rss_2.0Communications in Applied and Industrial Mathematics FeedSciendo RSS Feed for Communications in Applied and Industrial Mathematics in Applied and Industrial Mathematics 's Cover interaction simulations with a LES filtering approach in<abstract> <title style='display:none'>Abstract</title> <p>The goal of this paper is to test solids4Foam, the fluid-structure interaction (FSI) toolbox developed for foam-extend (a branch of OpenFOAM), and assess its flexibility in handling more complex flows. For this purpose, we consider the interaction of an incompressible fluid described by a Leray model with a hyperelastic structure modeled as a Saint Venant-Kirchho material. We focus on a strongly coupled, partitioned fluid-structure interaction (FSI) solver in a finite volume environment, combined with an arbitrary Lagrangian-Eulerian approach to deal with the motion of the fluid domain. For the implementation of the Leray model, which features a nonlinear differential low-pass filter, we adopt a three-step algorithm called Evolve-Filter-Relax. We validate our approach against numerical data available in the literature for the 3D cross flow past a cantilever beam at Reynolds number 100 and 400.</p> </abstract>ARTICLE2021-08-10T00:00:00.000+00:00Double-stage discretization approaches for biomarker-based bladder cancer survival modeling<abstract> <title style='display:none'>Abstract</title> <p>Bioinformatic techniques targeting gene expression data require specific analysis pipelines with the aim of studying properties, adaptation, and disease outcomes in a sample population. Present investigation compared together results of four numerical experiments modeling survival rates from bladder cancer genetic profiles. Research showed that a sequence of two discretization phases produced remarkable results compared to a classic approach employing one discretization of gene expression data. Analysis involving two discretization phases consisted of a primary discretizer followed by refinement or pre-binning input values before the main discretization scheme. Among all tests, the best model encloses a sequence of data transformation to compensate skewness, data discretization phase with class-attribute interdependence maximization algorithm, and final classification by voting feature intervals, a classifier that also provides discrete interval optimization.</p> </abstract>ARTICLE2021-08-10T00:00:00.000+00:00Numerical methods for a system of coupled Cahn-Hilliard equations<abstract> <title style='display:none'>Abstract</title> <p>In this work, we consider a system of coupled Cahn-Hilliard equations describing the phase separation of a copolymer and a homopolymer blend. We propose some numerical methods to approximate the solution of the system which are based on suitable combinations of existing schemes for the single Cahn-Hilliard equation. As a verification for our experimental approach, we present some tests and a detailed description of the numerical solutions’ behaviour obtained by varying the values of the system’s characteristic parameters.</p> </abstract>ARTICLE2021-03-30T00:00:00.000+00:00A study of the interactions between uniform and pointwise vortices in an inviscid fluid<abstract><title style='display:none'>Abstract</title><p>The planar interactions between pair of vortices in an inviscid fluid are analytically investigated, by assuming one of the two vortices pointwise and the other one uniform. A novel approach using the Schwarz function of the boundary of the uniform vortex is adopted. It is based on a new integral relation between the (complex) velocity induced by the uniform vortex and its Schwarz function and on the time evolution equation of this function. They lead to a singular integrodifferential problem. Even if this problem is strongly nonlinear, its nonlinearities are confined inside two terms, only. As a consequence, its solution can be analytically approached by means of successive approximations. The ones at 0th (nonlinear terms neglected) and 1st (nonlinear terms evaluated on the 0-order solution) orders are calculated and compared with contour dynamics simulations of the vortex motion. A satisfactory agreement is keept for times which are small with respect to the turn-over time of the vortex pair.</p></abstract>ARTICLE2016-05-20T00:00:00.000+00:00Sequential quadrature methods for RDO<abstract><title style='display:none'>Abstract</title><p>This paper presents a comparative study between a large number of different existing sequential quadrature schemes suitable for Robust Design Optimization (RDO), with the inclusion of two partly original approaches. Efficiency of the different integration strategies is evaluated in terms of accuracy and computational effort: main goal of this paper is the identification of an integration strategy able to provide the integral value with a prescribed accuracy using a limited number of function samples. Identification of the different qualities of the various integration schemes is obtained utilizing both algebraic and practical test cases. Differences in the computational effort needed by the different schemes is evidenced, and the implications on their application to practical RDO problems is highlighted.</p></abstract>ARTICLE2016-05-20T00:00:00.000+00:00A note from the Editor of a bubble rising in gravitational field<abstract><title style='display:none'>Abstract</title><p>The rising motion in free space of a pulsating spherical bubble of gas and vapour driven by the gravitational force, in an isochoric, inviscid liquid is investigated. The liquid is at rest at the initial time, so that the subsequent flow is irrotational. For this reason, the velocity field due to the bubble motion is described by means of a potential, which is represented through an expansion based on Legendre polynomials. A system of two coupled, ordinary and nonlinear differential equations is derived for the vertical position of the bubble center of mass and for its radius. This latter equation is a modified form of the Rayleigh-Plesset equation, including a term proportional to the kinetic energy associated to the translational motion of the bubble.</p></abstract>ARTICLE2016-05-20T00:00:00.000+00:00On the linear stability of some finite difference schemes for nonlinear reaction-diffusion models of chemical reaction networks<p> We identify sufficient conditions for the stability of some well-known finite difference schemes for the solution of the multivariable reaction-diffusion equations that model chemical reaction networks. Since the equations are mainly nonlinear, these conditions are obtained through local linearization. A recurrent condition is that the Jacobian matrix of the reaction part evaluated at some positive unknown solution is either D-semi-stable or semi-stable. We demonstrate that for a single reversible chemical reaction whose kinetics are monotone, the Jacobian matrix is D-semi-stable and therefore such schemes are guaranteed to work well.</p>ARTICLE2018-12-05T00:00:00.000+00:00Loss of mass and performance in skeletal muscle tissue: a continuum model<p> We present a continuum hyperelastic model which describes the mechanical response of a skeletal muscle tissue when its strength and mass are reduced by aging. Such a reduction is typical of a geriatric syndrome called sarcopenia. The passive behavior of the material is described by a hyperelastic, polyconvex, transversely isotropic strain energy function, and the activation of the muscle is modeled by the so called active strain approach. The loss of ability of activating of an elder muscle is then obtained by lowering of some percentage the active part of the stress, while the loss of mass is modeled through a multiplicative decomposition of the deformation gradient. The obtained stress-strain relations are graphically represented and discussed in order to study some of the effects of sarcopenia. </p>ARTICLE2018-02-28T00:00:00.000+00:00Comparison of minimization methods for nonsmooth image segmentation<p> Segmentation is a typical task in image processing having as main goal the partitioning of the image into multiple segments in order to simplify its interpretation and analysis. One of the more popular segmentation model, formulated by Chan-Vese, is the piecewise constant Mumford-Shah model restricted to the case of two-phase segmentation. We consider a convex relaxation formulation of the segmentation model, that can be regarded as a nonsmooth optimization problem, because the presence of the l1-term. Two basic approaches in optimization can be distinguished to deal with its non differentiability: the smoothing methods and the nonsmoothing methods. In this work, a numerical comparison of some first order methods belongs of both approaches are presented. The relationships among the different methods are shown, and accuracy and efficiency tests are also performed on several images.</p>ARTICLE2018-03-24T00:00:00.000+00:00The chord length distribution function of a non-convex hexagon<p> In this paper we obtain the chord length distribution function of a non-convex equilateral hexagon and then derive the associated density function. Finally, we calculate the expected value of the chord length. </p>ARTICLE2018-02-28T00:00:00.000+00:00Dynamics of a spherical bubble rising in gravity, subject to traveling pressure disturbance<p> The motion of a spherical bubble rising in a gravitational field in presence of a traveling pressure step wave is investigated. Equations of motion for the bubble radius and center of mass are deduced and several sample cases are analysed by means of their numerical integration. The crucial role played by the traveling speed of the wave front and by the intensity of the pressure step are discussed. A first comparison with the axisymmetric dynamics is discussed.</p>ARTICLE2018-12-14T00:00:00.000+00:00On preconditioner updates for sequences of saddle-point linear systems<p> Updating preconditioners for the solution of sequences of large and sparse saddle- point linear systems via Krylov methods has received increasing attention in the last few years, because it allows to reduce the cost of preconditioning while keeping the efficiency of the overall solution process. This paper provides a short survey of the two approaches proposed in the literature for this problem: updating the factors of a preconditioner available in a block LDL<sup>T</sup> form, and updating a preconditioner via a limited-memory technique inspired by quasi-Newton methods.</p>ARTICLE2018-02-28T00:00:00.000+00:00Semi-Analytical method for the pricing of barrier options in case of time-dependent parameters (with Matlab codes)<p> A Semi-Analytical method for pricing of Barrier Options (SABO) is presented. The method is based on the foundations of Boundary Integral Methods which is recast here for the application to barrier option pricing in the Black-Scholes model with time-dependent interest rate, volatility and dividend yield. The validity of the numerical method is illustrated by several numerical examples and comparisons.</p>ARTICLE2018-03-24T00:00:00.000+00:00A new two-component approach in modeling red blood cells<p>This work consists in the presentation of a computational modelling approach to study normal and pathological behavior of red blood cells in slow transient processes that can not be accompanied by pure particle methods (which require very small time steps). The basic model, inspired by the best models currently available, considers the cytoskeleton as a discrete non-linear elastic structure. The novelty of the proposed work is to couple this skeleton with continuum models instead of the more common discrete models (molecular dynamics, particle methods) of the lipid bilayer. The interaction of the solid cytoskeleton with the bilayer, which is a two-dimensional fluid, will be done through adhesion forces adapting e cient solid-solid adhesion algorithms. The continuous treatment of the fluid parts is well justified by scale arguments and leads to much more stable and precise numerical problems when, as is the case, the size of the molecules (0.3 <italic>nm</italic>) is much smaller than the overall size (≃ 8000 <italic>nm</italic>). In this paper we display some numerical simulations that show how our approach can describe the interaction of an RBC with an exogenous body as well as the relaxation of the shape of an RBC toward its equilibrium configuration in absence of external forces.</p>ARTICLE2020-10-31T00:00:00.000+00:00Tihonov theory and center manifolds for inhibitory mechanisms in enzyme kinetics<p> In this paper we study the chemical reaction of inhibition, determine the appropriate parameter ε for the application of Tihonov's Theorem, compute explicitly the equations of the center manifold of the system and find sufficient conditions to guarantee that in the phase space the curves which relate the behavior of the complexes to the substrates by means of the tQSSA are asymptotically equivalent to the center manifold of the system. Some numerical results are discussed. </p>ARTICLE2017-07-20T00:00:00.000+00:00A forecasting performance comparison of dynamic factor models based on static and dynamic methods<p> We present a comparison of the forecasting performances of three Dynamic Factor Models on a large monthly data panel of macroeconomic and financial time series for the UE economy. The first model relies on static principal-component and was introduced by Stock and Watson (2002a, b). The second is based on generalized principal components and it was introduced by Forni, Hallin, Lippi and Reichlin (2000, 2005). The last model has been recently proposed by Forni, Hallin, Lippi and Zaffaroni (2015, 2016). The data panel is split into two parts: the calibration sample, from February 1986 to December 2000, is used to select the most performing specification for each class of models in a in- sample environment, and the proper sample, from January 2001 to November 2015, is used to compare the performances of the selected models in an out-of-sample environment. The metholodogical approach is analogous to Forni, Giovannelli, Lippi and Soccorsi (2016), but also the size of the rolling window is empirically estimated in the calibration process to achieve more robustness. We find that, on the proper sample, the last model is the most performing for the Inflation. However, mixed evidencies appear over the proper sample for the Industrial Production.</p>ARTICLE2017-03-22T00:00:00.000+00:00A hierarchy of hydrodynamic models for silicon carbide semiconductors<p> The electro-thermal transport in silicon carbide semiconductors can be described by an extended hydrodynamic model, obtained by taking moments from kinetic equations, and using the Maximum Entropy Principle. By performing appropriate scaling, one can obtain reduced transport models such as the Energy transport and the drift-diffusion ones, where the transport coefficients are explicitly determined.</p>ARTICLE2017-12-22T00:00:00.000+00:00Integral equations for free-molecule ow in MEMS: recent advancements<p> We address a Boundary Integral Equation (BIE) approach for the analysis of gas dissipation in near-vacuum for Micro Electro Mechanical Systems (MEMS). Inspired by an analogy with the radiosity equation in computer graphics, we discuss an efficient way to compute the visible domain of integration. Moreover, we tackle the issue of near singular integrals by developing a set of analytical formulas for planar polyhedral domains. Finally a validation with experimental results taken from the literature is presented. </p>ARTICLE2017-03-22T00:00:00.000+00:00A numerical investigation of multi space reduced basis preconditioners for parametrized elliptic advection-diffusion equations<p> We analyze the numerical performance of a preconditioning technique recently proposed in [1] for the efficient solution of parametrized linear systems arising from the finite element (FE) discretization of parameterdependent elliptic partial differential equations (PDEs). In order to exploit the parametric dependence of the PDE, the proposed preconditioner takes advantage of the reduced basis (RB) method within the preconditioned iterative solver employed to solve the linear system, and combines a RB solver, playing the role of coarse component, with a traditional fine grid (such as Additive Schwarz or block Jacobi) preconditioner. A sequence of RB spaces is required to handle the approximation of the error-residual equation at each step of the iterative method at hand, whence the name of Multi Space Reduced Basis (MSRB) method. In this paper, a numerical investigation of the proposed technique is carried on in the case of a Richardson iterative method, and then extended to the flexible GMRES method, in order to solve parameterized advection-diffusion problems. Particular attention is payed to the impact of anisotropic diffusion coefficients and (possibly dominant) transport terms on the proposed preconditioner, by carrying out detailed comparisons with the current state of the art algebraic multigrid preconditioners.</p>ARTICLE2017-12-22T00:00:00.000+00:00en-us-1