�ݺ�ߣshows by User: iomsn

�ݺ�ߣshows by User: iomsn / http://www.slideshare.net/images/logo.gif �ݺ�ߣshows by User: iomsn / Mon, 30 Sep 2024 14:26:05 GMT �ݺ�ߣShare feed for �ݺ�ߣshows by User: iomsn Adaptive Multiphysics Simulations Coupled in Trixi.jl /slideshow/adaptive-multiphysics-simulations-coupled-in-trixi-jl/272107642 koenigswinter24-240930142605-9bd27335
Using Trixi.jl we present an implementation for adaptive multiphysics coupling. The coupling is done via the exchange of boundary values and converter functions. We can then freely prescribe conditions for which our sub-domains change, if needed by the physics.]]>
Using Trixi.jl we present an implementation for adaptive multiphysics coupling. The coupling is done via the exchange of boundary values and converter functions. We can then freely prescribe conditions for which our sub-domains change, if needed by the physics.]]> Mon, 30 Sep 2024 14:26:05 GMT /slideshow/adaptive-multiphysics-simulations-coupled-in-trixi-jl/272107642 iomsn@slideshare.net(iomsn) Adaptive Multiphysics Simulations Coupled in Trixi.jl iomsn Using Trixi.jl we present an implementation for adaptive multiphysics coupling. The coupling is done via the exchange of boundary values and converter functions. We can then freely prescribe conditions for which our sub-domains change, if needed by the physics. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/koenigswinter24-240930142605-9bd27335-thumbnail.jpg?width=120&height=120&fit=bounds" /> Using Trixi.jl we present an implementation for adaptive multiphysics coupling. The coupling is done via the exchange of boundary values and converter functions. We can then freely prescribe conditions for which our sub-domains change, if needed by the physics.

Adaptive Multiphysics Simulations Coupled in Trixi.jl from Simon Candelaresi

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0 Adaptively coupled multiphysics simulations with Trixi.jl /slideshow/adaptively-coupled-multiphysics-simulations-with-trixi-jl/270437630 zurich24-240723134805-79474c9d
We extended the capabilities of the numerical simulation framework Trixi.jl to be able to simulate adaptively coupled multiphysics systems. Coupling is performed through the boundary values of the systems where the coupling functions can be freely defined, depending on the physical nature of the interface. This allows us to couple any pair of systems, like Navier-Stokes equations with magnetohydrodynamic equations. This is particularly useful for hierarchical systems found in e.g. Astrophysics where we can have a complex model for a small part of the domain and a simplified model on a larger part. This can greatly reduce the computational cost and decrease the computational time. To account for dynamic changes in the physics that need to be solved at any given point in space, we support adaptively coupled domains. The criteria for changing the domain boundaries can be freely defined and tailored to the problem. One application is the propagation of magnetic fields in space where we solve the magnetohydrodynamic equations only for the part of the domain with a significant magnetic field.]]>
We extended the capabilities of the numerical simulation framework Trixi.jl to be able to simulate adaptively coupled multiphysics systems. Coupling is performed through the boundary values of the systems where the coupling functions can be freely defined, depending on the physical nature of the interface. This allows us to couple any pair of systems, like Navier-Stokes equations with magnetohydrodynamic equations. This is particularly useful for hierarchical systems found in e.g. Astrophysics where we can have a complex model for a small part of the domain and a simplified model on a larger part. This can greatly reduce the computational cost and decrease the computational time. To account for dynamic changes in the physics that need to be solved at any given point in space, we support adaptively coupled domains. The criteria for changing the domain boundaries can be freely defined and tailored to the problem. One application is the propagation of magnetic fields in space where we solve the magnetohydrodynamic equations only for the part of the domain with a significant magnetic field.]]> Tue, 23 Jul 2024 13:48:05 GMT /slideshow/adaptively-coupled-multiphysics-simulations-with-trixi-jl/270437630 iomsn@slideshare.net(iomsn) Adaptively coupled multiphysics simulations with Trixi.jl iomsn We extended the capabilities of the numerical simulation framework Trixi.jl to be able to simulate adaptively coupled multiphysics systems. Coupling is performed through the boundary values of the systems where the coupling functions can be freely defined, depending on the physical nature of the interface. This allows us to couple any pair of systems, like Navier-Stokes equations with magnetohydrodynamic equations. This is particularly useful for hierarchical systems found in e.g. Astrophysics where we can have a complex model for a small part of the domain and a simplified model on a larger part. This can greatly reduce the computational cost and decrease the computational time. To account for dynamic changes in the physics that need to be solved at any given point in space, we support adaptively coupled domains. The criteria for changing the domain boundaries can be freely defined and tailored to the problem. One application is the propagation of magnetic fields in space where we solve the magnetohydrodynamic equations only for the part of the domain with a significant magnetic field. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/zurich24-240723134805-79474c9d-thumbnail.jpg?width=120&height=120&fit=bounds" /> We extended the capabilities of the numerical simulation framework Trixi.jl to be able to simulate adaptively coupled multiphysics systems. Coupling is performed through the boundary values of the systems where the coupling functions can be freely defined, depending on the physical nature of the interface. This allows us to couple any pair of systems, like Navier-Stokes equations with magnetohydrodynamic equations. This is particularly useful for hierarchical systems found in e.g. Astrophysics where we can have a complex model for a small part of the domain and a simplified model on a larger part. This can greatly reduce the computational cost and decrease the computational time. To account for dynamic changes in the physics that need to be solved at any given point in space, we support adaptively coupled domains. The criteria for changing the domain boundaries can be freely defined and tailored to the problem. One application is the propagation of magnetic fields in space where we solve the magnetohydrodynamic equations only for the part of the domain with a significant magnetic field.

Adaptively coupled multiphysics simulations with Trixi.jl from Simon Candelaresi

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0 Twisted magnetic knots and links and their current alignment /slideshow/twisted-magnetic-knots-and-links-and-their-current-alignment/270434595 newcastle24-240723120022-1e37879c
In magnetohydrodynamics, astrophysics and plasma physics, the most used quantifier of the magnetic field line topology is the magnetic helicity. We know that its presence restricts the dynamics of the fluid which would not be the case for a non-helical magnetic field of similar energy. Various magnetic field geometries contribute to the magnetic helicity content, such as twisting, knotting, braiding and linking. Here I will present recent progress on relaxing magnetic field and their dynamics in plasmas, including work on twisted structures. The latter show a strong helicity creation and annihilation that can only be explained by taking into account the alignment of the magnetic field and the electric current density, which has implications on our understanding on the topology of large-scale magnetic structures.]]>
In magnetohydrodynamics, astrophysics and plasma physics, the most used quantifier of the magnetic field line topology is the magnetic helicity. We know that its presence restricts the dynamics of the fluid which would not be the case for a non-helical magnetic field of similar energy. Various magnetic field geometries contribute to the magnetic helicity content, such as twisting, knotting, braiding and linking. Here I will present recent progress on relaxing magnetic field and their dynamics in plasmas, including work on twisted structures. The latter show a strong helicity creation and annihilation that can only be explained by taking into account the alignment of the magnetic field and the electric current density, which has implications on our understanding on the topology of large-scale magnetic structures.]]> Tue, 23 Jul 2024 12:00:22 GMT /slideshow/twisted-magnetic-knots-and-links-and-their-current-alignment/270434595 iomsn@slideshare.net(iomsn) Twisted magnetic knots and links and their current alignment iomsn In magnetohydrodynamics, astrophysics and plasma physics, the most used quantifier of the magnetic field line topology is the magnetic helicity. We know that its presence restricts the dynamics of the fluid which would not be the case for a non-helical magnetic field of similar energy. Various magnetic field geometries contribute to the magnetic helicity content, such as twisting, knotting, braiding and linking. Here I will present recent progress on relaxing magnetic field and their dynamics in plasmas, including work on twisted structures. The latter show a strong helicity creation and annihilation that can only be explained by taking into account the alignment of the magnetic field and the electric current density, which has implications on our understanding on the topology of large-scale magnetic structures. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/newcastle24-240723120022-1e37879c-thumbnail.jpg?width=120&height=120&fit=bounds" /> In magnetohydrodynamics, astrophysics and plasma physics, the most used quantifier of the magnetic field line topology is the magnetic helicity. We know that its presence restricts the dynamics of the fluid which would not be the case for a non-helical magnetic field of similar energy. Various magnetic field geometries contribute to the magnetic helicity content, such as twisting, knotting, braiding and linking. Here I will present recent progress on relaxing magnetic field and their dynamics in plasmas, including work on twisted structures. The latter show a strong helicity creation and annihilation that can only be explained by taking into account the alignment of the magnetic field and the electric current density, which has implications on our understanding on the topology of large-scale magnetic structures.

Twisted magnetic knots and links and their current alignment from Simon Candelaresi

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0 Methods for Quantifying Magnetic Field Topology /slideshow/methods-for-quantifying-magnetic-field-topology/270434492 glasgow24-240723115629-a7820030
For the dynamics of a magnetised plasma, the magnetic field line topology is an important factor. Tangled, linked or knotted fields are not easily broken apart without any violent reconnection events, while topologically trivial fields freely and quickly relax to a force-free state. Magnetic helicity is a long established quantifier of the field line topology. It can be easily used for turbulent and non-turbulent systems. Its presence has been shown to restrict the energy conversion rate from magnetic to kinetic energy. The field-line magnetic helicity is related to the magnetic helicity and can be applied to cases where there is a dominant magnetic field, while being of less use in fully developed turbulence. This is particularly useful for fusion plasmas. The two quadratic helicities are somewhat of an underappreciated pair of helicity quantifiers. While they are ideal invariants, in practical cases they can vanish quickly during reconnection events. Lastly, I am going to show how we can use knot invariants to put numbers on the topology of the field lines.]]>
For the dynamics of a magnetised plasma, the magnetic field line topology is an important factor. Tangled, linked or knotted fields are not easily broken apart without any violent reconnection events, while topologically trivial fields freely and quickly relax to a force-free state. Magnetic helicity is a long established quantifier of the field line topology. It can be easily used for turbulent and non-turbulent systems. Its presence has been shown to restrict the energy conversion rate from magnetic to kinetic energy. The field-line magnetic helicity is related to the magnetic helicity and can be applied to cases where there is a dominant magnetic field, while being of less use in fully developed turbulence. This is particularly useful for fusion plasmas. The two quadratic helicities are somewhat of an underappreciated pair of helicity quantifiers. While they are ideal invariants, in practical cases they can vanish quickly during reconnection events. Lastly, I am going to show how we can use knot invariants to put numbers on the topology of the field lines.]]> Tue, 23 Jul 2024 11:56:29 GMT /slideshow/methods-for-quantifying-magnetic-field-topology/270434492 iomsn@slideshare.net(iomsn) Methods for Quantifying Magnetic Field Topology iomsn For the dynamics of a magnetised plasma, the magnetic field line topology is an important factor. Tangled, linked or knotted fields are not easily broken apart without any violent reconnection events, while topologically trivial fields freely and quickly relax to a force-free state. Magnetic helicity is a long established quantifier of the field line topology. It can be easily used for turbulent and non-turbulent systems. Its presence has been shown to restrict the energy conversion rate from magnetic to kinetic energy. The field-line magnetic helicity is related to the magnetic helicity and can be applied to cases where there is a dominant magnetic field, while being of less use in fully developed turbulence. This is particularly useful for fusion plasmas. The two quadratic helicities are somewhat of an underappreciated pair of helicity quantifiers. While they are ideal invariants, in practical cases they can vanish quickly during reconnection events. Lastly, I am going to show how we can use knot invariants to put numbers on the topology of the field lines. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/glasgow24-240723115629-a7820030-thumbnail.jpg?width=120&height=120&fit=bounds" /> For the dynamics of a magnetised plasma, the magnetic field line topology is an important factor. Tangled, linked or knotted fields are not easily broken apart without any violent reconnection events, while topologically trivial fields freely and quickly relax to a force-free state. Magnetic helicity is a long established quantifier of the field line topology. It can be easily used for turbulent and non-turbulent systems. Its presence has been shown to restrict the energy conversion rate from magnetic to kinetic energy. The field-line magnetic helicity is related to the magnetic helicity and can be applied to cases where there is a dominant magnetic field, while being of less use in fully developed turbulence. This is particularly useful for fusion plasmas. The two quadratic helicities are somewhat of an underappreciated pair of helicity quantifiers. While they are ideal invariants, in practical cases they can vanish quickly during reconnection events. Lastly, I am going to show how we can use knot invariants to put numbers on the topology of the field lines.

Methods for Quantifying Magnetic Field Topology from Simon Candelaresi

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0 Numerical Wave Damping in the Pencil Code /slideshow/numerical-wave-damping-in-the-pencil-code/262160753 pcum22-231013163708-4b6730d6
Eularian numerical methods introduce a numerical error that can lead to energy dissipation. The exact form of this dissipation can be very complex and depends on the spatial and temporal resolution. For the simple linear wave we perform numerical experiments and determine the numerical viscosity and diffusion coefficient.]]>
Eularian numerical methods introduce a numerical error that can lead to energy dissipation. The exact form of this dissipation can be very complex and depends on the spatial and temporal resolution. For the simple linear wave we perform numerical experiments and determine the numerical viscosity and diffusion coefficient.]]> Fri, 13 Oct 2023 16:37:08 GMT /slideshow/numerical-wave-damping-in-the-pencil-code/262160753 iomsn@slideshare.net(iomsn) Numerical Wave Damping in the Pencil Code iomsn Eularian numerical methods introduce a numerical error that can lead to energy dissipation. The exact form of this dissipation can be very complex and depends on the spatial and temporal resolution. For the simple linear wave we perform numerical experiments and determine the numerical viscosity and diffusion coefficient. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/pcum22-231013163708-4b6730d6-thumbnail.jpg?width=120&height=120&fit=bounds" /> Eularian numerical methods introduce a numerical error that can lead to energy dissipation. The exact form of this dissipation can be very complex and depends on the spatial and temporal resolution. For the simple linear wave we perform numerical experiments and determine the numerical viscosity and diffusion coefficient.

Numerical Wave Damping in the Pencil Code from Simon Candelaresi

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0 Polynomial knot invariants in the dynamics of braided magnetic fields /slideshow/polynomial-knot-invariants-in-the-dynamics-of-braided-magnetic-fields/262159876 nam22-231013161816-3de683c4
We model topologically complex solar magnetic fields in the form of magnetic braids and study the evolution of their topology quantified in terms of knot polynomials. As it is not possible to define a single knot polynomial for a complex and volume filling magnetic field, even in the shape of a simple braid, we compute the polynomials for an ensemble of magnetic streamlines, which gives us a distribution. As the magnetic field relaxes and simplifies over time, we observe a distinct change in the distribution from a high probability of complex polynomials to a larger probability of simpler ones. ]]>
We model topologically complex solar magnetic fields in the form of magnetic braids and study the evolution of their topology quantified in terms of knot polynomials. As it is not possible to define a single knot polynomial for a complex and volume filling magnetic field, even in the shape of a simple braid, we compute the polynomials for an ensemble of magnetic streamlines, which gives us a distribution. As the magnetic field relaxes and simplifies over time, we observe a distinct change in the distribution from a high probability of complex polynomials to a larger probability of simpler ones. ]]> Fri, 13 Oct 2023 16:18:16 GMT /slideshow/polynomial-knot-invariants-in-the-dynamics-of-braided-magnetic-fields/262159876 iomsn@slideshare.net(iomsn) Polynomial knot invariants in the dynamics of braided magnetic fields iomsn We model topologically complex solar magnetic fields in the form of magnetic braids and study the evolution of their topology quantified in terms of knot polynomials. As it is not possible to define a single knot polynomial for a complex and volume filling magnetic field, even in the shape of a simple braid, we compute the polynomials for an ensemble of magnetic streamlines, which gives us a distribution. As the magnetic field relaxes and simplifies over time, we observe a distinct change in the distribution from a high probability of complex polynomials to a larger probability of simpler ones. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/nam22-231013161816-3de683c4-thumbnail.jpg?width=120&height=120&fit=bounds" /> We model topologically complex solar magnetic fields in the form of magnetic braids and study the evolution of their topology quantified in terms of knot polynomials. As it is not possible to define a single knot polynomial for a complex and volume filling magnetic field, even in the shape of a simple braid, we compute the polynomials for an ensemble of magnetic streamlines, which gives us a distribution. As the magnetic field relaxes and simplifies over time, we observe a distinct change in the distribution from a high probability of complex polynomials to a larger probability of simpler ones.

Polynomial knot invariants in the dynamics of braided magnetic fields from Simon Candelaresi

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0 Twist and Current Alignment within non-trivial Magnetic Field Topologies /slideshow/twist-and-current-alignment-within-nontrivial-magnetic-field-topologies/262159553 dundee22-231013161211-cf1a8581
In magnetohydrodynamics, astrophysics and plasma physics, the most used quantifier of the magnetic field line topology is the magnetic helicity. We know that its presence restricts the dynamics of the fluid which would not be the case for a non-helical magnetic field of similar energy. Various magnetic field geometries contribute to the magnetic helicity content, such as twisting, knotting, braiding and linking. Here I will present the past and recent progress on relaxing magnetic field and their dynamics in plasmas, including unpublished work on twisted structures. The latter show a strong helicity creation and annihilation that can only be explained by taking into account the alignment of the magnetic field and the electric current density, which has implications on our images on large-scale magnetic structures.]]>
In magnetohydrodynamics, astrophysics and plasma physics, the most used quantifier of the magnetic field line topology is the magnetic helicity. We know that its presence restricts the dynamics of the fluid which would not be the case for a non-helical magnetic field of similar energy. Various magnetic field geometries contribute to the magnetic helicity content, such as twisting, knotting, braiding and linking. Here I will present the past and recent progress on relaxing magnetic field and their dynamics in plasmas, including unpublished work on twisted structures. The latter show a strong helicity creation and annihilation that can only be explained by taking into account the alignment of the magnetic field and the electric current density, which has implications on our images on large-scale magnetic structures.]]> Fri, 13 Oct 2023 16:12:11 GMT /slideshow/twist-and-current-alignment-within-nontrivial-magnetic-field-topologies/262159553 iomsn@slideshare.net(iomsn) Twist and Current Alignment within non-trivial Magnetic Field Topologies iomsn In magnetohydrodynamics, astrophysics and plasma physics, the most used quantifier of the magnetic field line topology is the magnetic helicity. We know that its presence restricts the dynamics of the fluid which would not be the case for a non-helical magnetic field of similar energy. Various magnetic field geometries contribute to the magnetic helicity content, such as twisting, knotting, braiding and linking. Here I will present the past and recent progress on relaxing magnetic field and their dynamics in plasmas, including unpublished work on twisted structures. The latter show a strong helicity creation and annihilation that can only be explained by taking into account the alignment of the magnetic field and the electric current density, which has implications on our images on large-scale magnetic structures. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/dundee22-231013161211-cf1a8581-thumbnail.jpg?width=120&height=120&fit=bounds" /> In magnetohydrodynamics, astrophysics and plasma physics, the most used quantifier of the magnetic field line topology is the magnetic helicity. We know that its presence restricts the dynamics of the fluid which would not be the case for a non-helical magnetic field of similar energy. Various magnetic field geometries contribute to the magnetic helicity content, such as twisting, knotting, braiding and linking. Here I will present the past and recent progress on relaxing magnetic field and their dynamics in plasmas, including unpublished work on twisted structures. The latter show a strong helicity creation and annihilation that can only be explained by taking into account the alignment of the magnetic field and the electric current density, which has implications on our images on large-scale magnetic structures.

Twist and Current Alignment within non-trivial Magnetic Field Topologies from Simon Candelaresi

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0 Stabilizing Effect of Magnetic Helicity on Magnetic Cavities in the Intergalactic Medium /slideshow/stabilizing-effect-of-magnetic-helicity-on-magnetic-cavities-in-the-intergalactic-medium/262158272 glasgow21b-231013155340-421a76ba
Intergalactic bubbles have been observed to live up to 100,00,00 years. Since they rise it is expected that the Kelvin-Helmholtz instability should disrupt them after only a few million years. Here we show in numerical simulations that a helical magnetic field contained in the bubbles can stabilize them long enough to explain the observations. With the right amount of magnetic helicity there is no need for a large amount of magnetic energy.]]>
Intergalactic bubbles have been observed to live up to 100,00,00 years. Since they rise it is expected that the Kelvin-Helmholtz instability should disrupt them after only a few million years. Here we show in numerical simulations that a helical magnetic field contained in the bubbles can stabilize them long enough to explain the observations. With the right amount of magnetic helicity there is no need for a large amount of magnetic energy.]]> Fri, 13 Oct 2023 15:53:40 GMT /slideshow/stabilizing-effect-of-magnetic-helicity-on-magnetic-cavities-in-the-intergalactic-medium/262158272 iomsn@slideshare.net(iomsn) Stabilizing Effect of Magnetic Helicity on Magnetic Cavities in the Intergalactic Medium iomsn Intergalactic bubbles have been observed to live up to 100,00,00 years. Since they rise it is expected that the Kelvin-Helmholtz instability should disrupt them after only a few million years. Here we show in numerical simulations that a helical magnetic field contained in the bubbles can stabilize them long enough to explain the observations. With the right amount of magnetic helicity there is no need for a large amount of magnetic energy. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/glasgow21b-231013155340-421a76ba-thumbnail.jpg?width=120&height=120&fit=bounds" /> Intergalactic bubbles have been observed to live up to 100,00,00 years. Since they rise it is expected that the Kelvin-Helmholtz instability should disrupt them after only a few million years. Here we show in numerical simulations that a helical magnetic field contained in the bubbles can stabilize them long enough to explain the observations. With the right amount of magnetic helicity there is no need for a large amount of magnetic energy.

Stabilizing Effect of Magnetic Helicity on Magnetic Cavities in the Intergalactic Medium from Simon Candelaresi

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0 Numerical Viscosity and Diffusion in Finite Difference Eulerian Codes /slideshow/numerical-viscosity-and-diffusion-in-finite-difference-eulerian-codes/250601676 pcum21-211106150732
Numerical discretizations of partial differential equations, like Navier-Stokes and magnetohydrodynamics, using fixed grid Eulerian methods lead to numerical viscosity, resistivity and dissipation. This is manifested in acoustic and Alfvenic wave damping. Here we show how to derive such dissipation from the truncation error of the numerical method.]]>
Numerical discretizations of partial differential equations, like Navier-Stokes and magnetohydrodynamics, using fixed grid Eulerian methods lead to numerical viscosity, resistivity and dissipation. This is manifested in acoustic and Alfvenic wave damping. Here we show how to derive such dissipation from the truncation error of the numerical method.]]> Sat, 06 Nov 2021 15:07:32 GMT /slideshow/numerical-viscosity-and-diffusion-in-finite-difference-eulerian-codes/250601676 iomsn@slideshare.net(iomsn) Numerical Viscosity and Diffusion in Finite Difference Eulerian Codes iomsn Numerical discretizations of partial differential equations, like Navier-Stokes and magnetohydrodynamics, using fixed grid Eulerian methods lead to numerical viscosity, resistivity and dissipation. This is manifested in acoustic and Alfvenic wave damping. Here we show how to derive such dissipation from the truncation error of the numerical method. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/pcum21-211106150732-thumbnail.jpg?width=120&height=120&fit=bounds" /> Numerical discretizations of partial differential equations, like Navier-Stokes and magnetohydrodynamics, using fixed grid Eulerian methods lead to numerical viscosity, resistivity and dissipation. This is manifested in acoustic and Alfvenic wave damping. Here we show how to derive such dissipation from the truncation error of the numerical method.

Numerical Viscosity and Diffusion in Finite Difference Eulerian Codes from Simon Candelaresi

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0 Magnetic Helicity in Periodic Domains /iomsn/helicity20 helicity20-211106145711
The magnetic vector potential does not exist in double and triply periodic domains when the net magnetic flux through a periodic axis is non-zero. We show case some contradiction in such domains for the magnetic helicity.]]>
The magnetic vector potential does not exist in double and triply periodic domains when the net magnetic flux through a periodic axis is non-zero. We show case some contradiction in such domains for the magnetic helicity.]]> Sat, 06 Nov 2021 14:57:10 GMT /iomsn/helicity20 iomsn@slideshare.net(iomsn) Magnetic Helicity in Periodic Domains iomsn The magnetic vector potential does not exist in double and triply periodic domains when the net magnetic flux through a periodic axis is non-zero. We show case some contradiction in such domains for the magnetic helicity. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/helicity20-211106145711-thumbnail.jpg?width=120&height=120&fit=bounds" /> The magnetic vector potential does not exist in double and triply periodic domains when the net magnetic flux through a periodic axis is non-zero. We show case some contradiction in such domains for the magnetic helicity.

Magnetic Helicity in Periodic Domains from Simon Candelaresi

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0 Vortex Reconnection and the Role of Topology /slideshow/vortex-reconnection-and-the-role-of-topology/249368563 ukmhd21-210615141326
We perform numerical experiments of relaxing and reconnecting vortex braids. While these braids have no net kinetic helicity, they are topologically non-trivial. Similar experiments with magnetic braids in MHD have shown a non-trivial relaxation behavior that resulted in two distinct twisted flux tubes. Here we observe the same separation behavior. Furthermore, we show analytically and experimentally that the presence of unsigned kinetic helicity poses a lower bound for the enstrophy of the system, similar to the realizability condition in MHD. Lastly, even the kinetic energy appears limited from below by the unsigned helicity, although we do not have an analytical explanation for this.]]>
We perform numerical experiments of relaxing and reconnecting vortex braids. While these braids have no net kinetic helicity, they are topologically non-trivial. Similar experiments with magnetic braids in MHD have shown a non-trivial relaxation behavior that resulted in two distinct twisted flux tubes. Here we observe the same separation behavior. Furthermore, we show analytically and experimentally that the presence of unsigned kinetic helicity poses a lower bound for the enstrophy of the system, similar to the realizability condition in MHD. Lastly, even the kinetic energy appears limited from below by the unsigned helicity, although we do not have an analytical explanation for this.]]> Tue, 15 Jun 2021 14:13:26 GMT /slideshow/vortex-reconnection-and-the-role-of-topology/249368563 iomsn@slideshare.net(iomsn) Vortex Reconnection and the Role of Topology iomsn We perform numerical experiments of relaxing and reconnecting vortex braids. While these braids have no net kinetic helicity, they are topologically non-trivial. Similar experiments with magnetic braids in MHD have shown a non-trivial relaxation behavior that resulted in two distinct twisted flux tubes. Here we observe the same separation behavior. Furthermore, we show analytically and experimentally that the presence of unsigned kinetic helicity poses a lower bound for the enstrophy of the system, similar to the realizability condition in MHD. Lastly, even the kinetic energy appears limited from below by the unsigned helicity, although we do not have an analytical explanation for this. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/ukmhd21-210615141326-thumbnail.jpg?width=120&height=120&fit=bounds" /> We perform numerical experiments of relaxing and reconnecting vortex braids. While these braids have no net kinetic helicity, they are topologically non-trivial. Similar experiments with magnetic braids in MHD have shown a non-trivial relaxation behavior that resulted in two distinct twisted flux tubes. Here we observe the same separation behavior. Furthermore, we show analytically and experimentally that the presence of unsigned kinetic helicity poses a lower bound for the enstrophy of the system, similar to the realizability condition in MHD. Lastly, even the kinetic energy appears limited from below by the unsigned helicity, although we do not have an analytical explanation for this.

Vortex Reconnection and the Role of Topology from Simon Candelaresi

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0 Stabilizing Effect of Magnetic Helicity on Magnetic Cavities in the Intergalactic Medium /slideshow/quy-nhon20/229023514 quynhon20-200224125319
We investigate the effect of magnetic helicity for the stability of buoyant magnetic cavities as found in the intergalactic medium. In these cavities we insert helical magnetic fields and test whether or not helicity can increase their stability to shredding through the Kelvin-Helmholtz instability and with that their life time. This is compared to the case of an external magnetic field which is known to reduce the growth rate of the Kelvin-Helmholtz instability. By comparing a low and high helicity configuration with the same magnetic energy we find that an internal helical magnetic field stabilizes the cavity. This effect increases as we increase the helicity content. Stabilizing the cavity with an external magnetic field requires a significantly stronger field.]]>
We investigate the effect of magnetic helicity for the stability of buoyant magnetic cavities as found in the intergalactic medium. In these cavities we insert helical magnetic fields and test whether or not helicity can increase their stability to shredding through the Kelvin-Helmholtz instability and with that their life time. This is compared to the case of an external magnetic field which is known to reduce the growth rate of the Kelvin-Helmholtz instability. By comparing a low and high helicity configuration with the same magnetic energy we find that an internal helical magnetic field stabilizes the cavity. This effect increases as we increase the helicity content. Stabilizing the cavity with an external magnetic field requires a significantly stronger field.]]> Mon, 24 Feb 2020 12:53:19 GMT /slideshow/quy-nhon20/229023514 iomsn@slideshare.net(iomsn) Stabilizing Effect of Magnetic Helicity on Magnetic Cavities in the Intergalactic Medium iomsn We investigate the effect of magnetic helicity for the stability of buoyant magnetic cavities as found in the intergalactic medium. In these cavities we insert helical magnetic fields and test whether or not helicity can increase their stability to shredding through the Kelvin-Helmholtz instability and with that their life time. This is compared to the case of an external magnetic field which is known to reduce the growth rate of the Kelvin-Helmholtz instability. By comparing a low and high helicity configuration with the same magnetic energy we find that an internal helical magnetic field stabilizes the cavity. This effect increases as we increase the helicity content. Stabilizing the cavity with an external magnetic field requires a significantly stronger field. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/quynhon20-200224125319-thumbnail.jpg?width=120&height=120&fit=bounds" /> We investigate the effect of magnetic helicity for the stability of buoyant magnetic cavities as found in the intergalactic medium. In these cavities we insert helical magnetic fields and test whether or not helicity can increase their stability to shredding through the Kelvin-Helmholtz instability and with that their life time. This is compared to the case of an external magnetic field which is known to reduce the growth rate of the Kelvin-Helmholtz instability. By comparing a low and high helicity configuration with the same magnetic energy we find that an internal helical magnetic field stabilizes the cavity. This effect increases as we increase the helicity content. Stabilizing the cavity with an external magnetic field requires a significantly stronger field.

Stabilizing Effect of Magnetic Helicity on Magnetic Cavities in the Intergalactic Medium from Simon Candelaresi

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0 Estimating the rate of field line braiding in the solar corona by photospheric flows. /slideshow/estimating-the-rate-of-field-line-braiding-in-the-solar-corona-by-photospheric-flows/95223002 standrews18-180427102908
We study the effect of photospheric motions on the braiding and tangling of coronal magnetic fields. For that we make use of horizontal velocity data that was extracted from magnetograms using the local correlation tracking technique. By tracing trajectories we are able to compute the injected field line winding and finite time topological entropy. Both are quantitative measures of tangling that can be compared to the blinking vortex motion as a benchmark. Here we show that through photospheric motions there can indeed be substantial injection of winding into the system that can potentially be transfered into magnetic loops. This can potentially lead to thin magnetic structures that are potential sites of magnetic energy loss. ]]>
We study the effect of photospheric motions on the braiding and tangling of coronal magnetic fields. For that we make use of horizontal velocity data that was extracted from magnetograms using the local correlation tracking technique. By tracing trajectories we are able to compute the injected field line winding and finite time topological entropy. Both are quantitative measures of tangling that can be compared to the blinking vortex motion as a benchmark. Here we show that through photospheric motions there can indeed be substantial injection of winding into the system that can potentially be transfered into magnetic loops. This can potentially lead to thin magnetic structures that are potential sites of magnetic energy loss. ]]> Fri, 27 Apr 2018 10:29:08 GMT /slideshow/estimating-the-rate-of-field-line-braiding-in-the-solar-corona-by-photospheric-flows/95223002 iomsn@slideshare.net(iomsn) Estimating the rate of field line braiding in the solar corona by photospheric flows. iomsn We study the effect of photospheric motions on the braiding and tangling of coronal magnetic fields. For that we make use of horizontal velocity data that was extracted from magnetograms using the local correlation tracking technique. By tracing trajectories we are able to compute the injected field line winding and finite time topological entropy. Both are quantitative measures of tangling that can be compared to the blinking vortex motion as a benchmark. Here we show that through photospheric motions there can indeed be substantial injection of winding into the system that can potentially be transfered into magnetic loops. This can potentially lead to thin magnetic structures that are potential sites of magnetic energy loss. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/standrews18-180427102908-thumbnail.jpg?width=120&height=120&fit=bounds" /> We study the effect of photospheric motions on the braiding and tangling of coronal magnetic fields. For that we make use of horizontal velocity data that was extracted from magnetograms using the local correlation tracking technique. By tracing trajectories we are able to compute the injected field line winding and finite time topological entropy. Both are quantitative measures of tangling that can be compared to the blinking vortex motion as a benchmark. Here we show that through photospheric motions there can indeed be substantial injection of winding into the system that can potentially be transfered into magnetic loops. This can potentially lead to thin magnetic structures that are potential sites of magnetic energy loss.

Estimating the rate of field line braiding in the solar corona by photospheric flows. from Simon Candelaresi

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0 Topology Conserving Magnetic Field Evolution /slideshow/topology-conserving-magnetic-field-evolution/95222855 tokyo17-180427102714
Magnetic helicity is a conserved quantity under an ideal evolution. Here we present methods for simulating such topology conserving systems. We make use of Lagrangian grids and mimetic differential operators. It is shown that the magnetic field topology is exactly conserved. This method is then used to study equilibria of configurations like the Hopf fibration.]]>
Magnetic helicity is a conserved quantity under an ideal evolution. Here we present methods for simulating such topology conserving systems. We make use of Lagrangian grids and mimetic differential operators. It is shown that the magnetic field topology is exactly conserved. This method is then used to study equilibria of configurations like the Hopf fibration.]]> Fri, 27 Apr 2018 10:27:13 GMT /slideshow/topology-conserving-magnetic-field-evolution/95222855 iomsn@slideshare.net(iomsn) Topology Conserving Magnetic Field Evolution iomsn Magnetic helicity is a conserved quantity under an ideal evolution. Here we present methods for simulating such topology conserving systems. We make use of Lagrangian grids and mimetic differential operators. It is shown that the magnetic field topology is exactly conserved. This method is then used to study equilibria of configurations like the Hopf fibration. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/tokyo17-180427102714-thumbnail.jpg?width=120&height=120&fit=bounds" /> Magnetic helicity is a conserved quantity under an ideal evolution. Here we present methods for simulating such topology conserving systems. We make use of Lagrangian grids and mimetic differential operators. It is shown that the magnetic field topology is exactly conserved. This method is then used to study equilibria of configurations like the Hopf fibration.

Topology Conserving Magnetic Field Evolution from Simon Candelaresi

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0 Magnetic Field Line Tangling and Topological Entropy /slideshow/durham17/75350200 durham17-170424132258
Mixing of two-dimensional flows or three-dimensional magnetic fields is quantified using the finite time topological entropy FTTE. Similar to the finite time Lyapunov exponent it quantifies the amount of mixing of the fluid or chaotic dynamics in the system. Here we present an efficient method on how to compute the FTTE for periodic magnetic fields, like in Tokamaks, or for time periodic two-dimensional flows. Our method is both precise and highly time efficient. To show case the method we apply it to such cases that describe tangled or twisted magnetic fields.]]>
Mixing of two-dimensional flows or three-dimensional magnetic fields is quantified using the finite time topological entropy FTTE. Similar to the finite time Lyapunov exponent it quantifies the amount of mixing of the fluid or chaotic dynamics in the system. Here we present an efficient method on how to compute the FTTE for periodic magnetic fields, like in Tokamaks, or for time periodic two-dimensional flows. Our method is both precise and highly time efficient. To show case the method we apply it to such cases that describe tangled or twisted magnetic fields.]]> Mon, 24 Apr 2017 13:22:58 GMT /slideshow/durham17/75350200 iomsn@slideshare.net(iomsn) Magnetic Field Line Tangling and Topological Entropy iomsn Mixing of two-dimensional flows or three-dimensional magnetic fields is quantified using the finite time topological entropy FTTE. Similar to the finite time Lyapunov exponent it quantifies the amount of mixing of the fluid or chaotic dynamics in the system. Here we present an efficient method on how to compute the FTTE for periodic magnetic fields, like in Tokamaks, or for time periodic two-dimensional flows. Our method is both precise and highly time efficient. To show case the method we apply it to such cases that describe tangled or twisted magnetic fields. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/durham17-170424132258-thumbnail.jpg?width=120&height=120&fit=bounds" /> Mixing of two-dimensional flows or three-dimensional magnetic fields is quantified using the finite time topological entropy FTTE. Similar to the finite time Lyapunov exponent it quantifies the amount of mixing of the fluid or chaotic dynamics in the system. Here we present an efficient method on how to compute the FTTE for periodic magnetic fields, like in Tokamaks, or for time periodic two-dimensional flows. Our method is both precise and highly time efficient. To show case the method we apply it to such cases that describe tangled or twisted magnetic fields.

Magnetic Field Line Tangling and Topological Entropy from Simon Candelaresi

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0 Magnetic field line braiding in the solar atmosphere /slideshow/magnetic-field-line-braiding-in-the-solar-atmosphere/70232748 cartagena16-161217174234
We study the effect of the magnetic field line braiding in the solar atmosphere using topological methods. By measuring the topological entropy of the magnetic field line mapping we show that footpoint motions are capable of inducing highly non-trivial braided structures, which has a fundamental effect on the formation of current layers. Those braids can reach further up in the solar atmosphere, through which energy is transported. Depending on the structure of the field close to the photosphere, such energy transport can be very efficient.]]>
We study the effect of the magnetic field line braiding in the solar atmosphere using topological methods. By measuring the topological entropy of the magnetic field line mapping we show that footpoint motions are capable of inducing highly non-trivial braided structures, which has a fundamental effect on the formation of current layers. Those braids can reach further up in the solar atmosphere, through which energy is transported. Depending on the structure of the field close to the photosphere, such energy transport can be very efficient.]]> Sat, 17 Dec 2016 17:42:34 GMT /slideshow/magnetic-field-line-braiding-in-the-solar-atmosphere/70232748 iomsn@slideshare.net(iomsn) Magnetic field line braiding in the solar atmosphere iomsn We study the effect of the magnetic field line braiding in the solar atmosphere using topological methods. By measuring the topological entropy of the magnetic field line mapping we show that footpoint motions are capable of inducing highly non-trivial braided structures, which has a fundamental effect on the formation of current layers. Those braids can reach further up in the solar atmosphere, through which energy is transported. Depending on the structure of the field close to the photosphere, such energy transport can be very efficient. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/cartagena16-161217174234-thumbnail.jpg?width=120&height=120&fit=bounds" /> We study the effect of the magnetic field line braiding in the solar atmosphere using topological methods. By measuring the topological entropy of the magnetic field line mapping we show that footpoint motions are capable of inducing highly non-trivial braided structures, which has a fundamental effect on the formation of current layers. Those braids can reach further up in the solar atmosphere, through which energy is transported. Depending on the structure of the field close to the photosphere, such energy transport can be very efficient.

Magnetic field line braiding in the solar atmosphere from Simon Candelaresi

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0 Fractional approaches in dielectric broadband spectroscopy /slideshow/berlin08/49802791 berlin08-150624203753-lva1-app6892
A fractional approach is used to describe data from dielectric spectroscopy for several glassy materials. Using composite fractional time evolution propagators a modified law for relaxation in glasses is found that describes the experimental data for broadband dielectric spectroscopy. Properties and solutions of some particular fractional differential equations (fDEQs) are investigated both for rational and irrational order. The laws of Debye, Kohlrausch, Cole-Cole, ColeDavidson and Havriliak-Negam]]>
A fractional approach is used to describe data from dielectric spectroscopy for several glassy materials. Using composite fractional time evolution propagators a modified law for relaxation in glasses is found that describes the experimental data for broadband dielectric spectroscopy. Properties and solutions of some particular fractional differential equations (fDEQs) are investigated both for rational and irrational order. The laws of Debye, Kohlrausch, Cole-Cole, ColeDavidson and Havriliak-Negam]]> Wed, 24 Jun 2015 20:37:53 GMT /slideshow/berlin08/49802791 iomsn@slideshare.net(iomsn) Fractional approaches in dielectric broadband spectroscopy iomsn A fractional approach is used to describe data from dielectric spectroscopy for several glassy materials. Using composite fractional time evolution propagators a modified law for relaxation in glasses is found that describes the experimental data for broadband dielectric spectroscopy. Properties and solutions of some particular fractional differential equations (fDEQs) are investigated both for rational and irrational order. The laws of Debye, Kohlrausch, Cole-Cole, ColeDavidson and Havriliak-Negam <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/berlin08-150624203753-lva1-app6892-thumbnail.jpg?width=120&height=120&fit=bounds" /> A fractional approach is used to describe data from dielectric spectroscopy for several glassy materials. Using composite fractional time evolution propagators a modified law for relaxation in glasses is found that describes the experimental data for broadband dielectric spectroscopy. Properties and solutions of some particular fractional differential equations (fDEQs) are investigated both for rational and irrational order. The laws of Debye, Kohlrausch, Cole-Cole, ColeDavidson and Havriliak-Negam

Fractional approaches in dielectric broadband spectroscopy from Simon Candelaresi

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0 Superflares in G, K and M Type Dwarfs from Kepler Observations /slideshow/warwick15/49793337 warwick15-150624163255-lva1-app6892
We study the occurrence of superflares in G, K and M type dwarfs from lightcurves obtained by the Kepler mission. From that set 380 stars are detected with flares above 10^34 erg with 1690 such events. Various stellar parameters are considered here to find what circumstances are favorable for the occurrence of superflares. With decreasing effective temperature the flaring rate increases, as well as with an increase in the star's rotation rate. Star spots, which are a proxy for the magnetic field strength and dynamo activity, are seen more frequently in flaring stars and cover a larger proportion of the star's. surface. Using Ohmic dissipation as proxy for flare events, we perform simulations for a turbulent dynamo and find an increase of Ohmic dissipation as the dynamo number increases, in line with the observations.]]>
We study the occurrence of superflares in G, K and M type dwarfs from lightcurves obtained by the Kepler mission. From that set 380 stars are detected with flares above 10^34 erg with 1690 such events. Various stellar parameters are considered here to find what circumstances are favorable for the occurrence of superflares. With decreasing effective temperature the flaring rate increases, as well as with an increase in the star's rotation rate. Star spots, which are a proxy for the magnetic field strength and dynamo activity, are seen more frequently in flaring stars and cover a larger proportion of the star's. surface. Using Ohmic dissipation as proxy for flare events, we perform simulations for a turbulent dynamo and find an increase of Ohmic dissipation as the dynamo number increases, in line with the observations.]]> Wed, 24 Jun 2015 16:32:55 GMT /slideshow/warwick15/49793337 iomsn@slideshare.net(iomsn) Superflares in G, K and M Type Dwarfs from Kepler Observations iomsn We study the occurrence of superflares in G, K and M type dwarfs from lightcurves obtained by the Kepler mission. From that set 380 stars are detected with flares above 10^34 erg with 1690 such events. Various stellar parameters are considered here to find what circumstances are favorable for the occurrence of superflares. With decreasing effective temperature the flaring rate increases, as well as with an increase in the star's rotation rate. Star spots, which are a proxy for the magnetic field strength and dynamo activity, are seen more frequently in flaring stars and cover a larger proportion of the star's. surface. Using Ohmic dissipation as proxy for flare events, we perform simulations for a turbulent dynamo and find an increase of Ohmic dissipation as the dynamo number increases, in line with the observations. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/warwick15-150624163255-lva1-app6892-thumbnail.jpg?width=120&height=120&fit=bounds" /> We study the occurrence of superflares in G, K and M type dwarfs from lightcurves obtained by the Kepler mission. From that set 380 stars are detected with flares above 10^34 erg with 1690 such events. Various stellar parameters are considered here to find what circumstances are favorable for the occurrence of superflares. With decreasing effective temperature the flaring rate increases, as well as with an increase in the star's rotation rate. Star spots, which are a proxy for the magnetic field strength and dynamo activity, are seen more frequently in flaring stars and cover a larger proportion of the star's. surface. Using Ohmic dissipation as proxy for flare events, we perform simulations for a turbulent dynamo and find an increase of Ohmic dissipation as the dynamo number increases, in line with the observations.

Superflares in G, K and M Type Dwarfs from Kepler Observations from Simon Candelaresi

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0 Current Formation During Magnetic Field Relaxation /slideshow/current-formation-during-magnetic-field-relaxation/48219788 newcastle15-150516103736-lva1-app6891
Using an ideal Lagrangian relaxation scheme for magnetic fields we investigate the formation of current concentrations for various magnetic field configurations. For sufficiently braided fields Parker (1972) hypothesizes the formation of singular current structures and subsequent reconnection. Here we find that even for highly braided fields current concentrations are well resolved and of finite magnitude. In presence of magnetic nulls, however, we confirm previous results of singular current structures at the nulls.]]>
Using an ideal Lagrangian relaxation scheme for magnetic fields we investigate the formation of current concentrations for various magnetic field configurations. For sufficiently braided fields Parker (1972) hypothesizes the formation of singular current structures and subsequent reconnection. Here we find that even for highly braided fields current concentrations are well resolved and of finite magnitude. In presence of magnetic nulls, however, we confirm previous results of singular current structures at the nulls.]]> Sat, 16 May 2015 10:37:36 GMT /slideshow/current-formation-during-magnetic-field-relaxation/48219788 iomsn@slideshare.net(iomsn) Current Formation During Magnetic Field Relaxation iomsn Using an ideal Lagrangian relaxation scheme for magnetic fields we investigate the formation of current concentrations for various magnetic field configurations. For sufficiently braided fields Parker (1972) hypothesizes the formation of singular current structures and subsequent reconnection. Here we find that even for highly braided fields current concentrations are well resolved and of finite magnitude. In presence of magnetic nulls, however, we confirm previous results of singular current structures at the nulls. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/newcastle15-150516103736-lva1-app6891-thumbnail.jpg?width=120&height=120&fit=bounds" /> Using an ideal Lagrangian relaxation scheme for magnetic fields we investigate the formation of current concentrations for various magnetic field configurations. For sufficiently braided fields Parker (1972) hypothesizes the formation of singular current structures and subsequent reconnection. Here we find that even for highly braided fields current concentrations are well resolved and of finite magnitude. In presence of magnetic nulls, however, we confirm previous results of singular current structures at the nulls.

Current Formation During Magnetic Field Relaxation from Simon Candelaresi

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0 Magnetic Vector Potentials and Helicity in Periodic Domains /slideshow/trondheim15/48219635 trondheim15-150516102943-lva1-app6892
Magnetic helicity is often assumed to be gauge independend in periodic domains. Here I show that for triply periodic domains this is no the case if we allow for gauge fields which are not periodic. Using methods of p-forms from differential geometry it is shown that the magnetic vector potential does not exist for periodic domains with net magnetic flux through the boundaries. This has ramifications for numerical codes which make use of the magnetic vector potential, rather than the magnetic field.]]>
Magnetic helicity is often assumed to be gauge independend in periodic domains. Here I show that for triply periodic domains this is no the case if we allow for gauge fields which are not periodic. Using methods of p-forms from differential geometry it is shown that the magnetic vector potential does not exist for periodic domains with net magnetic flux through the boundaries. This has ramifications for numerical codes which make use of the magnetic vector potential, rather than the magnetic field.]]> Sat, 16 May 2015 10:29:43 GMT /slideshow/trondheim15/48219635 iomsn@slideshare.net(iomsn) Magnetic Vector Potentials and Helicity in Periodic Domains iomsn Magnetic helicity is often assumed to be gauge independend in periodic domains. Here I show that for triply periodic domains this is no the case if we allow for gauge fields which are not periodic. Using methods of p-forms from differential geometry it is shown that the magnetic vector potential does not exist for periodic domains with net magnetic flux through the boundaries. This has ramifications for numerical codes which make use of the magnetic vector potential, rather than the magnetic field. <img style="border:1px solid #C3E6D8;float:right;" alt="" src="https://cdn.slidesharecdn.com/ss_thumbnails/trondheim15-150516102943-lva1-app6892-thumbnail.jpg?width=120&height=120&fit=bounds" /> Magnetic helicity is often assumed to be gauge independend in periodic domains. Here I show that for triply periodic domains this is no the case if we allow for gauge fields which are not periodic. Using methods of p-forms from differential geometry it is shown that the magnetic vector potential does not exist for periodic domains with net magnetic flux through the boundaries. This has ramifications for numerical codes which make use of the magnetic vector potential, rather than the magnetic field.

Magnetic Vector Potentials and Helicity in Periodic Domains from Simon Candelaresi

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0 https://public.slidesharecdn.com/v2/images/profile-picture.png simoncandelaresi.com https://cdn.slidesharecdn.com/ss_thumbnails/koenigswinter24-240930142605-9bd27335-thumbnail.jpg?width=320&height=320&fit=bounds slideshow/adaptive-multiphysics-simulations-coupled-in-trixi-jl/272107642 Adaptive Multiphysics ... https://cdn.slidesharecdn.com/ss_thumbnails/zurich24-240723134805-79474c9d-thumbnail.jpg?width=320&height=320&fit=bounds slideshow/adaptively-coupled-multiphysics-simulations-with-trixi-jl/270437630 Adaptively coupled mul... https://cdn.slidesharecdn.com/ss_thumbnails/newcastle24-240723120022-1e37879c-thumbnail.jpg?width=320&height=320&fit=bounds slideshow/twisted-magnetic-knots-and-links-and-their-current-alignment/270434595 Twisted magnetic knots...