Jacobian-free Newton-Krylov methods with GPU acceleration for computing nonlinear ship wave patterns

The nonlinear problem of steady free-surface flow past a submerged source is considered as a case study for three-dimensional ship wave problems. Of particular interest is the distinctive wedge-shaped wave pattern that forms on the surface of the fluid. By reformulating the governing equations with a standard boundary-integral method, we derive a system of nonlinear algebraic equations that enforce a singular integro-differential equation at each midpoint on a two-dimensional mesh. Our contribution is to solve the system of equations with a Jacobian-free Newton-Krylov method together with a banded preconditioner that is carefully constructed with entries taken from the Jacobian of the linearised problem. Further, we are able to utilise graphics processing unit acceleration to significantly increase the grid refinement and decrease the run-time of our solutions in comparison to schemes that are presently employed in the literature. Our approach provides opportunities to explore the nonlinear features of three-dimensional ship wave patterns, such as the shape of steep waves close to their limiting configuration, in a manner that has been possible in the two-dimensional analogue for some time.

Eigenstrain boundary integral equations with local Eshelby matrix for stress analysis of ellipsoidal particles

Aiming at the large scale numerical simulation of particle reinforced materials, the concept of local Eshelby matrix has been introduced into the computational model of the eigenstrain boundary integral equation (BIE) to solve the problem of interactions among particles. The local Eshelby matrix can be considered as an extension of the concepts of Eshelby tensor and the equivalent inclusion in numerical form. Taking the subdomain boundary element method as the control, three-dimensional stress analyses are carried out for some ellipsoidal particles in full space with the proposed computational model. Through the numerical examples, it is verified not only the correctness and feasibility but also the high efficiency of the present model with the corresponding solution procedure, showing the potential of solving the problem of large scale numerical simulation of particle reinforced materials.

Regulation and integral control of an underactuated robotic system using IDA-PBC with dynamic extension

This paper proposes a method for design of a set-point regulation controller with integral action for an underactuated robotic system. The robot is described as a port-Hamiltonian system, and the control design is based on a coordinate transformation and a dynamic extension. Both the change of coordinates and the dynamic extension add extra degrees of freedom that facilitate the solution of the matching equation associated with interconnection and damping assignment passivity-based control designs (IDA-PBC). The stability of the controlled system is proved using the closed loop Hamiltonian as a Lyapunov candidate function. The performance of the proposed controller is shown in simulation.

A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations. © 2011 Cambridge University Press.

Estimate of Lagrangian integral scales in shallow tidal water using high resolution GPS-tracked drifters

In estuaries and natural water channels, the estimate of velocity and dispersion coefficients is critical to the knowledge of scalar transport and mixing. This estimate is rarely available experimentally at sub-tidal time scale in shallow water channels where high frequency is required to capture its spatio-temporal variation. This study estimates Lagrangian integral scales and autocorrelation curves, which are key parameters for obtaining velocity fluctuations and dispersion coefficients, and their spatio-temporal variability from deployments of Lagrangian drifters sampled at 10 Hz for a 4-hour period. The power spectral densities of the velocities between 0.0001 and 0.8 Hz were well fitted with a slope of 5/3 predicted by Kolmogorov’s similarity hypothesis within the inertial subrange, and were similar to the Eulerian power spectral previously observed within the estuary. The result showed that large velocity fluctuations determine the magnitude of the integral time scale, TL. Overlapping of short segments improved the stability of the estimate of TL by taking advantage of the redundant data included in the autocorrelation function. The integral time scales were about 20 s and varied by up to a factor of 8. These results are essential inputs for spatial binning of velocities, Lagrangian stochastic modelling and single particle analysis of the tidal estuary.

Universal crack closure integral for SIF estimation

Numerical analysis of cracked structures often involves numerical estimation of stress intensity factors (SIFs) at a crack tip/front. A newly developed formulation called universal crack closure integral (UCCI) for the evaluation of potential energy release rates (PERRs) and the corresponding SIFs is presented in this paper. Unlike the existing element dedicated forms of crack closure integrals (MCCI, VCCI) with application limited to finite element analysis, this new numerical SIF/PERR estimation technique is independent of the basic stress analysis procedure, making it universally applicable. The second merit of this procedure is that it avoids the generally error-producing zones close to the crack tip/front singularity. The UCCI procedure, based on Irwin's original CCI, is formulated and explored using a simple 2D problem of a straight crack in an infinite sheet. It is then applied to some three-dimensional crack geometries with the stresses and displacements obtained from a boundary element program.

Integral Formulation of the Problem of Current Distribution in Compulsator Wires of Electromagnetic Launchers and Railguns

Compulsators are power sources of choice for use in electromagnetic launchers and railguns. These devices hold the promise of reducing unit costs of payload to orbit. In an earlier work, the author had calculated the current distribution in compulsator wires by considering the wire to be split into a finite number of separate wires. The present work develops an integral formulation of the problem of current distribution in compulsator wires which leads to an integrodifferential equation. Analytical solutions, including those for the integration constants, are obtained in closed form. The analytical solutions present a much clearer picture of the effect of various input parameters on the cross-sectional current distribution and point to ways in which the desired current density distribution can be achieved. Results are graphically presented and discussed, with particular reference to a 50-kJ compulsator in Bangalore. Finite-element analysis supports the results.

Solution of a System of Generalized Abel Integral Equations Using Fractional Calculus

A method is presented for obtaining useful closed form solution of a system of generalized Abel integral equations by using the ideas of fractional integral operators and their applications. This system appears in solving certain mixed boundary value problems arising in the classical theory of elasticity.

Approximate Controllability Of Semilinear Systems Using Integral Contractors

In this article, a non-autonomous (time-varying) semilinear system is considered and its approximate controllability is investigated. The notion of 'bounded integral contractor', introduced by Altman, has been exploited to obtain sufficient conditions for approximate controllability. This condition is weaker than Lipschitz condition. The main theorems of Naito [11, 12] are obtained as corollaries of our main results. An example is also given to show how our results weaken the conditions assumed by Sukavanam[17].

Inverse Sensitivity Analysis of Singular Solutions of FRF matrix in Structural System Identification

The problem of structural damage detection based on measured frequency response functions of the structure in its damaged and undamaged states is considered. A novel procedure that is based on inverse sensitivity of the singular solutions of the system FRF matrix is proposed. The treatment of possibly ill-conditioned set of equations via regularization scheme and questions on spatial incompleteness of measurements are considered. The application of the method in dealing with systems with repeated natural frequencies and (or) packets of closely spaced modes is demonstrated. The relationship between the proposed method and the methods based on inverse sensitivity of eigensolutions and frequency response functions is noted. The numerical examples on a 5-degree of freedom system, a one span free-free beam and a spatially periodic multi-span beam demonstrate the efficacy of the proposed method and its superior performance vis-a-vis methods based on inverse eigensensitivity.

On the eigenvalues and eigenfunctions of some integral operators

Some properties of the eigenvalues of the integral operator Kgt defined as Kτf(x) = ∫0τK(x − y) f (y) dy were studied by [1.], 554–566), with some assumptions on the kernel K(x). In this paper the eigenfunctions of the operator Kτ are shown to be continuous functions of τ under certain circumstances. Also, the results of Vittal Rao and the continuity of eigenfunctions are shown to hold for a larger class of kernels.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Approximate solutions of Fredholm integral equations of the second kind

This note is concerned with the problem of determining approximate solutions of Fredholm integral equations of the second kind. Approximating the solution of a given integral equation by means of a polynomial, an over-determined system of linear algebraic equations is obtained involving the unknown coefficients, which is finally solved by using the least-squares method. Several examples are examined in detail. (c) 2009 Elsevier Inc. All rights reserved.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Uso del pronombre personal sujeto de la primera persona del singular en español y portugués hablados: factores semánticos y pragmáticos

Tutkimuksen aihe on subjektipronominin ei-pakollinen käyttö finiittisten verbimuotojen yhteydessä espanjan ja portugalin kielessä. Tutkimuskohteena ovat yksikön ensimmäisen persoonan verbimuodot Espanjassa ja Portugalissa kerätyissä puhekielen korpuksissa. Tutkimuksen tarkoitus on selvittää, mitkä semanttiset ja pragmaattiset tekijät vaikuttavat subjektipronominin ei-pakollisen käytön yleisyyteen ja mitä systemaattisia eroja subjektipronominin käytössä on espanjan ja portugalin välillä. Tutkimus kuuluu korpuslingvistiikan alaan ja ensisijaisena tutkimusmetodina on kvantitatiivinen vertailu. Tutkimus osoittaa, että yksikön ensimmäisen persoonan subjektipronominin ei-pakollinen käyttö on käytännössä kaikissa konteksteissa yleisempää portugalissa kuin espanjassa. Tätä eroa voidaan selittää kielten konstituenttirakenteen typologisella erilaisuudella. Subjektin semanttinen rooli on tutkimuksen perusteella sidoksissa subjektipronominin käyttöön enemmän espanjassa kuin portugalissa, mutta kummassakaan kielessä subjektipronominin käyttöä ei voida selittää pelkästään subjektin semanttisella roolilla. Molemmissa kielissä samanviitteisyys edellisen subjektin kanssa vähentää subjektipronominin käyttöä, kun taas subjektipronominin ei-referentiaalinen käyttö ja toisaalta verbin ilmaiseman toiminnan irreaalisuus lisäävät sitä. Tutkimustulokset antavat aihetta lisätutkimukseen pronominien ja verbien ei-referentiaalisesta ja irreaalisesta käytöstä espanjassa ja portugalissa sekä typologi-seen tutkimukseen subjektipronominien käyttöön vaikuttavista tekijöistä eri kielissä.