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Wataru Takahashi - One of the best experts on this subject based on the ideXlab platform.
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The split common Null Point problem for generalized resolvents in two banach spaces
Numerical Algorithms, 2016Co-Authors: Wataru TakahashiAbstract:In this paper, we consider the split common Null Point problem in two Banach spaces. Then, using the generalized resolvents of maximal monotone operators and the generalized projections, we prove a strong convergence theorem for finding a solution of the split common Null Point problem in two Banach spaces. It seems that such a theorem for generalized resolvents is the first of its kind outside Hilbert spaces.
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a strong convergence theorem by the shrinking projection method for the split common Null Point problem in banach spaces
Numerical Functional Analysis and Optimization, 2016Co-Authors: Mayumi Hojo, Wataru TakahashiAbstract:ABSTRACTIn this article, we consider the split common Null Point problem in Banach spaces. Then, using the shrinking projection method, we prove a strong convergence theorem for finding a solution of the split common Null Point problem in Banach spaces. It appears that such a theorem is a first in Banach spaces.
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strong convergence theorems by hybrid methods for the split common Null Point problem in banach spaces
Fixed Point Theory and Applications, 2015Co-Authors: Wataru TakahashiAbstract:In this paper, we consider the split common Null Point problem in Banach spaces. Then using the hybrid method and the shrinking projection method in mathematical programming, we prove strong convergence theorems for finding a solution of the split common Null Point problem in Banach spaces.
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The split common Null Point problem and the shrinking projection method in Banach spaces
Optimization, 2015Co-Authors: Satoru Takahashi, Wataru TakahashiAbstract:In this paper, we consider the split common Null Point problem with resolvents of maximal monotone operators in Banach spaces. Then, using the shrinking projection method, we prove a strong convergence theorem for finding a solution of the split common Null Point problem in Banach spaces.
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The split common Null Point problem in Banach spaces
Archiv der Mathematik, 2015Co-Authors: Wataru TakahashiAbstract:In this paper, we consider the split common Null Point problem in Banach spaces. Then using the metric resolvents of maximal monotone operators and the metric projections, we prove a strong convergence theorem for finding a solution of the split common Null Point problem in Banach spaces. The result of this paper seems to be the first one to study it outside Hilbert spaces.
Truong Minh Tuyen - One of the best experts on this subject based on the ideXlab platform.
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Parallel iterative methods for solving the generalized split common Null Point problem in Hilbert spaces
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales. Serie A. Matemáticas, 2020Co-Authors: Simeon Reich, Truong Minh TuyenAbstract:We study the recently introduced generalized split common Null Point problem in Hilbert spaces. In order to solve this problem, we propose two new parallel algorithms and establish strong convergence theorems for both of them. Our schemes combine the hybrid and shrinking projection methods with the proximal Point algorithm.
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Two projection methods for solving the multiple-set split common Null Point problem in Hilbert spaces
Optimization, 2019Co-Authors: Simeon Reich, Truong Minh TuyenAbstract:ABSTRACTWe study the multiple-set split common Null Point problem in two Hilbert spaces. In order to solve this problem, we propose two new parallel algorithms and establish strong convergence theo...
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Iterative methods for solving the generalized split common Null Point problem in Hilbert spaces
Optimization, 2019Co-Authors: Simeon Reich, Truong Minh TuyenAbstract:We propose and study new iterative methods for solving the generalized split common Null Point problem in Hilbert spaces.
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A shrinking projection method for solving the split common Null Point problem in Banach spaces
Numerical Algorithms, 2019Co-Authors: Truong Minh Tuyen, Nguyen Thi Thu ThuyAbstract:In this paper, in order to solve the split common Null Point problem, we investigate a new explicit iteration method, base on the shrinking projection method and ε -enlargement of a maximal monotone operator. We also give some applications of our main results for the problem of split minimum Point, multiple-sets split feasibility, and split variational inequality. Two numerical examples also are given to illustrate the effectiveness of the proposed algorithm.
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A new algorithm for solving the split common Null Point problem in Hilbert spaces
Numerical Algorithms, 2019Co-Authors: Simeon Reich, Truong Minh TuyenAbstract:We study the split common Null Point problem in two Hilbert spaces. In order to solve this problem, we propose a new algorithm and establish a strong convergence theorem for it. Our scheme combines the hybrid projection method with the proximal Point algorithm.
Klaus Galsgaard - One of the best experts on this subject based on the ideXlab platform.
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On the nature of reconnection at a solar coronal Null Point above a separatrix dome
The Astrophysical Journal, 2013Co-Authors: David Pontin, E. R. Priest, Klaus GalsgaardAbstract:Three-dimensional magnetic Null Points are ubiquitous in the solar corona and in any generic mixed-polarity magnetic field. We consider magnetic reconnection at an isolated coronal Null Point whose fan field lines form a dome structure. Using analytical and computational models, we demonstrate several features of spine-fan reconnection at such a Null, including the fact that substantial magnetic flux transfer from one region of field line connectivity to another can occur. The flux transfer occurs across the current sheet that forms around the Null Point during spine-fan reconnection, and there is no separator present. Also, flipping of magnetic field lines takes place in a manner similar to that observed in the quasi-separatrix layer or slip-running reconnection.
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3D Solar Null Point Reconnection MHD Simulations
Solar Physics, 2012Co-Authors: G. Baumann, Klaus Galsgaard, Åke NordlundAbstract:Numerical MHD simulations of 3D reconnection events in the solar corona have improved enormously over the last few years, not only in resolution, but also in their complexity, enabling more and more realistic modeling. Various ways to obtain the initial magnetic field, different forms of solar atmospheric models as well as diverse driving speeds and patterns have been employed. This study considers differences between simulations with stratified and non-stratified solar atmospheres, addresses the influence of the driving speed on the plasma flow and energetics, and provides quantitative formulas for mapping electric fields and dissipation levels obtained in numerical simulations to the corresponding solar quantities. The simulations start out from a potential magnetic field containing a Null-Point, obtained from a Solar and Heliospheric Observatory (SOHO) Michelson Doppler Imager (MDI) magnetogram magnetogram extrapolation approximately 8 hours before a C-class flare was observed. The magnetic field is stressed with a boundary motion pattern similar to – although simpler than – horizontal motions observed by SOHO during the period preceding the flare. The general behavior is nearly independent of the driving speed, and is also very similar in stratified and non-stratified models, provided only that the boundary motions are slow enough. The boundary motions cause a build-up of current sheets, mainly in the fan-plane of the magnetic Null-Point, but do not result in a flare-like energy release. The additional free energy required for the flare could have been partly present in non-potential form at the initial state, with subsequent additions from magnetic flux emergence or from components of the boundary motion that were not represented by the idealized driving pattern.
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Steady state reconnection at a single 3D magnetic Null Point
Astronomy & Astrophysics, 2011Co-Authors: Klaus Galsgaard, David PontinAbstract:Aims. We systematically stress a rotationally symmetric 3D magnetic Null Point by advecting the opposite footPoints of the spine axis in opposite directions. This stress eventually concentrates in the vicinity of the Null Point, thereby forming a local current sheet through which magnetic reconnection takes place. The aim is to look for a steady state evolution of the current sheet dynamics, which may provide scaling relations for various characteristic parameters of the system. Methods. The evolution is followed by solving numerically the non-ideal MHD equations in a Cartesian domain. The Null Point is embedded in an initially constant density and temperature plasma. Results. It is shown that a quasi-steady reconnection process can be set up at a 3D Null by continuous shear driving. It appears that a true steady state is unlikely to be realised because the current layer tends to grow until it is restricted by the geometry of the computational domain and the imposed driving profile. However, ratios between characteristic quantities clearly settle after some time to stable values, so that the evolution is quasi-steady. The experiments show a number of scaling relations, but they do not provide a clear consensus for extending to lower magnetic resistivity or faster driving velocities. More investigations are needed to fully clarify the properties of current sheets at magnetic Null Points.
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Is Null-Point Reconnection Important for Solar Flux Emergence?
Solar Physics, 2009Co-Authors: R. C. Maclean, Clare E. Parnell, Klaus GalsgaardAbstract:The role of Null-Point reconnection in a three-dimensional numerical magnetohydrodynamic (MHD) model of solar emerging flux is investigated. The model consists of a twisted magnetic flux tube rising through a stratified convection zone and atmosphere to interact and reconnect with a horizontal overlying magnetic field in the atmosphere. Null Points appear as the reconnection begins and persist throughout the rest of the emergence, where they can be found mostly in the model photosphere and transition region, forming two loose clusters on either side of the emerging flux tube. Up to 26 Nulls are present at any one time, and tracking in time shows that there is a total of 305 overall, despite the initial simplicity of the magnetic field configuration. We find evidence for the reality of the Nulls in terms of their methods of creation and destruction, their balance of signs, their long lifetimes, and their geometrical stability. We then show that due to the low parallel electric fields associated with the Nulls, Null-Point reconnection is not the main type of magnetic reconnection involved in the interaction of the newly emerged flux with the overlying field. However, the large number of Nulls implies that the topological structure of the magnetic field must be very complex and the importance of reconnection along separators or separatrix surfaces for flux emergence cannot be ruled out.
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Current amplification and magnetic reconnection at a three-dimensional Null Point: Physical characteristics: MAGNETIC RECONNECTION AT A 3D Null Point
Journal of Geophysical Research: Space Physics, 2007Co-Authors: David Pontin, Klaus GalsgaardAbstract:[1] The behavior of magnetic perturbations of an initially potential three-dimensional equilibrium magnetic Null Point is investigated. The basic components which constitute a typical disturbance are taken to be rotations and shears, in line with previous work. The spine and fan of the Null Point (the field lines which asymptotically approach or recede from the Null) are subjected to such rotational and shear perturbations, using three-dimensional magnetohydrodynamic simulations. It is found that rotations of the fan plane and about the spine lead to current sheets which are spatially diffuse in at least one direction and form in the locations of the spine and fan. However, shearing perturbations lead to 3-D-localized current sheets focused at the Null Point itself. In addition, rotations are associated with a growth of current parallel to the spine, driving rotational flows and a type of rotational reconnection. Shears, on the other hand, cause a current through the Null which is parallel to the fan plane and are associated with stagnation-type flows and field line reconnection across both the spine and fan. The importance of the parallel electric field, and its meaning as a reconnection rate, are discussed.
Suthep Suantai - One of the best experts on this subject based on the ideXlab platform.
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A Self-Adaptive Algorithm for Split Null Point Problems and Fixed Point Problems for Demicontractive Multivalued Mappings
Acta Applicandae Mathematicae, 2020Co-Authors: Suthep Suantai, Pachara JailokaAbstract:In this work, we study the split Null Point problem and the fixed Point problem in Hilbert spaces. We introduce a self-adaptive algorithm based on the viscosity approximation method without prior knowledge of the operator norm for finding a common solution of the considered problem for maximal monotone mappings and demicontractive multivalued mappings. A strong convergence result of our proposed algorithm is established under some suitable conditions. Some convergence results for the split feasibility problem and the split minimization problem are consequences of our main result. Finally, we also give numerical examples for supporting our main result.
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Split Null Point Problems and Fixed Point Problems for Demicontractive Multivalued Mappings
Mediterranean Journal of Mathematics, 2018Co-Authors: Pachara Jailoka, Suthep SuantaiAbstract:In this paper, we consider the split Null Point problem and the fixed Point problem for multivalued mappings in Hilbert spaces. We introduce a Halpern-type algorithm for solving the problem for maximal monotone operators and demicontractive multivalued mappings, and establish a strong convergence result under some suitable conditions. Also, we apply our problem of main result to other split problems, that is, the split feasibility problem, the split equilibrium problem, and the split minimization problem. Finally, a numerical result for supporting our main result is also supplied.
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Nonlinear iterative methods for solving the split common Null Point problem in Banach spaces
Optimization Methods and Software, 2018Co-Authors: Suthep Suantai, Yekini Shehu, Prasit CholamjiakAbstract:ABSTRACTIn this work, we study the split common Null Point problem in the framework of Banach spaces. We propose an iterative scheme for solving the problem and then prove strong convergence theorem of the sequences generated by our iterative scheme under suitable conditions. We finally provide some numerical examples to support the main theorem.
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Convergence theorems for finding the split common Null Point in Banach spaces
Applied General Topology, 2017Co-Authors: Suthep Suantai, Kittipong Srisap, Natthapong Naprang, Manatsawin Mamat, Vithoon Yundon, Prasit CholamjiakAbstract:In this paper, we introduce a new iterative scheme for solving the split common Null Point problem. We then prove the strong convergence theorem under suitable conditions. Finally, we give some numerical examples for our results.
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Split common fixed Point and Null Point problems for demicontractive operators in Hilbert spaces
Optimization Methods and Software, 2017Co-Authors: Pachara Jailoka, Suthep SuantaiAbstract:In this article, we consider a split common fixed Point and Null Point problem which includes the split common fixed Point problem, the split common Null problem and other problems related to the fixed Point problem and the Null Point problem. We introduce an algorithm for studying the split common fixed Point and Null problem for demicontractive operators and maximal monotone operators in real Hilbert spaces. We establish a strong convergence result under some suitable conditions and reduce our main result to above-mentioned problems. Moreover, we also apply our main results to the split equilibrium problem. Finally, we give numerical results to demonstrate the convergence of our algorithms.
David Pontin - One of the best experts on this subject based on the ideXlab platform.
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Non-linear tearing of 3D Null Point current sheets
Physics of Plasmas, 2014Co-Authors: Peter F. Wyper, David PontinAbstract:The manner in which the rate of magnetic reconnection scales with the Lundquist number in realistic three-dimensional (3D) geometries is still an unsolved problem. It has been demonstrated that in 2D rapid non-linear tearing allows the reconnection rate to become almost independent of the Lundquist number (the “plasmoid instability”). Here, we present the first study of an analogous instability in a fully 3D geometry, defined by a magnetic Null Point. The 3D Null current layer is found to be susceptible to an analogous instability but is marginally more stable than an equivalent 2D Sweet-Parker-like layer. Tearing of the sheet creates a thin boundary layer around the separatrix surface, contained within a flux envelope with a hyperbolic structure that mimics a spine-fan topology. Efficient mixing of flux between the two topological domains occurs as the flux rope structures created during the tearing process evolve within this envelope. This leads to a substantial increase in the rate of reconnection between the two domains.
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On the nature of reconnection at a solar coronal Null Point above a separatrix dome
The Astrophysical Journal, 2013Co-Authors: David Pontin, E. R. Priest, Klaus GalsgaardAbstract:Three-dimensional magnetic Null Points are ubiquitous in the solar corona and in any generic mixed-polarity magnetic field. We consider magnetic reconnection at an isolated coronal Null Point whose fan field lines form a dome structure. Using analytical and computational models, we demonstrate several features of spine-fan reconnection at such a Null, including the fact that substantial magnetic flux transfer from one region of field line connectivity to another can occur. The flux transfer occurs across the current sheet that forms around the Null Point during spine-fan reconnection, and there is no separator present. Also, flipping of magnetic field lines takes place in a manner similar to that observed in the quasi-separatrix layer or slip-running reconnection.
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Steady state reconnection at a single 3D magnetic Null Point
Astronomy & Astrophysics, 2011Co-Authors: Klaus Galsgaard, David PontinAbstract:Aims. We systematically stress a rotationally symmetric 3D magnetic Null Point by advecting the opposite footPoints of the spine axis in opposite directions. This stress eventually concentrates in the vicinity of the Null Point, thereby forming a local current sheet through which magnetic reconnection takes place. The aim is to look for a steady state evolution of the current sheet dynamics, which may provide scaling relations for various characteristic parameters of the system. Methods. The evolution is followed by solving numerically the non-ideal MHD equations in a Cartesian domain. The Null Point is embedded in an initially constant density and temperature plasma. Results. It is shown that a quasi-steady reconnection process can be set up at a 3D Null by continuous shear driving. It appears that a true steady state is unlikely to be realised because the current layer tends to grow until it is restricted by the geometry of the computational domain and the imposed driving profile. However, ratios between characteristic quantities clearly settle after some time to stable values, so that the evolution is quasi-steady. The experiments show a number of scaling relations, but they do not provide a clear consensus for extending to lower magnetic resistivity or faster driving velocities. More investigations are needed to fully clarify the properties of current sheets at magnetic Null Points.
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Current amplification and magnetic reconnection at a three-dimensional Null Point: Physical characteristics: MAGNETIC RECONNECTION AT A 3D Null Point
Journal of Geophysical Research: Space Physics, 2007Co-Authors: David Pontin, Klaus GalsgaardAbstract:[1] The behavior of magnetic perturbations of an initially potential three-dimensional equilibrium magnetic Null Point is investigated. The basic components which constitute a typical disturbance are taken to be rotations and shears, in line with previous work. The spine and fan of the Null Point (the field lines which asymptotically approach or recede from the Null) are subjected to such rotational and shear perturbations, using three-dimensional magnetohydrodynamic simulations. It is found that rotations of the fan plane and about the spine lead to current sheets which are spatially diffuse in at least one direction and form in the locations of the spine and fan. However, shearing perturbations lead to 3-D-localized current sheets focused at the Null Point itself. In addition, rotations are associated with a growth of current parallel to the spine, driving rotational flows and a type of rotational reconnection. Shears, on the other hand, cause a current through the Null which is parallel to the fan plane and are associated with stagnation-type flows and field line reconnection across both the spine and fan. The importance of the parallel electric field, and its meaning as a reconnection rate, are discussed.
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current amplification and magnetic reconnection at a three dimensional Null Point physical characteristics
Journal of Geophysical Research, 2007Co-Authors: David Pontin, Klaus GalsgaardAbstract:[1] The behavior of magnetic perturbations of an initially potential three-dimensional equilibrium magnetic Null Point is investigated. The basic components which constitute a typical disturbance are taken to be rotations and shears, in line with previous work. The spine and fan of the Null Point (the field lines which asymptotically approach or recede from the Null) are subjected to such rotational and shear perturbations, using three-dimensional magnetohydrodynamic simulations. It is found that rotations of the fan plane and about the spine lead to current sheets which are spatially diffuse in at least one direction and form in the locations of the spine and fan. However, shearing perturbations lead to 3-D-localized current sheets focused at the Null Point itself. In addition, rotations are associated with a growth of current parallel to the spine, driving rotational flows and a type of rotational reconnection. Shears, on the other hand, cause a current through the Null which is parallel to the fan plane and are associated with stagnation-type flows and field line reconnection across both the spine and fan. The importance of the parallel electric field, and its meaning as a reconnection rate, are discussed.
