58 resultados para Calculus of variations.

em Indian Institute of Science - Bangalore - Índia


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The problem of determining optimal power spectral density models for earthquake excitation which satisfy constraints on total average power, zero crossing rate and which produce the highest response variance in a given linear system is considered. The solution to this problem is obtained using linear programming methods. The resulting solutions are shown to display a highly deterministic structure and, therefore, fail to capture the stochastic nature of the input. A modification to the definition of critical excitation is proposed which takes into account the entropy rate as a measure of uncertainty in the earthquake loads. The resulting problem is solved using calculus of variations and also within linear programming framework. Illustrative examples on specifying seismic inputs for a nuclear power plant and a tall earth dam are considered and the resulting solutions are shown to be realistic.

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Raman bandwidths and bandshapes of some molecular and ionic glasses have been investigated through the glass-transition region. Widths of both polarised and depolarised bands exhibit step-like changes during the glass transition. Molecular and ionic glasses differ with respect to the magnitude and the nature of variations in bandwidths and reorientational times. An attempt has been made to understand the changes in bandwidths around the glass-transition temperature.

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We obtained the images of the eastern part of the solar corona in the Fe xiv 530.3 nm (green) and Fe x 637.4 nm (red) coronal emission lines during the total solar eclipse of 29 March 2006 at Manavgat, Antalya, Turkey. The images were obtained using a 35 cm Meade telescope equipped with a Peltier-cooled 2k x 2k CCD and 0.3 nm pass-band interference filters at the rates of 2.95 s (exposure times of 100 ms) and 2.0 s (exposure times of 300 ms) in the Fe xiv and Fe x emission lines,respectively. The analysis of the data indicates intensity variations at some locations with period of strongest power around 27 s for the green line and 20 s for the red line. These results confirm earlier findings of variations in the continuum intensity with periods in the range of 5 to 56 s by Singh et al. (Solar Phys. 170, 235, 1997). The wavelet analysis has been used to identify significant intensity oscillations at all pixels within our field of view. Significant oscillations with high probability estimates were detected for some locations only. These locations seem to follow the boundary of an active region and in the neighborhood, rather than within the loops themselves. These intensity oscillations may be caused by fast magneto-sonic waves in the solar corona and partly account for heating of the plasma in the corona.

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The supramolecular structures of eight aryl protected ethyl-6-methyl-4-phenyl-2-thioxo-1,2,3,4 tetrahydropyrimidine-5-carboxyl ates were analyzed in order to understand the effect of variations in functional groups on molecular geometry, conformation and packing of molecules in the crystalline lattice. It is observed that the existence of a short intra-molecular C-H center dot center dot center dot pi interaction between the aromatic hydrogen of the aryl ring with the isolated double bond of the six-membered tetrahydropyrimidine ring is a key feature which imparts additional stability to the molecular conformation in the solid state. The compounds pack via the cooperative involvement of both N-H center dot center dot center dot S=C and N-H center dot center dot center dot O=C intermolecular dimers forming a sheet like structure. In addition, weak C-H center dot center dot center dot O and C-H center dot center dot center dot pi intermolecular interactions provide additional stability to the crystal packing.

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Results of an investigation dealing with the behaviour of grid-connected induction generators (GCIGs) driven by typical prime movers such as mini-hydro/wind turbines are presented. Certain practical operational problems of such systems are identified. Analytical techniques are developed to study the behavior of such systems. The system consists of the induction generator (IG) feeding a 11 kV grid through a step-up transformer and a transmission line. Terminal capacitors to compensate for the lagging VAr are included in the study. Computer simulation was carried out to predict the system performance at the given input power from the turbine. Effects of variations in grid voltage, frequency, input power, and terminal capacitance on the machine and system performance are studied. An analysis of self-excitation conditions on disconnection of supply was carried out. The behavior of a 220 kW hydel system and 55/11 kW and 22 kW wind driven system corresponding to actual field conditions is discussed

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A general model of a foam bed reactor has been developed which rigorously accounts for the extent of gas absorption with chemical reaction occurring in both the storage and foam sections. Its applicability extends to a wide spectrum of reaction velocities. The possibilities of the predominance of the bulk-liquid reaction in the storage section or the absorption with reaction in the foam section can be handled as merely special cases of the general analysis. The importance of foam for carrying out a particular gas-liquid reaction is characterised by a criterion in terms of the fractional rate of reaction in the foam section. Trends of variations in the concentrations of dissolved free A, solute B, and gas-phase A with time of operation of the reactor are presented. The nature of the variation in the fractional rate of reaction in the foam section with time, at different reaction velocities, and the effect of the liquid flow rate (across the storage section) on the transience are also illustrated. Finally, the predictions of the general model have been validated using the available experimental data on the oxidation of sodium sulphide in a foam bed reactor. The agreement between the experimental and the present theoretical information is fairly good, apart from being more insightful than all the previous models of this reactor.

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The constitutive flow behaviour of OFHC copper under working conditions is studied using hot compression in the temperature range 650 to 900-degrees-C and strain rate range 0.001 to 100 s-1. The variation of the efficiency of power dissipation given by [2m/(m + 1)] (where m is the strain rate sensitivity) with temperature and strain rate is represented in the form of a power dissipation map and interpreted on the basis of the Dynamic Materials Model. The map prominently exhibited a domain centered at 850-degrees-C and 100 s-1 with a peak efficiency of 35 %. On the basis of the correlation of variations of grain size, efficiency of power dissipation and hot workability with temperature, the domain is identified to represent dynamic recrystallization (DRX).

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The results of the structural and conformational studies carried out using C-13 CPMAS NMR technique on several glycine and alanine containing peptides in the solid state are reported. The study demonstrates the effects of variations in C-13 chemical shifts due to conformation and hydrogen bonding. The possibility of applying this technique to obtain insight into the conformational characteristics of peptides of unknown structures is discussed.

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Seismic design of reinforced soil structures involves many uncertainties that arise from the backfill soil properties and tensile strength of the reinforcement which is not addressed in current design guidelines. This paper highlights the significance of variability in the internal stability assessment of reinforced soil structures. Reliability analysis is applied to estimate probability of failure and pseudo‐static approach has been used for the calculation of the tensile strength and length of the reinforcement needed to maintain the internal stability against tension and pullout failures. Logarithmic spiral failure surface has been considered in conjunction with the limit equilibrium method. Two modes of failure namely, tension failure and pullout failure have been considered. The influence of variations of the backfill soil friction angle, the tensile strength of reinforcement, horizontal seismic acceleration on the reliability index against tension failure and pullout failure of reinforced earth structure have been discussed.

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We present a simplified theoretical formulation of the Fowler-Nordheim field emission (FNFE) under magnetic quantization and also in quantum wires of optoelectronic materials on the basis of a newly formulated electron dispersion law in the presence of strong electric field within the framework of k.p formalism taking InAs, InSb, GaAs, Hg(1-x)Cd(x)Te and In(1-x)Ga(x) As(y)P(1-y) lattice matched to InP as examples. The FNFE exhibits oscillations with inverse quantizing magnetic field and electron concentration due to SdH effect and increases with increasing electric field. For quantum wires the FNFE increases with increasing film thickness due to the existence van-Hove singularity and the magnitude of the quantum jumps are not of same height indicating the signature of the band structure of the material concerned. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the field current varies in various manners with all the variables in all the limiting cases as evident from all the curves, the rates of variations are totally band-structure dependent. Under certain limiting conditions, all the results as derived in this paper get transformed in to well known Fowler-Nordheim formula. (C) 2011 Elsevier Ltd. All rights reserved.

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An attempt is made to study the two dimensional (2D) effective electron mass (EEM) in quantum wells (Qws), inversion layers (ILs) and NIPI superlattices of Kane type semiconductors in the presence of strong external photoexcitation on the basis of a newly formulated electron dispersion laws within the framework of k.p. formalism. It has been found, taking InAs and InSb as examples, that the EEM in Qws, ILs and superlattices increases with increasing concentration, light intensity and wavelength of the incident light waves, respectively and the numerical magnitudes in each case is band structure dependent. The EEM in ILs is quantum number dependent exhibiting quantum jumps for specified values of the surface electric field and in NIPI superlattices; the same is the function of Fermi energy and the subband index characterizing such 2D structures. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the EEM varies in various manners with all the variables as evident from all the curves, the rates of variations totally depend on the specific dispersion relation of the particular 2D structure. Under certain limiting conditions, all the results as derived in this paper get transformed into well known formulas of the EEM and the electron statistics in the absence of external photo-excitation and thus confirming the compatibility test. The results of this paper find three applications in the field of microstructures. (C) 2011 Elsevier Ltd. All rights reserved.

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Experimental conditions or the presence of interacting components can lead to variations in the structural models of macromolecules. However, the role of these factors in conformational selection is often omitted by in silico methods to extract dynamic information from protein structural models. Structures of small peptides, considered building blocks for larger macromolecular structural models, can substantially differ in the context of a larger protein. This limitation is more evident in the case of modeling large multi-subunit macromolecular complexes using structures of the individual protein components. Here we report an analysis of variations in structural models of proteins with high sequence similarity. These models were analyzed for sequence features of the protein, the role of scaffolding segments including interacting proteins or affinity tags and the chemical components in the experimental conditions. Conformational features in these structural models could be rationalized by conformational selection events, perhaps induced by experimental conditions. This analysis was performed on a non-redundant dataset of protein structures from different SCOP classes. The sequence-conformation correlations that we note here suggest additional features that could be incorporated by in silico methods to extract dynamic information from protein structural models.

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Lime–fly ash reactions play a key role in improving the mechanical strength and tailoring the permeability characteristics of compacted fly ash. Activation of fly ash–lime pozzolanic reactions should accelerate the rate of strength development and possibly mobilize higher compressive strengths, facilitating improved engineering performance of fly ash amended materials. This paper makes an assessment of activation of lime–fly ash reactions by curing compacted fly ash–lime specimens at ambient (25°C) and at elevated temperature (80°C). The kinetics of fly ash–lime reactions are examined by monitoring the reacted lime as a function of curing period and temperature. The influence of variations in fly ash/lime content and dry density on the compressive strength developed by specimens at both temperatures is evaluated. The thermodynamic parameters for the fly ash–lime reactions have also been examined. Experimental results showed that curing at 80°C for 24 h accelerated fly ash–lime reactions such that it caused the steam cured (SC) specimens to evelop 1.21–2.44 fold larger strengths than room-temperature cured (RTC) specimens cured at 25°C for 28 days. Analysis of thermodynamic parameters indicated that the fly ash–lime reactions are thermodynamically favored at fly ash contents of 50–70% and lime additions of 16–20%, and the reactions are endothermic in nature. DOI: 10.1061/(ASCE)MT.1943-5533.0000482. © 2012 American Society of Civil Engineers.

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The two-step particle synthesis mechanism, also known as the Finke-Watzky (1997) mechanism, has emerged as a significant development in the field of nanoparticle synthesis. It explains a characteristic feature of the synthesis of transition metal nanoparticles, an induction period in precursor concentration followed by its rapid sigmoidal decrease. The classical LaMer theory (1950) of particle formation fails to capture this behavior. The two-step mechanism considers slow continuous nucleation and autocatalytic growth of particles directly from precursor as its two kinetic steps. In the present work, we test the two-step mechanism rigorously using population balance models. We find that it explains precursor consumption very well, but fails to explain particle synthesis. The effect of continued nucleation on particle synthesis is not suppressed sufficiently by the rapid autocatalytic growth of particles. The nucleation continues to increase breadth of size distributions to unexpectedly large values as compared to those observed experimentally. A number of variations of the original mechanism with additional reaction steps are investigated next. The simulations show that continued nucleation from the beginning of the synthesis leads to formation of highly polydisperse particles in all of the tested cases. A short nucleation window, realized with delayed onset of nucleation and its suppression soon after in one of the variations, appears as one way to explain all of the known experimental observations. The present investigations clearly establish the need to revisit the two-step particle synthesis mechanism.

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Extending the work of earlier papers on the relativistic-front description of paraxial optics and the formulation of Fourier optics for vector waves consistent with the Maxwell equations, we generalize the Jones calculus of axial plane waves to describe the action of the most general linear optical system on paraxial Maxwell fields. Several examples are worked out, and in each case it is shown that the formalism leads to physically correct results. The importance of retaining the small components of the field vectors along the axis of the system for a consistent description is emphasized.