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Relevant bibliographies by topics / Stokeslet

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Academic literature on the topic 'Stokeslet'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Stokeslet"

1

Aboelkassem, Yasser. "Chaotic mixing by oscillating a Stokeslet in a circular Hele-Shaw microfluidic device." Mathematics of Quantum Technologies 5, no. 1 (January 1, 2016): 1–8. http://dx.doi.org/10.1515/nsmmt-2016-0001.

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AbstractChaotic mixing by oscillating a Stokeslet in a circular Hele-Shaw microffluidic device is presented in this article. Mathematical modeling for the induced flow motions by moving a Stokeslet along the x-axis is derived using Fourier expansion method. The solution is formulated in terms of the velocity stream function. The model is then used to explore different stirring dynamics as function of the Stokeslet parameters. For instance, the effects of using various oscillation amplitudes and force strengths are investigated. Mixing patterns using Poincaré maps are obtained numerically and have been used to characterize the mixing efficiency. Results have shown that, for a given Stokeslet’s strength, efficient mixing can be obtained when small oscillation amplitudes are used. The present mixing platform is expected to be useful for many of biomicrofluidic applications.

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Cortez, Ricardo. "Regularized Stokeslet segments." Journal of Computational Physics 375 (December 2018): 783–96. http://dx.doi.org/10.1016/j.jcp.2018.08.055.

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Chan, A. T., and A. T. Chwang. "The unsteady stokeslet and oseenlet." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 214, no. 1 (January 1, 2000): 175–79. http://dx.doi.org/10.1243/0954406001522895.

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The unsteady low Reynolds number flow of an incompressible viscous fluid past a singular forcelet is investigated analytically. New fundamental three-dimensional solutions for a concentrated impulsive force are derived for the Stokes and the Oseen equations. These elementary solutions can be used as fundamental Green's functions to obtain solutions for flows over singularities with any time-dependent nature. The fundamental singularities are employed to construct some well-known solutions to demonstrate their validity and usefulness in solving unsteady problems governed by the Stokes and the Oseen equations. A new solution is presented for an unsteady Oseen flow with a constant acceleration.

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Gallagher, M. T., and D. J. Smith. "The art of coarse Stokes: Richardson extrapolation improves the accuracy and efficiency of the method of regularized stokeslets." Royal Society Open Science 8, no. 5 (May 2021): 210108. http://dx.doi.org/10.1098/rsos.210108.

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The method of regularized stokeslets is widely used in microscale biological fluid dynamics due to its ease of implementation, natural treatment of complex moving geometries, and removal of singular functions to integrate. The standard implementation of the method is subject to high computational cost due to the coupling of the linear system size to the numerical resolution required to resolve the rapidly varying regularized stokeslet kernel. Here, we show how Richardson extrapolation with coarse values of the regularization parameter is ideally suited to reduce the quadrature error, hence dramatically reducing the storage and solution costs without loss of accuracy. Numerical experiments on the resistance and mobility problems in Stokes flow support the analysis, confirming several orders of magnitude improvement in accuracy and/or efficiency.

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Popov, I. Yu. "On operator treatment of a Stokeslet." Siberian Mathematical Journal 35, no. 5 (September 1994): 1022–26. http://dx.doi.org/10.1007/bf02104580.

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Walker, B. J., K. Ishimoto, H. Gadêlha, and E. A. Gaffney. "Filament mechanics in a half-space via regularised Stokeslet segments." Journal of Fluid Mechanics 879 (October 1, 2019): 808–33. http://dx.doi.org/10.1017/jfm.2019.723.

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We present a generalisation of efficient numerical frameworks for modelling fluid–filament interactions via the discretisation of a recently developed, non-local integral equation formulation to incorporate regularised Stokeslets with half-space boundary conditions, as motivated by the importance of confining geometries in many applications. We proceed to utilise this framework to examine the drag on slender inextensible filaments moving near a boundary, firstly with a relatively simple example, evaluating the accuracy of resistive force theories near boundaries using regularised Stokeslet segments. This highlights that resistive force theories do not accurately quantify filament dynamics in a range of circumstances, even with analytical corrections for the boundary. However, there is the notable and important exception of movement in a plane parallel to the boundary, where accuracy is maintained. In particular, this justifies the judicious use of resistive force theories in examining the mechanics of filaments and monoflagellate microswimmers with planar flagellar patterns moving parallel to boundaries. We proceed to apply the numerical framework developed here to consider how filament elastohydrodynamics can impact drag near a boundary, analysing in detail the complex responses of a passive cantilevered filament to an oscillatory flow. In particular, we document the emergence of an asymmetric periodic beating in passive filaments in particular parameter regimes, which are remarkably similar to the power and reverse strokes exhibited by motile$9+2$cilia. Furthermore, these changes in the morphology of the filament beating, arising from the fluid–structure interactions, also induce a significant increase in the hydrodynamic drag of the filament.

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Blake, J. R., and S. R. Otto. "Ciliary propulsion, chaotic filtration and a ?blinking? stokeslet." Journal of Engineering Mathematics 30, no. 1-2 (March 1996): 151–68. http://dx.doi.org/10.1007/bf00118828.

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Blake, J. R., S. R. Otto, and D. A. Blake. "Filter Feeding, Chaotic Filtration, and a Blinking Stokeslet." Theoretical and Computational Fluid Dynamics 10, no. 1-4 (January 1, 1998): 23–36. http://dx.doi.org/10.1007/s001620050049.

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Falade, A., and H. Brenner. "Stokes wall effects for particles moving near cylindrical boundaries." Journal of Fluid Mechanics 154 (May 1985): 145–62. http://dx.doi.org/10.1017/s002211208500146x.

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An asymptotic scheme is derived for calculating values of the ‘reflected’ Stokeslet-field velocity dyadic V and its gradient ${\boldmath \nabla V}$ back at the Stokeslet location for situations in which this singular point lies in close proximity to the wall of an infinitely long circular cylinder. The asymptotic formulas furnished by this scheme permit calculations of first- and second-order wall effects in the non-dimensional parameter κ = a/R0 (a ≡ characteristic particle radius, R0 ≡ cylinder radius) upon the Stokes resistance of a particle of arbitrary shape, location and orientation when translating and/or rotating near the wall of an otherwise quiescent fluid-filled or fluid-surrounded circular cylinder. This reflection-type calculation is applicable for circumstances in which the inequalities κ [Lt ] 1 and 1 − β [Lt ] 1 are each separately satisfied, while simultaneously K/(1 − β) [Lt ] 1. (Here β = b/R0 is the fractionally eccentric Stokeslet location, or equivalently the centre of reaction of the particle, with b its distance from the tube axis.) The main result of this paper is the development of the pair of asymptotic wall-correction formulas \[ W_{jk}\sim {}_0C_{jk}(1-\beta)^{-1}+{}_1C_{jk}+{}_2C_{jk}(1-\beta)+O(1-\beta)^2 \] and \[ W_{jk,\,l}\sim {}_0D_{jkl}(1-\beta)^{-2}+{}_1D_{jkl}(1-\beta)^{-1}+{}_2D_{jkl}+O(1-\beta) \] to particle resistance, with W ≡ Wjk and ${\boldmath \nabla W}\equiv W_{kl,j}$ respectively the non-dimensional normalized wall-effect dyadic and its gradient at the Stokeslet location β. The numerical, rational fraction, β-independent, nCjk and nDjkl coefficients (n = 0, 1, 2) appearing above are evaluated by solving a recursive sequence of Stokes-flow boundary-value problems in the semi-infinite fluid domain bounded by a plane wall. These simple asymptotic formulas are shown to agree excellently in the range near β = 1 with existing values derived from the exact solution of the original circular-cylinder boundary-value problem, involving tedious infinite-series summations of complicated Bessel-function integrands extended over infinite integration domains. Generalizations of the scheme to particle motion in the space external to a circular cylinder is briefly sketched, as too is the case of cylinders of non-circular cross-section.

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Usha, R., and S. D. Nigam. "Flow in a spherical cavity due to a stokeslet." Fluid Dynamics Research 11, no. 1-2 (January 1993): 75–78. http://dx.doi.org/10.1016/0169-5983(93)90006-v.

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Dissertations / Theses on the topic "Stokeslet"

1

Berzig, Maher. "Etude des interactions hydrodynamiques entre particules et parois par la méthode des éléments de frontière." Paris 6, 2007. https://tel.archives-ouvertes.fr/tel-00325418.

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Berzig, Maher. "Étude des interactions hydrodynamiques entre particules et parois par la méthode des éléments de frontière." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2007. http://tel.archives-ouvertes.fr/tel-00325418.

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Cette thèse présente une étude numérique des interactions hydrodynamiques entre des particules et une paroi plane dans un fluide Newtonien, dans l'hypothèse d'un petit nombre de Reynolds. Les équations de Stokes sont d'abord transformées sous la forme classique d'une équation intégrale de surface donnant les contraintes sur la surface entourant le fluide. Nous avons calculé ainsi les forces et les couples exercés sur les particules. Une étude préliminaire correspond au problème axisymétrique pour une chaîne de particules sphériques arrangées suivant une ligne perpendiculaire à la paroi et en mouvement suivant cette ligne dans un fluide au repos. Puis nous avons abordé le problème général de particules non sphériques, la position des particules étant quelconque et le fluide loin des particules pouvant être en écoulement. Pour le cas axisymétrique, les points de collocation (qui sont aussi les emplacements des singularités de Stokes ou ``stokeslets'') sont choisis sur les surfaces des particules de façon que leurs distance relatives soient proportionnelles à la distance entre surfaces proches. Pour traiter le cas général, nous avons mis au point un code de calcul utilisant la méthode des éléments de frontière (BEM). Les stokeslets sont ici répartis de façon à prendre en compte les interactions hydrodynamiques et la complexité géométrique des configurations. En effet, le maillage est adapté à la variation du gradient de contraintes de façon que les zones de la surface qui entrent en forte interaction hydrodynamique soient les plus raffinées. La technique de raffinement dynamique de maillages que nous avons mise au point nous a permis de mieux détecter les zones de lubrification entre particules et paroi ainsi que les interactions entre particules. Les contraintes ont ainsi été calculées pour de nouvelles configurations géométriques. Enfin, les relations linéaires entre les forces et couples qui s'exercent sur les particules et leurs vitesses de translation et rotation sont exprimées au moyen de la « grande matrice de résistance » (ou de son inverse la « grande matrice de mobilité ») qui est alors introduite dans la relation fondamentale de la dynamique. En intégrant, nous avons déterminé les trajectoires des particules dans diverses configurations: en sédimentation dans un fluide au repos au voisinage d'une paroi, tournant librement dans un écoulement donné, ... La méthode permet aussi d'obtenir les champs de vitesse du fluide dans ces conditions.

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Zhao, Shunliu. "Development of Boundary Singularity Method for Partial-Slip and Transition Molecular-Continuum Flow Regimes with Application to Filtration." University of Akron / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=akron1247718304.

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4

Aboelkassem, Yasser. "Novel Bioinspired Pumping Models for Microscale Flow Transport." Diss., Virginia Tech, 2012. http://hdl.handle.net/10919/28674.

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Bioinspiration and biomimetics are two increasingly important fields in applied science and mechanics that seek to imitate systems or processes in nature to design improved engineering devices. Here, we are inspired and motivated by microscale internal flow transport phenomena in insect tracheal networks, which are observed to be induced by the rhythmic tracheal wall contractions. These networks have been shown to mange fluid very efficiently compared to current state-of-the-art microfluidic devises. This dissertation presents two versions of a novel bioinspired pumping mechanism that is neither peristaltic nor belongs to impedance mismatch class of pumping mechanisms. The insect-inspired pumping models presented here are expected to function efficiently in the microscale flow regime in a simple channel/tube geometries or a complex network of channels. The first pumping approach shows the ability of inducing a unidirectional net flow by using an inelastic tube or channel with at least two moving contractions. The second pumping approach presents a new concept for directional pumping, namely ``selective pumping in a network.". The results presented here might help in mimicking features of physiological systems in insects and guide efforts to fabricate novel microfluidic devices with improved efficiency. In this study, both theoretical analysis and Stokeslets-meshfree computational methods are used to solve for the 2D and 3D viscous flow transport in several micro-geometries (tubes, channels and networks) with prescribed moving wall contractions. The derived theoretical analysis is based on both lubrication theory and quasi-steady approximations at low Reynolds numbers. The meshfree numerical method is based on the method of fundamental solutions (MFS) that uses a set of singularized force elements ``Stokeslets'' to induce the flow motions. Moreover, the passive particle tracking simulation approach in the Lagrangian frame of reference is also used to strengthen and support our pumping paradigm developed in this dissertation.
Ph. D.

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Garcia, Gonzalez Jesus. "Numerical analysis of fluid motion at low Reynolds numbers." Thesis, University of Manchester, 2017. https://www.research.manchester.ac.uk/portal/en/theses/numerical-analysis-of-fluid-motion-at-low-reynolds-numbers(4cf30194-0155-439d-879a-c49787549e8c).html.

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At low Reynolds number flows, the effect of inertia becomes negligible and the fluid motion is dominated by the effect of viscous forces. Understanding of the behaviour of low Reynolds number flows underpins the prediction of the motion of microorganisms and particle sedimentation as well as the development of micro-robots that could potentially swim inside the human body to perform targeted drug/cell delivery and non-invasive microsurgery. The work in this thesis focuses on developing an understanding in the mathematical analysis of objects moving at low Reynolds numbers. A boundary element implementation of the Method of regularized Stokeslets (MRS) is applied to analyse the low Reynolds number flow field around an object of simple shape (sphere and cube). It also showed that the results obtained by a boundary element implementation for an unbounded cube, where singularities are presented in the corners of the cube, agrees with more complex solutions methods such as a GBEM and FEM.A methodology for analysing the effect of walls by locating collocation points on the surface of the walls and the object is presented. First at all, this methodology is validated with a boundary element implementation of the method of images for a sphere at different locations. Then, the method is extended when more than one wall is presented. This methodology is applied to predict the velocity filed of a cube moving in a tow tank at low Reynolds numbers for two different cases with a supporting rod similar to an experimental set-up, and without the supporting rod as in the CFD simulations based on the FVM. The results indicate a good match between CFD and the MRS, and an excellent approximation between the MRS and experimental data from PIV measurements. The drag, thrust and torque generated by helices moving at low Reynolds numbers in an unbounded medium is analysed by the resistive force theory, a slender body theory, and a boundary element method of the MRS. The results show that the resistive force theory predict accurately the drag, thrust and torque of moving helices when the resistive force coefficients are calculated from a slender body theory approximation by calculating independently the resistive force coefficients for translation and rotation, because it is observed that the resistive force coefficients depend also of the nature of motion. Moreover, the thrust generated by helices of different pitch angles is analysed calculated by a CFD numerical simulation based on the FVM and a boundary element implementation, an compared with experimental data. The results also show an excellent prediction between the boundary element implementation, the CFD results and the experimental data. Finally, a boundary element implementation of the MRS is applied to predict swimming of a biomimetic swimmer that mimics the motion of E.coli bacteria in an unbounded medium. The results are compared with the propulsive velocity and induced angular velocity measurement by recording the motion of the biomimetic swimmer in a square tank. It is observed that special care needs to be taken when the biomimetic swimmer is modelled inside the tank, as there is an apparent increment in the calculate thrust propulsion which does not represent a real situation of the biometic swimmer which propels by a power supply. However, this increment does not represent the condition of the biomimetic swimmer and a suggested methodology based on the solution from an unbounded case and when the swimmer is moving inside the tank is presented. In addition, the prediction of the free-swimming velocity for the biomimetic swimmer agrees with the results obtained by the MRS when the resistive force coefficients are calculated from a SBT implementation. The results obtained in this work have showed that a boundary element implementation of the MRS produces results comparable with more complex numerical implementations such as GBEM, FEM, FVM, and also an excellent agreement with results obtained from experimentation. Therefore, it is a suitable and easy to apply methodology to analyse the motion of swimmers at low Reynolds numbers, such as the biomimetic swimmer modelled in this work.

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Λινάρδος, Χάρης. "Προσδιορισμός του πεδίου ροής πέριξ διατάξεων σωματιδίων με τη μέθοδο των προτύπων ροών : εισαγωγή στη μέθοδο των πρότυπων ροών." Thesis, 2013. http://hdl.handle.net/10889/7530.

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Η περιγραφή των αλληλεπιδράσεων που αναπτύσσονται μεταξύ ενός συνόλου σωμάτων που είτε είναι ακίνητα είτε κινούνται και ενός ρευστού, ρέοντος ή ηρεμούντος, βρίσκεται στον πυρήνα ενός μεγάλου αριθμού επιστημονικών προσπαθειών. Η μοντελοποίηση των αλληλεπιδράσεων αυτών μπορεί να γίνει με πολλούς τρόπους, καθένας από τους οποίους εμφανίζει πλεονεκτήματα και μειονεκτήματα, ανάλογα με το είδος του συστήματος στο οποίο επιχειρείται να εφαρμοστεί. Σκοπός της εργασίας αυτής είναι η ανάδειξη ενός εξ αυτών που είναι η Μέθοδος των Προτύπων Ροών.
The description of interactions between a number of solid particles, which may be in motion or fixed in space and a fluid which in turn may either be flowing or resting, is placed at the core of a large number of scientific publications. Modelling such interactions may follow a variety of approaches. Each approach has its own pros and cons, regarding the nature and the specific features of the system which is aimed to describe. Current thesis goal is to describe one of these approaches, which is the approach of Singularities or the Method of Elementary Flows.

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"Computational modeling of peristaltic pumping using the method of regularized Stokeslets." Tulane University, 2008.

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In this thesis, we provide a starting point for the development of computational models of both uterine and oviductal fluid mechanics. The method of regularized Stokeslets provides a framework that is easily implemented and may be adapted to include the full fluid-structure interactions that are observed physiologically We compare our computational results to analytic results in settings where the geometry of the channel (in 213) or tube (in 3D) undergoes small amplitude, symmetric contractions. These comparisons allow us to validate our numerics, and give us insight into the choice of our numerical parameters We demonstrate that our results for tapered channels and non-symmetric channels in two dimensions match the lubrication theory of Elad et al. [6]. We extend these simulations to three dimensions. In addition, we include an inserted catheter in our two-dimensional model, as in the finite element calculations presented by [25]. Finally, we present preliminary results of a full, three-dimensional model of a peristaltic tube with an inserted catheter
acase@tulane.edu

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"The Interaction between Toroidal Swimmers in Stokes Flow." Tulane University, 2014.

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he focus of this research has been devoted to study the interaction between two or more self-propelled toroidal swimmers in Stokes flow by applying the method of regularized Stokeslets and also study the effect of a nearby wall to the movement of a helical ring by using the method of regurlarized Stokeslets with images. In the study of the interaction between two or more toroidal swimmers, we interpret these as three-dimensional, zero Reynolds number analogues of finite vortex dipoles in an ideal fluid. Then, we examine the stability of relative equilibria that can form for these swimmers when they are initially placed in tandem or abreast. In addition, we examine the dynamics of the torus when a spherical cell body is placed at its center. This gives us an insight into the mechanical role of the transverse flagellum of dinoflagellates. Moreover, we show that the torus with a sphere moves more efficiently than one without. Lastly, we model the transverse flagellum of a dinoflagellate as a helical ring and study the effect of a nearby wall on its movement. The numerical results show that the wall baffles the movement of the helical ring, which is consistent with the phenomenon of sperm accumulation near surfaces.
acase@tulane.edu

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Books on the topic "Stokeslet"

1

Henry VIII's conservative scholar: Bishop John Stokesley and the divorce, royal supremacy and doctrinal reform. Bern: P. Lang, 1997.

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Mary, Yonge Charlotte. The Stokesley Secret. 1st World Library - Literary Society, 2005.

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Mary, Yonge Charlotte. The Stokesley Secret. Hard Press, 2006.

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Mary, Yonge Charlotte. The Stokesley Secret. Kessinger Publishing, 2004.

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Mary, Yonge Charlotte. The Stokesley Secret. BiblioBazaar, 2007.

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Mary, Yonge Charlotte. The Stokesley Secret. ReadHowYouWant.com, 2006.

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Mary, Yonge Charlotte. The Stokesley Secret. IndyPublish.com, 2002.

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Mary, Yonge Charlotte. The Stokesley Secret. 1st World Library, 2004.

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Mary, Yonge Charlotte. The Stokesley Secret. Pinnacle Press, 2017.

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Mary, Yonge Charlotte. The Stokesley Secret. 1st World Library - Literary Society, 2006.

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Book chapters on the topic "Stokeslet"

1

Blake, J. R., and S. R. Otto. "Ciliary propulsion, chaotic filtration and a ‘blinking’ stokeslet." In The Centenary of a Paper on Slow Viscous Flow by the Physicist H.A. Lorentz, 151–68. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-009-0225-1_9.

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Lighthill, James. "Helical distributions of stokeslets." In The Centenary of a Paper on Slow Viscous Flow by the Physicist H.A. Lorentz, 35–78. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-009-0225-1_4.

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Liron, Nadav. "Stokes flow due to infinite arrays of stokeslets in three dimensions." In The Centenary of a Paper on Slow Viscous Flow by the Physicist H.A. Lorentz, 267–97. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-009-0225-1_16.

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Davis, A. M. J. "The use of stokeslets to describe the arbitrary translation of a disk near a plane wall." In The Centenary of a Paper on Slow Viscous Flow by the Physicist H.A. Lorentz, 239–52. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-009-0225-1_14.

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Lu, Dong-Qiang, and Allen Chwang. "Free-surface waves due to a Stokeslet in a viscous fluid of infinite depth." In Hydrodynamics VI: Theory and Applications, 611–17. Taylor & Francis, 2004. http://dx.doi.org/10.1201/b16815-90.

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Wright, Thomas. "59 I. Wright to CM [Stokesley?] 17 December 1668." In Markets and Merchants of the Late Seventeenth Century: The Marescoe-David Letters, 1668–1680, edited by Henry Roseveare, 260. British Academy, 1987. http://dx.doi.org/10.1093/oseo/instance.00102790.

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Wright, Thomas. "127 T. Wright to CM [Stokesley] 13 December 1669." In Markets and Merchants of the Late Seventeenth Century: The Marescoe-David Letters, 1668–1680, edited by Henry Roseveare. British Academy, 1987. http://dx.doi.org/10.1093/oseo/instance.00102859.

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Wright, Thomas. "13 Thomas Wright to CM Stokesley1 2 May 1668." In Markets and Merchants of the Late Seventeenth Century: The Marescoe-David Letters, 1668–1680, edited by Henry Roseveare. British Academy, 1987. http://dx.doi.org/10.1093/oseo/instance.00102744.

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Conference papers on the topic "Stokeslet"

1

Ahsan, Syed N., and Matteo Aureli. "Three-Dimensional Analysis of Shape-Morphing Cantilever Oscillations in Viscous Fluids." In ASME 2017 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/dscc2017-5402.

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In this paper, we study the linear flexural oscillations of a cantilever beam undergoing chord-wise shape-morphing deformation in a quiescent, Newtonian, viscous fluid. The shape-morphing deformation is prescribed for the beam cross section to an arc of a circle by specifying a periodic maximum curvature continuously along the axis of the structure. This particular strategy is investigated as a possible way to manipulate fluid-structure interaction mechanisms by modifying the hydrodynamic interactions in the vicinity of the submerged structure. Since we focus on the linear vibration of the beam, the fluid flow is described using three-dimensional unsteady Stokes hydrodynamics. By solving the linear unsteady Stokes problem in the frequency domain with a Stokeslet method, we identify the effect of the proposed shape-morphing strategy on the propulsion performance by estimating thrust, lift, and hydrodynamic power dissipation for a range of prescribed deformations. We verify the results obtained from our boundary element method against results from the existing literature. Our findings show a possible improvement in propulsion characteristics and minimization of hydrodynamic power dissipation, for an optimum level of shape-morphing deformation which is aspect ratio-dependent. Results from this study can aid in designing and operating cantilever-based underwater actuation systems for which the multi-objective goal of power losses reduction and propulsion performance improvement is sought.

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Martins, Nuno F. M., and Magda Rebelo. "A stokeslets approach for the numerical solution of Brinkman systems." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825601.

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