Mathematical Modelling and Physical Applications of Magnetic Systems

Wang, S.; Jiang, J., and Cao, W., 2019. Sealing performance evaluation method of nano-scale magnetic thin film materials in marine tanks. In: Guido-Aldana, P.A. and Mulahasan, S. (eds.), Advances in Water Resources and Exploration. Journal of Coastal Research, Special Issue No. 93, pp. 941–946. Coconut Creek (Florida), ISSN 0749-0208.In order to evaluate the sealing performance of nano-scale magnetic thin film materials in marine tanks, a method for evaluating the sealing performance of nano-scale magnetic thin film materials in marine tanks based on spatial visual image feature extraction is proposed. The differential frame point scanning and spatial vision high resolution imaging analysis method are used to collect the image information of ship tank nano-scale magnetic thin film material. The sealing gap of ship tank nano-scale magnetic film material, the weakening of material mechanics, the sealing frame point and other parts of the three-dimensional frame structure reconstitute image modeling. The edge structure feature decomposition and texture segmentation of ship tank nanoscale magnetic film material images are carried out. The stress fitting model of structural seal gap of ship tank nano-scale magnetic film material is constructed. The feature point extraction and mechanical state dynamic estimation of ship tank nano-scale magnetic film material seal gap are carried out by using three-dimensional frame structure reconstruction image feature extraction method, and the accurate prediction and evaluation of seal gap state of ship tank nano-scale magnetic film material seal are realized. The simulation results show that the sealing performance of nano-scale magnetic thin film material in ship tank is tested by this method, and the positioning accuracy of sealing gap point of nano-scale magnetic thin film material in ship tank is higher, the reliability index of closed performance evaluation is better, and the failure probability is the smallest.

The global Riemann problem for a nonstrictly hyperbolic system of conservation laws modeling polymer flooding is solved. In particular, the system contains a term that models adsorption effects.

Mathematical Applications and Modelling in Singapore Schools Communities of Mathematical Inquiry to Support Engagement in Rich Tasks Using ICT in Applications of Primary School Mathematics Applications of Mathematical Application Problems in Primary School Mathematics Collaborative Problem Solving as Modelling in the Primary Years of Schooling Word Problems and Modelling in Primary School Mathematics Mathematical Modelling in a PBL Setting for Pupils: Features and Task Design Initial Experiences of Primary School Teachers with Mathematical Modelling Why Study Mathematics? Applications of Mathematics in Our Daily Life Using ICT in Applications of Secondary School Mathematics Developing Pupils' Analysis and Interpretation of Graphs and Tables Using a Five Step Framework Theoretical Approaches and Examples for Modelling in Mathematics Education Mathematical Modelling in the Singapore Secondary School Mathematics Curriculum Making Decisions with Mathematics: From Mathematical Problem Solving to Modelling The Cable Drum - Description of a Challenging Mathematical Modelling Example and a Few Experiences Implementing Applications and Modelling in Secondary School: Issues for Teaching and Learning What's Next.

These proceedings collect the academic and scientific contributions presented at the X International Conference Days of Mathematical Modeling in Sciences (X ICDMMS), which continues the legacy of the “Days of Applied Mathematics” (ICDAM) previously held at Universidad Simón Bolívar, San José de Cúcuta, Colombia. The X ICDMMS took place in Talca, Chile, on October 2–25, 2024. The primary objective of this conference is to promote the exchange of concrete experiences in applying mathematical knowledge to address complex problems across diverse scientific contexts. In line with this mission, the event has brought together a vibrant academic and scientific community, including postgraduate students, professors, and researchers from across Latin America, who have not only presented their research but have also had the opportunity to publish their work (since the fourth edition) in the Journal of Physics: Conference Series, the journal associated with the conference. This event is an initiative led by three academic research groups with a presence in Chile and Colombia: the Mathematical Modeling Group of Maule (GM3), the Scientific Modeling and Business Innovation Group of Universidad Simón Bolívar (GIMCINE), and the Mathematical Modeling Group of Biological Systems at Universidad Tecnológica Metropolitana (MATBIO-UTEM). Its purpose is to serve as a platform for disseminating knowledge in the basic and applied sciences through the lens of mathematical modeling. A key focus of the conference is to continue encouraging a space for the scientific contributions of graduate students and to promote interactions that strengthen their integration into the research community. The topics developed in the X ICDMMS were the following: (i) Computer Science in Mathematics and Engineering (ii) Modeling in Basic Sciences (iii) Modeling in Social Sciences (iv) Mathematical Biology (v) Modeling, Simulation, and Diagnostics (vi) Education and Communication in Science and Engineering The ICDMMS forms an integral part of the training and research processes within the academic programs in Applied Mathematical Modeling, Mathematics Education, and Experimental Sciences Education at the Faculty of Basic Sciences of the Universidad Católica del Maule. It aligns with the institution's commitment to high-quality education and responds to the demands of the digital era by emphasizing the modeling of scientific knowledge across diverse fields, including mathematics, physics, biology, and chemistry, as well as applications in medicine, engineering, management, business, and education. The ICDMMS offers emerging researchers opportunities for participation and growth through meaningful interactions and dialogue with established researchers from various scientific disciplines represented at the conference. It also allows students, faculty, and researchers a valuable space for professional development and knowledge acquisition through thematic sessions. List of Organizing Committee, National Scientific Committee, International Scientific Committee, Organizing groups and partners and Sponsors are available in this PDF.

We formulate and study a one–dimensional single–species diffusive–delay population model. The time delay is the time taken from birth to maturity. Without diffusion, the delay differential model extends the well–known logistic differential equation by allowing delayed constant birth processes and instantaneous quadratically regulated death processes. This delayed model is known to have simple global dynamics similar to that of the logistic equation. Through the use of a sub/supersolution pair method, we show that the diffusive delay model continues to generate simple global dynamics. This has the important biological implication that quadratically regulated death processes dramatically simplify the growth dynamics. We also consider the possibility of travelling wavefront solutions of the scalar equation for the mature population, connecting the zero solution of that equation with the positive steady state. Our main finding here is that our fronts appear to be all monotone, regardless of the size of the delay. This is in sharp contrast to the frequently reported findings that delay causes a loss of monotonicity, with the front developing a prominent hump in some other delay models.

Previous article Next article Estimation of Linear Functionals on Sobolev Spaces with Application to Fourier Transforms and Spline InterpolationJ. H. Bramble and S. R. HilbertJ. H. Bramble and S. R. Hilberthttps://doi.org/10.1137/0707006PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] G. Birkhoff, , M. H. Schultz and , R. S. Varga, Piecewise Hermite interpolation in one and two variables with applications to partial differential equations, Numer. Math., 11 (1968), 232–256 10.1007/BF02161845 MR0226817 0159.20904 CrossrefISIGoogle Scholar[2] J. H. Bramble, , B. E. Hubbard and , Vidar Thomée, Convergence estimates for essentially positive type discrete Dirichlet problems, Math. Comp., 23 (1969), 695–709 MR0266444 0217.21902 CrossrefISIGoogle Scholar[3] Michael Golomb, Approximation by periodic spline interpolants on uniform meshes, J. Approximation Theory, 1 (1968), 26–65 10.1016/0021-9045(68)90055-5 MR0233121 0185.30901 CrossrefGoogle Scholar[4] Charles B. Morrey, Jr., Multiple integrals in the calculus of variations, Die Grundlehren der mathematischen Wissenschaften, Band 130, Springer-Verlag New York, Inc., New York, 1966ix+506 MR0202511 0142.38701 CrossrefGoogle Scholar[5] Arthur Sard, Linear approximation, American Mathematical Society, Providence, R.I., 1963xi+544, Math. Surveys, No. 9 MR0158203 0115.05403 CrossrefGoogle Scholar[6] I. J. Schoenberg, On cardinal spline interpolation and a summability method for the cardinal series, Symposium on Approximation, Lecture Notes, University of Cincinnati, Cincinnati, Ohio, 1969 Google Scholar[7] J. M. Whittaker, Interpolatory Function Theory, Cambridge University Press, Cambridge, 1935 0012.15503 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails An Interpolated Galerkin Finite Element Method for the Poisson EquationJournal of Scientific Computing, Vol. 92, No. 2 | 30 June 2022 Cross Ref Virtual element approximation of two-dimensional parabolic variational inequalitiesComputers & Mathematics with Applications, Vol. 116 | 1 Jun 2022 Cross Ref Direct serendipity and mixed finite elements on convex quadrilateralsNumerische Mathematik, Vol. 150, No. 4 | 26 March 2022 Cross Ref Nonlinear systems of parabolic IBVP: A stable super-supraconvergent fully discrete piecewise linear FEMApplied Mathematics and Computation, Vol. 419 | 1 Apr 2022 Cross Ref Convergence of Renormalized Finite Element Methods for Heat Flow of Harmonic MapsXinping Gui, Buyang Li, and Jilu WangSIAM Journal on Numerical Analysis, Vol. 60, No. 1 | 8 February 2022AbstractPDF (572 KB)Drug delivery enhanced by ultrasound: Mathematical modeling and simulationComputers & Mathematics with Applications, Vol. 107 | 1 Feb 2022 Cross Ref A C1 virtual element method for an elliptic distributed optimal control problem with pointwise state constraintsMathematical Models and Methods in Applied Sciences, Vol. 31, No. 14 | 10 January 2022 Cross Ref A Probabilistic Approach for Solutions of Deterministic PDE’s as Well as Their Finite Element ApproximationsAxioms, Vol. 10, No. 4 | 20 December 2021 Cross Ref NUMERICAL VALIDATION OF PROBABILISTIC LAWS TO EVALUATE FINITE ELEMENT ERROR ESTIMATESMathematical Modelling and Analysis, Vol. 26, No. 4 | 26 Nov 2021 Cross Ref A Weak Galerkin Harmonic Finite Element Method for Laplace EquationCommunications on Applied Mathematics and Computation, Vol. 3, No. 3 | 3 January 2021 Cross Ref The virtual element method for resistive magnetohydrodynamicsComputer Methods in Applied Mechanics and Engineering, Vol. 381 | 1 Aug 2021 Cross Ref A convexity enforcing $${C}^{{0}}$$ interior penalty method for the Monge–Ampère equation on convex polygonal domainsNumerische Mathematik, Vol. 148, No. 3 | 26 June 2021 Cross Ref A unified study on superconvergence analysis of Galerkin FEM for singularly perturbed systems of multiscale natureJournal of Applied Mathematics and Computing, Vol. 66, No. 1-2 | 10 September 2020 Cross Ref Predicting residual properties of ball screw raceway in whirling milling based on machine learningMeasurement, Vol. 173 | 1 Mar 2021 Cross Ref Some estimates of virtual element methods for fourth order problemsElectronic Research Archive, Vol. 29, No. 6 | 1 Jan 2021 Cross Ref Mesh quality metrics for isogeometric Bernstein–Bézier discretizationsComputer Methods in Applied Mechanics and Engineering, Vol. 371 | 1 Nov 2020 Cross Ref A New Mixed Functional-probabilistic Approach for Finite Element AccuracyComputational Methods in Applied Mathematics, Vol. 20, No. 4 | 15 April 2020 Cross Ref A General Superapproximation ResultComputational Methods in Applied Mathematics, Vol. 20, No. 4 | 1 September 2020 Cross Ref A cubic C0 interior penalty method for elliptic distributed optimal control problems with pointwise state and control constraintsResults in Applied Mathematics, Vol. 7 | 1 Aug 2020 Cross Ref Conforming and nonconforming harmonic finite elementsApplicable Analysis, Vol. 99, No. 4 | 1 August 2018 Cross Ref Model of approximation of a velocity, vorticity and pressure in an incompressible fluidJournal of Physics: Conference Series, Vol. 1514, No. 1 | 1 Mar 2020 Cross Ref Distribution model of toxic agents and runoff phenomenon in flat aquatic regionsJournal of Physics: Conference Series, Vol. 1514, No. 1 | 1 Mar 2020 Cross Ref Precision fertilization method of field crops based on the Wavelet-BP neural network in ChinaJournal of Cleaner Production, Vol. 246 | 1 Feb 2020 Cross Ref Virtual enriching operatorsCalcolo, Vol. 56, No. 4 | 14 October 2019 Cross Ref C0 interior penalty methods for an elliptic state-constrained optimal control problem with Neumann boundary conditionJournal of Computational and Applied Mathematics, Vol. 350 | 1 Apr 2019 Cross Ref Full H(div) -approximation of linear elasticity on quadrilateral meshes based on ABF finite elementsComputer Methods in Applied Mechanics and Engineering, Vol. 347 | 1 Apr 2019 Cross Ref Interpolation Error Bounds for Curvilinear Finite Elements and Their Implications on Adaptive Mesh RefinementJournal of Scientific Computing, Vol. 78, No. 2 | 10 August 2018 Cross Ref An overlapping Schwarz method for virtual element discretizations in two dimensionsComputers & Mathematics with Applications, Vol. 77, No. 4 | 1 Feb 2019 Cross Ref An isogeometric collocation method for efficient random field discretizationInternational Journal for Numerical Methods in Engineering, Vol. 117, No. 3 | 23 October 2018 Cross Ref An IMEX finite element method for a linearized Cahn–Hilliard–Cook equation driven by the space derivative of a space–time white noiseComputational and Applied Mathematics, Vol. 37, No. 5 | 24 May 2018 Cross Ref Approximating coupled hyperbolic–parabolic systems arising in enhanced drug deliveryComputers & Mathematics with Applications, Vol. 76, No. 1 | 1 Jul 2018 Cross Ref On the approximation of a virtual coarse space for domain decomposition methods in two dimensionsMathematical Models and Methods in Applied Sciences, Vol. 28, No. 07 | 19 June 2018 Cross Ref Virtual element methods on meshes with small edges or facesMathematical Models and Methods in Applied Sciences, Vol. 28, No. 07 | 19 June 2018 Cross Ref Multigrid methods for saddle point problems: Darcy systemsNumerische Mathematik, Vol. 138, No. 2 | 30 August 2017 Cross Ref A morley finite element method for an elliptic distributed optimal control problem with pointwise state and control constraintsESAIM: Control, Optimisation and Calculus of Variations, Vol. 24, No. 3 | 11 July 2018 Cross Ref Optimal stencils in Sobolev spacesIMA Journal of Numerical Analysis, Vol. 32 | 28 December 2017 Cross Ref Interpolation and Quasi-Interpolation in h - and hp -Version Finite Element SpacesEncyclopedia of Computational Mechanics Second Edition | 15 December 2017 Cross Ref Finite Element MethodsEncyclopedia of Computational Mechanics Second Edition | 15 December 2017 Cross Ref Superconvergence similarities in standard and mixed finite element methodsfinite element methods | 22 Nov 2017 Cross Ref Second order approximations for kinetic and potential energies in Maxwell's wave equationsApplied Numerical Mathematics, Vol. 120 | 1 Oct 2017 Cross Ref Finite element quasi-interpolation and best approximationESAIM: Mathematical Modelling and Numerical Analysis, Vol. 51, No. 4 | 21 July 2017 Cross Ref A New Convergence Analysis of Finite Element Methods for Elliptic Distributed Optimal Control Problems with Pointwise State ConstraintsSusanne C. Brenner and Li-yeng SungSIAM Journal on Control and Optimization, Vol. 55, No. 4 | 26 July 2017AbstractPDF (472 KB)Density estimation for $\tilde{\beta}$-dependent sequencesElectronic Journal of Statistics, Vol. 11, No. 1 | 1 Jan 2017 Cross Ref Superconvergence of both the Crouzeix–Raviart and Morley elementsNumerische Mathematik, Vol. 132, No. 3 | 27 May 2015 Cross Ref Two Families of $H$(div) Mixed Finite Elements on Quadrilaterals of Minimal DimensionTodd Arbogast and Maicon R. CorreaSIAM Journal on Numerical Analysis, Vol. 54, No. 6 | 22 November 2016AbstractPDF (529 KB)A generalized Peano Kernel Theorem for distributions of exponential decayJournal of Mathematical Analysis and Applications, Vol. 433, No. 1 | 1 Jan 2016 Cross Ref Forty Years of the Crouzeix-Raviart elementNumerical Methods for Partial Differential Equations, Vol. 31, No. 2 | 23 July 2014 Cross Ref Integration by interpolation and look-up for Galerkin-based isogeometric analysisComputer Methods in Applied Mechanics and Engineering, Vol. 284 | 1 Feb 2015 Cross Ref Convergence of Finite Difference Schemes for Nonlinear Complex Reaction-Diffusion ProcessesAdérito Araújo, Sílvia Barbeiro, and Pedro SerranhoSIAM Journal on Numerical Analysis, Vol. 53, No. 1 | 13 January 2015AbstractPDF (371 KB)A Partition of Unity Method for the Obstacle Problem of Simply Supported Kirchhoff PlatesMeshfree Methods for Partial Differential Equations VII | 5 November 2014 Cross Ref The Finite Difference Method for Boundary Value Problem with SingularityFinite Difference Methods,Theory and Applications | 17 June 2015 Cross Ref Gradient superconvergence post-processing of the tensor-product quadratic pentahedral finite elementDiscrete & Continuous Dynamical Systems - B, Vol. 20, No. 2 | 1 Jan 2015 Cross Ref Discretization of time-dependent quantum systems: real-time propagation of the evolution operatorApplicable Analysis, Vol. 93, No. 12 | 6 February 2014 Cross Ref Superconvergence patch recovery for the gradient of the tensor-product linear triangular prism elementBoundary Value Problems, Vol. 2014, No. 1 | 2 January 2014 Cross Ref A partition of unity method for the displacement obstacle problem of clamped Kirchhoff platesJournal of Computational and Applied Mathematics, Vol. 265 | 1 Aug 2014 Cross Ref A Partition of Unity Method with Penalty for Fourth Order ProblemsJournal of Scientific Computing, Vol. 60, No. 1 | 25 October 2013 Cross Ref Elliptic Boundary-Value ProblemsAnalysis of Finite Difference Schemes | 1 Jan 2014 Cross Ref High order geometric methods with exact conservation propertiesJournal of Computational Physics, Vol. 257 | 1 Jan 2014 Cross Ref Interpolation error estimates for mean value coordinates over convex polygonsAdvances in Computational Mathematics, Vol. 39, No. 2 | 12 October 2012 Cross Ref A $\Gamma$-Convergence Analysis of the Quasicontinuum MethodMalena I. Espan͂ol, Dennis M. Kochmann, Sergio Conti, and Michael OrtizMultiscale Modeling & Simulation, Vol. 11, No. 3 | 1 August 2013AbstractPDF (1702 KB)A Low-Storage Curvilinear Discontinuous Galerkin Method for Wave ProblemsT. WarburtonSIAM Journal on Scientific Computing, Vol. 35, No. 4 | 6 August 2013AbstractPDF (1034 KB)Analytical and Numerical Study of Memory Formalisms in Diffusion ProcessesModelling and Simulation in Fluid Dynamics in Porous Media | 3 November 2012 Cross Ref PreliminariesFinite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems | 24 September 2012 Cross Ref One-Level FETI/BETI MethodsFinite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems | 24 September 2012 Cross Ref Multiscale ProblemsFinite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems | 24 September 2012 Cross Ref Unbounded DomainsFinite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems | 24 September 2012 Cross Ref Dual-Primal MethodsFinite and Boundary Element Tearing and Interconnecting Solvers for Multiscale Problems | 24 September 2012 Cross Ref Finite element approximations for a linear Cahn-Hilliard-Cook equation driven by the space derivative of a space-time white noiseDiscrete & Continuous Dynamical Systems - B, Vol. 18, No. 7 | 1 Jan 2013 Cross Ref Stochastic Galerkin techniques for random ordinary differential equationsNumerische Mathematik, Vol. 122, No. 3 | 18 April 2012 Cross Ref Error estimates for generalized barycentric interpolationAdvances in Computational Mathematics, Vol. 37, No. 3 | 29 September 2011 Cross Ref New six-node and seven-node hexagonal finite elementsApplied Mathematics and Computation, Vol. 218, No. 24 | 1 Aug 2012 Cross Ref ANALYTIC REGULARITY FOR LINEAR ELLIPTIC SYSTEMS IN POLYGONS AND POLYHEDRAMathematical Models and Methods in Applied Sciences, Vol. 22, No. 08 | 28 May 2012 Cross Ref Polynomial approximation on domains bounded by diffeomorphic images of graphsJournal of Approximation Theory, Vol. 164, No. 7 | 1 Jul 2012 Cross Ref Numerical integration for high order pyramidal finite elementsESAIM: Mathematical Modelling and Numerical Analysis, Vol. 46, No. 2 | 12 October 2011 Cross Ref Average Interpolation under the Maximum Angle ConditionAlexander RandSIAM Journal on Numerical Analysis, Vol. 50, No. 5 | 23 October 2012AbstractPDF (673 KB)A Quadratic $C^0$ Interior Penalty Method for the Displacement Obstacle Problem of Clamped Kirchhoff PlatesSusanne C. Brenner, Li-Yeng Sung, Hongchao Zhang, and Yi ZhangSIAM Journal on Numerical Analysis, Vol. 50, No. 6 | 6 December 2012AbstractPDF (1270 KB)A Quadratic $C^0$ Interior Penalty Method for Linear Fourth Order Boundary Value Problems with Boundary Conditions of the Cahn--Hilliard TypeSusanne C. Brenner, Shiyuan Gu, Thirupathi Gudi, and Li-yeng SungSIAM Journal on Numerical Analysis, Vol. 50, No. 4 | 21 August 2012AbstractPDF (1368 KB)Weak Approximation Properties of Elliptic Projections with Functional ConstraintsRobert Scheichl, Panayot S. Vassilevski, and Ludmil T. ZikatanovMultiscale Modeling & Simulation, Vol. 9, No. 4 | 6 December 2011AbstractPDF (2657 KB)Stability and convergence analysis of a one step approximation of a linear partial integro-differential equationNumerical Methods for Partial Differential Equations, Vol. 27, No. 5 | 29 March 2010 Cross Ref Global error bounds for the Petrov-Galerkin discretization of the neutron transport equationNumerical Linear Algebra with Applications, Vol. 18, No. 1 | 24 March 2010 Cross Ref Numerical Methods for Non-Linear Hyperbolic Equations of Mathematical PhysicsHyperbolicity | 1 Jan 2011 Cross Ref Anisotropic Triangulation Methods in Adaptive Image ApproximationApproximation Algorithms for Complex Systems | 13 December 2010 Cross Ref C 0 Interior Penalty MethodsFrontiers in Numerical Analysis - Durham 2010 | 20 October 2011 Cross Ref High order compact schemes for gradient approximationScience China Mathematics, Vol. 53, No. 7 | 27 April 2010 Cross Ref Error estimate of the P 1 nonconforming finite element method for the penalized unsteady Navier-Stokes equationsNumerische Mathematik, Vol. 115, No. 2 | 2 December 2009 Cross Ref Finite element exterior calculus: from Hodge theory to numerical stabilityBulletin of the American Mathematical Society, Vol. 47, No. 2 | 25 January 2010 Cross Ref Fully-discrete finite element approximations for a fourth-order linear stochastic parabolic equation with additive space-time white noiseESAIM: Mathematical Modelling and Numerical Analysis, Vol. 44, No. 2 | 27 January 2010 Cross Ref Boundary element tearing and interconnecting methods in unbounded domainsApplied Numerical Mathematics, Vol. 59, No. 11 | 1 Nov 2009 Cross Ref Local projection methods on layer-adapted meshes for higher order discretisations of convection–diffusion problemsApplied Numerical Mathematics, Vol. 59, No. 10 | 1 Oct 2009 Cross Ref An unfitted finite element method using discontinuous GalerkinInternational Journal for Numerical Methods in Engineering, Vol. 79, No. 12 | 17 Sep 2009 Cross Ref New expansions of numerical eigenvalues by Wilson’s elementJournal of Computational and Applied Mathematics, Vol. 225, No. 1 | 1 Mar 2009 Cross Ref Galerkin Methods for Parabolic and Schrödinger Equations with Dynamical Boundary Conditions and Applications to Underwater AcousticsD. C. Antonopoulou, V. A. Dougalis, and G. E. ZourarisSIAM Journal on Numerical Analysis, Vol. 47, No. 4 | 6 August 2009AbstractPDF (397 KB)Numerical homogenization of the acoustic wave equations with a continuum of scalesComputer Methods in Applied Mechanics and Engineering, Vol. 198, No. 3-4 | 1 Dec 2008 Cross Ref New expansions of numerical eigenvalues by finite elementsJournal of Computational and Applied Mathematics, Vol. 217, No. 1 | 1 Jul 2008 Cross Ref A Priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Optimal Control Problems Part I: Problems Without Control ConstraintsDominik Meidner and Boris VexlerSIAM Journal on Control and Optimization, Vol. 47, No. 3 | 19 March 2008AbstractPDF (288 KB)Inf-sup stable nonconforming finite elements of higher order on quadrilaterals and hexahedraESAIM: Mathematical Modelling and Numerical Analysis, Vol. 41, No. 5 | 23 October 2007 Cross Ref A computational method for approximating a Darcy–Stokes system governing a vuggy porous mediumComputational Geosciences, Vol. 11, No. 3 | 21 February 2007 Cross Ref A new quadratic nonconforming finite element on rectanglesNumerical Methods for Partial Differential Equations, Vol. 22, No. 4 | 1 January 2006 Cross Ref ISOGEOMETRIC ANALYSIS: APPROXIMATION, STABILITY AND ERROR ESTIMATES FOR h-REFINED MESHESMathematical Models and Methods in Applied Sciences, Vol. 16, No. 07 | 21 November 2011 Cross Ref C 0 Interior Penalty Methods for Fourth Order Elliptic Boundary Value Problems on Polygonal DomainsJournal of Scientific Computing, Vol. 22-23, No. 1-3 | 1 Jun 2005 Cross Ref Nonstationary tight wavelet frames, II: unbounded intervalsApplied and Computational Harmonic Analysis, Vol. 18, No. 1 | 1 Jan 2005 Cross Ref Partition of unity method on nonmatching grids for the Stokes problemJournal of Numerical Mathematics, Vol. 13, No. 3 | 1 Jan 2005 Cross Ref Interpolation in h -Version Finite Element SpacesEncyclopedia of Computational Mechanics | 15 November 2004 Cross Ref Finite Element MethodsEncyclopedia of Computational Mechanics | 15 November 2004 Cross Ref Mixed projection-mesh scheme of the finite-element method for the solution of the boundary-value problems of the theory of small elastic-plastic strainsStrength of Materials, Vol. 36, No. 6 | 1 Nov 2004 Cross Ref The Bramble--Hilbert Lemma for Convex DomainsS. Dekel and D. LeviatanSIAM Journal on Mathematical Analysis, Vol. 35, No. 5 | 1 August 2006AbstractPDF (158 KB)Stability and Convergence of Collocation Schemes for Retarded Potential Integral EquationsPenny J. Davies and Dugald B. DuncanSIAM Journal on Numerical Analysis, Vol. 42, No. 3 | 25 July 2006AbstractPDF (249 KB)Postfiltering versus prefiltering for signal recovery from noisy samplesIEEE Transactions on Information Theory, Vol. 49, No. 12 | 1 Dec 2003 Cross Ref Poincaré--Friedrichs Inequalities for Piecewise H1 FunctionsSusanne C. BrennerSIAM Journal on Numerical Analysis, Vol. 41, No. 1 | 26 July 2006AbstractPDF (206 KB)The Semidiscrete Filtered Backprojection Algorithm Is Optimal for Tomographic InversionAndreas Rieder and Adel FaridaniSIAM Journal on Numerical Analysis, Vol. 41, No. 3 | 26 July 2006AbstractPDF (282 KB)Using finite element tools in proving shift theorems for elliptic boundary value problemsNumerical Linear Algebra with Applications, Vol. 10, No. 1-2 | 1 January 2002 Cross Ref Numerical Stability of Collocation Schemes for Time Domain Boundary Integral EquationsComputational Electromagnetics | 1 Jan 2003 Cross Ref Convergence of a Collocation Scheme for a Retarded Potential Integral EquationMathematical and Numerical Aspects of Wave Propagation WAVES 2003 | 1 Jan 2003 Cross Ref ReferencesNumerical Analysis of Wavelet Methods | 1 Jan 2003 Cross Ref Regularity estimates for elliptic boundary value problems with smooth data on polygonal domainsJournal of Numerical Mathematics, Vol. 11, No. 2 | 1 Jan 2003 Cross Ref Analysis of the hybrid finite element/finite volume methods for linear hyperbolic and convection-dominated convection–diffusion problemsJournal of Computational and Applied Mathematics, Vol. 139, No. 2 | 1 Feb 2002 Cross Ref Signal Sampling and Recovery Under Dependent NoiseSampling Theory in Signal and Image Vol. No. 1 | 1 January 2002 Cross Ref OF FOR Theory and Physics, Vol. No. 1 | 30 Apr Cross Ref finite to finite elementsJournal of Computational and Applied Mathematics, Vol. No. 1-2 | 1 Mar Cross Ref finite to finite elements A of numerical analysis of partial differential Differential Equations | 1 Jan Cross Ref finite to finite elements A of numerical analysis of partial differential in the | 1 Jan Cross Ref Theory and Numerical Methods | 1 Jan Cross Ref and a for Dirichlet Mathematical Modelling and Numerical Analysis, Vol. No. 6 | 15 April 2002 Cross Ref Superconvergence on Methods in Applied Mechanics and Engineering, Vol. No. 1 | 1 Aug Cross Ref A Method for Nonlinear Problems and Application to Problems with Finite Element Journal on Numerical Analysis, Vol. 37, No. 6 | 25 July 2006AbstractPDF KB)The analysis of of in of Scientific | 1 Jan Cross Ref Wavelet methods in numerical of in of Scientific | 1 Jan Cross Ref of | 1 Jan Cross Ref A finite element interpolation estimate Functional Analysis and Optimization, Vol. 20, No. 3-4 | 1 Jan Cross Ref Convergence of nonconforming methods elliptic of Computation, Vol. No. | 1 January Cross Ref On Deterministic Methods for J. and Journal on Numerical Analysis, Vol. 35, No. 4 | 25 July 2006AbstractPDF control and to model the from Mathematical Modelling and Numerical Analysis, Vol. No. 1 | 4 May 2009 Cross Ref Convergence of the scheme to generalized of a coupled field theory problemJournal of Difference Equations and Applications, Vol. No. 2 | 1 Jan Cross Ref A of and Bounds for Interpolation Journal on Mathematical Analysis, Vol. 28, No. 1 | 1 August 2006AbstractPDF KB)A C0 method for elliptic equations on Journal of the Mathematical B. Applied Mathematics, Vol. No. 3 | 17 February 2009 Cross Ref Approximation methods for problems of of Nonlinear | Dec Cross Ref On for elliptic boundary value problemsJournal of Computational and Applied Mathematics, Vol. No. 1 | 1 Jul Cross Ref The Numerical Analysis of Methods Applied to J. and Journal on Numerical Analysis, Vol. No. 1 | 12 July 2006AbstractPDF KB)The Approximation Problem for Vol. 37, No. 4 | 17 February 2012AbstractPDF of the in interpolation problems of quadrilateral finite elementsJournal of Computational and Applied Mathematics, Vol. No. 1-3 | 1 Nov Cross Ref A Finite Element Method for Arbogast and Journal on Numerical Analysis, Vol. No. 2 | 14 July 2006AbstractPDF linear point of the theory of Functional Analysis and Optimization, Vol. 16, No. 3-4 | 1 Jan Cross Ref Pointwise superconvergence of the gradient for the linear elementNumerical Methods for Partial Differential Equations, Vol. 10, No. 5 | 1 Sep Cross Ref A mixed finite-element method for the numerical solution of the problemJournal of Computational and Applied Mathematics, Vol. 50, No. 1-3 | 1 May Cross Ref and Superconvergence for Solutions to the in and Numerical Analysis | 1 Jan Cross Ref schemes on quadrilateral Vol. 51, No. 3-4 | 1 Sep Cross Ref Convergence analysis of mixed finite Vol. 51, No. 2 | 1 Jun Cross Ref An of the mixed finite-element method for a elliptic of Computational and Applied Mathematics, Vol. 47, No. 1 | 1 Jun Cross Ref A Mixed Multigrid Method for the Displacement Problem in Linear C. BrennerSIAM Journal on Numerical Analysis, Vol. No. 1 | 17 July 2006AbstractPDF finite elements with numerical integration for and problems, Part Approximation of and Methods in Applied Mechanics and Engineering, Vol. No. 3 | 1 Feb Cross Ref Error estimates for approximations from control Vol. 10, No. 1 | 1 Feb Cross Ref finite elements with numerical integration for and problems, and interpolation properties of finite elementsComputer Methods in Applied Mechanics and Engineering, Vol. No. 2 | 1 Jan Cross Ref Linear finite element methods for linear of Computation, Vol. 59, No. | 1 January Cross Ref and method for boundary value problemsNumerical Methods for Partial Differential Equations, Vol. No. 5 | 1 Sep Cross Ref of approximation by cardinal and Approximation, Vol. No. 3 | 1 Sep Cross Ref Anisotropic interpolation with applications to the finite element Vol. 47, No. 3-4 | 1 Sep Cross Ref Spline approximation methods for periodic Equations and Theory, Vol. No. 4 | 1 Jul Cross Ref A Multigrid Algorithm for the Mixed Finite Element C. BrennerSIAM Journal on Numerical Analysis, Vol. 29, No. 3 | 14 July 2006AbstractPDF of in of in and Engineering, Vol. No. 2 | 1 Jun Cross Ref A discontinuous Galerkin method for the two-dimensional unsteady Vol. No. 1 | 1 Jan Cross Ref On Simulation Methods for Systems with J. and H. D. Journal on Numerical Analysis, Vol. 28, No. 6 | July 2006AbstractPDF KB)The Convergence Theory of Methods for D. and J. Journal on Numerical Analysis, Vol. 28, No. 5 | July 2006AbstractPDF KB)The Convergence Analysis of Methods for D. Jr., and Journal on Numerical Analysis, Vol. 28, No. 4 | 14 July 2006AbstractPDF KB)A spline collocation method for elliptic of order Equations and Theory, Vol. No. 3 | 1 May Cross Ref Superconvergence of of piecewise quadratic finite element Part Methods for Partial Differential Equations, Vol. No. 1 | 1 Jan Cross Ref error estimates for elliptic Element Methods | 1 Jan Cross Ref Local in finite element Element Methods | 1 Jan Cross Ref Element

Next article Singular Perturbation Theory and GeophysicsG. F. CarrierG. F. Carrierhttps://doi.org/10.1137/1012041PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] W. Eckhaus and , E. M. de Jager, Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type, Arch. Rational Mech. Anal., 23 (1966), 26–86 10.1007/BF00281135 MR0206464 0151.15101 CrossrefISIGoogle Scholar[2] A. B. Vasil'eva, Asymptotic behaviour of solutions of certain problems for ordinary non-linear differential equations with a small parameter multiplying the highest derivatives, Uspehi Mat. Nauk, 18 (1963), 15–86, Russian Math. Surveys, 18 (1963), no. 3 MR0158137 0135.14001 Google Scholar[3] G. F. Carrier and , C. E. Pearson, Ordinary Differential Equations, Blaisdell, New York, 1968 0165.40601 Google Scholar[4] A. R. Robinson, The Wind Driven Ocean Circulation, Blaisdell, New York, 1963 Google Scholar[5] S. F. Feshchenko, , N. I. Shkil and , L. D. Nīkolenko, Asymptotic methods in the theory of linear differential equations, Translated from the Russian by Scripta Technica, Inc. Translation editor, Herbert Eagle. Modern Analytic and Computational Methods in Science and Mathematics, No. 10, American Elsevier Publishing Co., Inc., New York, 1967xvi+270 MR0221029 0153.40501 Google Scholar[6] S. Kaplun, Fluid mechanics and singular perturbations: A collection of papers by Saul Kaplun, Edited by Paco A. Lagerstrom, Louis N. Howard and Ching-shi Lin, Academic Press, New York, 1967xii+369 MR0214326 Google Scholar[7] Wolfgang Wasow, Asymptotic expansions for ordinary differential equations, Pure and Applied Mathematics, Vol. XIV, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1965ix+362 MR0203188 0133.35301 Google Scholar[8] R. E. O'Malley, Jr., Topics in singular perturbations, Advances in Mathematics, Vol. 2, Academic Press, New York, 1968, 365–470 Google Scholar[9A] L. E. Fraenkel, On the method of matched asymptotic expansions. I. A matching principle, Proc. Cambridge Philos. Soc., 65 (1969), 209–231 MR0237898 0187.24104 CrossrefISIGoogle Scholar[9B] L. E. Fraenkel, On the method of matched asymptotic expansions. II. Some applications of the composite series, Proc. Cambridge Philos. Soc., 65 (1969), 233–261 MR0237899 0187.24104 CrossrefISIGoogle Scholar[9C] L. E. Fraenkel, On the method of matched asymptotic expansions. III. Two boundary-value problems, Proc. Cambridge Philos. Soc., 65 (1969), 263–284 MR0237900 0187.24104 CrossrefISIGoogle Scholar[10] W. E. Exkhaus, On the foundations of the method of matched asymptotic approximationsMathematisch Instituut der Technische Hogeschool, Delft, Nederland, 1968 Google Scholar[11] Julian D. Cole, Perturbation methods in applied mathematics, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1968vi+260 MR0246537 0162.12602 Google Scholar[12] Milton Van Dyke, Perturbation methods in fluid mechanics, Applied Mathematics and Mechanics, Vol. 8, Academic Press, New York, 1964x+229 MR0176702 0136.45001 Google Scholar[13] H. P. Greenspan, The Theory of Rotating Fluids, Cambridge University Press, Cambridge, 1968 0182.28103 Google Scholar Next article FiguresRelatedReferencesCited byDetails A Numerical Approach for Singularly Perturbed Nonlinear Delay Differential Equations Using a Trigonometric SplineComputational and Mathematical Methods, Vol. 2022 Cross Ref A System of Singularly Perturbed Periodic Boundary Value Problem: Hybrid Difference Scheme28 May 2020 | International Journal of Applied and Computational Mathematics, Vol. 6, No. 3 Cross Ref A Numerical Technique for Solving Nonlinear Singularly Perturbed Delay Differential Equations12 February 2018 | Mathematical Modelling and Analysis, Vol. 23, No. 1 Cross Ref Analysis of Carrier's ProblemS. J. Chapman and P. E. Farrell13 June 2017 | SIAM Journal on Applied Mathematics, Vol. 77, No. 3AbstractPDF (4863 KB)Applications11 November 2014 Cross Ref Geometrical effects on western intensification of wind-driven ocean currents: The rotated-channel Stommel model, coastal orientation, and curvatureDynamics of Atmospheres and Oceans, Vol. 65 Cross Ref Two-Timing, Geometric, and Multi-scale Methods6 October 2014 Cross Ref Uniform asymptotic expansions of solutions of an inhomogeneous equationJournal of Differential Equations, Vol. 253, No. 3 Cross Ref Uniformly convergent second-order difference scheme for a singularly perturbed periodical boundary value problemInternational Journal of Computer Mathematics, Vol. 88, No. 1 Cross Ref Shallow-Water Equations and Related Topics Cross Ref On the Number of Solutions to Carrier's ProblemStudies in Applied Mathematics, Vol. 120, No. 3 Cross Ref Multi-bump solutions to Carrier's problemJournal of Mathematical Analysis and Applications, Vol. 277, No. 2 Cross Ref Spline Techniques for Solving Singularly-Perturbed Nonlinear Problems on Nonuniform GridsJournal of Optimization Theory and Applications, Vol. 114, No. 3 Cross Ref Numerical Solution of Singularly Perturbed Non-Linear Two Point Boundary Value Problems by Spline in Compression15 September 2010 | International Journal of Computer Mathematics, Vol. 79, No. 2 Cross Ref A Singular Perturbation Problem of Carrier and PearsonJournal of Mathematical Analysis and Applications, Vol. 255, No. 2 Cross Ref Parallel initial-value algorithms for singularly perturbed boundary-value problemsJournal of Optimization Theory and Applications, Vol. 73, No. 3 Cross Ref Numerical solution of second-order nonlinear singularly perturbed boundary-value problems by initial-value methodsJournal of Optimization Theory and Applications, Vol. 73, No. 2 Cross Ref The Quasi-Steady-State Assumption: A Case Study in PerturbationLee A. Segel and Marshall Slemrod18 July 2006 | SIAM Review, Vol. 31, No. 3AbstractPDF (3028 KB)Collocation for Singular Perturbation Problems III: Nonlinear Problems without Turning PointsU. Ascher and R. Weiss14 July 2006 | SIAM Journal on Scientific and Statistical Computing, Vol. 5, No. 4AbstractPDF (2185 KB)A Hybrid Asymptotic-Finite Element Method for Stiff Two-Point Boundary Value ProblemsR. C. Y. Chin and R. Krasny14 July 2006 | SIAM Journal on Scientific and Statistical Computing, Vol. 4, No. 2AbstractPDF (1502 KB)Singular Perturbation Techniques: A Comparison of the Method of Matched Asymptotic Expansions with that of Multiple ScalesDavid J. Wollkind18 July 2006 | SIAM Review, Vol. 19, No. 3AbstractPDF (1331 KB)Oceanic Morphogenesis Cross Ref The flow past a fixed sphere in a slowly rotating viscous fluidZeitschrift für angewandte Mathematik und Physik ZAMP, Vol. 26, No. 4 Cross Ref The Multivariable Method in Singular Perturbation AnalysisDonald R. Smith18 July 2006 | SIAM Review, Vol. 17, No. 2AbstractPDF (4288 KB)A comparison of some numerical methods for two-point boundary value problems1 January 1974 | Mathematics of Computation, Vol. 28, No. 127 Cross Ref Applications of the Maximum Principle to Singular Perturbation ProblemsF. W. Dorr, S. V. Parter, and L. F. Shampine18 July 2006 | SIAM Review, Vol. 15, No. 1AbstractPDF (2993 KB)Multiple Asymptotic Expansions and Singular ProblemsKenneth D. Shere17 February 2012 | SIAM Journal on Mathematical Analysis, Vol. 3, No. 2AbstractPDF (649 KB)A collocation method for boundary value problemsNumerische Mathematik, Vol. 19, No. 1 Cross Ref Regular and singular perturbation expansions in the analysis of extensional vibrations of platesJournal of Sound and Vibration, Vol. 15, No. 4 Cross Ref Volume 12, Issue 2| 1970SIAM Review History Submitted:22 October 1969Published online:18 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1012041Article page range:pp. 175-193ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics

We have constructed an end station for nanoscale magnetic materials study at the soft X-ray beamline HiSOR BL-14 at Hiroshima Synchrotron Radiation Center. An ultrahigh-vacuum scanning tunneling microscope (STM) was installed for an in situ characterization of nanoscale magnetic materials in combination with soft X-ray magnetic circular dichroism (XMCD) spectroscopy experiment. The STM was connected to the XMCD experimental station via damper bellows to isolate it from environmental vibrations, thus achieving efficient spatial resolution for observing Si(111) surface at atomic resolution. We performed an in situ experiment with STM and XMCD spectroscopy on Co nanoclusters on an Au(111) surface and explored its practical application to investigate magnetic properties for well-characterized nanoscale magnetic materials.

We study a mathematical model for a quasistatic behavior of electro-viscoelastic materials. The problem is related to highly nonlinear and non-smooth phenomena like contact, friction and normal compliance with wear. Then, a fully discrete scheme is introduced based on the finite element method to approximate the spatial variable and the backward Euler scheme to discretize the time derivatives. For a numerical scheme, we prove the existence and uniqueness of the solutions, and derive optimal order error estimates under certain regularity assumption on the solution of the continuous problem. AMS subject classification. 35J85 · 49J40 · 47J20 · 74M15. REFERENCES [1] Aoun, M. S. M., Dehda, B., & Douib, B. (2024). Numerical study of a thermo-elasto-viscoplastic contact problem with adhesion using a hybrid method. Studies in Engineering and Exact Sciences, 5(2), e8308-e8308. Search in Google Scholar. https://doi.org/10.54021/seesv5n2-255 [2] Aoun, M. S. M., Selmani, M., & Ahmed, A. A. (2021). Variational analysis of a frictional contact problem with wear and damage. Mathematical Modelling and Analysis, 26(2), 170-187. Search in Google Scholar. https://doi.org/10.3846/mma.2021.11942 [3] Barboteu, M., Fernández, J. R., & Ouafik, Y. (2008). Numerical analysis of a frictionless viscoelastic piezoelectric contact problem. ESAIM: Mathematical Modelling and Numerical Analysis, 42(4), 667-682. Search in Google Scholar. https://doi.org/10.1051/m2an:2008022 [4] Barboteu, M., Fernández, J. R., & Tarraf, R. (2008). Numerical analysis of a dynamic piezoelectric contact problem arising in viscoelasticity. Computer methods in applied mechanics and engineering, 197(45-48), 3724-3732. Search in Google Scholar. https://doi.org/10.1016/j.cma.2008.02.023 [5] Batra, R. C., & Yang, J. (1995). Saint-Venant's principle in linear piezoelectricity. Journal of Elasticity, 38(2), 209-218. Search in Google Scholar. https://doi.org/10.1007/BF00042498 [6] Braess, D. (2001). Finite elements: Theory, fast solvers, and applications in solid mechanics. Cambridge University Press. Search in Google Scholar. https://doi.org/10.1017/CBO9780511618635 [7] Chau, O., Fernández, J. R., Shillor, M., & Sofonea, M. (2003). Variational and numerical analysis of a quasistatic viscoelastic contact problem with adhesion. Journal of Computational and Applied Mathematics, 159(2), 431-465. Search in Google Scholar. https://doi.org/10.1016/S0377-0427(03)00547-8. [8] Chau, O., Shillor, M., & Sofonea, M. (2004). Dynamic frictionless contact with adhesion. Zeitschrift für angewandte Mathematik und Physik ZAMP, 55, 32-47. Search in Google Scholar. https://doi.org/10.1007/s00033-003-1089-9 [9] Chau, O., & Oujja, R. (2015). Numerical treatment of a class of thermal contact problems. Mathematics and Computers in Simulation, 118, 163-176. Search in Google Scholar. https://doi.org/10.1016/j.matcom.2014.12.007 [10] Ciarlet, P. G. (1978). The finite element method for elliptic problems. Amsterdam: North-Holland Pub. Co.. Search in Google Scholar. https://lib.ugent.be/catalog/ebk01:1000000000549375 [11] Ciarlet, P. G. (1991). Basic error estimates for elliptic problems, Handbook of Numerical Analysis, Volume 2, Pages 17-351. Search in Google Scholar. https://doi.org/10.1016/S1570-8659(05)80039-0 [12] Fernández, J. R., Shillor, M., & Sofonea, M. (2003). Analysis and numerical simulations of a dynamic contact problem with adhesion. Mathematical and Computer Modelling, 37(12-13), 1317-1333. Search in Google Scholar. https://doi.org/10.1016/S0895-7177(03)90043-4 [13] Han, W., Shillor, M., & Sofonea, M. (2001). Variational and numerical analysis of a quasistatic viscoelastic problem with normal compliance, friction and damage. Journal of Computational and Applied Mathematics, 137(2), 377-398. Search in Google Scholar. https://doi.org/10.1016/S0377-0427(00)00707-X [14] Han, W., & Sofonea, M. (2007). On a dynamic contact problem for elastic-visco-plastic materials. Applied numerical mathematics, 57(5-7), 498-509. Search in Google Scholar. https://doi.org/10.1016/j.apnum.2006.07.003 [15] Han, W., Sofonea, M., & Kazmi, K. (2007). Analysis and numerical solution of a frictionless contact problem for electro-elastic–visco-plastic materials. Computer methods in applied mechanics and engineering, 196(37-40), 3915-3926. Search in Google Scholar. https://doi.org/10.1016/j.cma.2006.10.051 [16] Ikeda, T. (1996). Fundamentals of piezoelectricity. Oxford university press. Search in Google Scholar. https://doi.org/10.1524/zkri.1992.199.1-2.158 [17] Lerguet, Z., Shillor, M., & Sofonea, M. (2007). A frictional contact problem for an electro-viscoelastic body. Electronic Journal of Differential Equations (EJDE)[electronic only], 2007, Paper-No. Search in Google Scholar. https://ejde.math.txstate.edu/Volumes/2007/170/abstr.html [18] Maanani, A. A., Maanani, Y., Betka, A., & Benguessoum, A. (2024). PV-Battery hybrid system power management based on backstepping control. International Journal of Applied Mathematics and Simulation, 1(2). Search in Google Scholar. https://doi.org/10.69717/ijams.v1.i2.102 [19] Maceri, F., & Bisegna, P. (1998). The unilateral frictionless contact of a piezoelectric body with a rigid support. Mathematical and Computer Modelling, 28(4-8), 19-28. Search in Google Scholar. https://doi.org/10.1016/S0895-7177(98)00105-8 [20] Migórski, S. (2006). Hemivariational inequality for a frictional contact problem inelasto-piezoelectricity. Discrete and Continuous Dynamical Systems-B, 6(6), 1339-1356. Search in Google Scholar. https://doi.org/10.3934/dcdsb.2006.6.1339. [21] Migórski, S., Ochal, A., & Sofonea, M. (2011). Analysis of a quasistatic contact problem for piezoelectric materials. Journal of mathematical analysis and applications, 382(2), 701-713. Search in Google Scholar. https://doi.org/10.1016/j.jmaa.2011.04.082 [22] Moumen, L., & Rebiai, S. E. (2024). Stabilization of the transmission Schrodinger equation with boundary time-varying delay. International Journal of Applied Mathematics and Simulation, 1(1). Search in Google Scholar. https://doi.org/10.69717/ijams.v1.i1.95 [23] Selmani, M. (2013). Frictional contact problem with wear for electro-viscoelastic materials with long memory. Bulletin of the Belgian Mathematical Society-Simon Stevin, 20(3), 461-479. Search in Google Scholar. https://doi.org/10.36045/bbms/1378314510. [24] Selmani, M., & Selmani, L. (2010). A frictional contact problem with wear and damage for electro-viscoelastic materials. Applications of Mathematics, 55, 89-109. Search In Google Scholar. https://doi.org/10.1007/s10492-010-0004-x [25] Sofonea, M., Han, W., & Shillor, M. (2005). Analysis and approximation of contact problems with adhesion or damage. Chapman and Hall/CRC. SEarch in Google Scholar. https://doi.org/10.1201/9781420034837 [26] Sofonea, M., Kazmi, K., Barboteu, M., & Han, W. (2012). Analysis and numerical solution of a piezoelectric frictional contact problem. Applied mathematical modelling, 36(9), 4483-4501. Search in Google Scholar. https://doi.org/10.1016/j.apm.2011.11.077 Communicated Editor: T.J. RABEHERIMANAN Manuscript received Sep. 19, 2024; revised Feb 02, 2025; accepted Feb 11, 2025; published Feb 28, 2025.

Using mathematics to solve or make sense of real-world problem situations and examining how mathematics has been used in context is of growing interest and importance in research within Australasia. Simultaneously curricula writers are increasingly recognising the importance of educating mathematically literate citizens of the world who can solve real-world problems. This chapter considers the different perspectives on teaching through mathematical modelling and applications and briefly reviews exemplary literature focusing on the teaching of mathematical modelling and applications. Not surprisingly, clear differences emerge in classroom practices engaged in applications, using known mathematics, versus modelling—where the mathematics that might be useful needs to be determined by the student. Theoretical developments in the field are reviewed. Recently, the research field has expanded from being mainly school focused to include pre-service and in-service teacher education. Methodological tools used in modelling and applications research that are being adopted or adapted in the region are then reviewed. Finally, the current positive state of Australasian modelling and applications research and its progress since last being reviewed in 2008 is discussed with an eye to possible future developments.

PREFACEWelcome to 2018 8th International Conference on Applied Physics and Mathematics (ICAPM 2018) held in Phuket, Thailand during January 27-29, 2018 The aim objective of ICAPM 2018 is to provide a platform for researchers, engineers, academicians as well as industrial professionals from all over the world to present their research results and development activities on Applied Physics and Mathematics. This conference provides opportunities for the delegates to exchange new ideas and application experiences face to face, to establish business or research relations and to find global partners for future collaboration.The present volume contains the selected papers submitted to this conference and provides up-to-date, comprehensive and worldwide state-of-the art knowledge in the field of Applied Physics and Mathematics. All papers included in this collection had undergone the careful peer-review by the conference technical committee members and international reviewers before they’re selected for publication. Studies presented in this volume cover the following topics: Mathematical theory and calculation, Physical Mathematics and Applied Physics, System Design and Mathematical Modeling, Applied Mathematics and Engineering, Mathematical Modeling and Analysis in Medical Field, Applied mechanics, Instrument Design and MeasurementWe’d like to express our gratitude to all the committee members for their great professionalism and efforts. And thank all the sponsors and participants for their valuable contributions and support to ICAPM 2018ICAMP 2018Conference Committee

Mathematical modelling and applications is a well-established field within mathematics education. Research in mathematical modelling and applications has maintained a focus on how to enhance students’ capabilities in using mathematics learnt in school to solve problems identified in, or derived from, the real world. While significant progress has been made in understanding the processes that underpin the successful applications of mathematics in real world contexts, there has been limited research into how to design tasks that are authentic reflections of the role of digital technologies in solving problems situated in the work place or daily life. This chapter draws on data sourced from a research and development project that investigated the use of digital technologies in teaching and learning mathematical modelling and applications to identify principles of effective task design. The instantiation of these principles within classroom practice is illustrated through a classroom vignette. This chapter concludes with a reflection on the research needed to further develop understanding of the role of technology as an enabler of principles of design for mathematical modelling tasks.

In this chapter, practical engineering strategies for recyclable magnetic materials for biomass conversion are discussed, starting with the synthesis and chemical functionalization of magnetic nanoparticles and nanoscopic materials. Nanoscale magnetic materials are attractive for the design of various catalytic systems because of their large surfaces, temperature-stability and easy (magneto-)recovery. The applications discussed here are focused on transforming lignocellulosic biomass to sugars (and subsequent biofuel), as well as feedstock chemicals. The breaking down of lignocellulosic biomass can be achieved by subsequent biomass pretreatment and fractionation. Tailored magnetic nanocatalysts can be used in both processes. An alternative strategy for generating low molecular sugars from lignocellulosic biomass is the use of enzymes (e.g. catalase) on magnetic beads. It is an attribute of all systems discussed that they can be recycled magnetically, thus decreasing the required costs of “green materials”.

Magnetic refrigeration is a promising energy efficient and environmentally friendly refrigeration technology. The major problem in magnetic refrigeration is to find working materials with a large magnetocaloric effect (MCE) in different temperatures regions. MCE is the reversible temperature change of a magnetic materials upon the application or removal of a magnetic field. Nanoscale magnetic materials are good candidates for magnetic refrigeration due to a presence of a large MCE in the superparamagnetic system and reduced hysteresis losses. The critical behavior of Er0.98□0.02Co2 intermetallic system has been investigated via isothermal magnetizations around its ferromagnetic-paramagnetic (FM-PM) transition at Curie temperature TC = 62 K. This study was performed through different methods; Arrott-Noakes technique, Kouvel-Fisher analysis, and critical isotherms procedure. All these models could not explain the behavior of the studied system, which suggest that it belongs to an unconventional critical behavior. The critical exponents of the magnetization β, for the temperature dependence of the spontaneous magnetization below Curie Temperature (TC), and γ for the magnetic susceptibility, and δ for the magnetic isotherm at TC were calculated. Based on Modified Arrott plots; Er0.98□0.02Co2 gives TC = 62.57 K ± 0.01 K with β = 0.68 ± 0.005 and TC = 62.59 K ± 0.01 K with γ = 0.88 ± 0.008. Using Kouvel-Fisher technique, we get TC = 62.66 K ± 0.06 K with β = 0.71 ± 0.01 and TC = 62.54 K ± 0.02 K with γ = 0.90 ± 0.06. The extracted value of δ from the critical isotherms and the Widom scaling relation are so close confirming that the obtained critical exponents are suitable and accurate within experimental error values. With 536.45 J kg−1 at 5 T of relative cooling power, Er0.98□0.02Co2 is very promising as magnetic refrigerant.

The integration of hard magnetic alloys in the form of patterned layers is one of the most interesting challenges for the manufacturing of energy efficient magnetic microelectromechanical systems (MEMS) [1]. With respect to current state of the art devices, whose working principle mostly relies on the exploitation of Lorentzian forces, MEMS based on permanent magnets can potentially present lower power consumption, larger displacements and stronger actuation forces. However, despite these attractive advantages, it is generally difficult to integrate thick hard magnetic layers with currently employed MEMS fabrication techniques.Electrodeposition is a technique that can be exploited to accomplish this task and that is characterized by many significant advantages: high deposition rates, no necessity of a vacuum system, low cost, possibility to deposit both alloys and composites. In addition, Reverse Pulse Plating (RPP) [2] can be used to mitigate the challenges connected to the deposition of hard magnetic alloys: high residual stress, presence of cracks and inadequate surface finishing. It can also simplify electrolyte formulation, eliminating the need of excessive amounts of additives.Regardless of the material selected, electrodeposition needs a template in order to confer a specific shape to the magnetic layer. Such template is normally manufactured using state-of-the-art technologies like standard lithography. This technique, however, is characterized by the necessity to use photomasks, which are costly and poorly adaptable to geometrical variations. Furthermore, the initial investment for the lithography equipment is typically high. A possible alternative is represented by the use of inkjet printing (IJP). This technology is characterized by low costs, high flexibility and optimal productivity. It can be applied to the micrometric patterning of electroformed layers by following a novel approach described in the present work for the first time: inkjet-assisted lithography (IAL). Briefly, droplets of a dispersion of silver nanoparticles are printed on the surface of a spin coated layer of negative photoresist. Silver is opaque for the UV radiation and it constitutes a mask for the resist. The resist is exposed and developed, forming thus templates usable for electroforming.The present work investigates the application of this approach to the production of thick and crack-free CoNiP micromagnets, which are RPP deposited inside IAL templates. CoNiP was selected due to its low-cost and good magnetic properties (with HC up to 2000 Oe). The alloy is electrodeposited from a chloride based acidic electrolyte [3], using ultra-fast RPP, in micrometric circular pores created via IAL. The diameter of the pores, and consequently the diameter of the finished magnets, can be efficiently tuned by changing the speed of the jetted droplets of silver ink. Conversely, the thickness of the magnets can be tuned by varying the deposition time. The resulting micromagnets, characterized by diameters in the 20-50 µm range and thickness up to 10 µm, are characterized to assess their morphology, phase composition and magnetic properties. The micrometric magnets here described may potentially find application for the realization of powerless MEMS, energy harvesting systems or microelectronic components.[1] N. M. Dempsey, “Hard Magnetic Materials for MEMS Applications” in: Nanoscale Magnetic Materials and Applications, Springer, Boston, MA (2009)[2] S. Pané et al., Electrochim. Acta 56, 8979-8988 (2011)[3] D. Y. Park et al., Electrochim. Acta 47, 2893-2900 (2002)