Magnetic Field Line Tangling and Topological Entropy
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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.
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Twist and Current Alignment within non-trivial Magnetic Field Topologies
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 Here I will present the past and recent progress on relaxing magnetic field and their dynamics in plasmas, including unpublished work on twisted structures.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.
Stabilizing Effect of Magnetic Helicity on Magnetic Cavities in the Intergala...
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.
Numerical Viscosity and Diffusion in Finite Difference Eulerian Codes
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.
Magnetic Helicity in Periodic Domains
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.
Vortex Reconnection and the Role of Topology
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.
Stabilizing Effect of Magnetic Helicity on Magnetic Cavities in the Intergala...
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.
Topology Conserving Magnetic Field Evolution
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 Vector Potentials and Helicity in Periodic Domains
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.
Lagrangian Relaxation of Magnetic Fields
Magnetic fields are ubiquitous in the universe and fundamentally determine the dynamics of many astrophysical bodies. Their evolution shows a variety of characteristics like reconnection, forward and inverse cascade and relaxation to lower energy states. wen absence of any external forcing or driving of the system the field is expected relax to a lower energy state with vanishing Lorentz-force. How such a state is reached and how the evolution depends on the initial field topology is under debate.
Using mimetic numerical operators to compute the electric current density we developed a numerical code to study the relaxation of magnetic fields in an ideal environment, i.e. without viscosity or resistivity. Combined with a Lagrangian grid scheme we solve the magneto-frictional equations to study the ideal relaxation of magnetic fields into a force-free state, which is also the minimum energy state. The methods conserve the field line topology and the divergence freeness exactly. Compared to previous approaches the final state is by various measures closer to the expected force-free state and is able to reduce the free magnetic energy to almost zero. Using these tools we present results which contest the validity of the Parker conjecture in solar physics, which claims the formation of singular current sheets during the relaxation of some braided magnetic fields which are bounded within two planes.
How much helicity is needed to drive large-scale dynamos?
Magnetic field generation on scales large compared with the scale of the turbulent eddies is known to be possible via the so-called alpha effect when the turbulence is helical and if the domain is large enough for the alpha effect to dominate over turbulent diffusion. Using three-dimensional turbulence simulations, we show that the energy of the resulting mean magnetic field of the saturated state increases linearly with the product of normalized helicity and the ratio of domain scale to eddy scale, provided this product exceeds a critical value around unity. This implies that large-scale dynamo action commences when the normalized helicity is larger than the inverse scale ratio. Recent findings of a smaller minimal helicity may be due to the onset of small-scale dynamo action at large magnetic Reynolds numbers. The onset of large-scale dynamo action is difficult to establish when the kinetic helicity is small.
Topological restrictions in magnetic field dynamics and reconnection
The dominance of the magnetic helicity as the determining topological invariant in magnetohydrodynamics is revisited for helical and non-helical field configurations. For fields with positive z-components we determine the fixed points of the field line mapping. The sum of the Poincare indices at those fixed points, the fixed pints index, gives rise to further restrictions, not captured by the magnetic helicity alone. Various braided field configurations, which correspond to helical and non-helical knots, are simulated in fully resistive magnetohydrodynamics. We observe an evolution which confirms the importance of the fixed point index as additional restricting quantity. Moreover, a topological flux function, the field line helicity, is computed at the fixed points and monitored during turbulent relaxation. Its rate of change gives a proxy for the magnetic reconnection rate.
Magnetic Helicity Fluxes and their Effect on the Solar Dynamo
Magnetic helicity fluxes in turbulently driven $\alpha^{2}$ dynamos are studied to demonstrate their ability to alleviate catastrophic quenching. A one-dimensional mean-field formalism is used to achieve magnetic Reynolds numbers of $10^{5}$. We study both diffusive magnetic helicity fluxes through the mid-plane as well as those resulting from the recently proposed alternate dynamic quenching formalism. By adding shear we make a parameter scan for the critical values of the shear and forcing parameters for which dynamo action occurs. For this $\alpha\Omega$ dynamo we find that the preferred mode is antisymmetric about the equatorial plane. This is also verified in 3-D direct numerical simulations.
www.nordita.org/~iomsn/
Decay of helical and non-helical magnetic links and knots
The decay characteristics of magnetic fields of the form of interlinked structures and knots depends heavily on the magnetic helicity. However there are cases where other topological invariants may play are role.
www.nordita.org/~iomsn/
Decay of helical and non-helical magnetic knots
We present calculations of the relaxation of magnetic field structures that have the shape of particular knots and links. Those shapes are the IUCAA knot, Borromean rings and the trefoil and higher foil knots. Due to magnetic helicity conservation the decay of magnetic energy is slowed down via the realizability condition. This turns out to be important even when the total magnetic helicity is zero, because local helical structures can be formed without any external forcing.
www.nordita.org/~iomsn/
More from Simon Candelaresi (17)
Polynomial knot invariants in the dynamics of braided magnetic fields
Polynomial knot invariants in the dynamics of braided magnetic fields
Twist and Current Alignment within non-trivial Magnetic Field Topologies
Twist and Current Alignment within non-trivial Magnetic Field Topologies
Stabilizing Effect of Magnetic Helicity on Magnetic Cavities in the Intergala...
Stabilizing Effect of Magnetic Helicity on Magnetic Cavities in the Intergala...
Numerical Viscosity and Diffusion in Finite Difference Eulerian Codes
Numerical Viscosity and Diffusion in Finite Difference Eulerian Codes
Stabilizing Effect of Magnetic Helicity on Magnetic Cavities in the Intergala...
Stabilizing Effect of Magnetic Helicity on Magnetic Cavities in the Intergala...
Magnetic Vector Potentials and Helicity in Periodic Domains
Magnetic Vector Potentials and Helicity in Periodic Domains
How much helicity is needed to drive large-scale dynamos?
How much helicity is needed to drive large-scale dynamos?
Topological restrictions in magnetic field dynamics and reconnection
Topological restrictions in magnetic field dynamics and reconnection
Magnetic helicity transport in the advective gauge family
Magnetic helicity transport in the advective gauge family
Magnetic Helicity Fluxes and their Effect on the Solar Dynamo
Magnetic Helicity Fluxes and their Effect on the Solar Dynamo
Decay of helical and non-helical magnetic links and knots
Decay of helical and non-helical magnetic links and knots
Recently uploaded
Salas, V. (2024) "John of St. Thomas (Poinsot) on the Science of Sacred Theol...
I Introduction
II Subalternation and Theology
III Theology and Dogmatic Declarations
IV The Mixed Principles of Theology
V Virtual Revelation: The Unity of Theology
VI Theology as a Natural Science
VII Theology’s Certitude
VIII Conclusion
Notes
Bibliography
All the contents are fully attributable to the author, Doctor Victor Salas. Should you wish to get this text republished, get in touch with the author or the editorial committee of the Studia Poinsotiana. Insofar as possible, we will be happy to broker your contact.
Unveiling the Energy Potential of Marshmallow Deposits.pdf
Unveiling the Energy Potential of Marshmallow Deposits: A Revolutionary
Breakthrough in Sustainable Energy Science
Orion Air Quality Monitoring Systems - CWS
Professional air quality monitoring systems provide immediate, on-site data for analysis, compliance, and decision-making.
Monitor common gases, weather parameters, particulates.
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3:国家专业人才认证中心颁发入库证书
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Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
Richard's aventures in two entangled wonderlands
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Seminar of U.V. Spectroscopy by SAMIR PANDA
Spectroscopy is a branch of science dealing the study of interaction of electromagnetic radiation with matter.
Ultraviolet-visible spectroscopy refers to absorption spectroscopy or reflect spectroscopy in the UV-VIS spectral region.
Ultraviolet-visible spectroscopy is an analytical method that can measure the amount of light received by the analyte.
(May 29th, 2024) Advancements in Intravital Microscopy- Insights for Preclini...
(May 29th, 2024) Advancements in Intravital Microscopy- Insights for Preclini...Scintica Instrumentation
Intravital microscopy (IVM) is a powerful tool utilized to study cellular behavior over time and space in vivo. Much of our understanding of cell biology has been accomplished using various in vitro and ex vivo methods; however, these studies do not necessarily reflect the natural dynamics of biological processes. Unlike traditional cell culture or fixed tissue imaging, IVM allows for the ultra-fast high-resolution imaging of cellular processes over time and space and were studied in its natural environment. Real-time visualization of biological processes in the context of an intact organism helps maintain physiological relevance and provide insights into the progression of disease, response to treatments or developmental processes.
In this webinar we give an overview of advanced applications of the IVM system in preclinical research. IVIM technology is a provider of all-in-one intravital microscopy systems and solutions optimized for in vivo imaging of live animal models at sub-micron resolution. The system’s unique features and user-friendly software enables researchers to probe fast dynamic biological processes such as immune cell tracking, cell-cell interaction as well as vascularization and tumor metastasis with exceptional detail. This webinar will also give an overview of IVM being utilized in drug development, offering a view into the intricate interaction between drugs/nanoparticles and tissues in vivo and allows for the evaluation of therapeutic intervention in a variety of tissues and organs. This interdisciplinary collaboration continues to drive the advancements of novel therapeutic strategies.
Deep Software Variability and Frictionless Reproducibility
Deep Software Variability and Frictionless ReproducibilityUniversity of Rennes, INSA Rennes, Inria/IRISA, CNRS
The ability to recreate computational results with minimal effort and actionable metrics provides a solid foundation for scientific research and software development. When people can replicate an analysis at the touch of a button using open-source software, open data, and methods to assess and compare proposals, it significantly eases verification of results, engagement with a diverse range of contributors, and progress. However, we have yet to fully achieve this; there are still many sociotechnical frictions.
Inspired by David Donoho's vision, this talk aims to revisit the three crucial pillars of frictionless reproducibility (data sharing, code sharing, and competitive challenges) with the perspective of deep software variability.
Our observation is that multiple layers — hardware, operating systems, third-party libraries, software versions, input data, compile-time options, and parameters — are subject to variability that exacerbates frictions but is also essential for achieving robust, generalizable results and fostering innovation. I will first review the literature, providing evidence of how the complex variability interactions across these layers affect qualitative and quantitative software properties, thereby complicating the reproduction and replication of scientific studies in various fields.
I will then present some software engineering and AI techniques that can support the strategic exploration of variability spaces. These include the use of abstractions and models (e.g., feature models), sampling strategies (e.g., uniform, random), cost-effective measurements (e.g., incremental build of software configurations), and dimensionality reduction methods (e.g., transfer learning, feature selection, software debloating).
I will finally argue that deep variability is both the problem and solution of frictionless reproducibility, calling the software science community to develop new methods and tools to manage variability and foster reproducibility in software systems.
Exposé invité Journées Nationales du GDR GPL 2024
Recently uploaded (20)
Salas, V. (2024) "John of St. Thomas (Poinsot) on the Science of Sacred Theol...
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Lateral Ventricles.pdf very easy good diagrams comprehensive
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Unveiling the Energy Potential of Marshmallow Deposits.pdf
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Deep Software Variability and Frictionless Reproducibility
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Magnetic Field Line Tangling and Topological Entropy
- 1. Magnetic Field Line Tangling and Topological Entropy Simon Candelaresi, David Pontin, Gunnar Hornig
- 2. Magnetic Fields 2 NASA (Thiffeault et al. 2006) Field line tangling in solar and laboratory magnetic fields. Study the tangling of magnetic field lines.
- 3. Topological Entropy Finite Time Topological Entropy (FTTE): Adaptive refinement: Number of necessary points large! 3
- 4. Blinking Vortex Experiments Repeated applications of the blinking vortex motion. World lines correspond to 3d braided magnetic field. 4 twist parameter
- 5. Blinking Vortex Experiments Adaptive refinement successfully increases resolution where needed. Greatly decrease number of points. 5 (Candelaresi et al. 2017)
- 6. Blinking Vortex Experiments Speed up of 450x compared to previous methods. Accurately compute the FTTE 6 (Candelaresi et al. 2017)
- 7. Topological Entropy Distribution 7 Map circles and measure their exponential stretching. FTTE distribution shows areas of chaotic behavior.
- 8. Conclusions ● Measure field line tangling through topological entropy. ● Estimate the entropy through material line stretching. ● Adaptively refine calculations. ● Speed up of 450x. ● Spatial topological entropy distribution. simon.candelaresi@gmail.com