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Volume 10 (2019): Issue 2 (January 2019)
Special Issue on Mathematical Models and Methods in Biology, Medicine and Physiology. Guest Editors: Michele Piana, Luigi Preziosi

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Volume 9 (2018): Issue 2 (December 2018)
Special Issue on Mathematical modelling for complex systems: multi-agents methods. Guest Editor: Elena De Angelis

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Volume 8 (2017): Issue 1 (March 2017)

Volume 7 (2016): Issue 3 (September 2016)
"Special Issue on New Trends in Semi-Lagrangian Methods, Guest Editors: Luca Bonaventura, Maurizio Falcone and Roberto Ferretti

Volume 7 (2016): Issue 2 (June 2016)
Special Issue on Constitutive Equations for Heat Conduction in Nanosystems and Non-equilibrium Processes. Guest Editors: Vito Antonio Cimmelli and David Jou

Volume 7 (2016): Issue 1 (January 2016)
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Journal Details
Format
Journal
eISSN
2038-0909
First Published
15 Dec 2014
Publication timeframe
1 time per year
Languages
English

Search

Volume 8 (2017): Issue 1 (March 2017)

Journal Details
Format
Journal
eISSN
2038-0909
First Published
15 Dec 2014
Publication timeframe
1 time per year
Languages
English

Search

15 Articles
access type Open Access

A coherent modeling procedure to describe cell activation in biological systems

Published Online: 22 Mar 2017
Page range: 1 - 22

Abstract

Abstract

Biological systems are typically formed by different cell phenotypes, characterized by specific biological properties and behaviors. In particular, cells are able to undergo phenotypic transitions (i.e., activation or differentiation) upon internal or external stimuli. In order to take these phenomena into account, we here propose a modelling framework in which cell ensembles can be described collectively (i.e., through a distributed mass density) or individually (i.e., as a group of pointwise/concentrated particles) according to their biological determinants. A set of suitable rules involving the introduction of a cell shape function then defines a coherent procedure to model cell activation mechanisms, which imply a switch between the two mathematical representations. The theoretical environment describing cell transition is then enriched by including cell migratory dynamics and duplication/apoptotic processes, as well as the kinetics of selected diffusing chemicals inuencing the system evolution. Remarkably, our approach provides consistency of the same modeling framework across all types of cell representation, as it is suitable to cope with the often ambiguous translation of individual cell arguments (i.e., cell dimensions and interaction radii) into collective cell descriptions. Biologically relevant numerical realizations are also presented: in particular, they deal with phenotypic transitions within cell colonies and with the growth of a tumor spheroid. These phenomena constitute biological systems particularly suitable to assess the advantages of the proposed model and to analyze the role on cell dynamics both of relevant parameters and of the specific form given to the cell shape function.

Keywords

  • multiscale modeling
  • hybrid systems
  • cell differentiation
  • cell phenotypic transition
  • multiscale dynamics
access type Open Access

Hydrodynamic limits of kinetic equations for polyatomic and reactive gases

Published Online: 22 Mar 2017
Page range: 23 - 42

Abstract

Abstract

Starting from a kinetic BGK-model for a rarefied polyatomic gas, based on a molecular structure of discrete internal energy levels, an asymptotic Chapman-Enskog procedure is developed in the asymptotic continuum limit in order to derive consistent fluid-dynamic equations for macroscopic fields at Navier-Stokes level. In this way, the model allows to treat the gas as a mixture of mono-atomic species. Explicit expressions are given not only for dynamical pressure, but also for shear stress, diffusion velocities, and heat flux. The analysis is shown to deal properly also with a mixture of reactive gases, endowed for simplicity with translational degrees of freedom only, in which frame analogous results can be achieved.

Keywords

  • Kinetic models
  • Hydrodynamic limit
  • Polyatomic gases
  • Chemical reaction
  • Transport coefficients
access type Open Access

A forecasting performance comparison of dynamic factor models based on static and dynamic methods

Published Online: 22 Mar 2017
Page range: 43 - 66

Abstract

Abstract

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.

Keywords

  • Macroeconomic Forecasting
  • Dynamic Factor Models
  • Time domain methods
  • Frequency domain methods
access type Open Access

Integral equations for free-molecule ow in MEMS: recent advancements

Published Online: 22 Mar 2017
Page range: 67 - 80

Abstract

Abstract

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.

Keywords

  • Boundary Integral Equations
  • Rarefied Gas Dynamics
  • MEMS
access type Open Access

Tihonov theory and center manifolds for inhibitory mechanisms in enzyme kinetics

Published Online: 20 Jul 2017
Page range: 81 - 102

Abstract

Abstract

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.

Keywords

  • Enzyme Kinetics
  • Inhibition
  • Tihonov's Theorem
  • Center Manifold
  • Perturbation Theory
access type Open Access

Energetic BEM for the numerical analysis of 2D Dirichlet damped wave propagation exterior problems

Published Online: 20 Jul 2017
Page range: 103 - 127

Abstract

Abstract

Time-dependent problems modeled by hyperbolic partial differential equations can be reformulated in terms of boundary integral equations and solved via the boundary element method. In this context, the analysis of damping phenomena that occur in many physics and engineering problems is a novelty. Starting from a recently developed energetic space-time weak formulation for 1D damped wave propagation problems rewritten in terms of boundary integral equations, we develop here an extension of the so-called energetic boundary element method for the 2D case. Several numerical benchmarks, whose numerical results confirm accuracy and stability of the proposed technique, already proved for the numerical treatment of undamped wave propagation problems in several dimensions and for the 1D damped case, are illustrated and discussed.

Keywords

  • Damped wave equation
  • energy
  • boundary element method
access type Open Access

Large Eddy Simulation of gravity currents with a high order DG method

Published Online: 20 Jul 2017
Page range: 128 - 148

Abstract

Abstract

This work deals with Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) of a turbulent gravity current in a gas, performed by means of a Discontinuous Galerkin (DG) Finite Elements method employing, in the LES case, LES-DG turbulence models previously introduced by the authors. Numerical simulations of non-Boussinesq lock-exchange benchmark problems show that, in the DNS case, the proposed method allows to correctly reproduce relevant features of variable density gas ows with gravity. Moreover, the LES results highlight, also in this context, the excessively high dissipation of the Smagorinsky model with respect to the Germano dynamic procedure.

Keywords

  • Large Eddy Simulation
  • dynamical models
  • density currents
  • low Mach number flows
  • Discontinuous Galerkin method
access type Open Access

The Godunov method for a 2-phase model

Published Online: 20 Jul 2017
Page range: 149 - 164

Abstract

Abstract

We consider the Godunov numerical method to the phase-transition trafic model, proposed in [1], by Colombo, Marcellini, and Rascle. Numerical tests are shown to prove the validity of the method. Moreover we highlight the differences between such model and the one proposed in [2], by Blandin, Work, Goatin, Piccoli, and Bayen.

Keywords

  • 2--Phase Model
  • Continuum Traffic Models
  • Godunov Scheme
  • Hyperbolic Systems of Conservation Laws
access type Open Access

Electrostatic field in terms of geometric curvature in membrane MEMS devices

Published Online: 20 Jul 2017
Page range: 165 - 184

Abstract

Abstract

In this paper we present, in a framework of 1D-membrane Micro-Electro-Mechanical- Systems (MEMS) theory, a formalization of the problem of existence and uniqueness of a solution related to the membrane deformation u for electrostatic actuation in the steady- state case. In particular, we propose a new model in which the electric field magnitude E is proportional to the curvature of the membrane and, for it, we obtain results of existence by Schauder-Tychono's fixed point application and subsequently we establish conditions of uniqueness. Finally, some numerical tests have been carried out to further support the analytical results.

Keywords

  • mems
  • nems
  • electrostatic actuation
  • boundary semi-linear elliptic problems
  • green function
  • fixed-point theorem
access type Open Access

Computational modeling of the electromechanical response of a ventricular fiber affected by eccentric hypertrophy

Published Online: 22 Dec 2017
Page range: 185 - 209

Abstract

Abstract

The aim of this work is to study the effects of eccentric hypertrophy on the electromechanics of a single myocardial ventricular fiber by means of a one-dimensional finite-element strongly-coupled model. The electrical current ow model is written in the reference configuration and it is characterized by two geometric feedbacks, i.e. the conduction and convection ones, and by the mechanoelectric feedback due to stretchactivated channels. First, the influence of such feedbacks is investigated for both a healthy and a hypertrophic fiber in case of isometric simulations. No relevant discrepancies are found when disregarding one or more feedbacks for both fibers. Then, all feedbacks are taken into account while studying the electromechanical responses of fibers. The results from isometric tests do not point out any notable difference between the healthy and hypertrophic fibers as regards the action potential duration and conduction velocity. The length-tension relationships show increased stretches and reduced peak values for tension instead. The tension-velocity relationships derived from afterloaded isotonic and quick- release tests depict higher values of contraction velocity at smaller afterloads. Moreover, higher maximum shortenings are achieved during the isotonic contraction. In conclusion, our simulation results are innovative in predicting the electromechanical behavior of eccentric hypertrophic fibers.

Keywords

  • electromechanical model
  • mechanical feedback
  • eccentric hypertrophy
  • isometric test
  • afterloaded isotonic test
  • quick-release test

MSC 2010

  • 74A05
  • 74A10
  • 74B20
  • 74F99
  • 74G15
  • 74L15
  • 74S05
  • 74S20
  • 92C10
access type Open Access

POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder

Published Online: 22 Dec 2017
Page range: 210 - 236

Abstract

Abstract

Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. A Reduced Order Model (ROM) of the incompressible ow around a circular cylinder is presented in this work. The ROM is built performing a Galerkin projection of the governing equations onto a lower dimensional space. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pres- sure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) the projection of the Governing equations (momentum equation and Poisson equation for pressure) performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework. The accuracy of the reduced order model is assessed against full order results.

Keywords

  • ROM
  • POD-Galerkin
  • Finite Volumes
  • CFD
  • vortex shedding
access type Open Access

A benchmark study of the Signed-particle Monte Carlo algorithm for the Wigner equation

Published Online: 22 Dec 2017
Page range: 237 - 250

Abstract

Abstract

The Wigner equation represents a promising model for the simulation of electronic nanodevices, which allows the comprehension and prediction of quantum mechanical phenomena in terms of quasi-distribution functions. During these years, a Monte Carlo technique for the solution of this kinetic equation has been developed, based on the generation and annihilation of signed particles. This technique can be deeply understood in terms of the theory of pure jump processes with a general state space, producing a class of stochastic algorithms. One of these algorithms has been validated successfully by numerical experiments on a benchmark test case.

Keywords

  • Nanostructures
  • Wigner transport equation
  • Direct simulation Monte Carlo
access type Open Access

A hierarchy of hydrodynamic models for silicon carbide semiconductors

Published Online: 22 Dec 2017
Page range: 251 - 264

Abstract

Abstract

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.

Keywords

  • Semiconductors
  • Kinetic theory
  • Irreversible thermodynamics
access type Open Access

A local adaptive method for the numerical approximation in seismic wave modelling

Published Online: 22 Dec 2017
Page range: 265 - 281

Abstract

Abstract

We propose a new numerical approach for the solution of the 2D acoustic wave equation to model the predicted data in the field of active-source seismic inverse problems. This method consists in using an explicit finite difference technique with an adaptive order of approximation of the spatial derivatives that takes into account the local velocity at the grid nodes. Testing our method to simulate the recorded seismograms in a marine seismic acquisition, we found that the low computational time and the low approximation error of the proposed approach make it suitable in the context of seismic inversion problems.

Keywords

  • Finite difference
  • Seismic modelling
  • Seismic inversion
  • Optimization
  • Acoustic wave equation
access type Open Access

A numerical investigation of multi space reduced basis preconditioners for parametrized elliptic advection-diffusion equations

Published Online: 22 Dec 2017
Page range: 282 - 297

Abstract

Abstract

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.

Keywords

  • Finite elements
  • preconditioners
  • reduced basis
  • high performance computing
  • parametrized advection-diffusion
15 Articles
access type Open Access

A coherent modeling procedure to describe cell activation in biological systems

Published Online: 22 Mar 2017
Page range: 1 - 22

Abstract

Abstract

Biological systems are typically formed by different cell phenotypes, characterized by specific biological properties and behaviors. In particular, cells are able to undergo phenotypic transitions (i.e., activation or differentiation) upon internal or external stimuli. In order to take these phenomena into account, we here propose a modelling framework in which cell ensembles can be described collectively (i.e., through a distributed mass density) or individually (i.e., as a group of pointwise/concentrated particles) according to their biological determinants. A set of suitable rules involving the introduction of a cell shape function then defines a coherent procedure to model cell activation mechanisms, which imply a switch between the two mathematical representations. The theoretical environment describing cell transition is then enriched by including cell migratory dynamics and duplication/apoptotic processes, as well as the kinetics of selected diffusing chemicals inuencing the system evolution. Remarkably, our approach provides consistency of the same modeling framework across all types of cell representation, as it is suitable to cope with the often ambiguous translation of individual cell arguments (i.e., cell dimensions and interaction radii) into collective cell descriptions. Biologically relevant numerical realizations are also presented: in particular, they deal with phenotypic transitions within cell colonies and with the growth of a tumor spheroid. These phenomena constitute biological systems particularly suitable to assess the advantages of the proposed model and to analyze the role on cell dynamics both of relevant parameters and of the specific form given to the cell shape function.

Keywords

  • multiscale modeling
  • hybrid systems
  • cell differentiation
  • cell phenotypic transition
  • multiscale dynamics
access type Open Access

Hydrodynamic limits of kinetic equations for polyatomic and reactive gases

Published Online: 22 Mar 2017
Page range: 23 - 42

Abstract

Abstract

Starting from a kinetic BGK-model for a rarefied polyatomic gas, based on a molecular structure of discrete internal energy levels, an asymptotic Chapman-Enskog procedure is developed in the asymptotic continuum limit in order to derive consistent fluid-dynamic equations for macroscopic fields at Navier-Stokes level. In this way, the model allows to treat the gas as a mixture of mono-atomic species. Explicit expressions are given not only for dynamical pressure, but also for shear stress, diffusion velocities, and heat flux. The analysis is shown to deal properly also with a mixture of reactive gases, endowed for simplicity with translational degrees of freedom only, in which frame analogous results can be achieved.

Keywords

  • Kinetic models
  • Hydrodynamic limit
  • Polyatomic gases
  • Chemical reaction
  • Transport coefficients
access type Open Access

A forecasting performance comparison of dynamic factor models based on static and dynamic methods

Published Online: 22 Mar 2017
Page range: 43 - 66

Abstract

Abstract

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.

Keywords

  • Macroeconomic Forecasting
  • Dynamic Factor Models
  • Time domain methods
  • Frequency domain methods
access type Open Access

Integral equations for free-molecule ow in MEMS: recent advancements

Published Online: 22 Mar 2017
Page range: 67 - 80

Abstract

Abstract

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.

Keywords

  • Boundary Integral Equations
  • Rarefied Gas Dynamics
  • MEMS
access type Open Access

Tihonov theory and center manifolds for inhibitory mechanisms in enzyme kinetics

Published Online: 20 Jul 2017
Page range: 81 - 102

Abstract

Abstract

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.

Keywords

  • Enzyme Kinetics
  • Inhibition
  • Tihonov's Theorem
  • Center Manifold
  • Perturbation Theory
access type Open Access

Energetic BEM for the numerical analysis of 2D Dirichlet damped wave propagation exterior problems

Published Online: 20 Jul 2017
Page range: 103 - 127

Abstract

Abstract

Time-dependent problems modeled by hyperbolic partial differential equations can be reformulated in terms of boundary integral equations and solved via the boundary element method. In this context, the analysis of damping phenomena that occur in many physics and engineering problems is a novelty. Starting from a recently developed energetic space-time weak formulation for 1D damped wave propagation problems rewritten in terms of boundary integral equations, we develop here an extension of the so-called energetic boundary element method for the 2D case. Several numerical benchmarks, whose numerical results confirm accuracy and stability of the proposed technique, already proved for the numerical treatment of undamped wave propagation problems in several dimensions and for the 1D damped case, are illustrated and discussed.

Keywords

  • Damped wave equation
  • energy
  • boundary element method
access type Open Access

Large Eddy Simulation of gravity currents with a high order DG method

Published Online: 20 Jul 2017
Page range: 128 - 148

Abstract

Abstract

This work deals with Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) of a turbulent gravity current in a gas, performed by means of a Discontinuous Galerkin (DG) Finite Elements method employing, in the LES case, LES-DG turbulence models previously introduced by the authors. Numerical simulations of non-Boussinesq lock-exchange benchmark problems show that, in the DNS case, the proposed method allows to correctly reproduce relevant features of variable density gas ows with gravity. Moreover, the LES results highlight, also in this context, the excessively high dissipation of the Smagorinsky model with respect to the Germano dynamic procedure.

Keywords

  • Large Eddy Simulation
  • dynamical models
  • density currents
  • low Mach number flows
  • Discontinuous Galerkin method
access type Open Access

The Godunov method for a 2-phase model

Published Online: 20 Jul 2017
Page range: 149 - 164

Abstract

Abstract

We consider the Godunov numerical method to the phase-transition trafic model, proposed in [1], by Colombo, Marcellini, and Rascle. Numerical tests are shown to prove the validity of the method. Moreover we highlight the differences between such model and the one proposed in [2], by Blandin, Work, Goatin, Piccoli, and Bayen.

Keywords

  • 2--Phase Model
  • Continuum Traffic Models
  • Godunov Scheme
  • Hyperbolic Systems of Conservation Laws
access type Open Access

Electrostatic field in terms of geometric curvature in membrane MEMS devices

Published Online: 20 Jul 2017
Page range: 165 - 184

Abstract

Abstract

In this paper we present, in a framework of 1D-membrane Micro-Electro-Mechanical- Systems (MEMS) theory, a formalization of the problem of existence and uniqueness of a solution related to the membrane deformation u for electrostatic actuation in the steady- state case. In particular, we propose a new model in which the electric field magnitude E is proportional to the curvature of the membrane and, for it, we obtain results of existence by Schauder-Tychono's fixed point application and subsequently we establish conditions of uniqueness. Finally, some numerical tests have been carried out to further support the analytical results.

Keywords

  • mems
  • nems
  • electrostatic actuation
  • boundary semi-linear elliptic problems
  • green function
  • fixed-point theorem
access type Open Access

Computational modeling of the electromechanical response of a ventricular fiber affected by eccentric hypertrophy

Published Online: 22 Dec 2017
Page range: 185 - 209

Abstract

Abstract

The aim of this work is to study the effects of eccentric hypertrophy on the electromechanics of a single myocardial ventricular fiber by means of a one-dimensional finite-element strongly-coupled model. The electrical current ow model is written in the reference configuration and it is characterized by two geometric feedbacks, i.e. the conduction and convection ones, and by the mechanoelectric feedback due to stretchactivated channels. First, the influence of such feedbacks is investigated for both a healthy and a hypertrophic fiber in case of isometric simulations. No relevant discrepancies are found when disregarding one or more feedbacks for both fibers. Then, all feedbacks are taken into account while studying the electromechanical responses of fibers. The results from isometric tests do not point out any notable difference between the healthy and hypertrophic fibers as regards the action potential duration and conduction velocity. The length-tension relationships show increased stretches and reduced peak values for tension instead. The tension-velocity relationships derived from afterloaded isotonic and quick- release tests depict higher values of contraction velocity at smaller afterloads. Moreover, higher maximum shortenings are achieved during the isotonic contraction. In conclusion, our simulation results are innovative in predicting the electromechanical behavior of eccentric hypertrophic fibers.

Keywords

  • electromechanical model
  • mechanical feedback
  • eccentric hypertrophy
  • isometric test
  • afterloaded isotonic test
  • quick-release test

MSC 2010

  • 74A05
  • 74A10
  • 74B20
  • 74F99
  • 74G15
  • 74L15
  • 74S05
  • 74S20
  • 92C10
access type Open Access

POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder

Published Online: 22 Dec 2017
Page range: 210 - 236

Abstract

Abstract

Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. A Reduced Order Model (ROM) of the incompressible ow around a circular cylinder is presented in this work. The ROM is built performing a Galerkin projection of the governing equations onto a lower dimensional space. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pres- sure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) the projection of the Governing equations (momentum equation and Poisson equation for pressure) performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework. The accuracy of the reduced order model is assessed against full order results.

Keywords

  • ROM
  • POD-Galerkin
  • Finite Volumes
  • CFD
  • vortex shedding
access type Open Access

A benchmark study of the Signed-particle Monte Carlo algorithm for the Wigner equation

Published Online: 22 Dec 2017
Page range: 237 - 250

Abstract

Abstract

The Wigner equation represents a promising model for the simulation of electronic nanodevices, which allows the comprehension and prediction of quantum mechanical phenomena in terms of quasi-distribution functions. During these years, a Monte Carlo technique for the solution of this kinetic equation has been developed, based on the generation and annihilation of signed particles. This technique can be deeply understood in terms of the theory of pure jump processes with a general state space, producing a class of stochastic algorithms. One of these algorithms has been validated successfully by numerical experiments on a benchmark test case.

Keywords

  • Nanostructures
  • Wigner transport equation
  • Direct simulation Monte Carlo
access type Open Access

A hierarchy of hydrodynamic models for silicon carbide semiconductors

Published Online: 22 Dec 2017
Page range: 251 - 264

Abstract

Abstract

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.

Keywords

  • Semiconductors
  • Kinetic theory
  • Irreversible thermodynamics
access type Open Access

A local adaptive method for the numerical approximation in seismic wave modelling

Published Online: 22 Dec 2017
Page range: 265 - 281

Abstract

Abstract

We propose a new numerical approach for the solution of the 2D acoustic wave equation to model the predicted data in the field of active-source seismic inverse problems. This method consists in using an explicit finite difference technique with an adaptive order of approximation of the spatial derivatives that takes into account the local velocity at the grid nodes. Testing our method to simulate the recorded seismograms in a marine seismic acquisition, we found that the low computational time and the low approximation error of the proposed approach make it suitable in the context of seismic inversion problems.

Keywords

  • Finite difference
  • Seismic modelling
  • Seismic inversion
  • Optimization
  • Acoustic wave equation
access type Open Access

A numerical investigation of multi space reduced basis preconditioners for parametrized elliptic advection-diffusion equations

Published Online: 22 Dec 2017
Page range: 282 - 297

Abstract

Abstract

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.

Keywords

  • Finite elements
  • preconditioners
  • reduced basis
  • high performance computing
  • parametrized advection-diffusion

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