[Mesa-users] Mesa-users Digest, Vol 88, Issue 7

[Nicholas Rui]

help

On Fri, Nov 15, 2024 at 6:49 AM <mesa-users-request at lists.mesastar.org>
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> Today's Topics:
>
>    1. Re: Convergence issues solved by changing a_mlt
>       (Joergensen, Johannes Holm)
>    2. New model for galaxy formation, star-formation, the
>       derivation of natural laws, replacement to the Big Bang, etc
>       (Marco Pereira)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Fri, 15 Nov 2024 10:57:42 +0000
> From: "Joergensen, Johannes Holm" <Johannes.Joergensen at uibk.ac.at>
> To: "Farag, Ebraheem" <ebraheem.farag at yale.edu>, Jared Goldberg
>         <jgoldberg at flatironinstitute.org>
> Cc: "mesa-users at lists.mesastar.org" <mesa-users at lists.mesastar.org>
> Subject: Re: [Mesa-users] Convergence issues solved by changing a_mlt
> Message-ID: <5d568d37a07c4afba9f223833d142889 at uibk.ac.at>
> Content-Type: text/plain; charset="utf-8"
>
> Hi again Ebraheem and Jared,
>
>
> thanks for your suggestions - I've made some progress with them since.
>
> > if the model is crashing right then or shortly after, it must be
> somewhat catastrophic as opposed to a slow decent
>
>
> I have attached two figures illustrating gradT-grada for the last two
> profiles in my model that fails. To me, it does indeed look catastrophic,
> with values from -6 to 6.
>
>
> > Turning on this control could spot the issue as well !report_ierr = .true
>
>
> Yes, the output from this looks to be:
>
>
> hydro_mtx: change too large, dlogT, logT, logT_start        4065
>  582          13   -1.5246921351765414D+02   -1.4732967808573136D+02
> 5.1395354319227664D+00
> set_vars_for_solver failed: model, nz        4065        1716
> eval_equations: set_solver_vars returned ierr          -1
> adjust_correction: eval_equations returned ierr          -1
> 7.8236146823124006D-02    7.8236146823124006D-02
>
> This is the last line from the solver:
>
> "4065 40  coeff 0.3191 avg resid  0.183E-06      max resid equL   579
> 0.20933E-02 mix type 11111 avg corr  0.529E-07        max corr v     1
> 0.81727E-03 mix type xx111  max resid -- give up"
>
> > minor perturbations to your model can cause you to avoid or encounter
> some of these spurious zones.
>
> By here you mean that changing amlt is a minor pertubation? I agree and
> suspect that I would've found similar results had I fx chosen to perturb
> the masses of my models slightly instead of amlt.
>
> > highly encourage running a resolution test varying spatial and temporal
> resolution.
>
> I'm running the model that I expect to fail again, but now with "max_dq =
> 1d-3" in one case and "mesh_delta_coeff = 0.2" in another. The models are
> more computationally heavy, however, I'm noticing that the model with the
> "max-dq" criteria has actually managed to evolve pass the problematic
> age/mass, having now reached age = 20700 years.
>
> Thanks again, I hope to get around to more of your suggestions as soon as
> possible.
>
> Cheers, Johannes
>
>
>
>
>
> ________________________________
> Fra: Farag, Ebraheem <ebraheem.farag at yale.edu>
> Sendt: 7. november 2024 21:00:28
> Til: Jared Goldberg; Joergensen, Johannes Holm
> Cc: mesa-users at lists.mesastar.org
> Emne: Re: [Mesa-users] Convergence issues solved by changing a_mlt
>
> All great points from jared,
>
>
>   *
> When examining the MESA solver outputs, I believe one column should
> display the index of the problematic cell? Is there a way to connect a
> given cell index with a radius or mass coordinate to illustrate what is
> going in the problematic cell?
>
> In particular if this is a result of a single or few  superadiabatic zones
> crashing the solver, then one would expect that the largest residuals in
> the bad solver iterations would coincide with location (zone) of the
> largest values of gradT_sub_grada.
>
> One can inspect the solver iterations by setting
> report_solver_progress = .true.
>
> This will report some info on the individual iterations contained within
> the timestep. Before a retry, the last solver iteration will display the
> largest residual quantity and zone.
>
> For example
>   2126 19  coeff 0.1000 avg resid  0.230E-03   max resid dlnE_dt  1829
> 0.19703E+02 mix type 00000 avg corr  0.624E-08      max corr lnT  1829
> 0.34794E-05 mix type 00000  avg+max resid
>
> This one line states that at timestep 2126 on the 19th iteration the the
> zone with maximum residual is zone 1829 where the largest residual is
> coming out of the energy equation.
>
> Further debugging options are described here
> https://docs.mesastar.org/en/24.08.1/developing/debugging.html
>
>
> If your investigation leads to you finding that the spurious zones of high
> gradT_sub_grada are indeed the source of your issue and if the pruning
> isn't helping you then likely your  solutions will have to come from
> something like increasing alpha, turning on mlt++, or turning on
> superad_reduction, all are methods of bring delT closer to del_ad, therby
> decreasing the superadibicity. All of which will directly affect the radius
> of your star.
>
> The fact that decreasing alpha is resulting in convergence, could just be
> from the fact that the superadiabatic zone is radiative instead of
> convective over the same timestep and so it doesn't suffer this issue, or
> that like Jared mentioned, minor perturbations to your model can cause you
> to avoid or encounter some of these spurious zones.
>
> For context, I know Thomas ran into some similar issues when running some
> of his models, although i don't remember which.  As you are really
> investigating a new larger parameter space, I'm not surprised you're
> encountering similar difficulty. I think he managed to get his models to
> work without any issue in some circumstances, but I remember him suffering
> some similar numerical issues, particularly for the more massive models or
> higher accretion rates. We experimented with using superad_reduction
> (turned higher than the default) and we were able to get some of his models
> to work that way at the cost of changing the structure. Although I don't
> know if those were the models used in his paper as I remember him being
> concerned about the affect this would have on the structure of the envelope
> and by extension the surface properties and  pulsation of these accretion
> models.
>
> p.s. I see that you have "prune_bad_cz_min_log_eps_nuc = 99", which
> appears to be set high enough that you are not pruning any bad zones. See
> the definition here<
> https://docs.mesastar.org/en/24.08.1/reference/controls.html#prune-bad-cz-min-log-eps-nuc>,
> where the default is "=-99",
>
> One more solver hack to try which can sometimes help convergence is to
> prevent zones from flipping back and forth between convective and radiative
> over a solver iteration.
> Try "make_gradr_sticky_in_solver_iters = .true.", described here<
> https://docs.mesastar.org/en/24.08.1/reference/controls.html#min-logt-for-make-gradr-sticky-in-solver-iters
> >
>
> -EbF
>
>
> ________________________________
> From: Jared Goldberg <jgoldberg at flatironinstitute.org>
> Sent: Thursday, November 7, 2024 2:58 PM
> To: Joergensen, Johannes Holm <Johannes.Joergensen at uibk.ac.at>
> Cc: Farag, Ebraheem <ebraheem.farag at yale.edu>;
> mesa-users at lists.mesastar.org <mesa-users at lists.mesastar.org>
> Subject: Re: [Mesa-users] Convergence issues solved by changing a_mlt
>
>
> I'm using MESA-r22.11.1 where Steindl+ 2022 used v12778. The scheme is the
> same as in that paper, with an initial stellar seed.
>
> Got it. And indeed, a fair amount has changed between 12778 and 22.11.1 in
> terms of the treatment of convection and the turb module in general. Some
> of the advances are described in MESA VI (Jermyn+2023).
>
>
> I follow your intuition as well; that more efficient convection should
> help with the small convection zones.
>
> Yes, and the behavior you show strongly appears to be numerics rather than
> physics for why one alpha is happier than the other. For engineering
> purposes, it might be OK to use the value of alpha that works, but I'm not
> sure we'll find a good physical justification because one likely doesn't
> exist. With whatever value you choose, I highly encourage running a
> resolution test varying spatial and temporal resolution (generally
> following best practices
> https://docs.mesastar.org/en/24.08.1/using_mesa/best_practices.html ).
>
>
> For the MESA inlist controls in question, I can tell the following:
> - 'relax_until_radiative_core' is not in my inlist. I guess it's set to
> 'true' by default?
> https://docs.mesastar.org/en/22.11.1/reference/star_job.html#pre-ms-relax-to-start-radiative-core
>
> Got it. Since you're starting with a very small seed mass, this doesn't
> kick in, but for posterity it may be a nuisance (i.e. it should be set to
> .false.) for other cases where you're trying to create accreting pre-MS
> stars. This is only activated with an initial mass that's > 0.3 Msun, and
> also not starting from a seed mass.
>
>
> - 'do_conv_premix' is set to 'True'.
>
> - 'prune_bad_cz*' and 'min_convective_gap' have the following controls:
>
> i) prune_bad_cz_min_Hp_height = 0.1
> ii) prune_bad_cz_min_log_eps_nuc = 99
> iii) min_convective_gap = 0.1
>
> Great, then these will already be taking effect.
>
> > If I'm understanding correctly, by decreasing 'alpha_mlt' from
> 'alpha_mlt = 1.9' to 'alpha_mlt = 1.85', you were able to solver most of
> your convergence issues?
>
> In general yes, but sometimes I had the case where I also increased
> 'alpha_mlt' slightly and solved my issues. Overall I have a grid of models
> from 0.5-1.5 solar masses with 35 different accretion scenarios that gives
> a total of 735 models. I wanted to keep 'alpha_mlt' fixed at 1.9, but ended
> up varying it between 1.8-2.0 to get better grid coverage. In the end I
> ended up with ~85% grid coverage.
>
> Got it. This might be OK, but this sounds like your issues are likely
> numerical rather than physical. Run a resolution test!
> Also, for science results, it's important to be aware that varying
> alpha_MLT will change the temperature of your pre-main-sequence descending
> Hayashi track for a convective envelope. This may be important to be aware
> of depending on your science application. See review by Joyce & Tayar:
> https://ui.adsabs.harvard.edu/abs/2023Galax..11...75J/abstract
> Notice the faint hayashi tracks here:
> [image.png]
>
> > Finally, do the tiny spurious convection zones pop up near the base of
> the convective envelope, or the surface?
>
> As far as I can tell, the zones show up throughout the entire interior.
>
> Looks like they are present at larger T, so they're seeded at the base,
> but yes they're popping up throughout the envelope. From the kippenhahn
> diagram you can see that this is when the star develops a radiative
> envelope, not at the top of the outer subsurface convection zone.
>
> > I think two plots could help in diagnosing what's happening.
>
> I have attached the plots, although I have plotted the MESA 'schwarzschild
> criteria' against logT instead of ???ad, but this should convey the same
> information right? (I hope my naming scheme makes sense)
>
> The schwarzschild criterion typically is a "yes or no" -- is it stable to
> convection or not? So grad - grad_ad  contains much more information,
> namely, how close your thermodynamic gradient is to the adiabat. See
> gradT_sub_grada in your pgstar panels, it is very ratty.
>
> One thing I noticed, when examining the Kippenhahn diagrams in the MESA
> pngs, is that the model that fails with 'alpha_mlt'=1.9 has a larger region
> of strong burning in the outer parts  than the model with lower 'alpha_mlt'
> at the same age. At later stages the the model with lower 'alpha_mlt' will
> also develop strong off-center burning, yet still converges, so I'm not
> sure this is the cause of the problem in the model with higher 'alpha_mlt'.
>
> The off-center burning is deuterium burning at the base of the H-rich
> envelope. So, yes, it looks like the onset of deuterium burning may not be
> playing nicely with MLT. See also the change in h3 abundance in the
> abundance plot. I was looking for rattier behavior, though, which doesn't
> seem to be the issue, so I agree this likely isn't the fundamental problem.
>
> > I would also encourage you to stare at power profile plots.
>
> Yes, thanks for the tip, I will get around to these plots as soon as I
> can, but I wanted to get the first plots to you both right now.
>
> As with grad - grad_ad profiles, you also have this in your pgstar (and
> therefore, for your own diagnostics, in profileN.data files).
>
> Final question for now: When examining the MESA solver outputs, I believe
> one column should display the index of the problematic cell? Is there a way
> to connect a given cell index with a radius or mass coordinate to
> illustrate what is going in the problematic cell?
>
> The profile.data files for that and adjacent timesteps contain a bunch of
> information and map from zone to mass/radius.  Sometimes it's helpful to
> increase your profile output to every timestep just around the crash. For
> information during the solve step, you can tell MESA to print information
> in extras_check_model in run_star_extras.
> Note that this "problematic cell" is just the one with the highest
> residual, there may be multiple cells where there are issues.
>
>
> Thanks to both of you for taking the time to help me, I really appreciate
> it
>
> No problem!
>
> Cheers,
> ~Jared
>
>
>
>
>
>
>
>
>
>
> Cheers, Johannes
>
> ________________________________
> Fra: Jared Goldberg <jgoldberg at flatironinstitute.org<mailto:
> jgoldberg at flatironinstitute.org>>
> Sendt: 6. november 2024 20:38:52
> Til: Farag, Ebraheem
> Cc: mesa-users at lists.mesastar.org<mailto:mesa-users at lists.mesastar.org>;
> Joergensen, Johannes Holm
> Emne: Re: [Mesa-users] Convergence issues solved by changing a_mlt
>
> Hi Johannes,
>
> I've been playing around with accretion on the pre-main-sequence in
> support of a student's project this past summer, and we've been breaking
> MESA in many interesting ways. The tiny convection zones popping in and out
> of existence definitely become a problem in this regime. Like Eb
> speculated, in my experience making convection more efficient (increasing
> alpha_MLT) tended to behave slightly better near the convective boundary,
> which I justified intuitively by thinking that it brings convective
> gradients closer to the adiabatic gradient, and also may be a bit better
> for composition gradients which may cause the tiny convection zones popping
> in and out of existence. I have less intuition for why a lower alpha_mlt
> might help the solver -- perhaps this is a sign that some of the numerics
> are ill-converged in general, and kicking the solver around (e.g. by
> changing alpha) could help with convergence.
>
> Convective boundaries are a notorious problem, and have had much work in
> MESA IV and V devoted to doing better and better, though there's still room
> for improvement. One work-around here is setting prune_bad_cz_* and
> min_convective_gap to prune these numerical jitters. Similarly
> do_conv_premix = .true. seems to help with numerical stability. Playing
> with overshooting may also help to this end.
>
> A few more questions to be more helpful and gauge what's going on:
>
> > First, what MESA revision are you using? Are you using the old revision
> from Steindl+2022 (9000s, I think?) or are you using a recent revision?
> A number of changes have been made since then which have put resolution
> away from composition gradients, and similarly there have been changes with
> convective boundary mixing schemes and the turbulence module in general
> which may impact the setup. There were also resolution controls near the
> core boundaries / composition boundaries in that old revision (useful for
> asteroseismology) which Steindl et al used that don't exist in modern
> revisions.
>
> > Also, what are you initial conditions? (E.g. We found that things are
> better-converged if relax_until_reach_radiative_core = .false. on the
> pre-MS.)
> Are you starting from a seed stellar model as in Steindl et al, or from
> one of MESA's built-in constructors for pre-ms initial conditions?
>
> > Finally, do the tiny spurious convection zones pop up near the base of
> the convective envelope, or the surface?
>
> I agree with Eb that
> 1- logT vs logRho profile of the whole model (a pgstar will work well, and
> it shows where convection operates along the profile)
> 2- superadiabicity (???ad) vs logT (so we can match the superadiabatic
> regions with regions in trho profile)
> are good plots to make.
>
> I would also encourage you to stare at power profile plots (are Li and
> Deuterium burning messing things up?) and composition profile plots (does
> jagged behavior in the composition profile cause local Ledoux-unstable
> behavior) as a function of mass coordinate. A kippenhahn diagram would also
> be helpful to see *when* in the star's evolution these spurious convection
> zones start to appear.
>
> Cheers,
> ~Jared
>
>
>
>
> On Wed, Nov 6, 2024 at 10:41?AM Farag, Ebraheem via Mesa-users <
> mesa-users at lists.mesastar.org<mailto:mesa-users at lists.mesastar.org>>
> wrote:
> Hello Johannes,
>
> > For context, I am running some "complicated" accreting pre-MS models
> with the framework developed by Steindl+ 2022.
>
> Very cool! Thomas did some nice work on developing a framework for pre-MS
> accretion.
>
> > From examining the output of the solver I see that the issues arise in
> convection zones. By trial and error I solved a lot of my convergence
> issues by simply changing the mixing length parameter slightly (e.g. from
> 1.9 to 1.85). My question is: Is there any way to interpret this? My models
> show interesting interiors with often many tiny convection cells which I
> imagine are difficult to handle; could a change in a_mlt help in this
> regard?
>
> If I'm understanding correctly, by decreasing 'alpha_mlt' from 'alpha_mlt
> = 1.9' to 'alpha_mlt = 1.85', you were able to solver most of your
> convergence issues?
>
> if decreasing alpha_mlt is indeed solving your issue, are these
> problematic convective zones becoming radiative in the improved working
> model? Naively, I would imagine the problem would become worse with lower
> alpha_mlt unless the zone becomes entirely radiative.
>
> I think two plots could help in diagnosing what's happening.
>
> 1- logT vs logRho profile of the whole model (a pgstar will work well, and
> it shows where convection operates along the profile)
> 2- superadiabicity (???ad) vs logT (so we can match the superadiabatic
> regions with regions in trho profile)
>
> If you can answer these questions, I can attempt to provide an explanation.
>
> -EbF
>
>
>
>
>
> ________________________________
> From: Mesa-users <mesa-users-bounces at lists.mesastar.org<mailto:
> mesa-users-bounces at lists.mesastar.org>> on behalf of Joergensen, Johannes
> Holm via Mesa-users <mesa-users at lists.mesastar.org<mailto:
> mesa-users at lists.mesastar.org>>
> Sent: Wednesday, November 6, 2024 4:50 AM
> To: mesa-users at lists.mesastar.org<mailto:mesa-users at lists.mesastar.org> <
> mesa-users at lists.mesastar.org<mailto:mesa-users at lists.mesastar.org>>
> Subject: [Mesa-users] Convergence issues solved by changing a_mlt
>
>
> Hi everyone,
>
>
> I am having convergence issues in MESA. For context, I am running some
> "complicated" accreting pre-MS models with the framework developed by
> Steindl+ 2022. From examining the output of the solver I see that the
> issues arise in convection zones. By trial and error I solved a lot of my
> convergence issues by simply changing the mixing length parameter slightly
> (e.g. from 1.9 to 1.85). My question is: Is there any way to interpret
> this? My models show interesting interiors with often many tiny convection
> cells which I imagine are difficult to handle; could a change in a_mlt help
> in this regard? I would gladly provide figures that showcase this, or my
> inlists. Much gratitude for any help!
>
> Cheers, Johannes
>
> _______________________________________________
> mesa-users at lists.mesastar.org<mailto:mesa-users at lists.mesastar.org>
> https://lists.mesastar.org/mailman/listinfo/mesa-users
>
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>
> ------------------------------
>
> Message: 2
> Date: Fri, 15 Nov 2024 06:47:13 -0500
> From: Marco Pereira <ny2292000 at gmail.com>
> To: mesa-users <mesa-users at lists.mesastar.org>, Marco Pereira
>         <ny2292000 at gmail.com>
> Subject: [Mesa-users] New model for galaxy formation, star-formation,
>         the derivation of natural laws, replacement to the Big Bang, etc
> Message-ID:
>         <CABs1CmW5B8UAnR5VSdwdwgpamAezVbs7XuN_=
> Hho8_NGMVfSdw at mail.gmail.com>
> Content-Type: text/plain; charset="utf-8"
>
> I posted three papers covering everything.  The papers are here:
> Preprints ZENODO
> https://zenodo.org/records/14047261 # HU-The Big Pop Cosmogenesis
> https://zenodo.org/records/14047097 # The Kinetic Energy of Relativistic
> Particles
> https://zenodo.org/records/14047049 # The Hypergeometrical Universe
>
>
> and here are the Python Repositories on GitHub
> https://github.com/ny2292000/CMB_HU
> https://github.com/ny2292000/HU_GalaxyPackage
> https://github.com/ny2292000/HU_Papers
>
> As far as I know, it explains everything without Dark Matter and Dark
> Energy, including the Spiral Galaxy Rotation Curve.  The reasoning is
> simple: Currently one models spiral rotation curves assuming that the
> luminous mass density (observed from millions of light-years away is
> reliable. One cannot really detect the gas cloud density from this
> distance.  Instead, I assumed that the initial state of the gas cloud
> forming the galaxy could be described by three
> exponential radial distributions with a common center.  I imposed the
> conservation of the total mass and if there is a central black hole, that
> would be the second constraint and fitted the observed rotation curve.
>
> Here is M33 at z=0
> [image: RotationCurve_z_0.png]
> and at z=10
> [image: RotationCurve_z_10.png]
> Notice that the M33 radius decreases with increasing redshift because G is
> inversely proportional to the 4D radius (G proportional to 1+z)
> Here is the gif showing how it evolved since its creation:
> https://youtu.be/A3buediDHUU
>
> You might ask if this epoch-dependent G explains the Supernova Data:
> [image: HU_short_distances_with_16554778896012723_H06969.png]
> [image: HU_long_distances_with_16554778896012723_H06969.png]
> The distances are normalized to 14.04 billion light-years and corrected for
> the epoch-dependent G.
>
> With respect to the effect of epoch-dependent G on our Sun, I explained
> that the Sun started smaller and has been growing through hydrogen gas
> accretion since then. That would imply deposition along the path of travel
> (almost perpendicular to the ecliptic).
> Here, I presented the increasing sun's mass, Earth's temperature, and the
> radius of the initial cloud.
> I presented a new model for the creation of the Universe and a new model
> for matter - those go hand-in-hand.  I modeled the CMB as the result of two
> events:
> a) The Blackholium-Neutronium phase transition (Neutronium Acoustic
> Oscillations or NAO)
> b) The Neutronium Evaporation (Baryonic Acoustic Oscillations or BAO).
> NAO was modeled using Hyperspherical Harmonics. Since these are not a
> complete base for describing what happens in the surface of an embedded
> sphere in a hyperspherical hypersurface, I had to find Earth's location.
> Once found, I optimized the hyperspherical harmonic spectral composition:
> Here are the results:
> This is Planck Satellite's Observation:
> [image: SMICA.png]
> This is the simulation:
> [image: CMB_Best.png]
> This is the difference to be explained by the BAO:
>
> [image: 12e93199-cae5-4bab-ac7f-92a0149c774b.png]
>
> Once I had the Hyperspherical Harmonic Spectral Decomposition, I was able
> to create the 3D map (prediction) of the observable Universe:
> https://youtu.be/MLqkbCAzcJM
>
> The model for matter contains all the hyperon taxonomy and maps the
> Pati-Salam SU(4) GUT.
>
> Feel free to ask questions.
>
> The Hypergeometrical Universe Theory (HU) introduces a novel model of the
> universe and matter, fundamentally altering our understanding of cosmology,
> quantum mechanics, and classical forces[Smarandache, F.
> (2007)][Smarandache, F., & Christianto, V. (2007)][Pereira, M.,
> 2017][Pereira, M., 2018]. Central to HU is the concept of the Fundamental
> Dilator (FD), a quantum mechanical wave generator responsible for shaping
> space through metric waves. HU posits that all particles are polymers of
> FDs, existing as shapeshifting space deformation solitons spinning in 4D
> and traveling at the speed of light along a hyperspherical locus in a 4D
> spatial manifold. This model redefines matter and replaces conventional
> particle-wave dualism with the Quantum Trinity of the FD, the dilaton
> field, and the Quantum Lagrangian Principle (QLP).
>
> HU reinterprets spacetime as a mere proxy for events occurring in a 4D
> spatial manifold, introducing an absolute 4D reference frame and
> reinterpreting Lorentz transformations in reciprocal space. So, HU replaces
> all the discussion on metric, spacetime with rotation matrices in a 4D
> spatial manifold affecting not space but 4D k-vectors. In HU, forces are
> carried by the dilation field (4D metric waves).  Waves? 4D k-vectors
> transform according to Lorentz transformations. So, HU solves the dynamics
> problem in the inertial frame and then reverts the solution to the Absolute
> Reference frame.
>
> By doing so, HU derives the Laws of Nature from first principles and
> resolves fundamental issues in cosmology, dismissing the need for dark
> matter, dark energy, and inflation [Guth, A. ,1981]. The theory explains
> the horizon problem with an initial hyperspherical uniform mass
> distribution and galaxy dynamics with idiosyncratic mass distributions
> while showing that time dilation is an artifact of diminishing forces as
> absolute velocities approach the speed of light.
>
> One of HU's significant contributions is the derivation of the laws of
> gravitation and electromagnetism, demonstrating that both follow the same
> Lorentz force format. The radial dependence of gravitational forces is
> shown to be a consequence of reference frame selection, such as one
> centered on the Sun, where radial symmetry dictates the force's behavior.
> This revolutionary insight has profound implications for electrodynamics,
> promising to transform the design of magnetic bottles, stellarators,
> tokamaks, and space propulsion technologies.
>
> Additionally, HU interprets gravitation as a Van der Waals force, where the
> carrier dilaton field oscillates at a frequency of 1E24 Hertz. This
> high-frequency process leads to the dynamic screening of gravitational
> effects, unifying gravitation and electromagnetism. The theory also
> facilitates non-perturbative Quantum Chromodynamics (HU-QCD) by mapping its
> particle model to the Pati-Salam [Pati, J. C., & Salam, A.,1974] SU(4) GUT
> model and eliminating the need for an integral functional in the Lagrangian
> Principle through the use of the Quantum Lagrangian Principle (QLP).
>
> Lastly, HU addresses and resolves the Faint Sun Paradox, the Spiral Galaxy
> Rotation Curve Conundrum, the Early Galaxy Formation Conundrum, the
> HyperBright Early Galaxies Conundrum, and the Cylindrical Galaxy Conundrum
> (JWST observations), which will be presented in forthcoming work.
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> End of Mesa-users Digest, Vol 88, Issue 7
> *****************************************
>
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