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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 9 (2018): Issue 1 (February 2018)

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

Search

11 Articles
access type Open Access

Loss of mass and performance in skeletal muscle tissue: a continuum model

Published Online: 28 Feb 2018
Page range: 1 - 19

Abstract

Abstract

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.

Keywords

  • sarcopenia
  • active strain
  • hyperelasticity
  • damage
  • 74B20
  • 74L15
access type Open Access

The chord length distribution function of a non-convex hexagon

Published Online: 28 Feb 2018
Page range: 20 - 34

Abstract

Abstract

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.

Keywords

  • Non-convex hexagon
  • chord length distribution function
  • multiple chord distribution
  • chord power integrals

MSC 2010

  • 60D05
  • 52A22
access type Open Access

On preconditioner updates for sequences of saddle-point linear systems

Published Online: 28 Feb 2018
Page range: 35 - 41

Abstract

Abstract

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 LDLT form, and updating a preconditioner via a limited-memory technique inspired by quasi-Newton methods.

Keywords

  • saddle-point matrices
  • sequences of linear systems
  • preconditioning
  • factorization updates
  • limited-memory techniques

MSC 2010

  • 65F08
  • 65F10
  • 90C25
access type Open Access

Semi-Analytical method for the pricing of barrier options in case of time-dependent parameters (with Matlab® codes)

Published Online: 24 Mar 2018
Page range: 42 - 67

Abstract

Abstract

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.

Keywords

  • Boundary Element Method
  • Black-Scholes
  • Barrier Options
  • Greeks
  • Time-Dependent Parameters
  • Integral Equations
access type Open Access

Comparison of minimization methods for nonsmooth image segmentation

Published Online: 24 Mar 2018
Page range: 68 - 86

Abstract

Abstract

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.

Keywords

  • nonsmooth optimization
  • first order methods
  • image segmentation
access type Open Access

Some results on discrete eigenvalues for the Stochastic Nonlinear Schrödinger Equation in fiber optics

Published Online: 24 Mar 2018
Page range: 87 - 103

Abstract

Abstract

We study a stochastic Nonlinear Schrödinger Equation (NLSE), with additive white Gaussian noise, by means of the Nonlinear Fourier Transform (NFT). In particular, we focus on the propagation of discrete eigenvalues along a focusing fiber. Since the stochastic NLSE is not exactly integrable by means of the NFT, then we use a perturbation approach, where we assume that the signal-to-noise ratio is high. The zeroth-order perturbation leads to the deterministic NLSE while the first-order perturbation allows to describe the statistics of the discrete eigenvalues. This is important to understand the properties of the channel for recently devised optical transmission techniques, where the information is encoded in the nonlinear Fourier spectrum.

Keywords

  • Stochastic Nonlinear Schrödinger Equation
  • Nonlinear Fourier Transform
  • Eigenvalues
  • Solitons
  • Perturbation
  • Fiber Optics
access type Open Access

A fractional spline collocation-Galerkin method for the time-fractional diffusion equation

Published Online: 24 Mar 2018
Page range: 104 - 120

Abstract

Abstract

The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The main advantage is in that the derivatives of integer and fractional order of the fractional splines can be expressed in a closed form that involves just the generalized finite difference operator. This allows us to construct an accurate and efficient numerical method. Several numerical tests showing the effectiveness of the proposed method are presented.

Keywords

  • Fractional diffusion problem
  • Collocation method
  • Galerkin method
  • Fractional spline
access type Open Access

On the linear stability of some finite difference schemes for nonlinear reaction-diffusion models of chemical reaction networks

Published Online: 05 Dec 2018
Page range: 121 - 140

Abstract

Abstract

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.

Keywords

  • Reaction-diffusion equations
  • Finite difference method
  • Stability
  • Amplification matrix
  • Linearization
  • Monotone kinetics
access type Open Access

Heat rectification in He II counterflow in radial geometries

Published Online: 05 Dec 2018
Page range: 141 - 148

Abstract

Abstract

We consider heat rectification in radial flows of turbulent helium II, where heat flux is not described by Fourier's law, but by a more general law. This is different from previous analyses of heat rectification, based on such law. In our simplified analysis we show that the coupling between heat flux and the gradient of vortex line density plays a decisive role in such rectification. Such rectification will be low at low and high values of the heat rate, but it may exhibit a very high value at an intermediate value of the heat rate. In particular, for a given range of values for the incoming heat ow, the outgoing heat flow corresponding to the exchange of internal and external temperatures would be very small. This would imply difficulties in heat removal in a given range of temperature gradients.

Keywords

  • Heat rectification
  • Superfluid helium
  • Radial heat flux
  • Quantum turbulence
access type Open Access

Dynamics of a spherical bubble rising in gravity, subject to traveling pressure disturbance

Published Online: 14 Dec 2018
Page range: 149 - 158

Abstract

Abstract

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.

Keywords

  • cavitation
  • rising gas bubble
  • traveling pressure disturbance
access type Open Access

A particle model reproducing the effect of a conflicting flight information on the honeybee swarm guidance

Published Online: 14 Dec 2018
Page range: 159 - 173

Abstract

Abstract

The honeybee swarming process is steered by few scout individuals, which are the unique informed on the location of the target destination. Theoretical and experimental results suggest that bee coordinated flight arises from visual signals. However, how the information is passed within the population is still debated. Moreover, it has been observed that honeybees are highly sensitive to conflicting directional information. In fact, swarms exposed to fast-moving bees headed in the wrong direction show clear signs of disrupted guidance. In this respect, we here present a discrete mathematical model to investigate different hypotheses on the behaviour both of informed and uninformed bees. In this perspective, numerical realizations, specifically designed to mimic selected experiments, reveal that only one combination of the considered assumptions is able to reproduce the empirical outcomes, resulting thereby the most reliable mechanism underlying the swarm dynamics according to the proposed approach. Specifically, this study suggests that (i) leaders indicate the right flight direction by repeatedly streaking at high speed pointing towards the target and then slowly coming back to the trailing edge of the bee cloud; and (ii) uninformed bees, in turn, gather the route information by adapting their movement to all the bees sufficiently close to their position.

Keywords

  • Bee swarming
  • collective dynamics
  • alignment mechanisms
11 Articles
access type Open Access

Loss of mass and performance in skeletal muscle tissue: a continuum model

Published Online: 28 Feb 2018
Page range: 1 - 19

Abstract

Abstract

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.

Keywords

  • sarcopenia
  • active strain
  • hyperelasticity
  • damage
  • 74B20
  • 74L15
access type Open Access

The chord length distribution function of a non-convex hexagon

Published Online: 28 Feb 2018
Page range: 20 - 34

Abstract

Abstract

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.

Keywords

  • Non-convex hexagon
  • chord length distribution function
  • multiple chord distribution
  • chord power integrals

MSC 2010

  • 60D05
  • 52A22
access type Open Access

On preconditioner updates for sequences of saddle-point linear systems

Published Online: 28 Feb 2018
Page range: 35 - 41

Abstract

Abstract

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 LDLT form, and updating a preconditioner via a limited-memory technique inspired by quasi-Newton methods.

Keywords

  • saddle-point matrices
  • sequences of linear systems
  • preconditioning
  • factorization updates
  • limited-memory techniques

MSC 2010

  • 65F08
  • 65F10
  • 90C25
access type Open Access

Semi-Analytical method for the pricing of barrier options in case of time-dependent parameters (with Matlab® codes)

Published Online: 24 Mar 2018
Page range: 42 - 67

Abstract

Abstract

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.

Keywords

  • Boundary Element Method
  • Black-Scholes
  • Barrier Options
  • Greeks
  • Time-Dependent Parameters
  • Integral Equations
access type Open Access

Comparison of minimization methods for nonsmooth image segmentation

Published Online: 24 Mar 2018
Page range: 68 - 86

Abstract

Abstract

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.

Keywords

  • nonsmooth optimization
  • first order methods
  • image segmentation
access type Open Access

Some results on discrete eigenvalues for the Stochastic Nonlinear Schrödinger Equation in fiber optics

Published Online: 24 Mar 2018
Page range: 87 - 103

Abstract

Abstract

We study a stochastic Nonlinear Schrödinger Equation (NLSE), with additive white Gaussian noise, by means of the Nonlinear Fourier Transform (NFT). In particular, we focus on the propagation of discrete eigenvalues along a focusing fiber. Since the stochastic NLSE is not exactly integrable by means of the NFT, then we use a perturbation approach, where we assume that the signal-to-noise ratio is high. The zeroth-order perturbation leads to the deterministic NLSE while the first-order perturbation allows to describe the statistics of the discrete eigenvalues. This is important to understand the properties of the channel for recently devised optical transmission techniques, where the information is encoded in the nonlinear Fourier spectrum.

Keywords

  • Stochastic Nonlinear Schrödinger Equation
  • Nonlinear Fourier Transform
  • Eigenvalues
  • Solitons
  • Perturbation
  • Fiber Optics
access type Open Access

A fractional spline collocation-Galerkin method for the time-fractional diffusion equation

Published Online: 24 Mar 2018
Page range: 104 - 120

Abstract

Abstract

The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The main advantage is in that the derivatives of integer and fractional order of the fractional splines can be expressed in a closed form that involves just the generalized finite difference operator. This allows us to construct an accurate and efficient numerical method. Several numerical tests showing the effectiveness of the proposed method are presented.

Keywords

  • Fractional diffusion problem
  • Collocation method
  • Galerkin method
  • Fractional spline
access type Open Access

On the linear stability of some finite difference schemes for nonlinear reaction-diffusion models of chemical reaction networks

Published Online: 05 Dec 2018
Page range: 121 - 140

Abstract

Abstract

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.

Keywords

  • Reaction-diffusion equations
  • Finite difference method
  • Stability
  • Amplification matrix
  • Linearization
  • Monotone kinetics
access type Open Access

Heat rectification in He II counterflow in radial geometries

Published Online: 05 Dec 2018
Page range: 141 - 148

Abstract

Abstract

We consider heat rectification in radial flows of turbulent helium II, where heat flux is not described by Fourier's law, but by a more general law. This is different from previous analyses of heat rectification, based on such law. In our simplified analysis we show that the coupling between heat flux and the gradient of vortex line density plays a decisive role in such rectification. Such rectification will be low at low and high values of the heat rate, but it may exhibit a very high value at an intermediate value of the heat rate. In particular, for a given range of values for the incoming heat ow, the outgoing heat flow corresponding to the exchange of internal and external temperatures would be very small. This would imply difficulties in heat removal in a given range of temperature gradients.

Keywords

  • Heat rectification
  • Superfluid helium
  • Radial heat flux
  • Quantum turbulence
access type Open Access

Dynamics of a spherical bubble rising in gravity, subject to traveling pressure disturbance

Published Online: 14 Dec 2018
Page range: 149 - 158

Abstract

Abstract

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.

Keywords

  • cavitation
  • rising gas bubble
  • traveling pressure disturbance
access type Open Access

A particle model reproducing the effect of a conflicting flight information on the honeybee swarm guidance

Published Online: 14 Dec 2018
Page range: 159 - 173

Abstract

Abstract

The honeybee swarming process is steered by few scout individuals, which are the unique informed on the location of the target destination. Theoretical and experimental results suggest that bee coordinated flight arises from visual signals. However, how the information is passed within the population is still debated. Moreover, it has been observed that honeybees are highly sensitive to conflicting directional information. In fact, swarms exposed to fast-moving bees headed in the wrong direction show clear signs of disrupted guidance. In this respect, we here present a discrete mathematical model to investigate different hypotheses on the behaviour both of informed and uninformed bees. In this perspective, numerical realizations, specifically designed to mimic selected experiments, reveal that only one combination of the considered assumptions is able to reproduce the empirical outcomes, resulting thereby the most reliable mechanism underlying the swarm dynamics according to the proposed approach. Specifically, this study suggests that (i) leaders indicate the right flight direction by repeatedly streaking at high speed pointing towards the target and then slowly coming back to the trailing edge of the bee cloud; and (ii) uninformed bees, in turn, gather the route information by adapting their movement to all the bees sufficiently close to their position.

Keywords

  • Bee swarming
  • collective dynamics
  • alignment mechanisms

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