R-parameter: A local truncation error based adaptive framework for finite volume compressible flow solvers

A residual-based strategy to estimate the local truncation error in a finite volume framework for steady compressible flows is proposed. This estimator, referred to as the -parameter, is derived from the imbalance arising from the use of an exact operator on the numerical solution for conservation laws. The behaviour of the residual estimator for linear and non-linear hyperbolic problems is systematically analysed. The relationship of the residual to the global error is also studied. The -parameter is used to derive a target length scale and consequently devise a suitable criterion for refinement/derefinement. This strategy, devoid of any user-defined parameters, is validated using two standard test cases involving smooth flows. A hybrid adaptive strategy based on both the error indicators and the -parameter, for flows involving shocks is also developed. Numerical studies on several compressible flow cases show that the adaptive algorithm performs excellently well in both two and three dimensions.

A h-Adaptive Algorithm Using Residual Error Estimates for Fluid Flows

Algorithms for adaptive mesh refinement using a residual error estimator are proposed for fluid flow problems in a finite volume framework. The residual error estimator, referred to as the R-parameter is used to derive refinement and coarsening criteria for the adaptive algorithms. An adaptive strategy based on the R-parameter is proposed for continuous flows, while a hybrid adaptive algorithm employing a combination of error indicators and the R-parameter is developed for discontinuous flows. Numerical experiments for inviscid and viscous flows on different grid topologies demonstrate the effectiveness of the proposed algorithms on arbitrary polygonal grids.

Efficient Adaptive Mesh Refinement for MoM-based Package-Board 3D Full-wave Extraction

The accurate solution of 3D full-wave Method of Moments (MoM) on an arbitrary mesh of a package-board structure does not guarantee accuracy, since the discretizations may not be fine enough to capture rapid spatial changes in the solution variable. At the same time, uniform over-meshing on the entire structure generates large number of solution variables and therefore requires an unnecessarily large matrix solution. In this work, a suitable refinement criterion for MoM based electromagnetic package-board extraction is proposed and the advantages of the adaptive strategy are demonstrated from both accuracy and speed perspectives.

Adaptive Mesh Refinement for Fast Convergence of EFIE-Based 3-D Extraction

3-D full-wave method of moments (MoM) based electromagnetic analysis is a popular means toward accurate solution of Maxwell's equations. The time and memory bottlenecks associated with such a solution have been addressed over the last two decades by linear complexity fast solver algorithms. However, the accurate solution of 3-D full-wave MoM on an arbitrary mesh of a package-board structure does not guarantee accuracy, since the discretization may not be fine enough to capture spatial changes in the solution variable. At the same time, uniform over-meshing on the entire structure generates a large number of solution variables and therefore requires an unnecessarily large matrix solution. In this paper, different refinement criteria are studied in an adaptive mesh refinement platform. Consequently, the most suitable conductor mesh refinement criterion for MoM-based electromagnetic package-board extraction is identified and the advantages of this adaptive strategy are demonstrated from both accuracy and speed perspectives. The results are also compared with those of the recently reported integral equation-based h-refinement strategy. Finally, a new methodology to expedite each adaptive refinement pass is proposed.

Simultaneous Utilization of Glucose and Sucrose by Thermophilic Fungi

The utilization of mixtures of glucose and sucrose at nonlimiting concentrations was studied in batch cultures of two common thermophilic fungi, Thermomyces lanuginosus and Penicilium duponti. The sucrose-utilizing enzymes (sucrose permease and invertase) in both fungi were inducible. Both sugars were used concurrently,regardless of their relative proportion in the mixture. At the optimal growth temperature (50C), T.lanuginosus utilized sucrose earlier than it did glucose, but at a suboptimal growth temperature (30°C) the two sugars were utilized at nearly comparable rates. The coutilization of the two sugars was most likely possible because (i) invertase was insensitive to catabolite repression by glucose, (ii) the activity and affinity of the glucose transport system were lowered when sucrose was included in the growth medium, and (iii) the activity of the glucose uptake system was also subject to repression by high concentrations of glucose itself. The concurrent utilization of the available carbon sources by thermophilic fungi might be an adaptive strategy for opportunistic growth in nature under conditions of low nutrient availability and thermal fluctuations in the environment.

A Control Strategy for Reference Wave Adaptive Current Generation

Speed control of ac motors requires variable frequency, variable current, or variable voltage supply. Variable frequency supply can be obtained directly from a fixed frequency supply by using a frequency converter or from a dc source using inverters. In this paper a control technique for reference wave adaptive-current generation by modulating the inverter voltage is explained. Extension of this technique for three-phase induction-motor speed control is briefly explained. The oscillograms of the current waveforms obtained from the experimental setup are also shown.

New a posteriori error estimator and adaptive mesh refinement strategy for 2-D crack problems

A posteriori error estimation and adaptive refinement technique for fracture analysis of 2-D/3-D crack problems is the state-of-the-art. The objective of the present paper is to propose a new a posteriori error estimator based on strain energy release rate (SERR) or stress intensity factor (SIF) at the crack tip region and to use this along with the stress based error estimator available in the literature for the region away from the crack tip. The proposed a posteriori error estimator is called the K-S error estimator. Further, an adaptive mesh refinement (h-) strategy which can be used with K-S error estimator has been proposed for fracture analysis of 2-D crack problems. The performance of the proposed a posteriori error estimator and the h-adaptive refinement strategy have been demonstrated by employing the 4-noded, 8-noded and 9-noded plane stress finite elements. The proposed error estimator together with the h-adaptive refinement strategy will facilitate automation of fracture analysis process to provide reliable solutions.

An optimal dynamic inversion-based neuro-adaptive approach for treatment of chronic myelogenous leukemia

Combining the advanced techniques of optimal dynamic inversion and model-following neuro-adaptive control design, an innovative technique is presented to design an automatic drug administration strategy for effective treatment of chronic myelogenous leukemia (CML). A recently developed nonlinear mathematical model for cell dynamics is used to design the controller (medication dosage). First, a nominal controller is designed based on the principle of optimal dynamic inversion. This controller can treat the nominal model patients (patients who can be described by the mathematical model used here with the nominal parameter values) effectively. However, since the system parameters for a realistic model patient can be different from that of the nominal model patients, simulation studies for such patients indicate that the nominal controller is either inefficient or, worse, ineffective; i.e. the trajectory of the number of cancer cells either shows non-satisfactory transient behavior or it grows in an unstable manner. Hence, to make the drug dosage history more realistic and patient-specific, a model-following neuro-adaptive controller is augmented to the nominal controller. In this adaptive approach, a neural network trained online facilitates a new adaptive controller. The training process of the neural network is based on Lyapunov stability theory, which guarantees both stability of the cancer cell dynamics as well as boundedness of the network weights. From simulation studies, this adaptive control design approach is found to be very effective to treat the CML disease for realistic patients. Sufficient generality is retained in the mathematical developments so that the technique can be applied to other similar nonlinear control design problems as well.

Nonlinear structural dynamical system identification using adaptive particle filters

The problem of identifying parameters of nonlinear vibrating systems using spatially incomplete, noisy, time-domain measurements is considered. The problem is formulated within the framework of dynamic state estimation formalisms that employ particle filters. The parameters of the system, which are to be identified, are treated as a set of random variables with finite number of discrete states. The study develops a procedure that combines a bank of self-learning particle filters with a global iteration strategy to estimate the probability distribution of the system parameters to be identified. Individual particle filters are based on the sequential importance sampling filter algorithm that is readily available in the existing literature. The paper develops the requisite recursive formulary for evaluating the evolution of weights associated with system parameter states. The correctness of the formulations developed is demonstrated first by applying the proposed procedure to a few linear vibrating systems for which an alternative solution using adaptive Kalman filter method is possible. Subsequently, illustrative examples on three nonlinear vibrating systems, using synthetic vibration data, are presented to reveal the correct functioning of the method. (c) 2007 Elsevier Ltd. All rights reserved.

Effective treatment of infectious diseases: A nonlinear adaptive control theoretic approach

A nonlinear adaptive system theoretic approach is presented in this paper for effective treatment of infectious diseases that affect various organs of the human body. The generic model used does not represent any specific disease. However, it mimics the generic immunological dynamics of the human body under pathological attack, including the response to external drugs. From a system theoretic point of view, drugs can be interpreted as control inputs. Assuming a set of nominal parameters in the mathematical model, first a nonlinear controller is designed based on the principle of dynamic inversion. This treatment strategy was found to be effective in completely curing "nominal patients". However, in some cases it is ineffective in curing "realistic patients". This leads to serious (sometimes fatal) damage to the affected organ. To make the drug dosage design more effective, a model-following neuro-adaptive control design is carried out using neural networks, which are trained (adapted) online. From simulation studies, this adaptive controller is found to be effective in killing the invading microbes and healing the damaged organ even in the presence of parameter uncertainties and continuing pathogen attack.

A neuro-adaptive augmented optimal dynamic inversion approach for effective and efficient treatment of chronic myelogenous leukemia

Combining the advanced techniques of optimal dynamic inversion and model-following neuro-adaptive control design, an efficient technique is presented for effective treatment of chronic myelogenous leukemia (CML). A recently developed nonlinear mathematical model for cell dynamics is used for the control (medication) synthesis. First, taking a set of nominal parameters, a nominal controller is designed based on the principle of optimal dynamic inversion. This controller can treat nominal patients (patients having same nominal parameters as used for the control design) effectively. However, since the parameters of an actual patient can be different from that of the ideal patient, to make the treatment strategy more effective and efficient, a model-following neuro-adaptive controller is augmented to the nominal controller. In this approach, a neural network trained online (based on Lyapunov stability theory) facilitates a new adaptive controller, computed online. From the simulation studies, this adaptive control design approach (treatment strategy) is found to be very effective to treat the CML disease for actual patients. Sufficient generality is retained in the theoretical developments in this paper, so that the techniques presented can be applied to other similar problem as well. Note that the technique presented is computationally non-intensive and all computations can be carried out online.

Optimal Blood Glucose Regulation using Single Network Adaptive Critics

Diabetes is a serious disease during which the body's production and use of insulin is impaired, causing glucose concentration level toincrease in the bloodstream. Regulating blood glucose levels as close to normal as possible, leads to a substantial decrease in long term complications of diabetes. In this paper, an intelligent neural network on-line optimal feedback treatment strategy based on nonlinear optimal control theory is presented for the disease using subcutaneous treatment strategy. A simple mathematical model of the nonlinear dynamics of glucose and insulin interaction in the blood system is considered based on the Bergman's minimal model. A glucose infusion term representing the effect of glucose intake resulting from a meal is introduced into the model equations. The efficiency of the proposed controllers is shown taking random parameters and random initial conditions in presence of physical disturbances like food intake. A comparison study with linear quadratic regulator theory brings Out the advantages of the nonlinear control synthesis approach. Simulation results show that unlike linear optimal control, the proposed on-line continuous infusion strategy never leads to severe hypoglycemia problems.

Optimal management of beaver population using a reduced-order distributed parameter model and single network adaptive critics

Beavers are often found to be in conflict with human interests by creating nuisances like building dams on flowing water (leading to flooding), blocking irrigation canals, cutting down timbers, etc. At the same time they contribute to raising water tables, increased vegetation, etc. Consequently, maintaining an optimal beaver population is beneficial. Because of their diffusion externality (due to migratory nature), strategies based on lumped parameter models are often ineffective. Using a distributed parameter model for beaver population that accounts for their spatial and temporal behavior, an optimal control (trapping) strategy is presented in this paper that leads to a desired distribution of the animal density in a region in the long run. The optimal control solution presented, imbeds the solution for a large number of initial conditions (i.e., it has a feedback form), which is otherwise nontrivial to obtain. The solution obtained can be used in real-time by a nonexpert in control theory since it involves only using the neural networks trained offline. Proper orthogonal decomposition-based basis function design followed by their use in a Galerkin projection has been incorporated in the solution process as a model reduction technique. Optimal solutions are obtained through a "single network adaptive critic" (SNAC) neural-network architecture.

Optimal blood glucose regulation of diabetic patients using single network adaptive critics

Diabetes is a long-term disease during which the body's production and use of insulin are impaired, causing glucose concentration level to increase in the bloodstream. Regulating blood glucose levels as close to normal as possible leads to a substantial decrease in long-term complications of diabetes. In this paper, an intelligent online feedback-treatment strategy is presented for the control of blood glucose levels in diabetic patients using single network adaptive critic (SNAC) neural networks (which is based on nonlinear optimal control theory). A recently developed mathematical model of the nonlinear dynamics of glucose and insulin interaction in the blood system has been revised and considered for synthesizing the neural network for feedback control. The idea is to replicate the function of pancreatic insulin, i.e. to have a fairly continuous measurement of blood glucose and a situation-dependent insulin injection to the body using an external device. Detailed studies are carried out to analyze the effectiveness of this adaptive critic-based feedback medication strategy. A comparison study with linear quadratic regulator (LQR) theory shows that the proposed nonlinear approach offers some important advantages such as quicker response, avoidance of hypoglycemia problems, etc. Robustness of the proposed approach is also demonstrated from a large number of simulations considering random initial conditions and parametric uncertainties. Copyright (C) 2009 John Wiley & Sons, Ltd.

An adaptive system of vigilance in spotted deer (Axis axis) herds in response to predation

Spotted deer or chital (Axis axis), a major prey species in southern India, lives in large groups. To understand the benefits of group living, we carried out observations on chital herds under natural conditions. Individual and group vigilance showed a negative correlation with herd size, whereas the latter had a positive correlation with proportion of vigilant individuals. Furthermore, individual vigilance was negatively correlated with proportion of individuals vigilant and positively correlated with group vigilance. These results are explained in the context of a three-phase vigilance system, probably operative in the chital herd, under specified ecological conditions. We surmise that this system allows for adaptation to predation risk and has possibly co-evolved with the optimal hunting strategy of the predator.