A posteriori error estimates of discontinuous Galerkin methods for the Signorini problem

A reliable and efficient a posteriori error estimator is derived for a class of discontinuous Galerkin (DG) methods for the Signorini problem. A common property shared by many DG methods leads to a unified error analysis with the help of a constraint preserving enriching map. The error estimator of DG methods is comparable with the error estimator of the conforming methods. Numerical experiments illustrate the performance of the error estimator. (C) 2015 Elsevier B.V. All rights reserved.

Karnaugh map analysis and synthesis of threshold functions

A unate function can easily be identified on a Karnaugh map from the well-known property that it cons ist s only ofess en ti al prime implicante which intersect at a common implicant. The additional property that the plot of a unate function F(x, ... XII) on a Karnaugh map should possess in order that F may also be Ivrealizable (n';:; 6) has been found. It has been sh own that the I- realizability of a unate function F corresponds to the ' compac tness' of the plot of F. No resort to tho inequalities is made, and no pre-processing such as positivizing and ordering of the given function is required.

The potential of certification for conservation and management of wild MAP resources

Medicinal and aromatic plants (MAPs) are an integral part of our biodiversity. In majority of MAP rich countries, wild collection practices are the livelihood options for a large number of rural peoples and MAPs play a significant role in socio-economic development of their communities. Recent concern over the alarming situation of the status of wild MAP resources, raw material quality, as well as social exploitation of rural communities, leads to the idea of certification for MAP resource conservation and management. On one hand, while MAP certification addresses environmental, social and economic perspectives of MAP resources, on the other hand, it ensures multi-stakeholder participation in improvement of the MAP sector. This paper presents an overview of MAP certification encompassing its different parameters, current scenario (Indian background), implementation strategies as well as stakeholders’ role in MAP conservation. It also highlights Indian initiatives in this direction.

Shortcomings of discontinuous-pressure finite element methods on a class of transient problems

Past studies that have compared LBB stable discontinuous- and continuous-pressure finite element formulations on a variety of problems have concluded that both methods yield Solutions of comparable accuracy, and that the choice of interpolation is dictated by which of the two is more efficient. In this work, we show that using discontinuous-pressure interpolations can yield inaccurate solutions at large times on a class of transient problems, while the continuous-pressure formulation yields solutions that are in good agreement with the analytical Solution.

Analysis of the MAP/G(a,b)/1/N queue with multiple vacations

This paper deals with a batch service queue and multiple vacations. The system consists of a single server and a waiting room of finite capacity. Arrival of customers follows a Markovian arrival process (MAP). The server is unavailable for occasional intervals of time called vacations, and when it is available, customers are served in batches of maximum size ‘b’ with a minimum threshold value ‘a’. We obtain the queue length distributions at various epochs along with some key performance measures. Finally, some numerical results have been presented.

Conservation law with the flux function discontinuous in the space variable- II - Convex-concave type fluxes and generalized entropy solutions

We deal with a single conservation law with discontinuous convex-concave type fluxes which arise while considering sign changing flux coefficients. The main difficulty is that a weak solution may not exist as the Rankine-Hugoniot condition at the interface may not be satisfied for certain choice of the initial data. We develop the concept of generalized entropy solutions for such equations by replacing the Rankine-Hugoniot condition by a generalized Rankine-Hugoniot condition. The uniqueness of solutions is shown by proving that the generalized entropy solutions form a contractive semi-group in L-1. Existence follows by showing that a Godunov type finite difference scheme converges to the generalized entropy solution. The scheme is based on solutions of the associated Riemann problem and is neither consistent nor conservative. The analysis developed here enables to treat the cases of fluxes having at most one extrema in the domain of definition completely. Numerical results reporting the performance of the scheme are presented. (C) 2006 Elsevier B.V. All rights reserved.

Critical lattice size limit for synchronized chaotic state in one- and two-dimensional diffusively coupled map lattices

We consider diffusively coupled map lattices with P neighbors (where P is arbitrary) and study the stability of the synchronized state. We show that there exists a critical lattice size beyond which the synchronized state is unstable. This generalizes earlier results for nearest neighbor coupling. We confirm the analytical results by performing numerical simulations on coupled map lattices with logistic map at each node. The above analysis is also extended to two-dimensional P-neighbor diffusively coupled map lattices.

Hot deformation behaviour of Mg–3Al alloy—A study using processing map

The hot deformation behaviour of Mg–3Al alloy has been studied using the processing-map technique. Compression tests were conducted in the temperature range 250–550 °C and strain rate range 3 × 10−4 to 102 s−1 and the flow stress data obtained from the tests were used to develop the processing map. The various domains in the map corresponding to different dissipative characteristics have been identified as follows: (i) grain boundary sliding (GBS) domain accommodated by slip controlled by grain boundary diffusion at slow strain-rates (<10−3 s−1) in the temperature range from 350 to 450 °C, (ii) two different dynamic recrystallization (DRX) domains with a peak efficiency of 42% at 550 °C/10−1 s−1 and 425 °C/102 s−1 governed by stress-assisted cross-slip and thermally activated climb as the respective rate controlling mechanisms and (iii) dynamic recovery (DRV) domain below 300 °C in the intermediate strain rate range from 3 × 10−2 to 3 × 10−1 s−1. The regimes of flow instability have also been delineated in the processing map using an instability criterion. Adiabatic shear banding at higher strain rates (>101 s−1) and solute drag by substitutional Al atoms at intermediate strain rates (3 × 10−2 to 3 × 10−1 s−1) in the temperature range (350–450 °C) are responsible for flow instability. The relevance of these mechanisms with reference to hot working practice of the material has been indicated. The processing maps of Mg–3Al alloy and as-cast Mg have been compared qualitatively to elucidate the effect of alloying with aluminum on the deformation behaviour of magnesium.

Quantitative photoacoustic tomography from boundary pressure measurements: noniterative recovery of optical absorption coefficient from the reconstructed absorbed energy map

We describe a noniterative method for recovering optical absorption coefficient distribution from the absorbed energy map reconstructed using simulated and noisy boundary pressure measurements. The source reconstruction problem is first solved for the absorbed energy map corresponding to single- and multiple-source illuminations from the side of the imaging plane. It is shown that the absorbed energy map and the absorption coefficient distribution, recovered from the single-source illumination with a large variation in photon flux distribution, have signal-to-noise ratios comparable to those of the reconstructed parameters from a more uniform photon density distribution corresponding to multiple-source illuminations. The absorbed energy map is input as absorption coefficient times photon flux in the time-independent diffusion equation (DE) governing photon transport to recover the photon flux in a single step. The recovered photon flux is used to compute the optical absorption coefficient distribution from the absorbed energy map. In the absence of experimental data, we obtain the boundary measurements through Monte Carlo simulations, and we attempt to address the possible limitations of the DE model in the overall reconstruction procedure.

Analysis of connectivity map: Control to glutamate injured and phenobarbital treated neuronal network

We study the responses of a cultured neural network when it is exposed to epileptogenesis glutamate injury causing epilepsy and subsequent treatment with phenobarbital by constructing connectivity map of neurons using correlation matrix. This study is particularly useful in understanding the pharmaceutical drug induced changes in the neuronal network properties with insights into changes at the systems biology level. (C) 2010 American Institute of Physics. [doi:10.1063/1.3398025]

Design of rectangular reinforced concrete slabs supported on all the sides with a short discontinuous edge

Bending moment coefficients for the design of rectangular reinforced concrete panels supported on four sides with a short discontinuous edge are derived using the strip theory. The moment fields resulting from the use of proposed coefficients are examined in terms of the moment volume for possible savings in reinforcement and compared with other codified procedures. The strip coefficients averaged over the corresponding sides of the panel, besides resulting in considerable savings in reinforcement, are found to be identical with the coefficients predicted by simple yield line theory using an orthotropic layout of reinforcement.

Low-Complexity Near-MAP Decoding of Large Non-Orthogonal STBCs Using PDA

Non-orthogonal space-time block codes (STBC) from cyclic division algebras (CDA) are attractive because they can simultaneously achieve both high spectral efficiencies (same spectral efficiency as in V-BLAST for a given number of transmit antennas) as well as full transmit diversity. Decoding of non-orthogonal STBCs with hundreds of dimensions has been a challenge. In this paper, we present a probabilistic data association (PDA) based algorithm for decoding non-orthogonal STBCs with large dimensions. Our simulation results show that the proposed PDA-based algorithm achieves near SISO AWGN uncoded BER as well as near-capacity coded BER (within 5 dB of the theoretical capacity) for large non-orthogonal STBCs from CDA. We study the effect of spatial correlation on the BER, and show that the performance loss due to spatial correlation can be alleviated by providing more receive spatial dimensions. We report good BER performance when a training-based iterative decoding/channel estimation is used (instead of assuming perfect channel knowledge) in channels with large coherence times. A comparison of the performances of the PDA algorithm and the likelihood ascent search (LAS) algorithm (reported in our recent work) is also presented.

Karnaugh map synthesis of multigate threshold networks

It has been shown in an earlier paper that I-realizability of a unate function F of up to six variables corresponds to ' compactness ' of the plot of F on a Karnaugh map. Here, an algorithm has been presented to synthesize on a Karnaugh map a non-threahold function of up to Bix variables with the minimum number of threshold gates connected in cascade. Incompletely specified functions can also be treated. No resort to inequalities is made and no pre-processing (such as positivizing and ordering) of the given switching function is required.

Processing map for hot working of alpha-zirconium

The hot deformation characteristics of alpha-zirconium in the temperature range of 650 °C to 850 °C and in the strain-rate range of 10-3 to 102 s-1 are studied with the help of a power dissipation map developed on the basis of the Dynamic Materials Model.[7,8,9] The processing map describes the variation of the efficiency of power dissipation (η =2m/m + 1) calculated on the basis of the strain-rate sensitivity parameter (m), which partitions power dissipation between thermal and microstructural means. The processing map reveals a domain of dynamic recrystallization in the range of 730 °C to 850 °C and 10−2 to 1−1 with its peak efficiency of 40 pct at 800 °C and 0.1 s-1 which may be considered as optimum hot-working parameters. The characteristics of dynamic recrystallization are similar to those of static recrystallization regarding the sigmoidal variation of grain size (or hardness) with temperature, although the dynamic recrystallization temperature is much higher. When deformed at 650 °C and 10-3 s-1 texture-induced dynamic recovery occurred, while at strain rates higher than 1 s-1, alpha-zirconium exhibits microstructural instabilities in the form of localized shear bands which are to be avoided in processing.

A Smooth Finite Element Method Based on Reproducing Kernel DMS-Splines

The element-based piecewise smooth functional approximation in the conventional finite element method (FEM) results in discontinuous first and higher order derivatives across element boundaries Despite the significant advantages of the FEM in modelling complicated geometries, a motivation in developing mesh-free methods has been the ease with which higher order globally smooth shape functions can be derived via the reproduction of polynomials There is thus a case for combining these advantages in a so-called hybrid scheme or a `smooth FEM' that, whilst retaining the popular mesh-based discretization, obtains shape functions with uniform C-p (p >= 1) continuity One such recent attempt, a NURBS based parametric bridging method (Shaw et al 2008b), uses polynomial reproducing, tensor-product non-uniform rational B-splines (NURBS) over a typical FE mesh and relies upon a (possibly piecewise) bijective geometric map between the physical domain and a rectangular (cuboidal) parametric domain The present work aims at a significant extension and improvement of this concept by replacing NURBS with DMS-splines (say, of degree n > 0) that are defined over triangles and provide Cn-1 continuity across the triangle edges This relieves the need for a geometric map that could precipitate ill-conditioning of the discretized equations Delaunay triangulation is used to discretize the physical domain and shape functions are constructed via the polynomial reproduction condition, which quite remarkably relieves the solution of its sensitive dependence on the selected knotsets Derivatives of shape functions are also constructed based on the principle of reproduction of derivatives of polynomials (Shaw and Roy 2008a) Within the present scheme, the triangles also serve as background integration cells in weak formulations thereby overcoming non-conformability issues Numerical examples involving the evaluation of derivatives of targeted functions up to the fourth order and applications of the method to a few boundary value problems of general interest in solid mechanics over (non-simply connected) bounded domains in 2D are presented towards the end of the paper