Ward Identities for Scale and Special Conformal Transformations in Inflation

We derive the general Ward identities for scale and special conformal transformations in theories of single field inflation. Our analysis is model independent and based on symmetry considerations alone. The identities we obtain are valid to all orders in the slow roll expansion. For special conformal transformations, the Ward identities include a term which is non-linear in the fields that arises due to a compensating spatial reparametrization. Some observational consequences are also discussed.Comment: 42 Pages. v3: Section on checks of the Ward identities added. The JHEP accepted versio

Constraints from Conformal Symmetry on the Three Point Scalar Correlator in Inflation

Using symmetry considerations, we derive Ward identities which relate the three point function of scalar perturbations produced during inflation to the scalar four point function, in a particular limit. The derivation assumes approximate conformal invariance, and the conditions for the slow roll approximation, but is otherwise model independent. The Ward identities allow us to deduce that the three point function must be suppressed in general, being of the same order of magnitude as in the slow roll model. They also fix the three point function in terms of the four point function, upto one constant which we argue is generically suppressed. Our approach is based on analyzing the wave function of the universe, and the Ward identities arise by imposing the requirements of spatial and time reparametrization invariance on it.Comment: 35 pages; Extra references and comments added, The version published in JHE

Symmetry Constraints in Inflation, α\alpha-vacua, and the Three Point Function

The Ward identities for conformal symmetries in single field models of inflation are studied in more detail in momentum space. For a class of generalized single field models, where the inflaton action contains arbitrary powers of the scalar and its first derivative, we find that the Ward identities are valid. We also study a one-parameter family of vacua, called $\alpha$-vacua, which preserve conformal invariance in de Sitter space. We find that the Ward identities, upto contact terms, are met for the three point function of a scalar field in the probe approximation in these vacua. Interestingly, the corresponding non-Gaussian term in the wave function does not satisfy the operator product expansion. For scalar perturbations in inflation, in the $\alpha$-vacua, we find that the Ward identities are not satisfied. We argue that this is because the back-reaction on the metric of the full quantum stress tensor has not been self-consistently incorporated. We also present a calculation, drawing on techniques from the AdS/CFT correspondence, for the three point function of scalar perturbations in inflation in the Bunch-Davies vacuum.Comment: 51 pages, 3 figures, 6 appendices. v3: JHEP version. Minor typos correcte

Velocity correlations in dense granular flows observed with internal imaging

We show that the velocity correlations in uniform dense granular flows inside a silo are similar to the hydrodynamic response of an elastic hard-sphere liquid. The measurements are made using a fluorescent refractive index matched interstitial fluid in a regime where the flow is dominated by grains in enduring contact and fluctuations scale with the distance traveled, independent of flow rate. The velocity autocorrelation function of the grains in the bulk shows a negative correlation at short time and slow oscillatory decay to zero similar to simple liquids. Weak spatial velocity correlations are observed over several grain diameters. The mean square displacements show an inflection point indicative of caging dynamics. The observed correlations are qualitatively different at the boundaries.Comment: 11 pages, 4 figure

Optimal Decompositions of Barely Separable States

Two families of bipartite mixed quantum states are studied for which it is proved that the number of members in the optimal-decomposition ensemble --- the ensemble realizing the entanglement of formation --- is greater than the rank of the mixed state. We find examples for which the number of states in this optimal ensemble can be larger than the rank by an arbitrarily large factor. In one case the proof relies on the fact that the partial transpose of the mixed state has zero eigenvalues; in the other case the result arises from the properties of product bases that are completable only by embedding in a larger Hilbert space.Comment: 14 Pages (RevTeX), 1 figure (eps). Submitted to the special issue of the J. Mod. Opt. V2: Change in terminology from "ensemble length" to "ensemble cardinality

Modeling the impact of battery degradation within lifecycle cost based design optimization of heavy-duty hybrid electric vehicles

The optimal design of hybrid electric vehicle (HEV) powertrains from a systems perspective is critical to realize the maximum benefits for a given application. This is particularly true in the heavy-duty vehicle space where the major challenges are: (i) greater emphasis on economic viability, (ii) reluctance to take on risk associated with new technologies, and (iii) numerous diverse applications that preclude a one-size-fits-all approach to hybrid-electric powertrain design. Past studies on HEV powertrain design have either ignored battery degradation, or failed to holistically capture its impact from a lifecycle cost perspective. The focus of this effort is the development of a model-based framework that enables parametric optimization of the design and control of hybrid electric vehicles while accounting for the degradation of the lithium-ion battery and its impact on the total cost-of-ownership of the vehicle. Two different implementations of such a framework are described. The first implementation explores a very high-fidelity approach to enable engineering design optimization across a small parameter space. It captures the impact of battery degradation on fuel consumption and battery replacements over the vehicle life by incorporating a high-fidelity electrochemical battery model capable of predicting degradation, and degraded performance, into the powertrain simulation. An electric motor and battery size optimization problem is studied for a parallel HEV transit bus application. Results show that different optimal component sizes are obtained when different optimization objectives, such as net present value, payback period, internal rate of return, or simply the day 1 fuel consumption, are considered. Accounting for the battery degradation in the powertrain simulations shows fuel consumption increasing by up to 10% from day 1 to end-of-life of the battery. These results highlight the utility of the proposed implementation in enabling better design decisions as compared to methods that do not capture the evolution of vehicle performance and fuel consumption as the battery degrades. However, the high-fidelity electrochemical battery degradation model and the interval-by-interval simulation approach used in this implementation are computationally too expensive for a large-scale design study. In contrast, the second implementation uses a simpler empirical battery model to enable a large-scale study over a 10-parameter design space, over multiple architectures and vehicle applications. This implementation is designed to aid heavy-duty vehicle and powertrain component manufacturers in identifying market opportunities and planning future products. The design space explored in this work includes three powertrain component sizing parameters, four control strategy parameters and three vehicle uncertainty parameters. Multiple drive cycles were simulated across the Class 5-7 medium-duty truck and Class 7-8 transit bus applications for both parallel and series plug-in hybrid electric vehicle (PHEV) powertrain architectures with charge depleting and charge sustaining modes of operation. These simulation results were then evaluated for real-world economic viability under different economic assumptions corresponding to the 2015, 2020, 2025 and 2030 time frames. Sensitivity of the economic viability of solutions was also studied with respect to the vehicle uncertainty parameters, economic assumptions and vehicle utilization assumptions. (Abstract shortened by ProQuest.

Impact of Selected Banking System on Small Scale Industries with Special Reference to Gujarat

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Laboratory experiments on cohesive soil bed fluidization by water waves

Part I. Relationships between the rate of bed fluidization and the rate of wave energy dissipation, by Jingzhi Feng and Ashish J. Mehta and Part II. In-situ rheometry for determining the dynamic response of bed, by David J.A. Williams and P. Rhodri Williams. A series of preliminary laboratory flume experiments were carried out to examine the time-dependent behavior of a cohesive soil bed subjected to progressive, monochromatic waves. The bed was an aqueous, 50/50 (by weight) mixture of a kaolinite and an attapulgite placed in a plexiglass trench. The nominal bed thickness was 16 cm with density ranging from 1170 to 1380 kg/m 3, and water above was 16 to 20 cm deep. Waves of design height ranging from 2 to 8 cm and a nominal frequency of 1 Hz were run for durations up to 2970 min. Part I of this report describes experiments meant to examine the rate at which the bed became fluidized, and its relation to the rate of wave energy dissipation. Part II gives results on in-situ rheometry used to track the associated changes in bed rigidity. Temporal and spatial changes of the effective stress were measured during the course of wave action, and from these changes the bed fluidization rate was calculated. A wave-mud interaction model developed in a companion study was employed to calculate the rate of wave energy dissipation. The dependence of the rate of fluidization on the rate of energy dissipation was then explored. Fluidization, which seemingly proceeded down from the bed surface, occurred as a result of the loss of structural integrity of the soil matrix through a buildup of the excess pore pressure and the associated loss of effective stress. The rate of fluidization was typically greater at the beginning of wave action and apparently approached zero with time. This trend coincided with the approach of the rate of energy dissipation to a constant value. In general it was also observed that, for a given wave frequency, the larger the wave height the faster the rate of fluidization and thicker the fluid mud layer formed. On the other hand, increasing the time of bed consolidation prior to wave action decreased the fluidization rate due to greater bed rigidity. Upon cessation of wave action structural recovery followed. Dynamic rigidity was measured by specially designed, in situ shearometers placed in the bed at appropriate elevations to determine the time-dependence of the storage and loss moduli, G' and G", of the viscoelastic clay mixture under 1 Hz waves. As the inter-particle bonds of the space-filling, bed material matrix weakened, the shear propagation velocity decreased measurably. Consequently, G' decreased and G" increased as a transition from dynamically more elastic to more viscous response occurred. These preliminary experiments have demonstrated the validity of the particular rheometric technique used, and the critical need for synchronous, in-situ measurements of pore pressures and moduli characterizing bed rheology in studies on mud fluidization. This study was supported by WES contract DACW39-90-K-0010. (This document contains 151 pages.