Relaxation system based sub-grid scale modelling for large eddy simulation of Burgers' equation

An implicit sub-grid scale model for large eddy simulation is presented by utilising the concept of a relaxation system for one dimensional Burgers' equation in a novel way. The Burgers' equation is solved for three different unsteady flow situations by varying the ratio of relaxation parameter (epsilon) to time step. The coarse mesh results obtained with a relaxation scheme are compared with the filtered DNS solution of the same problem on a fine mesh using a fourth-order CWENO discretisation in space and third-order TVD Runge-Kutta discretisation in time. The numerical solutions obtained through the relaxation system have the same order of accuracy in space and time and they closely match with the filtered DNS solutions.

Time dependent deformations in concrete: A multi-scale approach

Estimation of creep and shrinkage are critical in order to compute loss of prestress with time in order to compute leak tightness and assess safety margins available in containment structures of nuclear power plants. Short-term creep and shrinkage experiments have been conducted using in-house test facilities developed specifically for the present research program on 35 and 45 MPa normal concrete and 25 MPa heavy density concrete. The extensive experimental program for creep, has cylinders subject to sustained levels of load typically for several days duration (till negligible strain increase with time is observed in the creep specimen), to provide the total creep strain versus time curves for the two normal density concrete grades and one heavy density concrete grade at different load levels, different ages at loading, and at different relative humidity’s. Shrinkage studies on prism specimen for concrete of the same mix grades are also being studied. In the first instance, creep and shrinkage prediction models reported in the literature has been used to predict the creep and shrinkage levels in subsequent experimental data with acceptable accuracy. While macro-scale short experiments and analytical model development to estimate time dependent deformation under sustained loads over long term, accounting for the composite rheology through the influence of parameters such as the characteristic strength, age of concrete at loading, relative humidity, temperature, mix proportion (cement: fine aggregate: coarse aggregate: water) and volume to surface ratio and the associated uncertainties in these variables form one part of the study, it is widely believed that strength, early age rheology, creep and shrinkage are affected by the material properties at the nano-scale that are not well established. In order to understand and improve cement and concrete properties, investigation of the nanostructure of the composite and how it relates to the local mechanical properties is being undertaken. While results of creep and shrinkage obtained at macro-scale and their predictions through rheological modeling are satisfactory, the nano and micro indenting experimental and analytical studies are presently underway. Computational mechanics based models for creep and shrinkage in concrete must necessarily account for numerous parameters that impact their short and long term response. A Kelvin type model with several elements representing the influence of various factors that impact the behaviour is under development. The immediate short term deformation (elastic response), effects of relative humidity and temperature, volume to surface ratio, water cement ratio and aggregate cement ratio, load levels and age of concrete at loading are parameters accounted for in this model. Inputs to this model, such as the pore structure and mechanical properties at micro/nano scale have been taken from scanning electron microscopy and micro/nano-indenting of the sample specimen.

Multi-scale interactions and predictability of the Indian summer monsoon

Following the seminal work of Charney and Shukla (198 1), the tropical climate is recognised to be more predictable than extra tropical climate as it is largely forced by 'external' slowly varying forcing and less sensitive to initial conditions. However, the Indian summer monsoon is an exception within the tropics where 'internal' low frequency (LF) oscillations seem to make significant contribution to its interannual variability (IAV) and makes it sensitive to initial conditions. Quantitative estimate of contribution of 'internal' dynamics to IAV of Indian monsoon is made using long experiments with an atmospheric general circulation model (AGCM) and through analysis of long daily observations. Both AGCM experiments and observations indicate that more than 50% of IAV of the monsoon is contributed by 'internal' dynamics making the predictable signal (external component) burried in unpredictable noise (internal component) of comparable amplitude. Better understanding of the nature of the 'internal' LF variability is crucial for any improvement in predicition of seasonal mean monsoon. Nature of 'internal' LF variability of the monsoon and mechanism responsible for it are investigated and shown that vigorous monsoon intraseasonal oscillations (ISO's) with time scale between 10-70 days are primarily responsible for generating the 'internal' IAV. The monsoon ISO's do this through scale interactions with synoptic disturbances (1-7 day time scale) on one hand and the annual cycle on the other. The spatial structure of the monsoon ISO's is similar to that of the seasonal mean. It is shown that frequency of occurance of strong (weak) phases of the ISO is different in different seasons giving rise to stronger (weaker) than normal monsoon. Change in the large scale circulation during strong (weak) phases of the ISO make it favourable (inhibiting) for cyclogenesis and gives rise to space time clustering of synoptic activity. This process leads to enhanced (reduced) rainfall in seasons of higher frequency of occurence strong (weak) phases of monsoon ISO.

A multi-level multi-scale approach to study essential genes in Mycobacterium tuberculosis

Background: The set of indispensable genes that are required by an organism to grow and sustain life are termed as essential genes. There is a strong interest in identification of the set of essential genes, particularly in pathogens, not only for a better understanding of the pathogen biology, but also for identifying drug targets and the minimal gene set for the organism. Essentiality is inherently a systems property and requires consideration of the system as a whole for their identification. The available experimental approaches capture some aspects but each method comes with its own limitations. Moreover, they do not explain the basis for essentiality in most cases. A powerful prediction method to recognize this gene pool including rationalization of the known essential genes in a given organism would be very useful. Here we describe a multi-level multi-scale approach to identify the essential gene pool in a deadly pathogen, Mycobacterium tuberculosis. Results: The multi-level workflow analyses the bacterial cell by studying (a) genome-wide gene expression profiles to identify the set of genes which show consistent and significant levels of expression in multiple samples of the same condition, (b) indispensability for growth by using gene expression integrated flux balance analysis of a genome-scale metabolic model, (c) importance for maintaining the integrity and flow in a protein-protein interaction network and (d) evolutionary conservation in a set of genomes of the same ecological niche. In the gene pool identified, the functional basis for essentiality has been addressed by studying residue level conservation and the sub-structure at the ligand binding pockets, from which essential amino acid residues in that pocket have also been identified. 283 genes were identified as essential genes with high-confidence. An agreement of about 73.5% is observed with that obtained from the experimental transposon mutagenesis technique. A large proportion of the identified genes belong to the class of intermediary metabolism and respiration. Conclusions: The multi-scale, multi-level approach described can be generally applied to other pathogens as well. The essential gene pool identified form a basis for designing experiments to probe their finer functional roles and also serve as a ready shortlist for identifying drug targets.

Computational framework to integrate the effect of antigen recognition on disease epidemiology outcome: multi-scale approach

Human Leukocyte Antigen (HLA) plays an important role, in presenting foreign pathogens to our immune system, there by eliciting early immune responses. HLA genes are highly polymorphic, giving rise to diverse antigen presentation capability. An important factor contributing to enormous variations in individual responses to diseases is differences in their HLA profiles. The heterogeneity in allele specific disease responses decides the overall disease epidemiological outcome. Here we propose an agent based computational framework, capable of incorporating allele specific information, to analyze disease epidemiology. This framework assumes a SIR model to estimate average disease transmission and recovery rate. Using epitope prediction tool, it performs sequence based epitope detection for a given the pathogenic genome and derives an allele specific disease susceptibility index depending on the epitope detection efficiency. The allele specific disease transmission rate, that follows, is then fed to the agent based epidemiology model, to analyze the disease outcome. The methodology presented here has a potential use in understanding how a disease spreads and effective measures to control the disease.

Retrieval and Multi-scale Validation of Soil Moisture from Multi-temporal SAR Data in a Semi-Arid Tropical Region

The current study presents an algorithm to retrieve surface Soil Moisture (SM) from multi-temporal Synthetic Aperture Radar (SAR) data. The developed algorithm is based on the Cumulative Density Function (CDF) transformation of multi-temporal RADARSAT-2 backscatter coefficient (BC) to obtain relative SM values, and then converts relative SM values into absolute SM values using soil information. The algorithm is tested in a semi-arid tropical region in South India using 30 satellite images of RADARSAT-2, SMOS L2 SM products, and 1262 SM field measurements in 50 plots spanning over 4 years. The validation with the field data showed the ability of the developed algorithm to retrieve SM with RMSE ranging from 0.02 to 0.06 m(3)/m(3) for the majority of plots. Comparison with the SMOS SM showed a good temporal behaviour with RMSE of approximately 0.05 m(3)/m(3) and a correlation coefficient of approximately 0.9. The developed model is compared and found to be better than the change detection and delta index model. The approach does not require calibration of any parameter to obtain relative SM and hence can easily be extended to any region having time series of SAR data available.

COMPOSITE AND MULTI-SCALE COMPLIANT MECHANISMS FOR MANIPULATION AND MECHANICAL CHARACTERIZATION

In this paper, we integrate two or more compliant mechanisms to get enhanced functionality for manipulating and mechanically characterizing the grasped objects of varied size (cm to sub-mm), stiffness (1e5 to 10 N/m), and materials (cement to biological cells). The concepts of spring-lever (SL) model, stiffness maps, and non-dimensional kinetoelastostatic maps are used to design composite and multi-scale compliant mechanisms. Composite compliant mechanisms comprise two or more different mechanisms within a single elastic continuum while multi-scale ones possess the additional feature of substantial difference in the sizes of the mechanisms that are combined into one. We present three applications: (i) a composite compliant device to measure the failure load of the cement samples; (ii) a composite multi-scale compliant gripper to measure the bulk stiffness of zebrafish embryos; and (iii) a compliant gripper combined with a negative-stiffness element to reduce the overall stiffness. The prototypes of all three devices are made and tested. The cement sample needed a breaking force of 22.5 N; the zebrafish embryo is found to have bulk stiffness of about 10 N/m; and the stiffness of a compliant gripper was reduced by 99.8 % to 0.2 N/m.

Multi-scale vulnerability assessment for adaptation planning

Vulnerability of communities and natural ecosystems, to potential impacts of climate change in developing countries like India, and the need for adaptation are rapidly emerging as central issues in the debate around policy responses to climate change. The present study presents an approach to identify and prioritize the most vulnerable districts, villages and households in Karnataka State, through a multi-scale assessment of inherent vulnerability to current climate variability. It also identifies the drivers of inherent vulnerability, thereby providing a tool for developing and mainstreaming adaptation strategies, in ongoing developmental or dedicated adaptation programmes. The multi-scale assessment was made for all 30 districts at the state level in Karnataka, about 1220 villages in Chikballapur district, and at the household level for two villages - Gundlapalli and Saddapalli - in Bagepalli taluk of Chikballapur district. At the district, village and household levels, low levels of education and skills are the dominant factors contributing to vulnerability. At the village and household level, the lack of income diversification and livelihood support institutions are key drivers of vulnerability. The approach of multi-scale vulnerability assessment facilitates identification and prioritization of the drivers of vulnerability at different scales, to focus adaptation interventions to address these drivers.

Characteristic Dimensionless Numbers in Multi-Scale and Rate-Dependent Processes

For this sake, the macroscopic equations of mechanics and the kinetic equations of the microstructural transformations should form a unified set that be solved simultaneously. As a case study of coupling length and time scales, the trans-scale formulation

Synchronous Multi-Scale Observations on Rock Damage and Rupture

This paper reports a multi-scale study on damage evolution process and rupture of gabbro under uniaxial compression with several experimental techniques, including MTS810 testing machine, white digital speckle correlation method, and acoustic emission technique. In particular, the synchronization of the three experimental systems is realized for the study of relationship of deformation and damage at multiple scales. It is found that there are significant correlation between damage evolution at small and large length scales, and rupture at sample scale, especially it displays critical sensitivity at multiple scales and trans-scale fluctuations.

Extended self-similar scaling law of multi-scale eddy structure in wall turbulence

The longitudinal fluctuating velocity of a turbulent boundary layer was measured in a water channel at a moderate Reynolds number. The extended self-similar scaling law of structure function proposed by Benzi was verified. The longitudinal fluctuating velocity, in the turbulent boundary layer was decomposed into many multi-scale eddy structures by wavelet transform. The extended self-similar scaling law of structure function for each scale eddy velocity was investigated. The conclusions are I) The statistical properties of turbulence could be self-similar not only at high Reynolds number, but also at moderate and low Reynolds number, and they could be characterized by the same set of scaling exponents xi (1)(n) = n/3 and xi (2)(n) = n/3 of the fully developed regime. 2) The range of scales where the extended self-similarity valid is much larger than the inertial range and extends far deep into the dissipation range,vith the same set of scaling exponents. 3) The extended selfsimilarity is applicable not only for homogeneous turbulence, but also for shear turbulence such as turbulent boundary layers.

Multi-scale analysis of AFM tip and surface interactions

Thoroughly understanding AFM tip-surface interactions is crucial for many experimental studies and applications. It is important to realize that despite its simple appearance, the system of tip and sample surface involves multiscale interactions. In fact, the system is governed by a combination of molecular force (like the van der Waals force), its macroscopic representations (such as surface force) and gravitational force (a macroscopic force). Hence, in the system, various length scales are operative, from sub-nanoscale (at the molecular level) to the macroscopic scale. By integrating molecular forces into continuum equations, we performed a multiscale analysis and revealed the nonlocality effect between a tip and a rough solid surface and the mechanism governing liquid surface deformation and jumping. The results have several significant implications for practical applications. For instance, nonlocality may affect the measurement accuracy of surface morphology. At the critical state of liquid surface jump, the ratio of the gap between a tip and a liquid dome (delta) over the dome height (y(o)) is approximately (n-4) (for a large tip), which depends on the power law exponent n of the molecular interaction energy. These findings demonstrate that the multiscale analysis is not only useful but also necessary in the understanding of practical phenomena involving molecular forces. (c) 2007 Elsevier Ltd. All rights reserved.