Nonlocal effects in the solar dynamo
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Nonlocal effects in the solar dynamo

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CC Attribution 3.0 Germany:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
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2019

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English

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Abstract 
Model of the solar dynamo hardly reproduce the observations of the solar magnetic field. In the presence of strong magnetic field in a turbulent fully ionized medium, such as the solar interior, temporal and spacial recorrelations can occur. In the frame of meanfield MHD, these can be treated as spacial and temporal nonlocalities (memory effect). We found that the magnetic buoyancy occurring in the convective solar interior implies a nonlinear temporal nonlocality. This additional nonlinearity leads to solutions that recover the morphological evolution of the solar magnetic field.

00:00
Goodness of fit
Resultant
Astrophysics
00:24
Group action
Field (agriculture)
Diagonal
Physicalism
Astrophysics
Local ring
00:45
Point (geometry)
Surface
Scale (map)
Scaling (geometry)
Concentric
Cycle (graph theory)
Multiplication sign
Surface
Algebraic structure
Electric dipole moment
Special unitary group
Electric dipole moment
Chemical polarity
Polarization (waves)
Frequency
Arithmetic mean
Field (agriculture)
Frequency
Phase transition
Cycle (graph theory)
Spacetime
Physical system
02:48
Surface
Scale (map)
Special unitary group
Line (geometry)
Electric dipole moment
Shift operator
Polarization (waves)
Oscillation
Field (agriculture)
Profil (magazine)
Phase transition
Diagram
Diagram
03:37
Group action
Euler angles
Differential (mechanical device)
State of matter
Multiplication sign
Sheaf (mathematics)
Rotation
Sign (mathematics)
Velocity
Phase transition
Diagram
Inductive reasoning
Social class
Area
Process (computing)
Differential (mechanical device)
Zirkulation <Strömungsmechanik>
Mass flow rate
Moment (mathematics)
Physicalism
Special unitary group
Perturbation theory
Electric dipole moment
Degree (graph theory)
Category of being
Arithmetic mean
Field (agriculture)
Crosscorrelation
Order (biology)
Nichtlineares Gleichungssystem
Right angle
Cycle (graph theory)
Flux
Topology
Electric dipole moment
Shift operator
Polarization (waves)
Scherbeanspruchung
Oscillation
Mach's principle
Term (mathematics)
Average
Nichtlineares Gleichungssystem
Helix
Turbulence
Set theory
Scale (map)
Scaling (geometry)
Graph (mathematics)
Forcing (mathematics)
Uniqueness quantification
Physical law
Diffuser (automotive)
Line (geometry)
Mortality rate
Evolute
Network topology
Universe (mathematics)
Vertex (graph theory)
Fiber bundle
Diagram
10:53
Point (geometry)
Surface
Zirkulation <Strömungsmechanik>
Dynamical system
Group action
Blind spot (vehicle)
Multiplication sign
Algebraic structure
Quadratic form
Process capability index
Theory
Mach's principle
Propagator
Profil (magazine)
Diagram
Liquid
Nichtlineares Gleichungssystem
Turbulence
Partition (number theory)
Descriptive statistics
Flux
Rotation
Blind spot (vehicle)
Matching (graph theory)
Zirkulation <Strömungsmechanik>
Mass flow rate
Surface
Chemical equation
Weight
Diffuser (automotive)
Theory
Special unitary group
Line (geometry)
Scherbeanspruchung
Quadratic form
Tube (container)
Wave
Arithmetic mean
Field (agriculture)
Frequency
Order (biology)
Right angle
Turbulence
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Pole (complex analysis)
Spacetime
16:23
Axiom of choice
Complex (psychology)
Group action
Interior (topology)
Multiplication sign
Time zone
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Negative number
Aerodynamics
Local ring
Position operator
Flux
Observational study
Theory of relativity
Mass flow rate
Adaptive behavior
Moment (mathematics)
Physicalism
Special unitary group
Knot
Category of being
Arithmetic mean
Field (agriculture)
Crosscorrelation
Relation <Mathematik>
Flux
Resultant
Spacetime
Point (geometry)
Functional (mathematics)
Observational study
Image resolution
Algebraic structure
Tube (container)
Student's ttest
Polarization (waves)
Theory
Mach's principle
Crosscorrelation
Population density
Gitterverfeinerung
Modulform
Spacetime
Nichtlineares Gleichungssystem
Turbulence
Set theory
Addition
Scaling (geometry)
Autocovariance
Forcing (mathematics)
Surface
Theory
Algebraic structure
Correlation and dependence
Greatest element
Tube (container)
Turbulence
Object (grammar)
Pressure
21:35
Point (geometry)
Group action
Functional (mathematics)
Euler angles
Multiplication sign
Mass diffusivity
Chemical polarity
Event horizon
Theory
Frequency
Sign (mathematics)
Mechanism design
Field (agriculture)
Manysorted logic
Average
Term (mathematics)
Moving average
Ranking
Diagram
Nichtlineares Gleichungssystem
Summierbarkeit
Pairwise comparison
Set theory
Linear map
Flux
Newton's law of universal gravitation
Complex analysis
Surface
Moment (mathematics)
Physical law
Curve
Algebraic structure
Special unitary group
Line (geometry)
Perturbation theory
Limit (category theory)
Arithmetic mean
Field (agriculture)
Radius
Order (biology)
Linearization
Diagram
Local ring
Directed graph
26:22
Blind spot (vehicle)
Perfect group
Blind spot (vehicle)
Diffuser (automotive)
Quadratic form
Mass diffusivity
Numerical analysis
Quadratic form
Power (physics)
Doubling the cube
Diagram
Linear map
Rhombus
00:00
Israeli so ladies genuine good morning so I'm very very happy to be here and so my name is Yuri Fullerton from the Backus Institute for Astrophysics in Boston and as I was introduced to to present you some results of we published in late
00:20
2018 in acid in astrophysics which is a main you use a
00:25
dual for foster physics and the title is nonlocal effect and so on that's what I'm going to talk about today is basically the
00:34
the how to understand all that is how we try to understand the made if field of sub it
00:40
and this is where the diagonal meets right so before going too much into the details so we
00:47
make a short introduction so if you look in the sun from far way what you see is basically a large dipole OK it's not a simple Bibles under stationary day able if they're dipole which is also lettering so what is it mean it means that it has some strength and then after some time it's going to to become weaker and weaker what you're going to see that's some although coalfiring to emerge also notes with something to the dipole anymore until its reach a certain point to a gold again which was opposite polarity so the of the the polarity of also this here is changing every 11 years and getting back former polarity every 22 years this is called magnetic cycle of this to many you heard about at about the earth in space is saying about the sun except that the IRS as no clear as cycle period the sun as a very key 1 OK but if you don't look
01:42
closer to what the sun and Happy this picture is not too bad I was afraid words so you're going to see some much more smaller structures and the surface which are basically hiding this largescale Dybul OK that hidden behind this small scale and this structures into here are basically regions we have a lot of mean field mode of concentration of meaning and there appear soon stochastic elusive phase of the sun and then the out very organized and like by that I mean that if you you may know that the sun is a basic you blow off very high and I is a gas or plasma which is irritating and the altar outlook of the sun is collected he unstable Swedes attributes OK so it's you have a lot of no organized system which we mean is smaller than my system as you just mentioned also have veering Korean structures which are the socalled active regions call like that because I need to key very active OK so
02:50
now I'm going to explain this very complex diagrams 2nd so basically that's comic was making this mistake Liskov like here so this is
02:58
basically some light that you see and from that you can see nicely this the the the line of the mean killed but if you not take the same picture of the sun looking at the polarity of the magnetic field which is coming toward us in the coming to what's years it's called I need to add this basically you're going to have a mole of white and and but the light and dark spot from the positive and negative polarity if you now average this made ground over the longitude not busy he went to gets and latitudinal profile of the polarity of the leadership and if you do that every day for fall it's a 45 years you obtain
03:38
this diver so he have time in 1955 ends like other set of vertical line is latitudes it's a Latin poll find all the polarity the many field the body of field you know being positive blue being made and you do that's for 45 years and you get this very nice butterfly diagram school butterflied as well because in these areas here that looks like a butterfly weeks OK it's nothing to do with physics is just that people keep that in mind OK this is easier so all right so this is a very featurerich diagram and went to do my best to explain it right now so the 1st thing you see there is a largescale dipolar few OK dipole I feel it's means the feel that going for the poll so if you look now at the 90 degree latitude in the minus 2 deg latitude you see the police so here I'm going to focus on these guys and these guys so what you see you see this patch which Pretty Boy Genius and both 1 priority and not see you clearly see that the alternations the not scale when he feels is here in the inner the opposite sign on also and this year and becomes positive and so on with a 20 year 2 years cycle as I said earlier but now if you look at the lower latitudes if in advance Fields is not in Norwegian use patching what's none of you got this is what I men's with this small scales here so these are the active regions OK and what is this what you see a list in a graph is that the the activity of the lower latitude is also oscillating from very active less active reverse sign again the reactant less active and so on so what you see here you have 2 cycles OK yeah that cycle of the dipolar field and the cycle of the and what is interesting that when the lowlatitude ought to be the most active it's about the moments where the dipole was less active and about to reverse this is exactly what I said at the beginning the dipole of the sun is just reducing strength you have this high modes that emerge active latitudes and then it reverse is and goes and the real rate of the higher modes just disappear OK so this is basically this 2 cycles which have phase shift of cycle and at what is now this is already a very interesting feature that we know about the meanfield sun from observation but another 1 which is quite nice to that and the beginning of the cycle of this of the law like each of the own attitudes you see the the this active regions have a tendency to emerge at higher latitude and as you go through the cycle that going closer then going to emerge on average closer and closer to the equator this is called the a quater migration so it's actually latitude as migrating to what they create OK is also very important feature of the Dynamo's some because we don't also that all stars much the of assigns key and as soon as you see some flux going the bold this setting the latitude in also start to to promulgates not to what they equivalent to a little OK so the real attitude that propagate toward a crater and the highlatitude provided to what so obviously if you want to understand the field of the sun and if you want to model it you model needs to reproduce these features OK but this this is a right so how do
07:17
we describe weighted feels than in NASA physics basically it's just that the induction equation because this is what governing the main field and so this is just telling that's that the time read evolution of the mean field is basically the advection although in a field with some diffusion to us so now let's say you have a steady velocity field so this term is just going to be and section OK it's not creating made this 1 is diffusion KCN basically going to defuse so make the flux density so the mining flux density which is the screen to become weaker and weaker so basically what's going to happen is that anywhere in the universe we of many fields and in everywhere I mean if you're tendency to defuse away OK and as I said before the sun is a very turbulent object and as we know chilblains is very good for mixing ends up for diffusing and this is also the case for the as Rabin it's also the case for the meaning of and in the case of the sun you would diffuse in that say 10 thousand years OK so intense thousand years of some should have no mediation the thing that we know that when my shoulders and still has a lot of media field so you need and the cans and to maintain the magnetic field in stocks and on him stars is bundles of a galaxy and so on and this is what we call the dynamic in this so there are 2 main classes of processes that can maintain the leadership either largescale motions on suitable topologies by that I mean for example a differential tation so shearing is going to be able to generate many ship all you go close also happened that effects of average small motions let's say some kind of tubulin fields which is casting but which has some intrinsic properties if you average and some of them have but net effect that can lead to the generation of unique and in order to to visualize that I'm going to take the mean induction equation so basically the induction equation of the mean fields we just think this equation average at and some leverage ability so the rails of it and what you see here that you have the advection of the mean in fields by the mean flow you again you have the diffusion of the mean field which have an internship which is that basically the 1st or among moment and which is basically the average of the perturbation around the OK so let's go back to the 1st example the other state flow so basically nor perturbation around me this goes away you have no way to maintain them in but as soon as you have perturbation of the flow ends all the mean field you may have a way in this all of you possibilities to generate and maintain my field against the diffusion and this term he is called an intuitive force just if you want to look at the literature the problem that's a this is an unknown and this is basically what we want to model OK and this we want to model it's because we cannot sold it's in a direct fashion we have to try to understand what this all means and it is difficult and we don't know yet what this means but these are few disabilities and depending on which of these possibilities you believe as are the most important thing to it because they're all there that you're going to end up with different ends
10:53
and this is something which is dividing the astrophysical community in dividing the the the still select community that and you can't discriminate this too a way of thinking so PCI by asking the question what all the active regions exactly the thing that we are observing on the spot so some people say OK the active regions said just a signature or what is happening below the surface with all the people say no the active regions actually that the drivers all the diet so what we see in the Surface is actually the dime and this is something which is dividing the community and the nobody have true answer all that so the the the violence into type of Xidan dynamos the Babcock lighting dynamos where the main drivers are the Shia due to differential going to talk about in a 2nd and what is happening on the surface which is called the backup light and OK so the active regions are the drivers of the dynamo they are helping for the maintenance of them in the field and the theory of basically supported by observations so a lot of observations group this is how it away but the theory behind it does not yet finished or not even started the Timmons Dynamo though they have 4 main drivers of sharing enough attention and the helical turbulence which provides the that we can close in space and it for them the active regions of the 2 signatures of these very complex phenomenon which is appearing just be this final was a supported by fury so they're very strong theory it doesn't match well the observation it OK so both of these dynamic can partly explain the butterfly diagram but as I said before we just what we just all want to expand partly the butterfly when we want to explaining to explain the butterfly 11 and that's
12:44
the issue the propagation of active regions where said the a quater won't are not easy to get from the model and arena seventies pokery wrong independently suggested that you could divide the mean meanfield description of the dynamo added at the weights OK so that a dynamic duo way and the propagation of this wave half to full which we called a differential station which that time was supposed to be very very cylindrical but nowadays we had the chance to have use mode so this is basically say small magical technique that you apply some OK so that and and basically you can look inside the cell and by looking inside someone of the mood of the great success of this method is that we could get the differential tations on so the sun is not solid gains will ball of gas so if you make it rotating it's love like the IRS something to regionally is going to recede differential so mean that the equator would it much faster than this than the pole but you also all the spot where the crater irritates lower than people or you have a stuff like Jupiter when you have these jets where everything is upside down and and the thing that as you see here this profiles king not cylindrical it's more on iconic OK so if you believe in this is actually the case that the partition the population will wave propagates along this is a line of the different rotation then you have no acquittal immigration is what you see here these new equatorward immigration whatsoever is just like a st right providing so this is an issue when you see this little dip here is called a sufficiently and some people claim while this is sufficient to gets liquid all immigration but the model since to say no it's not the case but it's not sufficient and then you have another possibility to get this acquittal of migration which is called the advection of the Medusa collection so as soon as you have differential take rotation they're creating an and balance and they are full of though flow has to adapt and you get you having to get somewhere you know circulation inside stuff OK they're just recognize so this is slice of the sun rights and he the crater he knew the poll so it's it's a it's rotating that's OK and he's just north this here and this is exactly the same size and you get this nice regional circulation that goes and it's a face full large and then the other region flow at some point in the all out and build on the stock that goes equatorward and if at this point we where the returned for is maximum the know Germans diffusivity meaning where is their determines as we you are going to get this nice equatorward migration back OK the problem that is that's supposing it's you have diffusion that I extreme this week so we know that there are actually unrealistic so there are about 100 times too low compared to what we expect so this was loft tuning in order to get it right and even when you get it right it's not really right because as you see here active regions actually not very active and is active regions are not active they're not active regions so OK you get the Quattro immigration back but you losing all the aspect of the butterfly there when removed in a case which you would clearly have a problem and then we wanted to check the question OK how we
16:23
can can we saw that and now I'm not going to show fence equations because it would take too long to explain them that of shunned trying to to do it phenomena due the phenomenological manner so let's start from the beginning I think the major question is how strong is something so 1st midterm and final what happened is that you some hey legal attributes and which has some properties and a few other objects it can generates made each of the sun before OK the thing that's these assumes that your chairman's is fully developed and that you have no no correlation between 2 points light in space while in time meaning that 2 points makes a choice doesn't know about themselves about the neighbors but they don't know neither what happened in the past about OK so these feel as no memory this is not for week Plainfield because the sun is FIR turbulence and that's all fine but as we said the net effect of the helical to rinse is going to generate mining so the mean field is going to become stronger and stronger and the tension force all the media field is going to smooth tube it's OK and as soon as you small students then you're killing the 2 and you're killing the generation of any killed his school the quenching mechanism which is good because as we see on the sun if he doesn't grow exposure the it a saturated to a certain point which is done by this morning effects OK and this is where fury stop your own that's we have no Suri whatsoever to help us to understand further means the problem that this is not entirely entirely correct this is this is true in the linear approximation but as soon as you go to only assistant and working more in this reason for that is that as soon as you have strongly fields you are recorded re correlating played places in space and time so basically your knots you have no no memory as soon as you have strongly fueled you get some memory effects so 2 point knows about each other is connected by many the lights and then also about the past it had been and that it exists field full time the other thing to put on top of that is that strong Koreans structures like Fortis's off maybe fields which are calling flux tubes and they have the pressure when the pressure inside which is basically making the density inside the structure we so this structure that actually be so where the the form in the so inside the star they're going to rise to what the face eventually merge and form active regions OK so that's a lot of completed physics and as a said there is no theory to to to do with these things and so basically people have been trying to to model them the best they could and at its gaining a perfect but I and I hope we having clues and folder to this to the things and more and more people will start to try to take into account this memory effect and so the 1st thing we said OK not a tool to model this the impact of this strong structures all the flow that we need to understand the dynamic 1st and this is what we did it
19:34
thousand 17 and it took us 3 years to do it so we it remain a large numerical study where we are solving the complex most complex set of equation I know so the physical personal hydrodynamic set of equations so by that I mean hydro plus many killed incompressible manner and we need that was a coach school new managers development of our institute which is also the possibility to an additive mesh refinement is is quite nice for the study of this Korean structures but because so here you have the picture on the song with the surface here here the radiating interior of the cost of saying the phone in his green thing is here obvious flux tubes and was talking about how this covariance structure of mean and here the red and blue edges positive and negative polarity to ship this book so this things thanks to Our result was an effective resolution of 4 thousand troops which is not too bad and so we've that's we could a make nice assimilation quite fast needs 100 stringy simulation in each of them runabouts results accused on a chair the chair and let 1 month so this was quite a big work in and out of these we can basically extract is very simple scaling relations which is many follow some but also for all the stars and which tells how long these guys are going to rise to this this whole how long they need from the moment you have been formed to reach the surface OK and this is as we can see here it's a nonlinear function of the minute few itself so strong that the magnetic field foster these things are going to to rise of surface weaker than in any field longer that take OK and this is what we call the memory so this is a time scale of the memory of these things are could connecting places which are up to 2 different places in the space but also places in the past so basically we have been on the at OK I know locally
21:39
Geneina Tumpel OK so now I I could not avoid to put some equations on trying to to give that's as simple as possible so we found that the tumble locality so this delayed the time as a structures need to reach a surface is a nonlinear function of the meaning of this was expected already from the nineties but we could show it in a very direct manner and so if I may remind you of the electromotive force which was the average of group on the line it basically compose on the source terms of something which is acting against diffusion because some all the higherorder terms like including 2 events that here and on and the thing to talk about this case that basically the stools tension looks like together Sulston which is a function of the latitude find the function of the radius in science I function of time but this AllStar as I said is nonlocal so it is a complex function of the mileage fields which was at another place at another time OK and this is here the store eyes were to see this tomfool nonlocality that we see here which is a nonlinear function of the meaningful exam and now trying to explain this confusable 1 so so basically in order to illustrate what's the point of of this today we just took the the mining field very simple minded set we say the main fuel of the sun just alternate like a standard science with some frequency and I was OK good so let's compute this delay and this is a green curve you see here something of a structured Let's is formed at this moment here have time the structure which is formed this moment with this might expect it is going to rise and as soon as you touch the the rank of the basic which that which a surface find OK now if you look at it later at this point another structure was formed with this strong remaining fuels streetwise as much faster and the reaches a surface about the same time as a structure which was formed only on so what is happening that you have a different structure the trades a surface at the same time but they were formed at different times before a different place OK and what happened is basically that you are going to have accumulation of this of this this thing doesn't look like a sign as a whole because like almost like a discrete peak of sorts so knowing on localities transforming minus is call into song very and very strong peaks OK of salsa so far so good but the effect of linearity what does it tell us for the butterfly diagram come butterflies
24:31
so here you have the butterflied I well is partly Yutian wrong waste time where you see no whatsoever a question it could all migration now we take the same simulation and we put this moment this memory effects in the model and what you see here is what you get and very nicely you obtain this equatorward migration and a a lot of all the features here that you see on this picture actually quantitatively comparable to what we get out of that what we observed on the surface of this model is actually very successful in reproducing all the features we have been saying so far and the reason for that is basically that and the the money the the the main fields and the higher latitudes is stronger and therefore the delay shorter but as soon as you go in law attitude is weaker and therefore the delays longer and this is actually the effect we so basically what we found is that this memory we can use the new mechanism to explain the a quater 1 migration so this is quite says was quite surprising because we nobody thought about this affecting took me a while to feed and that's what this is all about and but it is not as I said very powerful I'm not going to claim that this is the final answer it it's very still good and the small is very crude so we still need to put a lot 14 and standing was going on here and putting the pushing it further but what is that thing which is very interesting in that as soon as you start to think of of the limitation of the linear theory we have been working with full fall we need to push that's further to the nonlinear case and this memory effect seems to have a great deal of importance if we want to repeat use the main fuel cell OK I think
26:23
in about conclusion so I would just to let you some summary so this is like the general summary should contain the first one home that's perfect so that to double dynamos Wednesay's active regions of the driver of the dynamo number 1 say just a signature of the diamond that would be nice if you can take that home if you know again it's not in the you cannot gets the Equador migration without unrealistic diffusions so this where the problem we had and our contribution was basically to say that we could obtain a nonlinear model from global so the full power of the tool we actually have no and then to topple nonlocality if it's normally can open a new window to want to watch and solutions if we didn't know before which also like butterfly that which shows select that I went and very interestingly also let's show longterm viable solutions even Celtic solutions which is exactly what you have observed and the surface of OK I think you were much for your attention and if you have any questions I would be delighted to answer
27:27
and