Linear stability, transient growth and the role of viscosity stratification in compressible Couette flow

Linear stability and the nonmodal transient energy growth in compressible plane Couette flow are investigated for two prototype mean flows: (a) the uniform shear flow with constant viscosity, and (b) the nonuniform shear flow with stratified viscosity. Both mean flows are linearly unstable for a range of supersonic Mach numbers (M). For a given M, the critical Reynolds number (Re) is significantly smaller for the uniform shear flow than its nonuniform shear counterpart; for a given Re, the dominant instability (over all streamwise wave numbers, α) of each mean flow belongs to different modes for a range of supersonic M. An analysis of perturbation energy reveals that the instability is primarily caused by an excess transfer of energy from mean flow to perturbations. It is shown that the energy transfer from mean flow occurs close to the moving top wall for “mode I” instability, whereas it occurs in the bulk of the flow domain for “mode II.” For the nonmodal transient growth analysis, it is shown that the maximum temporal amplification of perturbation energy, Gmax, and the corresponding time scale are significantly larger for the uniform shear case compared to those for its nonuniform counterpart. For α=0, the linear stability operator can be partitioned into L∼L̅ +Re2 Lp, and the Re-dependent operator Lp is shown to have a negligibly small contribution to perturbation energy which is responsible for the validity of the well-known quadratic-scaling law in uniform shear flow: G(t∕Re)∼Re2. In contrast, the dominance of Lp is responsible for the invalidity of this scaling law in nonuniform shear flow. An inviscid reduced model, based on Ellingsen-Palm-type solution, has been shown to capture all salient features of transient energy growth of full viscous problem. For both modal and nonmodal instability, it is shown that the viscosity stratification of the underlying mean flow would lead to a delayed transition in compressible Couette flow.

Groundwater Management in India:Physical, Institutional and Policy Alternatives

Groundwater constitutes a vital natural resource for sustaining India’s agricultural economy and meeting the country’s social, ecological and environmental goals. It is a unique resource, widely available, providing security against droughts and yet it is closely linked to surface-water resources and the hydrological cycle. Its availability depends on geo-hydrological conditions and characteristics of aquifers, from deep to alluvium, sediment crystalline rocks to basalt formations; and agro-climate from humid to subhumid and semi-arid to arid. Its reliable supply, uniform quality and temperature, relative turbidity, pollution-safe, minimal evaporation losses, and low cost of development are attributes making groundwater more attractive compared to other resources. It plays a key role in the provision of safe drinking water to rural populations. For example, already almost 80% of domestic water use in rural areas in India is groundwater-supplied, and much of it is being supplied to farms, villages and small towns. Inadequate control of the use of groundwater, indiscriminate application of agrochemicals and unrestrained pollution of the rural environment by other human activities make groundwater usage unsustainable, necessitating proper management in the face of the twin demand for water of good quality for domestic supply and adequate supply for irrigation, ensuring equity, efficiency and sustainability of the resource. Groundwater irrigation has overtaken surface irrigation in the early 1980s, supported by well energization. It is estimated that there are about 24 million energised wells and tube wells now and it is driven by demand rather than availability, evident through the greater occurrence of wells in districts with high population densities. Apart from aquifer characteristics, land fragmentation and landholding size are the factors that decide the density of wells. The ‘rise and fall’ of local economies dependent on groundwater can be summarized as: the green revolution of 1980s, groundwaterbased agrarian boom, early symptoms of groundwater overdraft, and decline of the groundwater socio-ecology. The social characteristics and policy interventions typical of each stage provide a fascinating insight into the human-resource dynamics. This book is a compilation of nine research papers discussing various aspects of groundwater management. It attempts to integrate knowledge about the physical system, the socio-economic system, the institutional set-up and the policy environment to come out with a more realistic analysis of the situation with regard to the nature, characteristics and intensity of resource use, the size of the economy the use generates, and the negative socioeconomic consequences. Complex variables addressed in this regard focusing on northern Gujarat are the stock of groundwater available in the region, its hydrodynamics, its net outflows against inflows, the economics of its intensive use (particularly irrigation in semi-arid and arid regions), its criticality in the regional hydroecological regime, ethical aspects and social aspects of its use. The first chapter by Dinesh Kumar and Singh, dwells on complex groundwater socio-ecology of India, while emphasizing the need for policy measures to address indiscriminate over-exploitation of dwindling resources. The chapter also explores the nature of groundwater economy and the role of electricity prices on it. The next chapter on groundwater issue in north Gujarat provides a description of groundwater resource characteristics followed by a detailed analysis of the groundwater depletion and quality deterioration problems in the region and their undesirable consequences on the economy, ecosystem health and the society. Considering water-buyers and wellowning farmers individually, a methodology for economic valuation of groundwater in regions where its primary usage is in agriculture, and as assessment of the groundwater economy based on case studies from north Gujarat is presented in the fourth chapter. The next chapter focuses on the extent of dependency of milk production on groundwater, which includes the water embedded in green and dry fodder and animal feed. The study made a realistic estimate of irrigation water productivity in terms of the physics and economics of milk production. The sixth chapter analyses the extent of reduction in water usage, increase in yield and overall increase in physical productivity of alfalfa with the use of the drip irrigation system. The chapter also provides a detailed synthesis of the costs and benefits associated with the use of drip irrigation systems. A linear programmingbased optimization model with the objective to minimize groundwater use taking into account the interaction between two distinct components – farming and dairying under the constraints of food security and income stability for different scenarios, including shift in cropping pattern, introduction of water-efficient crops, water- saving technologies in addition to the ‘business as usual’ scenario is presented in the seventh chapter. The results show that sustaining dairy production in the region with reduced groundwater draft requires crop shifts and adoption of water-saving technologies. The eighth chapter provides evidences to prove that the presence of adequate economic incentive would encourage farmers to adopt water-saving irrigation devices, based on the findings of market research with reference to the level of awareness among farmers of technologies and the factors that decide the adoption of water-saving technologies. However, now the marginal cost of using electricity for agricultural pumping is almost zero. The economic incentives are strong and visible only when the farmers are either water-buyers or have to manage irrigation with limited water from tube-well partnerships. The ninth chapter explores the socio-economic viability of increasing the power tariff and inducing groundwater rationing as a tool for managing energy and groundwater demand, considering the current estimate of the country’s annual economic loss of Rs 320 billion towards electricity subsidy in the farm sector. The tenth chapter suggests private tradable property rights and development of water markets as the institutional tool for achieving equity, efficiency and sustainability of groundwater use. It identifies the externalities for local groundwater management and emphasizes the need for managing groundwater by local user groups, supported by a thorough analysis of groundwater socio-ecology in India. An institutional framework for managing the resource based on participatory approach that is capable of internalizing the externalities, comprising implementation of institutional and technical alternatives for resource management is also presented. Major findings of the analyses and key arguments in each chapter are summarized in the concluding chapter. Case studies of the social and economic benefits of groundwater use, where that use could be described as unsustainable, are interesting. The benefits of groundwater use are outlined and described with examples of social and economic impacts of groundwater and the negative aspects of groundwater development with the compilation of environmental problems based on up-to-date research results. This publication with a well-edited compilation of case studies is informative and constitutes a useful publication for students and professionals.

Modified Stability Checking for On-Line Error Detection

The paper propose a unified error detection technique, based on stability checking, for on-line detection of delay, crosstalk and transient faults in combinational circuits and SEUs in sequential elements. The proposed method, called modified stability checking (MSC), overcomes the limitations of the earlier stability checking methods. The paper also proposed a novel checker circuit to realize this scheme. The checker is self-checking for a wide set of realistic internal faults including transient faults. Extensive circuit simulations have been done to characterize the checker circuit. A prototype checker circuit for a 1mm2 standard cell array has been implemented in a 0.13mum process.

Steady-State Stability of Current-Mode Active-Clamp ZVS DC-DC Converters

Active-clamp dc-dc converters are pulsewidth-modulated converters having two switches featuring zero-voltage switching at frequencies beyond 100 kHz. Generalized equivalent circuits valid for steady-state and dynamic performance have been proposed for the family of active-clamp converters. The active-clamp converter is analyzed for its dynamic behavior under current control in this paper. The steady-state stability analysis is presented. On account of the lossless damping inherent in the active-clamp converters, it appears that the stability region in the current-controlled active-clamp converters get extended for duty ratios, a little greater than 0.5 unlike in conventional hard-switched converters. The conventional graphical approach fails to assess the stability of current-controlled active-clamp converters, due to the coupling between the filter inductor current and resonant inductor current. An analysis that takes into account the presence of the resonant elements is presented to establish the condition for stability. This method correctly predicts the stability of the current-controlled active-clamp converters. A simple expression for the maximum duty cycle for subharmonic-free operation is obtained. The results are verified experimentally.

Size and temperature dependent stability and phase transformation in single-crystal zirconium nanowire

A novel size dependent FCC (face-centered-cubic) -> HCP (hexagonally-closed-pack) phase transformation and stability of an initial FCC zirconium nanowire are studied. FCC zirconium nanowires with cross-sectional dimensions < 20 are found unstable in nature, and they undergo a FCC -> HCP phase transformation, which is driven by tensile surface stress induced high internal compressive stresses. FCC nanowire with cross-sectional dimensions > 20 , in which surface stresses are not enough to drive the phase transformation, show meta-stability. In such a case, an external kinetic energy in the form of thermal heating is required to overcome the energy barrier and achieve FCC -> HCP phase transformation. The FCC-HCP transition pathway is also studied using Nudged Elastic Band (NEB) method, to further confirm the size dependent stability/metastability of Zr nanowires. We also show size dependent critical temperature, which is required for complete phase transformation of a metastable-FCC nanowire.

Stability of domain structures in multi-domain proteins

Multi-domain proteins have many advantages with respect to stability and folding inside cells. Here we attempt to understand the intricate relationship between the domain-domain interactions and the stability of domains in isolation. We provide quantitative treatment and proof for prevailing intuitive ideas on the strategies employed by nature to stabilize otherwise unstable domains. We find that domains incapable of independent stability are stabilized by favourable interactions with tethered domains in the multi-domain context. Stability of such folds to exist independently is optimized by evolution. Specific residue mutations in the sites equivalent to inter-domain interface enhance the overall solvation, thereby stabilizing these domain folds independently. A few naturally occurring variants at these sites alter communication between domains and affect stability leading to disease manifestation. Our analysis provides safe guidelines for mutagenesis which have attractive applications in obtaining stable fragments and domain constructs essential for structural studies by crystallography and NMR.

Long term stability studies of particle storage rings using polynomial Maps

Long-term stability studies of particle storage rings can not be carried out using conventional numerical integration algorithms. We require symplectic integration algorithms which are both fast and accurate. In this paper, we study a symplectic integration method wherein the sym-plectic map representing the Hamiltonian system is refactorized using polynomial symplectic maps. This method is used to perform long term integration on a particle storage ring.