The alpha method for solving differential algebraic inequality (DAI) systems

This paper describes an algorithm for ``direct numerical integration'' of the initial value Differential-Algebraic Inequalities (DAI) in a time stepping fashion using a sequential quadratic programming (SQP) method solver for detecting and satisfying active path constraints at each time step. The activation of a path constraint generally increases the condition number of the active discretized differential algebraic equation's (DAE) Jacobian and this difficulty is addressed by a regularization property of the alpha method. The algorithm is locally stable when index 1 and index 2 active path constraints and bounds are active. Subject to available regularization it is seen to be stable for active index 3 active path constraints in the numerical examples. For the high index active path constraints, the algorithm uses a user-selectable parameter to perturb the smaller singular values of the Jacobian with a view to reducing the condition number so that the simulation can proceed. The algorithm can be used as a relatively cheaper estimation tool for trajectory and control planning and in the context of model predictive control solutions. It can also be used to generate initial guess values of optimization variables used as input to inequality path constrained dynamic optimization problems. The method is illustrated with examples from space vehicle trajectory and robot path planning.

Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws

Non-standard finite difference methods (NSFDM) introduced by Mickens [Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers–Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791–797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250–2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235–276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter (λ) is chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.

Crystal structure of 2-thiophene-2-yl-3(thiophene-2-carboxylideneamino)-1,2-dihydroquinazolin-4(3H)-one and the synthesis, spectral and thermal studies of its transition metal(II) complexes

The synthesis of manganese(II), cobalt(II), nickel(II), copper(II), zinc(II) and cadmium(II) complexes of a new ligand 2-thiophene-2-yl-3(thiophene-2-carboxylidene-amino)-1,2-dihydroquinazolin-4(3H)-one (TTCADQ) is described. The ligand and metal complexes were characterized by elemental analysis, conductivity measurements, spectral (u.v.-vis., i.r., 1D n.m.r., 2D hetcor and e.p.r.) and thermal studies. The formation of 1,2-dihydroquinazolin-4(3H)-one rather than hydrazone, in the reaction of aromatic aldehyde and o-aminobenzoylhydrazide is proved by single crystal X-ray diffraction and 2D hetcor n.m.r. studies. On the basis of elemental analysis, u.v.-vis.spectroscopy and magnetic moment studies, six coordinate geometry for all the complexes was proposed. The i.r. spectral studies reveal the bidentate behaviour of the ligand.

Correlation of helicopter rotor aeroelastic response with HART-II wind tunnel test data

Purpose - This paper aims to validate a comprehensive aeroelastic analysis for a helicopter rotor with the higher harmonic control aeroacoustic rotor test (HART-II) wind tunnel test data. Design/methodology/approach - Aeroelastic analysis of helicopter rotor with elastic blades based on finite element method in space and time and capable of considering higher harmonic control inputs is carried out. Moderate deflection and coriolis nonlinearities are included in the analysis. The rotor aerodynamics are represented using free wake and unsteady aerodynamic models. Findings - Good correlation between analysis and HART-II wind tunnel test data is obtained for blade natural frequencies across a range of rotating speeds. The basic physics of the blade mode shapes are also well captured. In particular, the fundamental flap, lag and torsion modes compare very well. The blade response compares well with HART-II result and other high-fidelity aeroelastic code predictions for flap and torsion mode. For the lead-lag response, the present analysis prediction is somewhat better than other aeroelastic analyses. Research limitations/implications - Predicted blade response trend with higher harmonic pitch control agreed well with the wind tunnel test data, but usually contained a constant offset in the mean values of lead-lag and elastic torsion response. Improvements in the modeling of the aerodynamic environment around the rotor can help reduce this gap between the experimental and numerical results. Practical implications - Correlation of predicted aeroelastic response with wind tunnel test data is a vital step towards validating any helicopter aeroelastic analysis. Such efforts lend confidence in using the numerical analysis to understand the actual physical behavior of the helicopter system. Also, validated numerical analyses can take the place of time-consuming and expensive wind tunnel tests during the initial stage of the design process. Originality/value - While the basic physics appears to be well captured by the aeroelastic analysis, there is need for improvement in the aerodynamic modeling which appears to be the source of the gap between numerical predictions and HART-II wind tunnel experiments.

Modeling of a reacting nanofilm on a composite substrate

This article provides a detailed computational analysis of the reaction of dense nanofilms and the heat transfer characteristics on a composite substrate. Although traditional energetic compounds based on organic materials have similar energy per unit weight, non-organic material in nanofilm configuration offers much higher energy density and higher flame speed. The reaction of a multilayer thin film of aluminum and copper oxide has been studied by varying the substrate material and thicknesses. The numerical analysis of the thermal transport of the reacting film deposited on the substrate combined a hybrid approach in which a traditional two-dimensional black box theory was used in conjunction with the sandwich model to estimate the appropriate heat flux on the substrate accounting for the heat loss to the surroundings. A procedure to estimate this heat flux using stoichiometric calculations is provided. This work highlights two important findings. One is that there is very little difference in the temperature profiles between a single substrate of silica and a composite substrate of silicon silica. Secondly, with increase in substrate thickness, the quenching effect is progressively diminished at a given speed. These findings show that the composite substrate is effective and that the average speed and quenching of flames depend on the thickness of the silica substrate, and can be controlled by a careful choice of the substrate configuration. (C) 2011 Elsevier Ltd. All rights reserved.

Spin and charge density waves in the extended Hubbard model: A slave-boson approach

We use the extended Hubbard model to investigate the properties of the charge- and spin-density-wave phases in the presence of a nearest-neighbors repulsion term in the framework of the slave-boson technique. We show that, contrary to Hartree-Fock results, an instablity may occur for sufficiently high values of the Hubbard repulsion, both in the spin- and charge-density-wave phase, which makes the system discontinuously jump to a phase with a smaller or zero wave amplitude. The limits of applicability of our approach are discussed and our results are compared with previous numerical analysis. The phase diagram of the model at half-filling is determined.

Capacity Optimizing Hop Distance in a Mobile Ad Hoc Network with Power Control

In a dense multi-hop network of mobile nodes capable of applying adaptive power control, we consider the problem of finding the optimal hop distance that maximizes a certain throughput measure in bit-metres/sec, subject to average network power constraints. The mobility of nodes is restricted to a circular periphery area centered at the nominal location of nodes. We incorporate only randomly varying path-loss characteristics of channel gain due to the random motion of nodes, excluding any multi-path fading or shadowing effects. Computation of the throughput metric in such a scenario leads us to compute the probability density function of random distance between points in two circles. Using numerical analysis we discover that choosing the nearest node as next hop is not always optimal. Optimal throughput performance is also attained at non-trivial hop distances depending on the available average network power.

An interior penalty method for a sixth-order elliptic equation

We derive and study a C(0) interior penalty method for a sixth-order elliptic equation on polygonal domains. The method uses the cubic Lagrange finite-element space, which is simple to implement and is readily available in commercial software. After introducing some notation and preliminary results, we provide a detailed derivation of the method. We then prove the well-posedness of the method as well as derive quasi-optimal error estimates in the energy norm. The proof is based on replacing Galerkin orthogonality with a posteriori analysis techniques. Using this approach, we are able to obtain a Cea-like lemma with minimal regularity assumptions on the solution. Numerical experiments are presented that support the theoretical findings.

Amplitude death in complex networks induced by environment

We present a mechanism for amplitude death in coupled nonlinear dynamical systems on a complex network having interactions with a common environment like external system. We develop a general stability analysis that is valid for any network topology and obtain the threshold values of coupling constants for the onset of amplitude death. An important outcome of our study is a universal relation between the critical coupling strength and the largest nonzero eigenvalue of the coupling matrix. Our results are fully supported by the detailed numerical analysis for different network topologies.

Finite Element Method For A Nonlocal Problem Of Kirchhoff Type

The nonlocal term in the nonlinear equations of Kirchhoff type causes difficulties when the equation is solved numerically by using the Newton-Raphson method. This is because the Jacobian of the Newton-Raphson method is full. In this article, the finite element system is replaced by an equivalent system for which the Jacobian is sparse. We derive quasi-optimal error estimates for the finite element method and demonstrate the results with numerical experiments.

An operator-splitting Galerkin/SUPG finite element method for population balance equations : stability and convergence

We present a heterogeneous finite element method for the solution of a high-dimensional population balance equation, which depends both the physical and the internal property coordinates. The proposed scheme tackles the two main difficulties in the finite element solution of population balance equation: (i) spatial discretization with the standard finite elements, when the dimension of the equation is more than three, (ii) spurious oscillations in the solution induced by standard Galerkin approximation due to pure advection in the internal property coordinates. The key idea is to split the high-dimensional population balance equation into two low-dimensional equations, and discretize the low-dimensional equations separately. In the proposed splitting scheme, the shape of the physical domain can be arbitrary, and different discretizations can be applied to the low-dimensional equations. In particular, we discretize the physical and internal spaces with the standard Galerkin and Streamline Upwind Petrov Galerkin (SUPG) finite elements, respectively. The stability and error estimates of the Galerkin/SUPG finite element discretization of the population balance equation are derived. It is shown that a slightly more regularity, i.e. the mixed partial derivatives of the solution has to be bounded, is necessary for the optimal order of convergence. Numerical results are presented to support the analysis.

SPLIT-STEP FORWARD MILSTEIN METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS

In this paper, we consider the problem of computing numerical solutions for stochastic differential equations (SDEs) of Ito form. A fully explicit method, the split-step forward Milstein (SSFM) method, is constructed for solving SDEs. It is proved that the SSFM method is convergent with strong order gamma = 1 in the mean-square sense. The analysis of stability shows that the mean-square stability properties of the method proposed in this paper are an improvement on the mean-square stability properties of the Milstein method and three stage Milstein methods.

A QUADRATIC C degrees INTERIOR PENALTY METHOD FOR LINEAR FOURTH ORDER BOUNDARY VALUE PROBLEMS WITH BOUNDARY CONDITIONS OF THE CAHN-HILLIARD TYPE

We develop a quadratic C degrees interior penalty method for linear fourth order boundary value problems with essential and natural boundary conditions of the Cahn-Hilliard type. Both a priori and a posteriori error estimates are derived. The performance of the method is illustrated by numerical experiments.

Modeling the vulnerability of an urban groundwater system due to the combined impacts of climate change and management scenarios

Climate change impact on a groundwater-dependent small urban town has been investigated in the semiarid hard rock aquifer in southern India. A distributed groundwater model was used to simulate the groundwater levels in the study region for the projected future rainfall (2012-32) obtained from a general circulation model (GCM) to estimate the impacts of climate change and management practices on groundwater system. Management practices were based on the human-induced changes on the urban infrastructure such as reduced recharge from the lakes, reduced recharge from water and wastewater utility due to an operational and functioning underground drainage system, and additional water extracted by the water utility for domestic purposes. An assessment of impacts on the groundwater levels was carried out by calibrating a groundwater model using comprehensive data gathered during the period 2008-11 and then simulating the future groundwater level changes using rainfall from six GCMs Institute of Numerical Mathematics Coupled Model, version 3.0 (INM-CM. 3.0); L'Institut Pierre-Simon Laplace Coupled Model, version 4 (IPSL-CM4); Model for Interdisciplinary Research on Climate, version 3.2 (MIROC3.2); ECHAM and the global Hamburg Ocean Primitive Equation (ECHO-G); Hadley Centre Coupled Model, version 3 (HadCM3); and Hadley Centre Global Environment Model, version 1 (HadGEM1)] that were found to show good correlation to the historical rainfall in the study area. The model results for the present condition indicate that the annual average discharge (sum of pumping and natural groundwater outflow) was marginally or moderately higher at various locations than the recharge and further the recharge is aided from the recharge from the lakes. Model simulations showed that groundwater levels were vulnerable to the GCM rainfall and a scenario of moderate reduction in recharge from lakes. Hence, it is important to sustain the induced recharge from lakes by ensuring that sufficient runoff water flows to these lakes.

Elastic-plastic contact conditions for frictionally constrained bodies under cyclic tangential loading

A Frictionally constrained condition implies dependence of friction force on tangential displacement amplitude. The condition may occur due to chemical, physical, and/or mechanical interaction between the contacting surfaces. The condition, sometimes also referred to as the presliding condition or partial slip condition, is characterized under fretting. Under such conditions, various experimental studies indicate the existence of two distinguishable regions, that is, stick region and slip region. In the present study, frictionally constrained conditions are identified and the evolutions of stick-slip regions are investigated in detail. Investigations have been performed on self-mated stainless steel and chromium carbide coated surfaces mated against stainless steel, under both vacuum and ambient conditions. Contact conditions prevailing at the contact interface were identified based on the mechanical responses and were correlated with the surface damage observed. Surface degradation has been observed in the form of microcracks and material transfer. Detailed numerical analysis has also been performed in order to understand the energy dissipation and the damage mode involved in the surface or subsurface damage. It has been observed that under frictionally constrained conditions, the occurrence of annular slip features are mainly due to the junction growth, resulting from elastic-plastic deformation at the contact interface. Ratcheting has been observed as the governing damage mode under cyclic tangential loading condition.