The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Manju Sharma - One of the best experts on this subject based on the ideXlab platform.
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a parameter uniform difference scheme for parabolic partial differential equation with a retarded argument
Applied Mathematical Modelling, 2010Co-Authors: Aditya Kaushik, Kapil K Sharma, Manju SharmaAbstract:The paper deals with the analysis of a non-stationary parabolic partial differential equation with a time delay. The highest order derivative Term is affected by the small parameter. This is precisely the case when the magnitude of the convective Term becomes much larger compare to that of Diffusion Term. The solution of problem exhibits steep gradients in the narrow intervals of space and short interval of times. In these cases a dissipative loss turned out to be more complex. Even for the one spatial dimension and one temporal variable, not all difference scheme can capture these steep variation. Although the analysis is restricted to the model in one space dimension, the technique and comparison principles developed should prove useful in assessing the merits of numerical solution of other nonlinear model equations too.
Henrik Madsen - One of the best experts on this subject based on the ideXlab platform.
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Evaluation of probabilistic flow predictions in sewer systems using grey box models and a skill score criterion
Stochastic Environmental Research and Risk Assessment, 2012Co-Authors: Fannar Örn Thordarson, Jan Kloppenborg Moller, Anders Breinholt, Peter Steen Mikkelsen, Morten Grum, Henrik MadsenAbstract:In this paper we show how the grey box methodology can be applied to find models that can describe the flow prediction uncertainty in a sewer system where rain data are used as input, and flow measurements are used for calibration and updating model states. Grey box models are composed of a drift Term and a Diffusion Term, respectively accounting for the deTerministic and stochastic part of the models. Furthermore, a distinction is made between the process noise and the observation noise. We compare five different model candidates’ predictive performances that solely differ with respect to the Diffusion Term description up to a 4 h prediction horizon by adopting the prediction performance measures; reliability, sharpness and skill score to pinpoint the preferred model. The prediction performance of a model is reliable if the observed coverage of the prediction intervals corresponds to the nominal coverage of the prediction intervals, i.e. the bias between these coverages should ideally be zero. The sharpness is a measure of the distance between the lower and upper prediction limits, and skill score criterion makes it possible to pinpoint the preferred model by taking into account both reliability and sharpness. In this paper, we illustrate the power of the introduced grey box methodology and the probabilistic performance measures in an urban drainage context.
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development of a restricted state space stochastic differential equation model for bacterial growth in rich media
Journal of Theoretical Biology, 2012Co-Authors: Jan Kloppenborg Moller, Kirsten Riber Bergmann, Lasse Engbo Christiansen, Henrik MadsenAbstract:In the present study, bacterial growth in a rich media is analysed in a Stochastic Differential Equation (SDE) framework. It is demonstrated that the SDE formulation and smoothened state estimates provide a systematic framework for data driven model improvements, using random walk hidden states. Bacterial growth is limited by the available substrate and the inclusion of Diffusion must obey this natural restriction. By inclusion of a modified logistic Diffusion Term it is possible to introduce a Diffusion Term flexible enough to capture both the growth phase and the stationary phase, while concentration is restricted to the natural state space (substrate and bacteria non-negative). The case considered is the growth of Salmonella and Enterococcus in a rich media. It is found that a hidden state is necessary to capture the lag phase of growth, and that a flexible logistic Diffusion Term is needed to capture the random behaviour of the growth model. Further, it is concluded that the Monod effect is not needed to capture the dynamics of bacterial growth in the data presented.
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grey box modelling of flow in sewer systems with state dependent Diffusion
Environmetrics, 2011Co-Authors: Anders Breinholt, Jan Kloppenborg Moller, Fannar Örn Thordarson, Peter Steen Mikkelsen, Morten Grum, Henrik MadsenAbstract:Generating flow forecasts with uncertainty limits from rain gauge inputs in sewer systems require simple models with identifiable parameters that can adequately describe the stochastic phenomena of the system. In this paper, a simple grey-box model is proposed that is attractive for both forecasting and control purposes. The grey-box model is based on stochastic differential equations and a key feature is the separation of the total noise into process and measurement noise. The grey-box approach is properly introduced and hypothesis regarding the noise Terms are formulated. Three different hypotheses for the Diffusion Term are investigated and compared: one that assumes additive Diffusion; one that assumes state proportional Diffusion; and one that assumes state exponentiated Diffusion. To implement the state dependent Diffusion Terms Ito's formula and the Lamperti transform are applied. It is shown that an additive Diffusion noise Term description leads to a violation of the physical constraints of the system, whereas a state dependent Diffusion noise avoids this problem and should be favoured. It is also shown that a logarithmic transformation of the flow measurements secures positive lower flow prediction limits, because the observation noise is proportionally scaled with the modelled output. Finally it is concluded that a state proportional Diffusion Term best and adequately describes the one-step flow prediction uncertainty, and a proper description of the system noise is important for ascertaining the physical parameters in question. Copyright © 2011 John Wiley & Sons, Ltd.
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parameter estimation in stochastic grey box models
Automatica, 2004Co-Authors: Niels Rode Kristensen, Henrik Madsen, Sten Bay JorgensenAbstract:An efficient and flexible parameter estimation scheme for grey-box models in the sense of discretely, partially observed Ito stochastic differential equations with measurement noise is presented along with a corresponding software implementation. The estimation scheme is based on the extended Kalman filter and features maximum likelihood as well as maximum a posteriori estimation on multiple independent data sets, including irregularly sampled data sets and data sets with occasional outliers and missing observations. The software implementation is compared to an existing software tool and proves to have better performance both in Terms of quality of estimates for nonlinear systems with significant Diffusion and in Terms of reproducibility. In particular, the new tool provides more accurate and more consistent estimates of the parameters of the Diffusion Term.
Georges Guiochon - One of the best experts on this subject based on the ideXlab platform.
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perspectives on the evolution of the column efficiency in liquid chromatography
Analytical Chemistry, 2013Co-Authors: Fabrice Gritti, Georges GuiochonAbstract:When analyses of mixtures of small molecules are carried out at mobile phase velocities close to (for isocratic runs) or somewhat above (for gradient runs) the optimum velocity, the eddy Diffusion Term contributes to at least 75% of the band broadening. Future improvements in column performance may come only from a reduction of the eddy Diffusion Term. The classical models of axial dispersion of Gunn and Giddings are revisited and their predictions compared to recently reported eddy dispersion data obtained by solving numerically the Navier–Stokes equations and simulating advective-diffusive transport in the bulk region and in confined geometries of reconstructed and computer-generated random sphere packings. The Gunn model fails to describe these data. In contrast, the Giddings model succeeds, provided that his original guesses regarding the values of two parameters of his model are adjusted. Accurate measurements of real eddy dispersion data in modern high-pressure liquid chromatography (HPLC) columns w...
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measurement of the eddy Diffusion Term in chromatographic columns i application to the first generation of 4 6 mm i d monolithic columns
Journal of Chromatography A, 2011Co-Authors: Fabrice Gritti, Georges GuiochonAbstract:Abstract The corrected heights equivalent to a theoretical plate (HETP) of three 4.6 mm I.D. monolithic Onyx-C18 columns (Onyx, Phenomenex, Torrance, CA) of different lengths (2.5, 5, and 10 cm) are reported for retained (toluene, naphthalene) and non-retained (uracil, caffeine) small molecules. The moments of the peak profiles were measured according to the accurate numerical integration method. Correction for the extra-column contributions was systematically applied. The peak parking method was used in order to measure the bulk Diffusion coefficients of the sample molecules, their longitudinal Diffusion Terms, and the eddy Diffusion Term of the three monolithic columns. The experimental results demonstrate that the maximum efficiency was 60 000 plates/m for retained compounds. The column length has a large impact on the plate height of non-retained species. These observations were unambiguously explained by a large trans-column eddy Diffusion Term in the van Deemter HETP equation. This large trans-rod eddy Diffusion Term is due to the combination of a large trans-rod velocity bias (≃3%), a small radial dispersion coefficient in silica monolithic columns, and a poorly designed distribution and collection of the sample streamlets at the inlet and outlet of the monolithic rod. Improving the performance of large I.D. monolithic columns will require (1) a detailed knowledge of the actual flow distribution across and along these monolithic rod and (2) the design of appropriate inlet and outlet distributors designed to minimize the nefarious impact of the radial flow heterogeneity on band broadening.
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relationship between trans column eddy Diffusion and retention in liquid chromatography theory and experimental evidence
Journal of Chromatography A, 2010Co-Authors: Fabrice Gritti, Georges GuiochonAbstract:Abstract Experimental results demonstrate that trans-column eddy Diffusion depends on the retention of compounds. The combination of elution profiles recorded in different points of the exit column cross-section and of the height equivalent to a theoretical plate (HETP) of small molecules clearly show a strong link between retention and column performance in liquid chromatography. These results validate a new model of trans-column eddy Diffusion in packed columns. The contribution to the column HETP of the trans-column eddy Diffusion Term decreases with increasing retention factor from k′ = 0 to k′ = 3 above which it becomes negligible. The best column performance in RPLC is observed for the most retained compounds. This is due to the combination of the lack of a residual trans-column eddy Diffusion contribution and the vanishing contribution of the instrument to band broadening.
Aditya Kaushik - One of the best experts on this subject based on the ideXlab platform.
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a parameter uniform difference scheme for parabolic partial differential equation with a retarded argument
Applied Mathematical Modelling, 2010Co-Authors: Aditya Kaushik, Kapil K Sharma, Manju SharmaAbstract:The paper deals with the analysis of a non-stationary parabolic partial differential equation with a time delay. The highest order derivative Term is affected by the small parameter. This is precisely the case when the magnitude of the convective Term becomes much larger compare to that of Diffusion Term. The solution of problem exhibits steep gradients in the narrow intervals of space and short interval of times. In these cases a dissipative loss turned out to be more complex. Even for the one spatial dimension and one temporal variable, not all difference scheme can capture these steep variation. Although the analysis is restricted to the model in one space dimension, the technique and comparison principles developed should prove useful in assessing the merits of numerical solution of other nonlinear model equations too.
Bashir Ahmad - One of the best experts on this subject based on the ideXlab platform.
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passivity analysis of delayed reaction Diffusion cohen grossberg neural networks via hardy poincare inequality
Journal of The Franklin Institute-engineering and Applied Mathematics, 2017Co-Authors: Ruoxia Li, Ahmed Alsaedi, Bashir AhmadAbstract:Abstract In this paper, we formulate and investigate the passivity analysis of delayed reaction-Diffusion neural networks with Cohen-Grossberg type. The derivative of the Lyapunov-Krasovskii functional was estimated by the new agencies of Hardy-Poincare inequality and some analysis techniques. Subsequently, some new and concise conditions to check the passivity of the given Cohen-Grossberg neural networks were summarized. The proposed criteria not only depends on the system parameters, reaction-Diffusion coefficients but also on the regional feature. Furthermore, as corollaries, some sufficient schemes are provided to achieve passive and exponential passive of delayed Cohen-Grossberg neural networks without reaction-Diffusion Term. The results obtained in this paper generalize and improve many known results. Finally, two numerical examples and its simulations are proposed to show the effectiveness and merits of the improved theoretical results.