Articles de revista
http://hdl.handle.net/2117/1137
20170429T21:40:41Z

A higher order frozen Jacobian iterative method for solving HamiltonJacobi equations
http://hdl.handle.net/2117/103758
A higher order frozen Jacobian iterative method for solving HamiltonJacobi equations
Alzahrani, Ebraheem O.; Alaidarous, Eman; Younas, Arshad M. M.; Ahmad, Fayyaz; Ahmad, Shamshad; Ahmad, Shahid
It is wellknown that the solution of HamiltonJacobi equation may have singularity i.e., the solution is nonsmooth or nearly nonsmooth. We construct a frozen Jacobian multistep iterative method for solving HamiltonJacobi equation under the assumption that the solution is nearly singular. The frozen Jacobian iterative methods are computationally very efficient because a single instance of the iterative method uses a single inversion (in the scene of LU factorization) of the frozen Jacobian. The multistep part enhances the convergence order by solving lower and upper triangular systems. The convergence order of our proposed iterative method is 3(m1) for m>=3. For attaining good numerical accuracy in the solution, we use Chebyshev pseudospectral collocation method. Some HamiltonJacobi equations are solved, and numerically obtained results show high accuracy.
20170426T14:48:38Z
Alzahrani, Ebraheem O.
Alaidarous, Eman
Younas, Arshad M. M.
Ahmad, Fayyaz
Ahmad, Shamshad
Ahmad, Shahid
It is wellknown that the solution of HamiltonJacobi equation may have singularity i.e., the solution is nonsmooth or nearly nonsmooth. We construct a frozen Jacobian multistep iterative method for solving HamiltonJacobi equation under the assumption that the solution is nearly singular. The frozen Jacobian iterative methods are computationally very efficient because a single instance of the iterative method uses a single inversion (in the scene of LU factorization) of the frozen Jacobian. The multistep part enhances the convergence order by solving lower and upper triangular systems. The convergence order of our proposed iterative method is 3(m1) for m>=3. For attaining good numerical accuracy in the solution, we use Chebyshev pseudospectral collocation method. Some HamiltonJacobi equations are solved, and numerically obtained results show high accuracy.

The white dwarf binary pathways survey  I. A sample of FGK stars with white dwarf companions
http://hdl.handle.net/2117/103080
The white dwarf binary pathways survey  I. A sample of FGK stars with white dwarf companions
Parsons, S. G.; Rebassa Mansergas, Alberto; Schreiber, Mathias R.; Gänsicke, Boris T.; Zorotovic, Mónica; Ren, J. J.
The number of spatially unresolved white dwarf plus mainsequence star binaries has increased rapidly in the last decade, jumping from only ~30 in 2003 to over 3000. However, in the majority of known systems the companion to the white dwarf is a lowmass M dwarf, since these are relatively easy to identify from optical colours and spectra. White dwarfs with more massive FGK type companions have remained elusive due to the large difference in optical brightness between the two stars. In this paper, we identify 934 mainsequence FGK stars from the Radial Velocity Experiment survey in the Southern hemisphere and the Large Sky Area MultiObject Fiber Spectroscopic Telescope survey in the Northern hemisphere, that show excess flux at ultraviolet wavelengths which we interpret as the likely presence of a white dwarf companion. We obtained Hubble Space Telescope ultraviolet spectra for nine systems which confirmed that the excess is indeed caused, in all cases, by a hot compact companion, eight being white dwarfs and one a hot subdwarf or prehelium white dwarf, demonstrating that this sample is very clean. We also address the potential of this sample to test binary evolution models and Type Ia supernovae formation channels.
20170330T08:58:22Z
Parsons, S. G.
Rebassa Mansergas, Alberto
Schreiber, Mathias R.
Gänsicke, Boris T.
Zorotovic, Mónica
Ren, J. J.
The number of spatially unresolved white dwarf plus mainsequence star binaries has increased rapidly in the last decade, jumping from only ~30 in 2003 to over 3000. However, in the majority of known systems the companion to the white dwarf is a lowmass M dwarf, since these are relatively easy to identify from optical colours and spectra. White dwarfs with more massive FGK type companions have remained elusive due to the large difference in optical brightness between the two stars. In this paper, we identify 934 mainsequence FGK stars from the Radial Velocity Experiment survey in the Southern hemisphere and the Large Sky Area MultiObject Fiber Spectroscopic Telescope survey in the Northern hemisphere, that show excess flux at ultraviolet wavelengths which we interpret as the likely presence of a white dwarf companion. We obtained Hubble Space Telescope ultraviolet spectra for nine systems which confirmed that the excess is indeed caused, in all cases, by a hot compact companion, eight being white dwarfs and one a hot subdwarf or prehelium white dwarf, demonstrating that this sample is very clean. We also address the potential of this sample to test binary evolution models and Type Ia supernovae formation channels.

The agemetallicity relation in the solar neighbourhood from a pilot sample of white dwarfmain sequence binaries
http://hdl.handle.net/2117/103078
The agemetallicity relation in the solar neighbourhood from a pilot sample of white dwarfmain sequence binaries
Rebassa Mansergas, Alberto; Anguiano, B.; GarcíaBerro Montilla, Enrique; Freeman, K. C.; Cojocaru, Elena Ruxandra; Manser, C. J.; Pala, A. F.; Gänsicke, Boris T.; Liu, X.
The age–metallicity relation (AMR) is a fundamental observational constraint for understanding how the Galactic disc formed and evolved chemically in time. However, there is not yet an agreement on the observational properties of the AMR for the solar neighbourhood, primarily due to the difficulty in obtaining accurate stellar ages for individual field stars. We have started an observational campaign for providing the much needed observational input by using wide whitedwarf–mainsequence (WDMS) binaries. White dwarfs are ‘natural’ clocks and can be used to derive accurate ages. Metallicities can be obtained from the mainsequence companions. Since the progenitors of white dwarfs and the mainsequence stars were born at the same time, WDMS binaries provide a unique opportunity to observationally constrain in a robust way the properties of the AMR. In this work we present the AMR derived from analysing a pilot sample of 23 WDMS binaries and provide clear observational evidence for the lack of correlation between age and metallicity at young and intermediate ages (0–7 Gyr).
20170330T08:41:28Z
Rebassa Mansergas, Alberto
Anguiano, B.
GarcíaBerro Montilla, Enrique
Freeman, K. C.
Cojocaru, Elena Ruxandra
Manser, C. J.
Pala, A. F.
Gänsicke, Boris T.
Liu, X.
The age–metallicity relation (AMR) is a fundamental observational constraint for understanding how the Galactic disc formed and evolved chemically in time. However, there is not yet an agreement on the observational properties of the AMR for the solar neighbourhood, primarily due to the difficulty in obtaining accurate stellar ages for individual field stars. We have started an observational campaign for providing the much needed observational input by using wide whitedwarf–mainsequence (WDMS) binaries. White dwarfs are ‘natural’ clocks and can be used to derive accurate ages. Metallicities can be obtained from the mainsequence companions. Since the progenitors of white dwarfs and the mainsequence stars were born at the same time, WDMS binaries provide a unique opportunity to observationally constrain in a robust way the properties of the AMR. In this work we present the AMR derived from analysing a pilot sample of 23 WDMS binaries and provide clear observational evidence for the lack of correlation between age and metallicity at young and intermediate ages (0–7 Gyr).

Comment on: "On the KungTraub Conjecture for iterative methods for solving quadratic equations" Algorithms 2016, 9, 1
http://hdl.handle.net/2117/102944
Comment on: "On the KungTraub Conjecture for iterative methods for solving quadratic equations" Algorithms 2016, 9, 1
Ahmad, Fayyaz
KungTraub conjecture states that an iterative method without memory for finding the simple zero of a scalar equation could achieve convergence order 2(d1), and d is the total number of function evaluations. In an article Babajee, D.K.R. On the KungTraub Conjecture for Iterative Methods for Solving Quadratic Equations, Algorithms 2016, 9, 1, doi:10.3390/a9010001, the author has shown that KungTraub conjecture is not valid for the quadratic equation and proposed an iterative method for the scalar and vector quadratic equations. In this comment, we have shown that we first reported the aforementioned iterative method.
20170328T09:49:30Z
Ahmad, Fayyaz
KungTraub conjecture states that an iterative method without memory for finding the simple zero of a scalar equation could achieve convergence order 2(d1), and d is the total number of function evaluations. In an article Babajee, D.K.R. On the KungTraub Conjecture for Iterative Methods for Solving Quadratic Equations, Algorithms 2016, 9, 1, doi:10.3390/a9010001, the author has shown that KungTraub conjecture is not valid for the quadratic equation and proposed an iterative method for the scalar and vector quadratic equations. In this comment, we have shown that we first reported the aforementioned iterative method.

Multistep derivativefree preconditioned Newton method for solving systems of nonlinear equations
http://hdl.handle.net/2117/101565
Multistep derivativefree preconditioned Newton method for solving systems of nonlinear equations
Ahmad, Fayyaz
Preconditioning of systems of nonlinear equations modifies the associated Jacobian and provides rapid convergence. The preconditioners are introduced in a way that they do not affect the convergence order of parent iterative method. The multistep derivativefree iterative method consists of a base method and multistep part. In the base method, the Jacobian of the system of nonlinear equation is approximated by finite difference operator and preconditioners add an extra term to modify it. The inversion of modified finite difference operator is avoided by computing LU factors. Once we have LU factors, we repeatedly use them to solve lower and upper triangular systems in the multistep part to enhance the convergence order. The convergence order of mstep Newton iterative method is m + 1. The claimed convergence orders are verified by computing the computational order of convergence and numerical simulations clearly show that the good selection of preconditioning provides numerical stability, accuracy and rapid convergence.
20170224T15:53:27Z
Ahmad, Fayyaz
Preconditioning of systems of nonlinear equations modifies the associated Jacobian and provides rapid convergence. The preconditioners are introduced in a way that they do not affect the convergence order of parent iterative method. The multistep derivativefree iterative method consists of a base method and multistep part. In the base method, the Jacobian of the system of nonlinear equation is approximated by finite difference operator and preconditioners add an extra term to modify it. The inversion of modified finite difference operator is avoided by computing LU factors. Once we have LU factors, we repeatedly use them to solve lower and upper triangular systems in the multistep part to enhance the convergence order. The convergence order of mstep Newton iterative method is m + 1. The claimed convergence orders are verified by computing the computational order of convergence and numerical simulations clearly show that the good selection of preconditioning provides numerical stability, accuracy and rapid convergence.

The evolution of white dwarfs resulting from heliumenhanced, lowmetallicity progenitor stars
http://hdl.handle.net/2117/101528
The evolution of white dwarfs resulting from heliumenhanced, lowmetallicity progenitor stars
Althaus, Leandro G.; de Geronimo, Francisco; Córsico, Alejandro H.; Torres Gil, Santiago; GarcíaBerro Montilla, Enrique
Context. Some globular clusters host multiple stellar populations with different chemical abundance patterns. This is particularly true for ¿ Centauri, which shows clear evidence of a heliumenriched subpopulation characterized by a helium abundance as high as Y = 0.4
Aims. We present a whole and consistent set of evolutionary tracks from the ZAMS to the white dwarf stage that is appropriate for the study of the formation and evolution of white dwarfs resulting from the evolution of heliumrich progenitors.
Methods. We derived white dwarf sequences from progenitors with stellar mass ranging from 0.60 to 2.0 M¿ and for an initial helium abundance of Y = 0.4. We adopted two values of metallicity: Z = 0.001 and Z = 0.0005.
Results. We explored different issues of white dwarf evolution and their heliumrich progenitors. In particular, the final mass of the remnants, the role of overshooting during the thermally pulsing phase, and the cooling of the resulting white dwarfs differ markedly from the evolutionary predictions of progenitor stars with the standard initial helium abundance. Finally, the pulsational properties of the resulting white dwarfs are also explored.
Conclusions. We find that, for the range of initial masses explored in this paper, the final mass of the heliumrich progenitors is markedly higher than the final mass expected from progenitors with the usual helium abundance. We also find that progenitors with initial mass lower than M ¿ 0.65 M¿ evolve directly into heliumcore white dwarfs in less than 14 Gyr, and that, for larger progenitor masses, the evolution of the resulting lowmass carbonoxygen white dwarfs is dominated by residual nuclear burning. For heliumcore white dwarfs, we find that they evolve markedly faster than their counterparts coming from standard progenitors. Also, in contrast with what occurs for white dwarfs resulting from progenitors with the standard helium abundance, the impact of residual burning on the cooling time of white dwarfs is not affected by the occurrence of overshooting during the thermally pulsing phase of progenitor stars.
20170224T11:47:47Z
Althaus, Leandro G.
de Geronimo, Francisco
Córsico, Alejandro H.
Torres Gil, Santiago
GarcíaBerro Montilla, Enrique
Context. Some globular clusters host multiple stellar populations with different chemical abundance patterns. This is particularly true for ¿ Centauri, which shows clear evidence of a heliumenriched subpopulation characterized by a helium abundance as high as Y = 0.4
Aims. We present a whole and consistent set of evolutionary tracks from the ZAMS to the white dwarf stage that is appropriate for the study of the formation and evolution of white dwarfs resulting from the evolution of heliumrich progenitors.
Methods. We derived white dwarf sequences from progenitors with stellar mass ranging from 0.60 to 2.0 M¿ and for an initial helium abundance of Y = 0.4. We adopted two values of metallicity: Z = 0.001 and Z = 0.0005.
Results. We explored different issues of white dwarf evolution and their heliumrich progenitors. In particular, the final mass of the remnants, the role of overshooting during the thermally pulsing phase, and the cooling of the resulting white dwarfs differ markedly from the evolutionary predictions of progenitor stars with the standard initial helium abundance. Finally, the pulsational properties of the resulting white dwarfs are also explored.
Conclusions. We find that, for the range of initial masses explored in this paper, the final mass of the heliumrich progenitors is markedly higher than the final mass expected from progenitors with the usual helium abundance. We also find that progenitors with initial mass lower than M ¿ 0.65 M¿ evolve directly into heliumcore white dwarfs in less than 14 Gyr, and that, for larger progenitor masses, the evolution of the resulting lowmass carbonoxygen white dwarfs is dominated by residual nuclear burning. For heliumcore white dwarfs, we find that they evolve markedly faster than their counterparts coming from standard progenitors. Also, in contrast with what occurs for white dwarfs resulting from progenitors with the standard helium abundance, the impact of residual burning on the cooling time of white dwarfs is not affected by the occurrence of overshooting during the thermally pulsing phase of progenitor stars.

The white dwarf population within 40 pc of the Sun
http://hdl.handle.net/2117/101451
The white dwarf population within 40 pc of the Sun
Torres Gil, Santiago; GarcíaBerro Montilla, Enrique
© 2016 ESO. Context. The white dwarf luminosity function is an important tool to understand the properties of the solar neighborhood, like its star formation history, and its age. Aims. Here we present a population synthesis study of the white dwarf population within 40 pc from the Sun, and compare the results of this study with the properties of the observed sample. Methods. We use a stateoftheart population synthesis code based on Monte Carlo techniques, which incorporates the most recent and reliable white dwarf cooling sequences, an accurate description of the Galactic neighborhood, and a realistic treatment of all the known observational biases and selection procedures. Results. We find a good agreement between our theoretical models and the observed data. In particular, our simulations reproduce a previously unexplained feature of the bright branch of the white dwarf luminosity function, which we argue is due to a recent episode of star formation. We also derive the age of the solar neighborhood employing the position of the observed cutoff of the white dwarf luminosity function, to obtain ~8.9 ± 0.2 Gyr. Conclusions. We conclude that a detailed description of the ensemble properties of the population of white dwarfs within 40 pc of the Sun allows us to obtain interesting constraints on the history of the Solar neighborhood.
20170223T11:34:51Z
Torres Gil, Santiago
GarcíaBerro Montilla, Enrique
© 2016 ESO. Context. The white dwarf luminosity function is an important tool to understand the properties of the solar neighborhood, like its star formation history, and its age. Aims. Here we present a population synthesis study of the white dwarf population within 40 pc from the Sun, and compare the results of this study with the properties of the observed sample. Methods. We use a stateoftheart population synthesis code based on Monte Carlo techniques, which incorporates the most recent and reliable white dwarf cooling sequences, an accurate description of the Galactic neighborhood, and a realistic treatment of all the known observational biases and selection procedures. Results. We find a good agreement between our theoretical models and the observed data. In particular, our simulations reproduce a previously unexplained feature of the bright branch of the white dwarf luminosity function, which we argue is due to a recent episode of star formation. We also derive the age of the solar neighborhood employing the position of the observed cutoff of the white dwarf luminosity function, to obtain ~8.9 ± 0.2 Gyr. Conclusions. We conclude that a detailed description of the ensemble properties of the population of white dwarfs within 40 pc of the Sun allows us to obtain interesting constraints on the history of the Solar neighborhood.

The effect of 22Ne diffusion in the evolution and pulsational properties of white dwarfs with solar metallicity prgenitors
http://hdl.handle.net/2117/101446
The effect of 22Ne diffusion in the evolution and pulsational properties of white dwarfs with solar metallicity prgenitors
Camisassa, Maria E; Althaus, Leandro G.; Corsico, Alejandro H.; Vinyoles, Núria; Serenelli, Aldo M.; Isem, Jordi; Miller Bertolami, Marcelo M; GarcíaBerro Montilla, Enrique
© 2016. The American Astronomical Society. All rights reserved. Because of the large neutron excess of 22Ne, sedimentation of this isotope occurs rapidly in the interior of white dwarfs. This process releases an additional amount of energy, thus delaying the cooling times of the white dwarf. This influences the ages of different stellar populations derived using white dwarf cosmochronology. Furthermore, the overabundance of 22Ne in the inner regions of the star modifies the BruntVäisälä frequency, thus altering the pulsational properties of these stars. In this work we discuss the impact of 22Ne sedimentation in white dwarfs resulting from solar metallicity progenitors (Z = 0.02). We performed evolutionary calculations of white dwarfs with masses of 0.528, 0.576, 0.657, and 0.833 derived from full evolutionary computations of their progenitor stars, starting at the zeroAge main sequence all the way through the central hydrogen and helium burning, the thermally pulsing asymptotic giant branch (AGB), and postAGB phases. Our computations show that at low luminosities (), 22Ne sedimentation delays the cooling of white dwarfs with solar metallicity progenitors by about 1 Gyr. Additionally, we studied the consequences of 22Ne sedimentation on the pulsational properties of ZZ Ceti white dwarfs. We find that 22Ne sedimentation induces differences in the periods of these stars larger than the present observational uncertainties, particularly in more massive white dwarfs.
20170223T11:03:37Z
Camisassa, Maria E
Althaus, Leandro G.
Corsico, Alejandro H.
Vinyoles, Núria
Serenelli, Aldo M.
Isem, Jordi
Miller Bertolami, Marcelo M
GarcíaBerro Montilla, Enrique
© 2016. The American Astronomical Society. All rights reserved. Because of the large neutron excess of 22Ne, sedimentation of this isotope occurs rapidly in the interior of white dwarfs. This process releases an additional amount of energy, thus delaying the cooling times of the white dwarf. This influences the ages of different stellar populations derived using white dwarf cosmochronology. Furthermore, the overabundance of 22Ne in the inner regions of the star modifies the BruntVäisälä frequency, thus altering the pulsational properties of these stars. In this work we discuss the impact of 22Ne sedimentation in white dwarfs resulting from solar metallicity progenitors (Z = 0.02). We performed evolutionary calculations of white dwarfs with masses of 0.528, 0.576, 0.657, and 0.833 derived from full evolutionary computations of their progenitor stars, starting at the zeroAge main sequence all the way through the central hydrogen and helium burning, the thermally pulsing asymptotic giant branch (AGB), and postAGB phases. Our computations show that at low luminosities (), 22Ne sedimentation delays the cooling of white dwarfs with solar metallicity progenitors by about 1 Gyr. Additionally, we studied the consequences of 22Ne sedimentation on the pulsational properties of ZZ Ceti white dwarfs. We find that 22Ne sedimentation induces differences in the periods of these stars larger than the present observational uncertainties, particularly in more massive white dwarfs.

Frozen Jacobian iterative method for solving systems of nonlinear equations: application to nonlinear IVPs and BVPs
http://hdl.handle.net/2117/101173
Frozen Jacobian iterative method for solving systems of nonlinear equations: application to nonlinear IVPs and BVPs
Ullah, Malik Zaka; Ahmad, Fayyaz; Alshomrani, Ali Saleh; Alzahrani, A. K.; Alghamdi, Metib Said; Ahmad, Shamshad; Ahmad, Shahid
Frozen Jacobian iterative methods are of practical interest to solve the system of nonlinear equations. A
frozen Jacobian multistep iterative method is presented. We divide the multistep iterative method into two
parts namely base method and multistep part. The convergence order of the constructed frozen Jacobian
iterative method is three, and we design the base method in a way that we can maximize the convergence
order in the multistep part. In the multistep part, we utilize a single evaluation of the function, solve four
systems of lower and upper triangular systems and a second frozen Jacobian. The attained convergence
order per multistep is four. Hence, the general formula for the convergence order is 3 + 4(m  2) for
m = 2 and m is the number of multisteps. In a single instance of the iterative method, we employ only
single inversion of the Jacobian in the form of LU factors that makes the method computationally cheaper
because the LU factors are used to solve four system of lower and upper triangular systems repeatedly. The
claimed convergence order is verified by computing the computational order of convergence for a system of
nonlinear equations. The efficiency and validity of the proposed iterative method are narrated by solving
many nonlinear initial and boundary value problems.
20170217T11:47:01Z
Ullah, Malik Zaka
Ahmad, Fayyaz
Alshomrani, Ali Saleh
Alzahrani, A. K.
Alghamdi, Metib Said
Ahmad, Shamshad
Ahmad, Shahid
Frozen Jacobian iterative methods are of practical interest to solve the system of nonlinear equations. A
frozen Jacobian multistep iterative method is presented. We divide the multistep iterative method into two
parts namely base method and multistep part. The convergence order of the constructed frozen Jacobian
iterative method is three, and we design the base method in a way that we can maximize the convergence
order in the multistep part. In the multistep part, we utilize a single evaluation of the function, solve four
systems of lower and upper triangular systems and a second frozen Jacobian. The attained convergence
order per multistep is four. Hence, the general formula for the convergence order is 3 + 4(m  2) for
m = 2 and m is the number of multisteps. In a single instance of the iterative method, we employ only
single inversion of the Jacobian in the form of LU factors that makes the method computationally cheaper
because the LU factors are used to solve four system of lower and upper triangular systems repeatedly. The
claimed convergence order is verified by computing the computational order of convergence for a system of
nonlinear equations. The efficiency and validity of the proposed iterative method are narrated by solving
many nonlinear initial and boundary value problems.

Simultaneous detection of the nonlinear restoring and excitation of a forced nonlinear oscillation: an integral approach
http://hdl.handle.net/2117/101056
Simultaneous detection of the nonlinear restoring and excitation of a forced nonlinear oscillation: an integral approach
Ahmad, Fayyaz; Jang, Taek Soo; Park, Jinsoo; Sung, Hong Gun
We address in this article, how to calculate the restoring characteristic and the excitation of a nonlinear forced oscillating system. Under the assumption that the forced nonlinear oscillator has a periodic solution with period, we constructed a system of linear equations by introducing timedependent multipliers. The periodicity assumption helps simplify the system of linear equations. The stability and uniqueness are also presented for the inverse problem. Numerical testing is conducted to show the effectiveness of our presented methodology.
20170215T09:34:46Z
Ahmad, Fayyaz
Jang, Taek Soo
Park, Jinsoo
Sung, Hong Gun
We address in this article, how to calculate the restoring characteristic and the excitation of a nonlinear forced oscillating system. Under the assumption that the forced nonlinear oscillator has a periodic solution with period, we constructed a system of linear equations by introducing timedependent multipliers. The periodicity assumption helps simplify the system of linear equations. The stability and uniqueness are also presented for the inverse problem. Numerical testing is conducted to show the effectiveness of our presented methodology.