Outward spherical solidification of a superheated melt with time dependent boundary flux

Short-time analytical solutions of solid and liquid temperatures and freezing front have been obtained for the outward radially symmetric spherical solidification of a superheated melt. Although results are presented here only for time dependent boundary flux, the method of solution can be used for other kinds of boundary conditions also. Later, the analytical solution has been compared with the numerical solution obtained with the help of a finite difference numerical scheme in which the grid points change with the freezing front position. An efficient method of execution of the numerical scheme has been discussed in details. Graphs have been drawn for the total solidification times and temperature distributions in the solid.

Algorithms for Colouring Random k-colourable Graphs

The k-colouring problem is to colour a given k-colourable graph with k colours. This problem is known to be NP-hard even for fixed k greater than or equal to 3. The best known polynomial time approximation algorithms require n(delta) (for a positive constant delta depending on k) colours to colour an arbitrary k-colourable n-vertex graph. The situation is entirely different if we look at the average performance of an algorithm rather than its worst-case performance. It is well known that a k-colourable graph drawn from certain classes of distributions can be ii-coloured almost surely in polynomial time. In this paper, we present further results in this direction. We consider k-colourable graphs drawn from the random model in which each allowed edge is chosen independently with probability p(n) after initially partitioning the vertex set into ii colour classes. We present polynomial time algorithms of two different types. The first type of algorithm always runs in polynomial time and succeeds almost surely. Algorithms of this type have been proposed before, but our algorithms have provably exponentially small failure probabilities. The second type of algorithm always succeeds and has polynomial running time on average. Such algorithms are more useful and more difficult to obtain than the first type of algorithms. Our algorithms work as long as p(n) greater than or equal to n(-1+is an element of) where is an element of is a constant greater than 1/4.

A kinetic Ising model study of dynamical correlations in confined fluids: Emergence of both fast and slow time scales

Experiments and computer simulation studies have revealed existence of rich dynamics in the orientational relaxation of molecules in confined systems such as water in reverse micelles, cyclodextrin cavities, and nanotubes. Here we introduce a novel finite length one dimensional Ising model to investigate the propagation and the annihilation of dynamical correlations in finite systems and to understand the intriguing shortening of the orientational relaxation time that has been reported for small sized reverse micelles. In our finite sized model, the two spins at the two end cells are oriented in the opposite directions to mimic the effects of surface that in real system fixes water orientation in the opposite directions. This produces opposite polarizations to propagate inside from the surface and to produce bulklike condition at the center. This model can be solved analytically for short chains. For long chains, we solve the model numerically with Glauber spin flip dynamics (and also with Metropolis single-spin flip Monte Carlo algorithm). We show that model nicely reproduces many of the features observed in experiments. Due to the destructive interference among correlations that propagate from the surface to the core, one of the rotational relaxation time components decays faster than the bulk. In general, the relaxation of spins is nonexponential due to the interplay between various interactions. In the limit of strong coupling between the spins or in the limit of low temperature, the nature of relaxation of the spins undergoes a qualitative change with the emergence of a homogeneous dynamics where decay is predominantly exponential, again in agreement with experiments. (C) 2010 American Institute of Physics. doi: 10.1063/1.3474948]

Search on a hypercubic lattice using a quantum random walk. I. d > 2

Random walks describe diffusion processes, where movement at every time step is restricted to only the neighboring locations. We construct a quantum random walk algorithm, based on discretization of the Dirac evolution operator inspired by staggered lattice fermions. We use it to investigate the spatial search problem, that is, to find a marked vertex on a d-dimensional hypercubic lattice. The restriction on movement hardly matters for d > 2, and scaling behavior close to Grover's optimal algorithm (which has no restriction on movement) can be achieved. Using numerical simulations, we optimize the proportionality constants of the scaling behavior, and demonstrate the approach to that for Grover's algorithm (equivalent to the mean-field theory or the d -> infinity limit). In particular, the scaling behavior for d = 3 is only about 25% higher than the optimal d -> infinity value.

On Minimization of Test Application Time for RAS

Conventional Random access scan (RAS) for testing has lower test application time, low power dissipation, and low test data volume compared to standard serial scan chain based design In this paper, we present two cluster based techniques, namely, Serial Input Random Access Scan and Variable Word Length Random Access Scan to reduce test application time even further by exploiting the parallelism among the clusters and performing write operations on multiple bits Experimental results on benchmarks circuits show on an average 2-3 times speed up in test write time and average 60% reduction in write test data volume

Rocking response of rectangular rigid blocks under random noise base excitations

The response of a rigid rectangular block resting on a rigid foundation and acted upon simultaneously by a horizontal and a vertical random white-noise excitation is considered. In the equation of motion, the energy dissipation is modeled through a viscous damping term. Under the assumption that the body does not topple, the steady-state joint probability density function of the rotation and the rotational velocity is obtained using the Fokker-Planck equation approach. Closed form solution is obtained for a specific combination of system parameters. A more general but approximate solution to the joint probability density function based on the method of equivalent non-linearization is also presented. Further, the problem of overturning of the block is approached in the framework of the diffusion methods for first passage failure studies. The overturning of the block is deemed incipient when the response trajectories in the phase plane cross the separatrix of the conservative unforced system. Expressions for the moments of first passage time are obtained via a series solution to the governing generalized Pontriagin-Vitt equations. Numerical results illustra- tive of the theoretical solutions are presented and their validity is examined through limited amount of digital simulations.

In-Network Computation in Random Wireless Networks: A PAC Approach to Constant Refresh Rates with Lower Energy Costs

We propose a method to compute a probably approximately correct (PAC) normalized histogram of observations with a refresh rate of Theta(1) time units per histogram sample on a random geometric graph with noise-free links. The delay in computation is Theta(root n) time units. We further extend our approach to a network with noisy links. While the refresh rate remains Theta(1) time units per sample, the delay increases to Theta(root n log n). The number of transmissions in both cases is Theta(n) per histogram sample. The achieved Theta(1) refresh rate for PAC histogram computation is a significant improvement over the refresh rate of Theta(1/log n) for histogram computation in noiseless networks. We achieve this by operating in the supercritical thermodynamic regime where large pathways for communication build up, but the network may have more than one component. The largest component however will have an arbitrarily large fraction of nodes in order to enable approximate computation of the histogram to the desired level of accuracy. Operation in the supercritical thermodynamic regime also reduces energy consumption. A key step in the proof of our achievability result is the construction of a connected component having bounded degree and any desired fraction of nodes. This construction may also prove useful in other communication settings on the random geometric graph.

Hydrologic drought prediction under climate change: Uncertainty modeling with Dempster-Shafer and Bayesian approaches

Representation and quantification of uncertainty in climate change impact studies are a difficult task. Several sources of uncertainty arise in studies of hydrologic impacts of climate change, such as those due to choice of general circulation models (GCMs), scenarios and downscaling methods. Recently, much work has focused on uncertainty quantification and modeling in regional climate change impacts. In this paper, an uncertainty modeling framework is evaluated, which uses a generalized uncertainty measure to combine GCM, scenario and downscaling uncertainties. The Dempster-Shafer (D-S) evidence theory is used for representing and combining uncertainty from various sources. A significant advantage of the D-S framework over the traditional probabilistic approach is that it allows for the allocation of a probability mass to sets or intervals, and can hence handle both aleatory or stochastic uncertainty, and epistemic or subjective uncertainty. This paper shows how the D-S theory can be used to represent beliefs in some hypotheses such as hydrologic drought or wet conditions, describe uncertainty and ignorance in the system, and give a quantitative measurement of belief and plausibility in results. The D-S approach has been used in this work for information synthesis using various evidence combination rules having different conflict modeling approaches. A case study is presented for hydrologic drought prediction using downscaled streamflow in the Mahanadi River at Hirakud in Orissa, India. Projections of n most likely monsoon streamflow sequences are obtained from a conditional random field (CRF) downscaling model, using an ensemble of three GCMs for three scenarios, which are converted to monsoon standardized streamflow index (SSFI-4) series. This range is used to specify the basic probability assignment (bpa) for a Dempster-Shafer structure, which represents uncertainty associated with each of the SSFI-4 classifications. These uncertainties are then combined across GCMs and scenarios using various evidence combination rules given by the D-S theory. A Bayesian approach is also presented for this case study, which models the uncertainty in projected frequencies of SSFI-4 classifications by deriving a posterior distribution for the frequency of each classification, using an ensemble of GCMs and scenarios. Results from the D-S and Bayesian approaches are compared, and relative merits of each approach are discussed. Both approaches show an increasing probability of extreme, severe and moderate droughts and decreasing probability of normal and wet conditions in Orissa as a result of climate change. (C) 2010 Elsevier Ltd. All rights reserved.

Heat conduction with a phase change in a cylindrical mould

Analytical short time solution of moving boundary in heat conduction in a cylindrical mould under prescribed flux boundary condition has been studied in this paper. Partial differential equations are converted to integro-differential equations. These integro-differential equations which are coupled have been solved analytically for short time by choosing suitable series expansions for the unknown quantitities.

On infinitesimal σ-fields generated by random processes

It is proved that the infinitesimal look-ahead and look-back σ-fields of a random process disagree at atmost countably many time instants.

Random sequential multilayer deposition of different‐sized k mers on a one dimensional infinite substrate

Kinetics of random sequential, irreversible multilayer deposition of macromolecules of two different sizes on a one dimensional infinite lattice is analyzed at the mean field level. A formal solution for the corresponding rate equation is obtained. The Jamming limits and the distribution of gaps of exact sizes are discussed. In the absence of screening, the jamming limits are shown to be the same for all the layers. A detailed analysis for the components differing by one monomer unit is presented. The small and large time behaviors and the dependence of the individual jamming limits of the k mers and (k−1) mers on k and the rate parameters are analyzed.

Implications of climate change on mitigation potential estimates for forest sector in India

Climate change is projected to impact forest ecosystems, including biodiversity and Net Primary Productivity (NPP). National level carbon forest sector mitigation potential estimates are available for India; however impacts of projected climate change are not included in the mitigation potential estimates. Change in NPP (in gC/m(2)/yr) is taken to represent the impacts of climate change. Long term impacts of climate change (2085) on the NPP of Indian forests are available; however no such regional estimates are available for short and medium terms. The present study based on GCM climatology scenarios projects the short, medium and long term impacts of climate change on forest ecosystems especially on NPP using BIOME4 vegetation model. We estimate that under A2 scenario by the year 2030 the NPP changes by (-5) to 40% across different agro-ecological zones (AEZ). By 2050 it increases by 15% to 59% and by 2070 it increases by 34 to 84%. However, under B2 scenario it increases only by 3 to 25%, 3.5 to 34% and (-2.5) to 38% respectively, in the same time periods. The cumulative mitigation potential is estimated to increase by up to 21% (by nearly 1 GtC) under A2 scenario between the years 2008 and 2108, whereas, under B2 the mitigation potential increases only by 14% (646 MtC). However, cumulative mitigation potential estimates obtained from IBIS-a dynamic global vegetation model suggest much smaller gains, where mitigation potential increases by only 6% and 5% during the period 2008 to 2108.

Computation of restoration of ligand response in the random kinetics of a prostate cancer cell signaling pathway

Mutation and/or dysfunction of signaling proteins in the mitogen activated protein kinase (MAPK) signal transduction pathway are frequently observed in various kinds of human cancer. Consistent with this fact, in the present study, we experimentally observe that the epidermal growth factor (EGF) induced activation profile of MAP kinase signaling is not straightforward dose-dependent in the PC3 prostate cancer cells. To find out what parameters and reactions in the pathway are involved in this departure from the normal dose-dependency, a model-based pathway analysis is performed. The pathway is mathematically modeled with 28 rate equations yielding those many ordinary differential equations (ODE) with kinetic rate constants that have been reported to take random values in the existing literature. This has led to us treating the ODE model of the pathways kinetics as a random differential equations (RDE) system in which the parameters are random variables. We show that our RDE model captures the uncertainty in the kinetic rate constants as seen in the behavior of the experimental data and more importantly, upon simulation, exhibits the abnormal EGF dose-dependency of the activation profile of MAP kinase signaling in PC3 prostate cancer cells. The most likely set of values of the kinetic rate constants obtained from fitting the RDE model into the experimental data is then used in a direct transcription based dynamic optimization method for computing the changes needed in these kinetic rate constant values for the restoration of the normal EGF dose response. The last computation identifies the parameters, i.e., the kinetic rate constants in the RDE model, that are the most sensitive to the change in the EGF dose response behavior in the PC3 prostate cancer cells. The reactions in which these most sensitive parameters participate emerge as candidate drug targets on the signaling pathway. (C) 2011 Elsevier Ireland Ltd. All rights reserved.

Fiber Bragg Grating Sensors for Real Time Monitoring of Evacuation Process

Fiber bragg grating (FBG) sensors have been widely used for number of sensing applications like temperature, pressure, acousto-ultrasonic, static and dynamic strain, refractive index change measurements and so on. Present work demonstrates the use of FBG sensors in in-situ measurement of vacuum process with simultaneous leak detection capability. Experiments were conducted in a bell jar vacuum chamber facilitated with conventional Pirani gauge for vacuum measurement. Three different experiments have been conducted to validate the performance of FBG sensor in monitoring vacuum creating process and air bleeding. The preliminary results of FBG sensors in vacuum monitoring have been compared with that of commercial Pirani gauge sensor. This novel technique offers a simple alternative to conventional method for real time monitoring of evacuation process. Proposed FBG based vacuum sensor has potential applications in vacuum systems involving hazardous environment such as chemical and gas plants, automobile industries, aeronautical establishments and leak monitoring in process industries, where the electrical or MEMS based sensors are prone to explosion and corrosion.

Test Application Time Minimization for RAS using Basis Optimization of Column Decoder

Random Access Scan, which addresses individual flip-flops in a design using a memory array like row and column decoder architecture, has recently attracted widespread attention, due to its potential for lower test application time, test data volume and test power dissipation when compared to traditional Serial Scan. This is because typically only a very limited number of random ``care'' bits in a test response need be modified to create the next test vector. Unlike traditional scan, most flip-flops need not be updated. Test application efficiency can be further improved by organizing the access by word instead of by bit. In this paper we present a new decoder structure that takes advantage of basis vectors and linear algebra to further significantly optimize test application in RAS by performing the write operations on multiple bits consecutively. Simulations performed on benchmark circuits show an average of 2-3 times speed up in test write time compared to conventional RAS.