target yield for dynamic voltage scaling applications.

Analysis of Lined Ducts With Mean Flow, With Application to Dissipative Mufflers

Mufflers with at least one acoustically absorptive duct are generally called dissipative mufflers. Generally, for want of systems approach, these mufflers are characterized by transmission loss of the lined duct with overriding corrections for the terminations, mean flow, etc. In this article, it is proposed that dissipative duct should be integrated with other muffler elements, source impedance and radiation impedance, by means of transfer matrix approach. Towards this end, the transfer matrix for rectangular duct with mean flow has been derived here, for the least attenuated mode. Mean flow introduces a coupling between transverse wave numbers and axial wave number, the evaluation of which therefore calls for simultaneous solution of two or three transcendental equations. This is done by means of a Newton-Raphson iteration scheme, which is illustrated here for square ducts lined with porous ceramic tiles.

Transfer matrix modeling of hyperbolic and parabolic ducts with incompressible mean flow

A general differential equation for the propagation of sound in a variable area duct or nozzle carrying incompressible mean flow (of low Mach number) is derived and solved for hyperbolic and parabolic shapes. Expressions for the state variables of acoustic pressure and acoustic mass velocity of the shapes are derived. Self‐consistent expressions for the four‐pole parameters are developed. The conical, exponential, catenoidal, sine, and cosine ducts are shown to be special cases of hyperbolic ducts. Finally, it is shown that if the mean flow in computing the transmission loss of the mufflers involving hyperbolic and parabolic shapes was not neglected, little practical benefit would be derived.