Solar differential rotation driven by baroclinic forcing

G. Guerrero; J. Zhang; L. S. Menicucci; M. Dikpati; P. K. Smolarkiewicz; R. Hester

REVIEW 3 major objections 8 minor 299 references

Solar differential rotation driven by baroclinic forcing

T0 review · 3 major / 8 minor · reviewed 2026-08-01 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The Sun's differential rotation—fast equator, slow poles—can be sustained by a small latitudinal entropy gradient in thermal wind balance, without needing vigorous convection or Reynolds stresses. The authors demonstrate this through 20 glo

desk verdict A careful spherical-shell demonstration that a prescribed baroclinic forcing can sustain solar-like differential rotation without strong convection, but the solar scenario rests on an unmodeled entropy gradient. read the letter →

arxiv 2607.19730 v1 pith:PEASFJEO submitted 2026-07-22 astro-ph.SR

L. S. Menicucci , G. Guerrero , M. Dikpati , R. Hester , J. Zhang , P. K. Smolarkiewicz This is my paper · ORCID

classification astro-ph.SR

keywords solardifferentialrotationbaroclinicforcingthermalwindbalanceconvectiveconundrumlatitudinalentropygradientglobalhydrodynamicsimulationsgyroscopicpumpingconvectionzone

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that the Sun's observed differential rotation (equator rotating faster than poles, with radially aligned mid-latitude contours) can be generated and maintained without requiring strong turbulent convection and its associated Reynolds stresses. Instead, the authors propose that a background latitudinal entropy gradient, held in thermal wind balance, is enough to drive the flow. They test this idea with a suite of global hydrodynamic simulations spanning stable, adiabatic, and weakly unstable stratifications, finding that all produce a solar-like rotation profile. The result offers a way around the 'convective conundrum', where mixing-length theory predicts much stronger convection than helioseismology observes.

What carries the argument

The central object is the prescribed latitudinal potential-temperature gradient Θ_B, built by integrating the thermal wind balance relation (Eq. A1) against the helioseismic rotation profile. The stratification is enforced through a Newtonian cooling term in the potential-temperature equation (Eq. 3) with a long timescale (2.4–4.9 yr). The dynamical balance is expressed in the thermal wind equation: the centrifugal term C = r sinθ ∂Ω²/∂z is balanced against the baroclinic term B = (g/(Θ₀ r)) ∂Θ′/∂θ. The small residual C−B drives gyroscopic pumping, producing meridional circulation cells that redistribute angular momentum and sustain the differential rotation without the need for turbulent st

What would settle it

A direct helioseismic measurement of the latitudinal entropy gradient in the convection zone, showing it to be absent or far smaller than the thermal-wind value needed to balance the observed rotation, would falsify the mechanism. Alternatively, detection of Reynolds stress torques dominating over meridional-circulation torques in the Sun (as deduced from inversions of flow correlations) would contradict the paper's central claim.

Watch

Extended reading notes

Core claim

The central claim is that solar-like differential rotation can be generated and maintained in the convection zone without relying on Reynolds stresses from vigorous turbulent convection, provided a large-scale latitudinal entropy gradient exists and is sustained in thermal wind balance. In a rotating spherical shell with anelastic equations and a nudged potential-temperature profile, all simulations—whether stably stratified, adiabatic, or weakly superadiabatic—produce a rotation profile with a faster equator and slower poles. The torque analysis shows that the meridional circulation, rather than Reynolds stresses, is the main carrier of angular momentum in these runs; the Reynolds stresses

Load-bearing premise

The Sun's convection zone must actually maintain a persistent large-scale latitudinal entropy gradient, in thermal wind balance with the observed rotation, over timescales of years; if convection mixes that gradient away faster than it can be replenished, the proposed mechanism will not operate in the real Sun.

Editorial extensions

If this is right

If correct, the solar convection zone can be much less turbulent than mixing-length theory predicts, easing the convective conundrum.
The observed differential rotation profile becomes a signature of large-scale thermodynamic balance rather than a direct measure of convective Reynolds stresses.
The same baroclinic mechanism could operate in other solar-type stars, giving a common explanation for their rotation profiles.
Models of the solar dynamo, which rely on differential rotation to stretch magnetic fields, may need to account for a rotation profile that is thermodynamically constrained rather than convectively driven.
The work suggests that the radial tilt of the rotation contours at mid-latitudes emerges naturally from gyroscopic pumping of the baroclinic imbalance, offering a direct explanation for this long-puzzling feature.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A testable corollary of the paper's logic is that the observed solar rotation profile implies the existence of a sustained latitudinal entropy gradient of roughly the magnitude of Θ_B plotted in Fig. 2; if helioseismic or other measurements ever rule out such a gradient over multi-year timescales, the mechanism would be in conflict.
The paper's preference for weak or stable stratifications suggests that the Sun's interior may contain subadiabatic layers (as in the Deardorff-layer picture); an inference is that the location and sharpness of such layers would control the shape of the rotation profile and could be constrained by the observed radial behavior near the tachocline.
Extending this hydrodynamical framework to include magnetic fields, as the authors suggest, would test whether the baroclinically maintained rotation can survive Lorentz forces; one might predict that the magnetically active cycle modifies the entropy gradient and hence the rotation profile, providing a link to the observed torsional oscillations.
The paper does not prescribe the origin of the entropy gradient; an inference is that any convective or tachocline-driven process that creates a large-scale latitudinal entropy variation (e.g., rotational modulation of heat transport or entropy rain) would suffice, meaning the mechanism is robust to the exact source as long as the gradient persists.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Honest, well-scoped numerical experiment. The new thing is not the thermal-wind idea — Balbus, Gunderson, Hester and others have been there — but the nonlinear spherical-shell demonstration. Across 20 runs spanning stable, adiabatic, and weakly unstable stratifications, the authors show that a prescribed latitudinal entropy gradient in thermal wind balance drives a steady, fast-equator/slower-pole rotation profile with mid-latitude radial contours, and their torque decomposition attributes the maintenance to meridional circulation rather than Reynolds stresses. That is real evidence for dynamical viability, and the diagnostics are careful: 456 years of evolution, 76-year averages, explicit equations and boundary conditions.

The soft spot is the load-bearing premise. The entropy gradient is not modeled; it is imposed as Θ_B, and that target is constructed from the very helioseismic Ω the paper aims to explain (Appendix A). The Newtonian cooling nudges toward it, so a solar-like outcome is partly inherited. The authors are open about this — they call it a controlled forcing and defer the origin — but it means the paper demonstrates consistency, not that the Sun possesses such a gradient. If convection mixes the gradient away, the mechanism fails. Their own results also show fragility: only weakly convective cases reproduce the observed radial increase at low latitudes, and strongly superadiabatic cases collapse to cylindrical contours. And the headline claim about not relying on Reynolds stresses is qualified even within the model, since §3 says Reynolds stresses help maintain that radial increase in the weakly convective cases.

Minor but real: no error bars on the time averages, no quantitative match metric against helioseismic Ω, and no released code or data. All addressable.

My overall take agrees with the reader's conditional verdict: this is a useful proof-of-concept that the baroclinic scenario is dynamically plausible, not a demonstration that it operates in the Sun. The paper is honest, internally consistent, and clearly scoped. It deserves a serious referee; the authors have done the work to make a referee's job straightforward. I'd want the entropy-gradient origin acknowledged more forcefully as a limitation, but it already is. Worth engaging with.

Referee Report

3 major / 8 minor

Summary. The paper investigates whether solar differential rotation can be sustained by a prescribed large-scale latitudinal entropy gradient rather than by Reynolds stresses from vigorous convection. Global anelastic EULAG-MHD simulations of a spherical shell (0.72–0.96 R_sun) are run for 20 combinations of polytropic index (stable, adiabatic, weakly unstable) and two Newtonian-cooling timescales, with a target potential-temperature profile Θ_B derived from helioseismic differential rotation via thermal-wind balance. Time-averaged results show a fast equator and slower poles across most runs, with radially aligned mid-latitude contours; torque analysis attributes the maintenance primarily to meridional circulation, with Reynolds stresses playing a smaller or auxiliary role. The authors conclude that baroclinic forcing can maintain solar-like differential rotation without strong convective Reynolds stresses, offering a possible resolution to the convective conundrum, while acknowledging that the physical origin of the imposed entropy gradient is not modeled.

Significance. The paper has genuine strengths: the equations, boundary conditions, grid, and parameter choices are fully specified; the parameter sweep is broad; and the simulations are evolved long enough for robust temporal averages. The torque decomposition and thermal-wind diagnostics are appropriate and clearly presented. If the claims are scoped carefully, the study is a useful dynamical proof-of-concept: it shows that a baroclinic state designed to be in thermal-wind balance is nonlinearly compatible with a fast-equator rotation profile across a range of stratifications. However, the central solar-application claim is weakened by the construction of Θ_B from the very differential-rotation profile the paper explains, and by the fact that the entropy gradient is externally maintained rather than shown to exist or persist in the Sun. The paper is therefore more convincing as a controlled dynamics study than as an explanation of the origin of solar differential rotation.

major comments (3)

[Appendix A, Eq. (A1); §4] The target profile Θ_B is constructed by integrating the thermal-wind balance using the observed helioseismic Ω profile (Eqs. A2–A3), and Eq. (3) relaxes the simulation toward this target. The solar-like Ω in the runs is therefore at least partly imposed: the forcing encodes the very observable being explained. The paper states explicitly that the physical origin of the entropy gradient is not modeled (§1, §4), but the abstract and conclusion present the result as an 'alternative scenario' for the solar rotation profile. As it stands, this is a demonstration of dynamical consistency, not a demonstration that the Sun possesses a sustained entropy gradient of the required amplitude and structure. Please narrow the claims accordingly, or provide a quantitative estimate of the required Θ_B and a discussion of whether such a gradient is consistent with observational constraints and with the r
[§2, boundary conditions after Eq. (3)] Eq. (3) relaxes Θ′ toward Θ_B, but the boundary conditions immediately below require Θ′=0 at r=0.72 and 0.96 R_sun. The target Θ_B shown in Fig. 2 has latitudinal structure at these radii (its latitudinal average is zero, but pointwise values are not), so the homogeneous Dirichlet condition is incompatible with the nudging target at the boundaries. This will create boundary layers in Θ′ and corresponding baroclinic torques. Please clarify how the boundary condition is imposed in the code, whether the source term is suppressed at the boundary cells, and whether the reported time averages—including Fig. 3 and the torque integrals of Fig. 4—are sensitive to this treatment.
[§3, first paragraph; §4] The paper's headline claim that solar-like differential rotation is maintained 'without relying on Reynolds stresses' is internally qualified. §3 states that 'weakly convective models ... are the only ones capable of reproducing the observed radial increase of Ω at low latitudes' and that 'the Reynolds stresses are responsible for torques capable of maintaining the radial increase of the rotation rate.' The radial increase at low latitudes is part of the observed solar profile, so the abstract and conclusions overstate the result. Please recast the claim to distinguish the baroclinically driven fast-equator/pole contrast from the low-latitude radial shear, which in the successful simulations is maintained with assistance from weak convective Reynolds stresses.

minor comments (8)

[Eq. (10)] The symbols C and B are used before they are defined; define them explicitly or insert a sentence introducing them.
[§2, paragraph on nudging] The phrase 'wavelength agnostic diffusivity' is vague. Since the Fourier-space form −τ^{-1}Θ̂′ is given, please explain the intended physical interpretation more concretely.
[Throughout] Spelling is inconsistent: 'superabadicity' vs. 'superadiabaticity' and 'heliosseismic' vs. 'helioseismic'. Please check the whole text.
[§4] The concluding paragraph ends with a stray 'a' after '...viable alternative to convection-dominated paradigms and contributes toward resolving long-standing discrepancies.'
[Fig. 2 caption] Please state the units and color-scale range for the potential-temperature panel; currently the reader cannot estimate the amplitude of Θ_B.
[Table 1] Entries in the second column like '1.5−1×10−4' are easy to misread as 1.5×10−4. Use explicit arithmetic (e.g., '1.4999') or add a space.
[References] In the reference for Stefan et al. 2026, 'Guerreo' appears to be a typo for 'Guerrero'. Please check.
[§2, numerical model] No explicit viscosity or diffusivity appears in Eqs. (1)–(3). If the runs rely on EULAG's numerical dissipation as an implicit subgrid model, please state this explicitly, since it is relevant for interpreting the Reynolds-stress torque decomposition.

Circularity Check

1 steps flagged · score 6.0 of 10

Solar-like rotation is partly an input: the prescribed entropy gradient Θ_B is derived from the observed helioseismic Ω profile, and the simulations are nudged toward it.

self definitional [Appendix A, Eq. (A1); Section 2, Eq. (3) and surrounding text]
"To obtain an entropy distribution compatible with the differential rotation profile inferred by helioseismic measurements, we integrate the thermal wind balance relation ... ΘB = C(r) − Θ0/g ∫ ∂Ω^2/∂z r dθ (A1). The nudging target profile Θ B implements an axis-symmetric potential temperature distribution in thermal wind balance with a velocity profile ... obtained by fitting the helioseismic observations ... into u 0 = a 0(r) + a 2(r) cos2(θ) + a 4(r) cos4(θ)."

Θ_B is constructed by integrating the thermal-wind balance from the observed helioseismic Ω profile (Eqs. A1–A3). The prognostic equation (3) then nudges Θ′ toward Θ_B on a τ ≈ 2.4–4.9 yr timescale. The simulated 'solar-like' rotation (fast equator, slow poles, radial contours) is therefore at least partly an input rather than an output: the forcing already encodes the target. The paper's own statement that the gradient is 'prescribed as a controlled forcing to test its dynamical consequences rather than to model its physical origin' confirms that the central driver is imported, not derived. Partial non-circular content remains in the departure from perfect TWB and the torque analysis.

full rationale

The paper makes a clear and honest distinction: it does not claim to derive the latitudinal entropy gradient from first principles, but rather prescribes it to test its dynamical consequences. However, the central result—that solar-like differential rotation can be generated without strong Reynolds stresses—is partially circular because the prescribed gradient itself is obtained by integrating the thermal-wind balance from the very helioseismic rotation profile that the simulations then reproduce. The Newtonian cooling term (Eq. 3) continuously relaxes the entropy perturbation toward this observed-derived target, so the pole-to-equator increase in Ω and the mid-latitude contour alignment are substantially built into the forcing. The non-vacuous content is the nonlinear dynamical consistency: the simulations show how the steady state departs from the imposed thermal-wind state via meridional circulation and how torques balance, which is a genuine result. There is no load-bearing self-citation or imported uniqueness theorem; the cited prior work (e.g., Hester et al. 2025) is used for comparison, not as a logical premise. The score of 6 reflects that one central 'prediction' (solar-like Ω) reduces by construction to the fitted input Θ_B, while the paper's own limitations statements are explicit and the dynamical analysis retains independent content.

Assumptions & free parameters 4 free parameters · 6 assumptions · 1 invented entities

The central claim rests on: (1) a forcing profile Θ_B constructed from the observed rotation through the thermal-wind integral — the target embeds the helioseismic Ω fit; (2) a Newtonian-cooling device (Eq. 3) that maintains this baroclinicity on multi-year timescales, standing in for an unmodeled physical process; (3) standard anelastic/polytropic modeling choices. Roughly a dozen hand-set or fitted numbers (Δ∇ scan values, τ values, the six DR-fit coefficients, and the gauge C(r)) enter the setup. No new physical entity beyond the prescribed entropy gradient is introduced, and its existence in the Sun is unverified.

free parameters (4)

Helioseismic DR fit coefficients α0, α2, α4, β0, β2, β4 (Eq. A2/A3) = Not tabulated (multiple linear regression to Larson & Schou 2018 data)
These coefficients define the smooth rotation profile that, via Eq. (A1), generates the forcing Θ_B. The solar-like character of the target is thus baked in from the fit.
Gauge function C(r) of the thermal-wind integral = Chosen by imposing vanishing latitudinal average of Θ_B
Eq. (A1) determines Θ_B only up to an arbitrary radial function; the chosen gauge sets the radial structure of the forced baroclinicity and therefore shapes the simulated radial Ω profile.
Nudging timescale τΘ = 7.8×10^7 s (~2.4 yr) and 1.5×10^8 s (~4.9 yr)
Hand-chosen values controlling the stiffness of the thermodynamic constraint in Eq. (3). The paper shows results depend on this choice (strongly convective models change behavior with τ).
Ambient superadiabaticity Δ∇ (10 values via polytropic index m_a) = Values in Table 1, ranging from −1.5×10^−7 to −1×10^−4, plus 0
Exploration parameters that set whether the layer is convectively unstable, neutral, or stable. The solar-likeness of the outcome is sensitive to this scan: strongly unstable cases become cylindrical.

assumptions (6)

domain assumption Anelastic (Lipps–Hemler) approximation is valid for the subsonic solar convection zone flow.
Invoked in §2, Eqs. (1)–(3). Standard for global solar convection modeling but filters acoustic modes and assumes small perturbations around a reference state.
ad hoc to paper Newtonian cooling with τ ≈ 2.4–4.9 yr (Eq. 3) is a faithful stand-in for whatever physical process would hold the entropy gradient in place.
The relaxation term is a numerical device whose solar counterpart is not identified. Without it, the prescribed baroclinicity would diffuse away; the mechanism's persistence in the Sun is therefore assumed, not shown.
standard math The constructed state satisfies steady thermal-wind/geostrophic balance, so Θ_B from Eq. (A1) is the correct entropy pattern for the fitted Ω.
Appendix A integrates the thermal-wind relation B = C, a standard derivation under the stated assumptions of a purely azimuthal flow and steady balance.
domain assumption The background stratification is polytropic with base-state index m_0 = 1.5 (adiabatic), matched to the solar standard model at r_min.
Used in §2, Eqs. (5)–(6) and Fig. 1. The quasi-adiabatic solar convection zone motivates this choice; departures near the boundaries are neglected.
domain assumption Stress-free, impermeable boundaries with vanishing potential-temperature fluctuation at r_min and r_max.
Stated in §2. These boundary conditions affect the torque balance and the meridional flow structure in the simulated shell.
domain assumption Gravity follows an inverse-square law with mass enclosed at r_min (Eq. 4).
Stated in §2. Standard for a thin spherical shell in the solar interior.

invented entities (1)

Externally prescribed, sustained latitudinal entropy (potential-temperature) gradient Θ_B in thermal wind balance with the observed rotation
purpose: Provides the baroclinic forcing that generates and maintains solar-like differential rotation without convective Reynolds stresses
Θ_B is constructed from the observed Ω via Eqs. (A1)–(A3) and maintained by the nudging term of Eq. (3). No observation, mechanism, or falsifiable handle outside the model establishes that such a gradient exists in the Sun; the paper explicitly states its origin is left open (§4).

how reviews work

0 comments

Cite this review

Pith. "Pith review of Solar differential rotation driven by baroclinic forcing." pith.science (2026). https://pith.science/paper/PEASFJEO

@misc{pith2026260719730,
  author       = {Pith},
  title        = {Pith review of: Solar differential rotation driven by baroclinic forcing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PEASFJEO}},
  note         = {Machine review of arXiv:2607.19730}
}

read the original abstract

A combination of recent observations and numerical simulations has called into question whether Sun's interior is characterized by strong turbulent convection, a problem known as convective conundrum. In light of a possible absence of vigorous convective motions, we examine whether the Sun's differential rotation, previously assumed to be tightly coupled to Reynolds stresses, may instead be sustained by the presence of a background latitudinal entropy gradient in thermal wind balance. By performing global hydrodynamical simulations of a rotating spherical shell representing the bulk of the solar convection zone, we demonstrate that solar-like differential rotation can be generated under a variety of thermal stratifications. This work proposes an alternative scenario for the origin of solar differential rotation that accommodates the previously reported discrepancies.

Figures

Figures reproduced from arXiv: 2607.19730 by the authors.

**Figure 1.** Top panel: polytropic background density, ρ0 (black line) and temperature, T0 (red line), profiles plotted as a solid line. The corresponding quantities extracted from the solar standard model of J. Christensen-Dalsgaard et al. (1996) are presented with dashed lines. Bottom panel: radial profiles of the ambient potential temperature for each class of simulations. The S, U and AD labels refer, respectively, to stab… view at source ↗

**Figure 2.** Angular velocities fitted from the heliosseismic data (T. P. Larson & J. Schou 2018) into Eqs. (A2) and (A3) (left), color limits are fixed to match the heliosseismic data. Potential temperature profile obtained after integration of Eq. (A1), using the fitted velocities, and imposition of a vanishing latitudinal average (right). The nudging target profile ΘB implements an axissymmetric potential temperature distri… view at source ↗

**Figure 3.** Time and longitudinal averages of the rotation rate (a, d, g), latitudinal velocity (b, e, h) and potential temperature perturbation (c, f, i) fields for three characteristic simulations chosen as so to represent the total set of simulations. Color levels on the first column is adjusted to match the limits of heliosseismic data (T. P. Larson & J. Schou 2018). Each row corresponds to a different simulation named aft… view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Time averaged radial (top row) and latitudinal (bottom row) integrals of the Reynolds stresses defined in Eq. (9) for the same simulations of [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: Time and longitudinal averages of the centrifugal (panels (a), (d), (g)) and baroclinic (panels (b), (e), (h)) terms, defined in Eq. (10), as well as their difference (panels (c), (f), (i)) for the same set simulations of [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: Time and longitudinal averages of the rotation rate, latitudinal velocity and potential temperature perturbation for the models listed in [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

299 extracted references · 102 canonical work pages

[1]

New Journal of Physics , author =

A quantum information processor with trapped ions , volume =. New Journal of Physics , author =. 2013 , note =. doi:10.1088/1367-2630/15/12/123012 , abstract =

work page doi:10.1088/1367-2630/15/12/123012 2013
[2]

Nature , author =

Experimental realization of. Nature , author =. 2001 , pages =. doi:10.1038/414883a , language =

work page doi:10.1038/414883a 2001
[3]

Science China Information Sciences , author =

Superconducting quantum computing: a review , volume =. Science China Information Sciences , author =. 2020 , pages =. doi:10.1007/s11432-020-2881-9 , abstract =

doi:10.1007/s11432-020-2881-9 2020
[4]

SIAM Journal on Computing , author =

Strengths and. SIAM Journal on Computing , author =. 1997 , note =. doi:10.1137/S0097539796300933 , abstract =

doi:10.1137/s0097539796300933 1997
[5]

Proceedings of the National Academy of Sciences , author =

Ensemble quantum computing by. Proceedings of the National Academy of Sciences , author =. 1997 , keywords =. doi:10.1073/pnas.94.5.1634 , abstract =

work page doi:10.1073/pnas.94.5.1634 1997
[6]

Advances in Physics , author =

The. Advances in Physics , author =. 2003 , note =. doi:10.1080/0001873021000049195 , abstract =

work page doi:10.1080/0001873021000049195 2003
[7]

Physical Review B , author =

Stochastic series expansion method with operator-loop update , volume =. Physical Review B , author =. 1999 , pages =. doi:10.1103/PhysRevB.59.R14157 , language =

doi:10.1103/physrevb.59.r14157 1999
[8]

Physical Review , author =

Residual. Physical Review , author =. 1967 , pages =. doi:10.1103/PhysRev.162.162 , language =

doi:10.1103/physrev.162.162 1967

Show all 299 references

[9]

Computers in Physics , author =

Quantum. Computers in Physics , author =. 1992 , pages =. doi:10.1063/1.4823122 , language =

1992 doi
[10]

Progress of Theoretical Physics , author =

Relationship between d-. Progress of Theoretical Physics , author =. 1976 , pages =. doi:10.1143/PTP.56.1454 , abstract =

1976 doi
[11]

Physical Review E , author =

Quantum. Physical Review E , author =. 2002 , pages =. doi:10.1103/PhysRevE.66.046701 , language =

2002 doi
[12]

Physical Review , author =

One-. Physical Review , author =. 1966 , pages =. doi:10.1103/PhysRev.150.321 , language =

1966 doi
[13]

Introduction to quantum integrability , volume =

Lamers, Jules , month = feb, year =. Introduction to quantum integrability , volume =. Proceedings of 10th. doi:10.22323/1.232.0001 , language =

doi
[14]

and Avella, Adolfo and Mancini, Ferdinando , year =

Sandvik, Anders W. and Avella, Adolfo and Mancini, Ferdinando , year =. Computational. doi:10.1063/1.3518900 , urldate =

doi
[15]

Physical Review Letters , author =

Cluster. Physical Review Letters , author =. 2001 , pages =. doi:10.1103/PhysRevLett.87.047203 , language =

2001 doi
[16]

Cluster algorithm for vertex models , volume =

Evertz, Hans Gerd and Lana, Gideon and Marcu, Mihai , year =. Cluster algorithm for vertex models , volume =
[17]

Journal of Fluid Mechanics , author =

Direct numerical simulation of laminar and turbulent. Journal of Fluid Mechanics , author =. 1982 , pages =. doi:10.1017/S0022112082001256 , abstract =

1982 doi
[18]

The Astrophysical Journal , author =

On the. The Astrophysical Journal , author =. 1965 , note =. doi:10.1086/148106 , abstract =

1965 doi
[19]

Physics of Fluids , author =

Thermal inertial waves in a rotating fluid layer:. Physics of Fluids , author =. 1997 , pages =. doi:10.1063/1.869317 , abstract =

1997 doi
[20]

and Margolin, Len G

Grinstein, Fenando F. and Margolin, Len G. and Rider, William , year =. Implicit large eddy simulation: computing turbulent fluid dynamics , isbn =
[21]

Haemorrhage and thrombosis for the

Harper, Ann , year =. Haemorrhage and thrombosis for the
[22]

, year =

Ballentine, Leslie E. , year =. Quantum mechanics: a modern development , isbn =
[23]

Living Reviews in Computational Astrophysics , author =

Modelling of stellar convection , volume =. Living Reviews in Computational Astrophysics , author =. 2017 , keywords =. doi:10.1007/s41115-017-0001-9 , abstract =

2017 doi
[24]

Journal of Computational Physics , author =

Computational design for long-term numerical integration of the equations of fluid motion:. Journal of Computational Physics , author =. 1966 , pages =. doi:10.1016/0021-9991(66)90015-5 , abstract =

1966 doi
[25]

Quarterly Journal of the Royal Meteorological Society , author =

Validity of anelastic and other equation sets as inferred from normal-mode analysis , volume =. Quarterly Journal of the Royal Meteorological Society , author =. 2003 , note =. doi:10.1256/qj.02.1951 , abstract =

2003 doi
[26]

Meteorology and Atmospheric Physics , author =

Review of numerical methods for nonhydrostatic weather prediction models , volume =. Meteorology and Atmospheric Physics , author =. 2003 , keywords =. doi:10.1007/s00703-001-0593-8 , abstract =

2003 doi
[27]

, month = mar, year =

Lorenz, Edward N. , month = mar, year =. Deterministic. Journal of the Atmospheric Sciences , publisher =. doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 , abstract =

1963 doi
[28]

and Rheinhardt, Matthias and Brandenburg, Axel and Arlt, Rainer and Käpylä, Maarit J

Käpylä, Petri J. and Rheinhardt, Matthias and Brandenburg, Axel and Arlt, Rainer and Käpylä, Maarit J. and Lagg, Andreas and Olspert, Nigul and Warnecke, Jörn , month = aug, year =. Extended. The Astrophysical Journal Letters , publisher =. doi:10.3847/2041-8213/aa83ab , abstract =

doi
[29]

The Astrophysical Journal Supplement Series , author =

Compressible convection in a rotating spherical shell. The Astrophysical Journal Supplement Series , author =. 1981 , note =. doi:10.1086/190714 , abstract =

1981 doi
[30]

Stein, R. F. and Nordlund, Å , month = jun, year =. Simulations of. The Astrophysical Journal , publisher =. doi:10.1086/305678 , language =

doi
[31]

Journal of Computational Physics , author =

Building resolving large-eddy simulations and comparison with wind tunnel experiments , volume =. Journal of Computational Physics , author =. 2007 , keywords =. doi:10.1016/j.jcp.2007.08.005 , abstract =

2007 doi
[32]

Computers & Fluids , author =

Don't suppress the wiggles—. Computers & Fluids , author =. 1981 , pages =. doi:10.1016/0045-7930(81)90026-8 , abstract =

1981 doi
[33]

and Smolarkiewicz, Piotr K

Klein, Rupert and Achatz, Ulrich and Bresch, Didier and Knio, Omar M. and Smolarkiewicz, Piotr K. , month = oct, year =. Regime of. Journal of the Atmospheric Sciences , publisher =. doi:10.1175/2010JAS3490.1 , abstract =

doi
[34]

and Brandenburg, A

Barekat, A. and Brandenburg, A. , month = nov, year =. Near-polytropic stellar simulations with a radiative surface , volume =. Astronomy & Astrophysics , publisher =. doi:10.1051/0004-6361/201322461 , abstract =

doi
[35]

The Astrophysical Journal , author =

The. The Astrophysical Journal , author =. 1991 , note =. doi:10.1086/170441 , abstract =

1991 doi
[36]

and Lecoanet, Daniel and Brown, Benjamin P

Anders, Evan H. and Lecoanet, Daniel and Brown, Benjamin P. , month = oct, year =. Entropy. The Astrophysical Journal , publisher =. doi:10.3847/1538-4357/ab3644 , abstract =

doi
[37]

Living Reviews in Solar Physics , author =

Solar. Living Reviews in Solar Physics , author =. 2009 , keywords =. doi:10.12942/lrsp-2009-2 , abstract =

2009 doi
[38]

Reports on Progress in Physics , author =

Astrophysical turbulence modeling , volume =. Reports on Progress in Physics , author =. 2011 , pages =. doi:10.1088/0034-4885/74/4/046901 , abstract =

2011 doi
[39]

and Hindman, Bradley W

Greer, Benjamin J. and Hindman, Bradley W. and Featherstone, Nicholas A. and Toomre, Juri , month = apr, year =. The Astrophysical Journal Letters , publisher =. doi:10.1088/2041-8205/803/2/L17 , abstract =

doi
[40]

Solar Physics , author =

Multichannel. Solar Physics , author =. 2012 , keywords =. doi:10.1007/s11207-011-9873-8 , abstract =

2012 doi
[41]

Journal of Computational Physics , author =

Simulations of stellar convection with. Journal of Computational Physics , author =. 2012 , keywords =. doi:10.1016/j.jcp.2011.09.026 , abstract =

2012 doi
[42]

Astronomy and Astrophysics , author =

Numerical simulations of convection at the surface of a. Astronomy and Astrophysics , author =. 1994 , note =

1994
[43]

, month = mar, year =

Trampedach, Regner and Stein, Robert F. , month = mar, year =. The Astrophysical Journal , publisher =. doi:10.1088/0004-637X/731/2/78 , abstract =

doi
[44]

, month = jun, year =

Durran, Dale R. , month = jun, year =. Improving the. Journal of the Atmospheric Sciences , publisher =. doi:10.1175/1520-0469(1989)046<1453:ITAA>2.0.CO;2 , abstract =

1989 doi
[45]

, month = jul, year =

Lipps, Frank B. , month = jul, year =. On the. Journal of the Atmospheric Sciences , publisher =. doi:10.1175/1520-0469(1990)047<1794:OTAAFD>2.0.CO;2 , abstract =

1990 doi
[46]

and Hemler, Richard S

Lipps, Franik B. and Hemler, Richard S. , month = oct, year =. A. Journal of the Atmospheric Sciences , publisher =. doi:10.1175/1520-0469(1982)039<2192:ASAODM>2.0.CO;2 , abstract =

1982 doi
[47]

, volume =

Turbulent plumes in stellar convective envelopes. , volume =. Astronomy and Astrophysics , author =. 1995 , note =

1995
[48]

The Astrophysical Journal , author =

Topology of. The Astrophysical Journal , author =. 1989 , note =. doi:10.1086/185493 , abstract =

1989 doi
[49]

Investigative Urology , author =

Computer evaluation of the effect of urecholine on the spontaneous activity of smooth muscle from the urinary bladder of the rabbit , volume =. Investigative Urology , author =. 1975 , keywords =

1975
[50]

The Astrophysical Journal , author =

Numerical. The Astrophysical Journal , author =. 2022 , pages =. doi:10.3847/1538-4357/ac54b7 , abstract =

2022 doi
[51]

and Weiss, A

Kippenhahn, Rudolf and Weigert, A. and Weiss, A. , year =. Stellar structure and evolution , isbn =
[52]

The Astrophysical Journal , publisher =

Brandenburg, Axel , month = nov, year =. The Astrophysical Journal , publisher =. doi:10.3847/0004-637X/832/1/6 , abstract =

doi
[53]

Journal of Computational Physics , author =

A fully multidimensional positive definite advection transport algorithm with small implicit diffusion , volume =. Journal of Computational Physics , author =. 1984 , pages =. doi:10.1016/0021-9991(84)90121-9 , abstract =

1984 doi
[54]

Deardorff, J. W. , month = sep, year =. The. Journal of the Atmospheric Sciences , publisher =. doi:10.1175/1520-0469(1966)023<0503:TCGHFI>2.0.CO;2 , abstract =

1966 doi
[55]

Journal of Fluid Mechanics , author =

Scaling of hard thermal turbulence in. Journal of Fluid Mechanics , author =. 1989 , pages =. doi:10.1017/S0022112089001643 , language =

1989 doi
[56]

and Castaing, B

Heslot, F. and Castaing, B. and Libchaber, A. , month = dec, year =. Transitions to turbulence in helium gas , volume =. Physical Review A , publisher =. doi:10.1103/PhysRevA.36.5870 , abstract =

doi
[57]

Lantz, S. R. and Fan, Y. , month = mar, year =. Anelastic. The Astrophysical Journal Supplement Series , publisher =. doi:10.1086/313187 , language =

doi
[59]

, year =

Chandrasekhar, S. , year =. Hydrodynamic and hydromagnetic stability , isbn =
[60]

Science , author =

The. Science , author =. 1996 , pages =. doi:10.1126/science.272.5266.1286 , language =

1996
[61]

2008 , pages =

Computers & Fluids , author =. 2008 , pages =. doi:10.1016/j.compfluid.2007.12.001 , abstract =

2008 doi
[62]

and Vasil, Geoffrey M

Brown, Benjamin P. and Vasil, Geoffrey M. and Zweibel, Ellen G. , month = aug, year =. The Astrophysical Journal , publisher =. doi:10.1088/0004-637X/756/2/109 , abstract =

doi
[63]

The Astrophysical Journal , publisher =

Verhoeven, Jan and Wiesehöfer, Thomas and Stellmach, Stephan , month = may, year =. The Astrophysical Journal , publisher =. doi:10.1088/0004-637X/805/1/62 , abstract =

doi
[64]

and Julien, Keith and Marti, Philippe , month = mar, year =

Calkins, Michael A. and Julien, Keith and Marti, Philippe , month = mar, year =. The breakdown of the anelastic approximation in rotating compressible convection: implications for astrophysical systems , volume =. Proceedings of the Royal Society A: Mathematical, Physical and ...

2014
[65]

, year =

Menicucci, L.S. , year =. Computational study of the phase transitions of a tridimensional anisotropic ferromagnetic model using the roots of the energy`s
[66]

Roger and Seldin, J

Hindley, J. Roger and Seldin, J. P. , year =. Lambda-calculus and combinators, an introduction , isbn =
[67]

The physics of fluids and plasmas: an introduction for astrophysicists , isbn =

Choudhuri, Arnab Rai , year =. The physics of fluids and plasmas: an introduction for astrophysicists , isbn =
[68]

International Journal for Numerical Methods in Fluids , author =

Multidimensional positive definite advection transport algorithm: an overview , volume =. International Journal for Numerical Methods in Fluids , author =. 2006 , note =. doi:10.1002/fld.1071 , abstract =

2006 doi
[69]

Journal of Computational Physics , author =

A consistent framework for discrete integrations of soundproof and compressible. Journal of Computational Physics , author =. 2014 , keywords =. doi:10.1016/j.jcp.2014.01.031 , abstract =

2014 doi
[70]

Where were you when? 180 unforgettable moments in living history , isbn =

Harrison, Ian , year =. Where were you when? 180 unforgettable moments in living history , isbn =
[71]

Thinking with type: a critical guide for designers, writers, editors, & students , isbn =

Lupton, Ellen , year =. Thinking with type: a critical guide for designers, writers, editors, & students , isbn =
[72]

a , month = mar, year =

Davidson, P. a , month = mar, year =. An
[73]

Living Reviews in Solar Physics , author =

Dynamo models of the solar cycle , volume =. Living Reviews in Solar Physics , author =. 2020 , keywords =. doi:10.1007/s41116-020-00025-6 , abstract =

2020 doi
[74]

The Astrophysical Journal , author =

On the. The Astrophysical Journal , author =. 1908 , pages =. doi:10.1086/141602 , language =

1908 doi
[75]

Solid State Communications , author =

Magnetic vortices in kekulene-like molecules , volume =. Solid State Communications , author =. 2021 , pages =. doi:10.1016/j.ssc.2021.114224 , language =

2021
[76]

Morningstar, Colin , month = feb, year =. The. doi:10.48550/arXiv.hep-lat/0702020 , abstract =

doi arXiv
[77]

and Wilmer, Elizabeth L

Levin, David Asher and Peres, Y. and Wilmer, Elizabeth L. and Propp, James and Wilson, David B. , year =. Markov chains and mixing times , isbn =
[78]

and Hibbs, Albert R

Feynman, Richard P. and Hibbs, Albert R. , year =. Quantum mechanics and path integrals , isbn =
[79]

, month = nov, year =

Jarzynski, C. , month = nov, year =. Equilibrium free-energy differences from nonequilibrium measurements:. Physical Review E , publisher =. doi:10.1103/PhysRevE.56.5018 , abstract =

doi
[80]

Out-of-equilibrium protocol for

Alba, Vincenzo , month = jun, year =. Out-of-equilibrium protocol for. Physical Review E , publisher =. doi:10.1103/PhysRevE.95.062132 , abstract =

doi
[81]

, month = apr, year =

Jarzynski, C. , month = apr, year =. Nonequilibrium. Physical Review Letters , publisher =. doi:10.1103/PhysRevLett.78.2690 , abstract =

doi
[82]

Entanglement

D'Emidio, Jonathan , month = mar, year =. Entanglement. Physical Review Letters , publisher =. doi:10.1103/PhysRevLett.124.110602 , abstract =

doi
[83]

Measuring

Zhao, Jiarui and Chen, Bin-Bin and Wang, Yan-Cheng and Yan, Zheng and Cheng, Meng and Meng, Zi Yang , month = jun, year =. Measuring. npj Quantum Materials , publisher =. doi:10.1038/s41535-022-00476-0 , abstract =

doi
[84]

and Vazirani, Umesh Virkumar , year =

Dasgupta, Sanjoy and Papadimitriou, Christos H. and Vazirani, Umesh Virkumar , year =. Algorithms , isbn =
[85]

Introductory functional analysis with applications , isbn =

Kreyszig, Erwin , year =. Introductory functional analysis with applications , isbn =
[86]

and Urbantke, Helmuth K

Sexl, Roman U. and Urbantke, Helmuth K. , month = mar, year =. Production of. Physical Review , publisher =. doi:10.1103/PhysRev.179.1247 , abstract =

doi
[87]

Field theory: a modern primer , isbn =

Ramond, Pierre , year =. Field theory: a modern primer , isbn =
[88]

Physics Physique Fizika , author =

On the. Physics Physique Fizika , author =. 1964 , pages =. doi:10.1103/PhysicsPhysiqueFizika.1.195 , language =

1964 doi
[89]

, month = jun, year =

Fursaev, Dmitri V. , month = jun, year =. Entanglement entropy in critical phenomena and analog models of quantum gravity , volume =. Physical Review D , publisher =. doi:10.1103/PhysRevD.73.124025 , abstract =

doi
[90]

Journal of High Energy Physics , author =

Entanglement entropy: a perturbative calculation , volume =. Journal of High Energy Physics , author =. 2014 , keywords =. doi:10.1007/JHEP12(2014)179 , abstract =

2014 doi
[91]

Journal of High Energy Physics , author =

Some calculable contributions to holographic entanglement entropy , volume =. Journal of High Energy Physics , author =. 2011 , keywords =. doi:10.1007/JHEP08(2011)039 , abstract =

2011 doi
[92]

, month = dec, year =

Hertzberg, Mark P. , month = dec, year =. Entanglement entropy in scalar field theory , volume =. Journal of Physics A: Mathematical and Theoretical , publisher =. doi:10.1088/1751-8113/46/1/015402 , abstract =

doi
[93]

and Wilczek, Frank , month = feb, year =

Hertzberg, Mark P. and Wilczek, Frank , month = feb, year =. Some. Physical Review Letters , publisher =. doi:10.1103/PhysRevLett.106.050404 , abstract =

doi
[94]

Physics Letters B , author =

Entanglement entropy, conformal invariance and extrinsic geometry , volume =. Physics Letters B , author =. 2008 , pages =. doi:10.1016/j.physletb.2008.05.071 , abstract =

2008 doi
[95]

Aspects of holographic entanglement entropy , volume =

Ryu, Shinsei and Takayanagi, Tadashi , month = aug, year =. Aspects of holographic entanglement entropy , volume =. Journal of High Energy Physics , publisher =. doi:10.1088/1126-6708/2006/08/045 , abstract =

2006 doi
[96]

Nuclear Physics B , author =

Geometric and renormalized entropy in conformal field theory , volume =. Nuclear Physics B , author =. 1994 , pages =. doi:10.1016/0550-3213(94)90402-2 , abstract =

1994 doi
[97]

Nuclear Physics B , author =

Entanglement entropy, trace anomalies and holography , volume =. Nuclear Physics B , author =. 2008 , pages =. doi:10.1016/j.nuclphysb.2008.04.015 , abstract =

2008 doi
[98]

and Morton, K

Richtmyer, Robert D. and Morton, K. W. , year =. Difference methods for initial-value problems , isbn =
[99]

Physics Reports , author =

The renormalization group and the ϵ expansion , volume =. Physics Reports , author =. 1974 , pages =. doi:10.1016/0370-1573(74)90023-4 , abstract =

1974 doi
[100]

Annals of Physics , author =

The density-matrix renormalization group in the age of matrix product states , volume =. Annals of Physics , author =. 2011 , pages =. doi:10.1016/j.aop.2010.09.012 , abstract =

2011 doi
[101]

Newman, M. E. J. and Barkema, G. T. , year =. Monte
[102]

Quantum. Do. 2019 , keywords =. doi:10.1017/9781108569361.010 , urldate =

2019 doi
[103]

, year =

Peskin, Michael Edward and Schroeder, Daniel V. , year =. An introduction to quantum field theory , isbn =
[104]

Jaynes, E. T. , month = may, year =. Information. Physical Review , publisher =. doi:10.1103/PhysRev.106.620 , abstract =

doi
[105]

, month = oct, year =

Werner, Reinhard F. , month = oct, year =. Quantum states with. Physical Review A , publisher =. doi:10.1103/PhysRevA.40.4277 , abstract =

doi
[106]

and Bruß, D

Lewenstein, M. and Bruß, D. and Cirac, J. I. and Kraus, B. and Kuś, M. and Samsonowicz, J. and Sanpera, A. and Tarrach, R. , month = nov, year =. Separability and distillability in composite quantum systems-a primer , volume =. Journal of Modern Optics , publisher =. doi:10.10...

doi
[107]

, month = oct, year =

Schrödinger, E. , month = oct, year =. Discussion of. Mathematical Proceedings of the Cambridge Philosophical Society , publisher =. doi:10.1017/S0305004100013554 , abstract =

doi
[108]

Entanglement entropy for a

Casini, Horacio and Huerta, Marina , month = nov, year =. Entanglement entropy for a. Physical Review D , publisher =. doi:10.1103/PhysRevD.90.105013 , abstract =

doi
[109]

Journal of High Energy Physics , author =

Exact and numerical results on entanglement entropy in (5 + 1)-dimensional. Journal of High Energy Physics , author =. 2012 , keywords =. doi:10.1007/JHEP12(2012)005 , abstract =

2012 doi
[110]

Journal of High Energy Physics , author =

A refinement of entanglement entropy and the number of degrees of freedom , volume =. Journal of High Energy Physics , author =. 2013 , note =. doi:10.1007/JHEP04(2013)162 , abstract =

2013 doi
[111]

Physics Reports , author =

Quantum entanglement in condensed matter systems , volume =. Physics Reports , author =. 2016 , pages =. doi:10.1016/j.physrep.2016.06.008 , abstract =

2016 doi
[112]

Reviews of Modern Physics , author =

Area laws for the entanglement entropy - a review , volume =. Reviews of Modern Physics , author =. 2010 , note =. doi:10.1103/RevModPhys.82.277 , abstract =

2010 doi
[113]

't , month = mar, year =

Hooft, G. 't , month = mar, year =. Dimensional
[114]

The world as a hologram , volume =

Susskind, Leonard , month = nov, year =. The world as a hologram , volume =. Journal of Mathematical Physics , publisher =. doi:10.1063/1.531249 , number =

doi
[115]

Journal of Geometry and Physics , author =

Ambiguity of the equivalence principle and. Journal of Geometry and Physics , author =. 1984 , pages =. doi:10.1016/0393-0440(84)90013-5 , abstract =

1984 doi
[116]

Reduced density matrices and entanglement entropy in free lattice models , volume =

Peschel, Ingo and Eisler, Viktor , month = dec, year =. Reduced density matrices and entanglement entropy in free lattice models , volume =. Journal of Physics A: Mathematical and Theoretical , publisher =. doi:10.1088/1751-8113/42/50/504003 , abstract =

doi
[117]

Hawking, S. W. , month = jan, year =. Black holes and thermodynamics , volume =. Physical Review D , publisher =. doi:10.1103/PhysRevD.13.191 , abstract =

doi
[118]

, month = feb, year =

Schiffer, Marcelo and Bekenstein, Jacob D. , month = feb, year =. Proof of the quantum bound on specific entropy for free fields , volume =. Physical Review D , publisher =. doi:10.1103/PhysRevD.39.1109 , abstract =

doi
[119]

Pramana , author =

The real symplectic groups in quantum mechanics and optics , volume =. Pramana , author =. 1995 , keywords =. doi:10.1007/BF02848172 , abstract =

1995 doi
[120]

Publications of the Research Institute for Mathematical Sciences , author =

On. Publications of the Research Institute for Mathematical Sciences , author =. 1970 , pages =. doi:10.2977/prims/1195193913 , number =

1970
[121]

, month = jun, year =

Adesso, Gerardo and Ragy, Sammy and Lee, Antony R. , month = jun, year =. Continuous. Open Systems & Information Dynamics , publisher =. doi:10.1142/S1230161214400010 , abstract =

doi
[122]

Communications in Mathematical Physics , author =

Black holes in general relativity , volume =. Communications in Mathematical Physics , author =. 1972 , keywords =. doi:10.1007/BF01877517 , abstract =

1972 doi
[123]

Communications in Mathematical Physics , author =

The commutation property of a stationary, axisymmetric system , volume =. Communications in Mathematical Physics , author =. 1970 , keywords =. doi:10.1007/BF01647092 , abstract =

1970 doi
[124]

Hawking, Stephen W and Ellis, G. F. R , year =. The
[125]

General Relativity and Gravitation , author =

". General Relativity and Gravitation , author =. 2002 , keywords =. doi:10.1023/A:1016578408204 , language =

2002 doi
[126]

, month = feb, year =

Bekenstein, Jacob D. , month = feb, year =. Transcendence of the. Physical Review Letters , publisher =. doi:10.1103/PhysRevLett.28.452 , abstract =

doi
[127]

, month = may, year =

Bekenstein, Jacob D. , month = may, year =. Nonexistence of. Physical Review D , publisher =. doi:10.1103/PhysRevD.5.2403 , abstract =

doi
[128]

Communications in Mathematical Physics , author =

The four laws of black hole mechanics , volume =. Communications in Mathematical Physics , author =. 1973 , keywords =. doi:10.1007/BF01645742 , abstract =

1973 doi
[129]

and Thorne, Kip S

Misner, Charles W. and Thorne, Kip S. and Wheeler, John Archibald , year =. Gravitation , isbn =
[130]

, month = feb, year =

Bekenstein, Jacob D. , month = feb, year =. Extraction of. Physical Review D , publisher =. doi:10.1103/PhysRevD.7.949 , abstract =

doi
[131]

, month = nov, year =

Bekenstein, Jacob D. , month = nov, year =. Statistical black-hole thermodynamics , volume =. Physical Review D , publisher =. doi:10.1103/PhysRevD.12.3077 , abstract =

doi
[132]

, month = jun, year =

Bekenstein, Jacob D. , month = jun, year =. Generalized second law of thermodynamics in black-hole physics , volume =. Physical Review D , publisher =. doi:10.1103/PhysRevD.9.3292 , abstract =

doi
[133]

Physics Letters B , author =

Numerical determination of the entanglement entropy for free fields in the cylinder , volume =. Physics Letters B , author =. 2012 , pages =. doi:10.1016/j.physletb.2012.03.044 , abstract =

2012 doi
[134]

Dowker, J. S. , month = oct, year =. Hyperspherical entanglement entropy , volume =. Journal of Physics A: Mathematical and Theoretical , publisher =. doi:10.1088/1751-8113/43/44/445402 , abstract =

doi
[135]

Physics Letters B , author =

Entanglement entropy for the n-sphere , volume =. Physics Letters B , author =. 2010 , keywords =. doi:10.1016/j.physletb.2010.09.054 , abstract =

2010 doi
[136]

Physics Letters B , author =

Numerical determination of entanglement entropy for a sphere , volume =. Physics Letters B , author =. 2010 , pages =. doi:10.1016/j.physletb.2010.01.053 , abstract =

2010 doi
[137]

1988 , keywords =

Numerical recipes in. 1988 , keywords =

1988
[138]

and Bosilca, George and Angskun, Thara and Dongarra, Jack J

Gabriel, Edgar and Fagg, Graham E. and Bosilca, George and Angskun, Thara and Dongarra, Jack J. and Squyres, Jeffrey M. and Sahay, Vishal and Kambadur, Prabhanjan and Barrett, Brian and Lumsdaine, Andrew and Castain, Ralph H. and Daniel, David J. and Graham, Richard L. and Woo...

2004 doi
[139]

Xianyi, Zhang , month = jun, year =
[140]

What's new , month = dec, year =
[141]

Annals of Physics , author =

Regularization and renormalization of quantum field theory in curved space-time , volume =. Annals of Physics , author =. 1977 , pages =. doi:10.1016/0003-4916(77)90210-X , language =

1977 doi
[142]

Physical Review D , author =

Nonuniqueness of. Physical Review D , author =. 1973 , pages =. doi:10.1103/PhysRevD.7.2850 , language =

1973 doi
[143]

A modern introduction to quantum field theory , isbn =

Maggiore, Michele , year =. A modern introduction to quantum field theory , isbn =
[144]

and Johnson, Charles R

Horn, Roger A. and Johnson, Charles R. , month = dec, year =. Matrix. doi:10.1017/CBO9780511810817 , urldate =

doi
[145]

arXiv:2204.09464 [hep-th] , author =

Instability of. arXiv:2204.09464 [hep-th] , author =. 2022 , note =

2022 arXiv
[146]

and Eisert, J

Audenaert, K. and Eisert, J. and Plenio, M. B. and Werner, R. F. , month = oct, year =. Entanglement properties of the harmonic chain , volume =. Physical Review A , publisher =. doi:10.1103/PhysRevA.66.042327 , abstract =

doi
[147]

Entanglement entropy of squeezed vacua on a lattice , volume =

Bianchi, Eugenio and Hackl, Lucas and Yokomizo, Nelson , month = oct, year =. Entanglement entropy of squeezed vacua on a lattice , volume =. Physical Review D , publisher =. doi:10.1103/PhysRevD.92.085045 , abstract =

doi
[148]

, month = dec, year =

Nicacio, F. , month = dec, year =. Williamson theorem in classical, quantum, and statistical physics , volume =. American Journal of Physics , publisher =. doi:10.1119/10.0005944 , number =

doi
[149]

Bosonic quadratic

Dereziński, Jan , month = dec, year =. Bosonic quadratic. Journal of Mathematical Physics , publisher =. doi:10.1063/1.5017931 , number =

doi
[150]

Rényi, Alfréd , month = jan, year =. On. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics , publisher =
[151]

and González, Iván and Kallin, Ann B

Hastings, Matthew B. and González, Iván and Kallin, Ann B. and Melko, Roger G. , month = apr, year =. Measuring. Physical Review Letters , publisher =. doi:10.1103/PhysRevLett.104.157201 , abstract =

doi
[152]

Journal of High Energy Physics , author =

Observations on entanglement entropy in massive. Journal of High Energy Physics , author =. 2013 , keywords =. doi:10.1007/JHEP04(2013)017 , abstract =

2013 doi
[153]

Holevo, A. S. and Sohma, M. and Hirota, O. , month = mar, year =. Capacity of quantum. Physical Review A , publisher =. doi:10.1103/PhysRevA.59.1820 , abstract =

doi
[154]

Wightman, A. S. , month = jan, year =. Quantum. Physical Review , publisher =. doi:10.1103/PhysRev.101.860 , abstract =

doi
[155]

Reviews of Modern Physics , author =

Entanglement entropy:. Reviews of Modern Physics , author =. 2018 , pages =. doi:10.1103/RevModPhys.90.035007 , language =

2018 doi
[156]

Calculation of reduced density matrices from correlation functions , volume =

Peschel, Ingo , month = mar, year =. Calculation of reduced density matrices from correlation functions , volume =. Journal of Physics A: Mathematical and General , publisher =. doi:10.1088/0305-4470/36/14/101 , abstract =

doi
[157]

Entanglement in continuous-variable systems: recent advances and current perspectives , volume =

Adesso, Gerardo and Illuminati, Fabrizio , month = jun, year =. Entanglement in continuous-variable systems: recent advances and current perspectives , volume =. Journal of Physics A: Mathematical and Theoretical , publisher =. doi:10.1088/1751-8113/40/28/S01 , abstract =

doi
[158]

, year =

Zee, A. , year =. Group theory in a nutshell for physicists , isbn =
[159]

arXiv:2111.05154 [cond-mat, physics:hep-th] , author =

On the continuum limit of the entanglement. arXiv:2111.05154 [cond-mat, physics:hep-th] , author =. 2021 , note =

2021 arXiv
[160]

Introduction to quantum fields on a lattice: 'a robust mate' , isbn =

Smit, Jan , year =. Introduction to quantum fields on a lattice: 'a robust mate' , isbn =
[161]

and Münster, Gernot , year =

Montvay, I. and Münster, Gernot , year =. Quantum fields on a lattice , isbn =
[162]

and Shapiro, Stuart L

Baumgarte, Thomas W. and Shapiro, Stuart L. , year =. Numerical relativity: starting from scratch , isbn =
[163]

and Schroeter, Darrell F

Griffiths, David J. and Schroeter, Darrell F. , year =. Introduction to quantum mechanics , isbn =
[164]

Physical Review D , author =

Universal terms of the entanglement entropy in a static closed universe , volume =. Physical Review D , author =. 2021 , pages =. doi:10.1103/PhysRevD.104.125016 , language =

2021 doi
[165]

An updated performance comparison of virtual machines and

Felter, Wes and Ferreira, Alexandre and Rajamony, Ram and Rubio, Juan , month = mar, year =. An updated performance comparison of virtual machines and. 2015. doi:10.1109/ISPASS.2015.7095802 , urldate =

2015
[166]

Álgebra linear , isbn =

Lima, Elon Lages , year =. Álgebra linear , isbn =
[167]

, year =

Wald, Robert M. , year =. General relativity , isbn =
[168]

, year =

Carroll, Sean M. , year =. Spacetime and geometry: an introduction to general relativity , isbn =
[169]

Wave and

Teller, Paul , editor =. Wave and. Perspectives on. 1996 , pages =. doi:10.1007/978-94-015-8656-6_11 , urldate =

1996 doi
[170]

Methods of modern mathematical physics , isbn =

Reed, Michael and Simon, Barry , year =. Methods of modern mathematical physics , isbn =
[171]

Greiner, Walter and Reinhardt, Joachim , year =. Field. doi:10.1007/978-3-642-61485-9 , language =

doi
[172]

D and Davies, P

Birrell, N. D and Davies, P. C. W , year =. Quantum
[173]

Journal of Mathematical Physics , author =

Characterizing entanglement , volume =. Journal of Mathematical Physics , author =. 2002 , pages =. doi:10.1063/1.1494474 , language =

2002 doi
[174]

Geometry of quantum states: an introduction to quantum entanglement , isbn =

Bengtsson, Ingemar and Życzkowski, Karol , year =. Geometry of quantum states: an introduction to quantum entanglement , isbn =
[175]

A , year =

Salinas, Sílvio R. A , year =. Introdução à física estatística , isbn =
[176]

Physical Review Letters , author =

Teleporting an unknown quantum state via dual classical and. Physical Review Letters , author =. 1993 , pages =. doi:10.1103/PhysRevLett.70.1895 , language =

1993 doi
[177]

, year =

Grover, Lov K. , year =. A fast quantum mechanical algorithm for database search , isbn =. Proceedings of the twenty-eighth annual. doi:10.1145/237814.237866 , language =
[178]

J and Napolitano, Jim , year =

Sakurai, J. J and Napolitano, Jim , year =. Modern quantum mechanics , isbn =
[179]

doi:10.1007/0-306-47120-5 , language =

Quantum. doi:10.1007/0-306-47120-5 , language =

doi
[180]

and Bai, Z

Anderson, E. and Bai, Z. and Bischof, C. and Blackford, L. S. and Demmel, J. and Dongarra, J. and Du Croz, J. and Greenbaum, A. and Hammarling, S. and McKenney, A. and Sorensen, D. , month = jan, year =. doi:10.1137/1.9780898719604 , language =

doi
[181]

Reviews of Modern Physics , author =

The holographic principle , volume =. Reviews of Modern Physics , author =. 2002 , pages =. doi:10.1103/RevModPhys.74.825 , language =

2002 doi
[182]

Nuclear Physics B , author =

On the quantum structure of a black hole , volume =. Nuclear Physics B , author =. 1985 , pages =. doi:10.1016/0550-3213(85)90418-3 , language =

1985 doi
[183]

General Relativity and Gravitation , author =

Building up spacetime with quantum entanglement , volume =. General Relativity and Gravitation , author =. 2010 , pages =. doi:10.1007/s10714-010-1034-0 , language =

2010 doi
[184]

Bell System Technical Journal , author =

A. Bell System Technical Journal , author =. 1948 , pages =. doi:10.1002/j.1538-7305.1948.tb01338.x , language =

1948
[185]

Physical Review , author =

Event. Physical Review , author =. 1967 , pages =. doi:10.1103/PhysRev.164.1776 , language =

1967 doi
[186]

Physical Review Letters , author =

Axisymmetric. Physical Review Letters , author =. 1971 , pages =. doi:10.1103/PhysRevLett.26.331 , language =

1971 doi
[187]

Physical Review Letters , author =

Reversible and. Physical Review Letters , author =. 1970 , pages =. doi:10.1103/PhysRevLett.25.1596 , language =

1970 doi
[188]

Physical Review D , author =

Reversible. Physical Review D , author =. 1971 , pages =. doi:10.1103/PhysRevD.4.3552 , language =

1971 doi
[189]

Nature Physical Science , author =

Extraction of. Nature Physical Science , author =. 1971 , pages =. doi:10.1038/physci229177a0 , language =

1971 doi
[190]

Physical Review , author =

Detection and. Physical Review , author =. 1960 , pages =. doi:10.1103/PhysRev.117.306 , language =

1960 doi
[191]

Physical Review Letters , author =

Anisotropy and. Physical Review Letters , author =. 1970 , pages =. doi:10.1103/PhysRevLett.25.180 , language =

1970 doi
[192]

Physical Review Letters , author =

Gravitational. Physical Review Letters , author =. 1971 , pages =. doi:10.1103/PhysRevLett.26.1344 , language =

1971 doi
[193]

Communications In Mathematical Physics , author =

Particle creation by black holes , volume =. Communications In Mathematical Physics , author =. 1975 , pages =. doi:10.1007/BF02345020 , language =

1975 doi
[194]

Physical Review D , author =

Probability distribution of particles created by a black hole , volume =. Physical Review D , author =. 1975 , pages =. doi:10.1103/PhysRevD.12.1519 , language =

1975 doi
[195]

Physical Review D , author =

Einstein. Physical Review D , author =. 1977 , pages =. doi:10.1103/PhysRevD.15.2775 , language =

1977 doi
[196]

Physical Review D , author =

Quantum source of entropy for black holes , volume =. Physical Review D , author =. 1986 , pages =. doi:10.1103/PhysRevD.34.373 , language =

1986 doi
[197]

Living Reviews in Relativity , author =

Entanglement. Living Reviews in Relativity , author =. 2011 , pages =. doi:10.12942/lrr-2011-8 , language =

2011 doi
[198]

Physical Review A , author =

Concentrating partial entanglement by local operations , volume =. Physical Review A , author =. 1996 , pages =. doi:10.1103/PhysRevA.53.2046 , language =

1996 doi
[199]

Quantum field theory and the standard model , isbn =

Schwartz, Matthew Dean , year =. Quantum field theory and the standard model , isbn =
[200]

Dirac, P. A. M. , year =. The principles of quantum mechanics , isbn =
[201]

and Chuang, Isaac L

Nielsen, Michael A. and Chuang, Isaac L. , year =. Quantum. doi:10.1017/CBO9780511976667 , urldate =

doi
[202]

Physical Review A , author =

Quantum, classical, and total amount of correlations in a quantum state , volume =. Physical Review A , author =. 2005 , pages =. doi:10.1103/PhysRevA.72.032317 , language =

2005 doi
[203]

Reviews of Modern Physics , author =

Entanglement in many-body systems , volume =. Reviews of Modern Physics , author =. 2008 , pages =. doi:10.1103/RevModPhys.80.517 , language =

2008 doi
[204]

Journal of Physics A: Mathematical and Theoretical , author =

Entanglement entropy in free quantum field theory , volume =. Journal of Physics A: Mathematical and Theoretical , author =. 2009 , pages =. doi:10.1088/1751-8113/42/50/504007 , number =

2009 doi
[205]

Physical Review D , author =

Black. Physical Review D , author =. 1973 , pages =. doi:10.1103/PhysRevD.7.2333 , language =

1973 doi
[206]

Physical Review Letters , author =

Entropy and area , volume =. Physical Review Letters , author =. 1993 , pages =. doi:10.1103/PhysRevLett.71.666 , language =

1993 doi
[207]

Science , author =

Bulk. Science , author =. 1997 , pages =. doi:10.1126/science.275.5298.350 , language =

1997 doi
[208]

Physics of Fluids , author =

Solar convective velocities:. Physics of Fluids , author =. 2024 , pages =. doi:10.1063/5.0216728 , abstract =

2024 doi
[209]

Information and Control , author =

On certain formal properties of grammars , volume =. Information and Control , author =. 1959 , pages =. doi:10.1016/S0019-9958(59)90362-6 , abstract =

1959 doi
[210]

Iterative methods for sparse linear systems , isbn =

Saad, Youcef and Saad, Yousef , year =. Iterative methods for sparse linear systems , isbn =
[211]

Iterative solution methods , isbn =

Axelsson, Owe , year =. Iterative solution methods , isbn =
[212]

Upgrading fortran source code using automatic refactoring , isbn =

Orchard, Dominic and Rice, Andrew , month = oct, year =. Upgrading fortran source code using automatic refactoring , isbn =. Proceedings of the 2013. doi:10.1145/2541348.2541356 , language =

2013
[213]

Observations of large-scale solar flows , url =

Proxauf, Bastian , year =. Observations of large-scale solar flows , url =. doi:10.53846/goediss-8502 , urldate =

doi
[214]

Journal of Geophysical Research: Space Physics , author =

The solar meridional circulation and sunspot cycle variability , volume =. Journal of Geophysical Research: Space Physics , author =. 2014 , note =. doi:10.1002/2013JA019432 , abstract =

2014 doi
[215]

The Astronomy and Astrophysics Review , author =

The solar dynamo , volume =. The Astronomy and Astrophysics Review , author =. 2003 , keywords =. doi:10.1007/s00159-003-0019-3 , abstract =

2003 doi
[216]

, editor =

Kosovichev, Alexander G. , editor =. Advances in. The. 2011 , pages =. doi:10.1007/978-3-642-19928-8_1 , abstract =

2011 doi
[217]

Zeitschrift fur Astrophysik , author =

Über die. Zeitschrift fur Astrophysik , author =. 1958 , pages =

1958
[218]

Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse , author =

Ueber das. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse , author =. 1906 , pages =

1906
[219]

International Journal for Numerical Methods in Fluids , author =

A rationale for implicit turbulence modelling , volume =. International Journal for Numerical Methods in Fluids , author =. 2002 , note =. doi:10.1002/fld.331 , abstract =

2002 doi
[220]

On maintained convective motion in a fluid heated from below , volume =

Pellew, Anne and Southwell, Richard Vynne , month = jan, year =. On maintained convective motion in a fluid heated from below , volume =. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences , publisher =. doi:10.1098/rspa.1940.0092 , abstract =

1940
[221]

2000 , file =

Variational methods for elliptic problems in fluid models , author =. 2000 , file =

2000
[222]

Momar , month = mar, year =

Irbah, Abdanour and Meftah, Mustapha and Hauchecorne, Alain and Djafer, Djelloul and Corbard, Thierry and Bocquier, Maxime and Cisse, E. Momar , month = mar, year =. The Astrophysical Journal , publisher =. doi:10.1088/0004-637X/785/2/89 , abstract =

doi
[223]

Variations of

Irbah, Abdanour and Mecheri, Redouane and Damé, Luc and Djafer, Djelloul , month = apr, year =. Variations of. The Astrophysical Journal Letters , publisher =. doi:10.3847/2041-8213/ab16e2 , abstract =

doi
[224]

ECMWF , author =

Spectral preconditioners for nonhydrostratic atmospheric models: extreme applications , shorttitle =. ECMWF , author =
[225]

and Miesch, Mark S

Featherstone, Nicholas A. and Miesch, Mark S. , month = may, year =. The Astrophysical Journal , publisher =. doi:10.1088/0004-637X/804/1/67 , abstract =

doi
[226]

Living Reviews in Computational Astrophysics , author =

Large. Living Reviews in Computational Astrophysics , author =. 2015 , keywords =. doi:10.1007/lrca-2015-2 , abstract =

2015 doi
[227]

Space Science Reviews , author =

Large-. Space Science Reviews , author =. 2015 , keywords =. doi:10.1007/s11214-015-0190-7 , abstract =

2015 doi
[228]

Proceedings of the International Astronomical Union , author =

A solar cycle 25 prediction based on. Proceedings of the International Astronomical Union , author =. 2019 , pages =. doi:10.1017/S1743921320003993 , abstract =

2019 doi
[229]

The Astrophysical Journal , author =

Magnetically. The Astrophysical Journal , author =. 2017 , pages =. doi:10.3847/1538-4357/aa6d60 , abstract =

2017 doi
[230]

, year =

Tritton, David J. , year =. Physical fluid dynamics , isbn =
[231]

Living Reviews in Solar Physics , author =

Magnetic. Living Reviews in Solar Physics , author =. 2009 , keywords =. doi:10.12942/lrsp-2009-4 , abstract =

2009 doi
[232]

The Astrophysical Journal , author =

Turbulent compressible convection in a deep atmosphere. The Astrophysical Journal , author =. 1986 , pages =. doi:10.1086/164409 , language =

1986 doi
[233]

The Astrophysical Journal , author =

Solar. The Astrophysical Journal , author =. 2003 , pages =. doi:10.1086/375492 , language =

2003 doi
[234]

and Kusano, K

Hotta, H. and Kusano, K. and Shimada, R. , month = jul, year =. Generation of. The Astrophysical Journal , publisher =. doi:10.3847/1538-4357/ac7395 , abstract =

doi
[235]

Advances in Space Research , author =

Modeling turbulent stellar convection zones:. Advances in Space Research , author =. 2016 , keywords =. doi:10.1016/j.asr.2016.05.043 , abstract =

2016 doi
[236]

Solar Physics , author =

Global-. Solar Physics , author =. 2018 , keywords =. doi:10.1007/s11207-017-1201-5 , abstract =

2018 doi
[237]

and Duvall, Thomas L

Hanasoge, Shravan M. and Duvall, Thomas L. and Sreenivasan, Katepalli R. , month = jul, year =. Anomalously weak solar convection , volume =. Proceedings of the National Academy of Sciences , publisher =. doi:10.1073/pnas.1206570109 , abstract =

doi
[238]

The Astrophysical Journal , author =

Helioseismic. The Astrophysical Journal , author =. 1998 , pages =. doi:10.1086/306146 , language =

1998 doi
[239]

and Cohen, Ira M

Kundu, Pijush K. and Cohen, Ira M. and Hu, Howard H. , year =. Fluid mechanics , isbn =
[240]

2013 , keywords =

Journal of Computational Physics , author =. 2013 , keywords =. doi:10.1016/j.jcp.2012.11.008 , abstract =

2013 doi
[241]

Computational fluid dynamics: the basics with applications , isbn =

Anderson, John David , file =. Computational fluid dynamics: the basics with applications , isbn =
[242]

Z3: an efficient

De Moura, Leonardo and Bjørner, Nikolaj , month = mar, year =. Z3: an efficient. Proceedings of the
[243]

, year =

Pratt, Vaughan R. , year =. Top down operator precedence , url =. Proceedings of the 1st annual. doi:10.1145/512927.512931 , language =
[244]

Space Science Reviews , author =

Simulations of. Space Science Reviews , author =. 2023 , keywords =. doi:10.1007/s11214-023-01005-6 , abstract =

2023 doi
[245]

Information technology —
[246]

, year =

Burge, William H. , year =. Recursive programming techniques , isbn =
[247]

The Astrophysical Journal , author =

Implicit. The Astrophysical Journal , author =. 2022 , pages =. doi:10.3847/1538-4357/ac9af3 , abstract =

2022 doi
[248]

tree-sitter/tree-sitter: v0.24.3 , copyright =

Max Brunsfeld and Amaan Qureshi and Andrew Hlynskyi and Patrick Thomson and ObserverOfTime and Josh Vera and Phil Turnbull and dundargoc and Timothy Clem and Douglas Creager and Andrew Helwer and Rob Rix and Daumantas Kavolis and Hendrik van Antwerpen and Michael Davis and Ika...
[249]

2007 , annote =

Compilers: principles, techniques, & tools , isbn =. 2007 , annote =

2007
[250]

2003 , pages =

Journal of the Atmospheric Sciences , author =. 2003 , pages =. doi:10.1175/1520-0469(2003)060<0847:MLCSSS>2.0.CO;2 , language =

2003 doi
[251]

The art of computer programming , isbn =

Knuth, Donald Ervin , year =. The art of computer programming , isbn =
[252]

Tomita, Masaru and Ng, See-Kiong , editor =. The. Generalized. 1991 , pages =. doi:10.1007/978-1-4615-4034-2_1 , language =

1991 doi
[253]

and Ullman, Jeffrey D

Aho, Alfred V. and Ullman, Jeffrey D. , year =. The theory of parsing, translation, and compiling. 1:
[254]

and Jasper, Daniel and Klimek, Manuel and Carruth, Chandler and Wan, Zhanyong , month = sep, year =

Wright, Hyrum K. and Jasper, Daniel and Klimek, Manuel and Carruth, Chandler and Wan, Zhanyong , month = sep, year =. Large-. 2013. doi:10.1109/ICSM.2013.93 , urldate =

2013 doi
[255]

Geophysical fluid dynamics , isbn =

Pedlosky, Joseph , year =. Geophysical fluid dynamics , isbn =
[256]

ESAIM: Proceedings and Surveys , author =

Krylov. ESAIM: Proceedings and Surveys , author =. 2018 , pages =. doi:10.1051/proc/201863001 , abstract =

2018
[257]

Journal of Fluid Mechanics , author =

Thermal instabilities in rapidly rotating systems , volume =. Journal of Fluid Mechanics , author =. 1970 , pages =. doi:10.1017/S0022112070001921 , abstract =

1970 doi
[258]

Journal of Fluid Mechanics , author =

Radius ratio dependency of the instability of fully compressible convection in rapidly rotating spherical shells , volume =. Journal of Fluid Mechanics , author =. 2021 , keywords =. doi:10.1017/jfm.2021.701 , abstract =

2021 doi
[259]

Journal of the ACM , author =

Pattern. Journal of the ACM , author =. 1982 , pages =. doi:10.1145/322290.322295 , language =

1982
[260]

Mathematics Magazine , author =

Tree. Mathematics Magazine , author =. 1991 , pages =. doi:10.1080/0025570X.1991.11977616 , language =

1991
[261]

Introduction to the theory of computation , isbn =

Sipser, Michael , year =. Introduction to the theory of computation , isbn =
[262]

Journal of Computational Science , author =

Efficient multicore-aware parallelization strategies for iterative stencil computations , volume =. Journal of Computational Science , author =. 2011 , keywords =. doi:10.1016/j.jocs.2011.01.010 , abstract =

2011 doi
[263]

and Hopcroft, John E

Aho, Alfred V. and Hopcroft, John E. and Ullman, Jeffrey D. , year =. The design and analysis of computer algorithms , isbn =
[264]

Curso de física básica1: mecânica , isbn =

Moysés , month = jun, year =. Curso de física básica1: mecânica , isbn =
[265]

Handbook of theoretical computer science , isbn =

Leeuwen, Jan van , year =. Handbook of theoretical computer science , isbn =
[266]

Term rewriting and all that , isbn =

Baader, Franz and Nipkow, Tobias , year =. Term rewriting and all that , isbn =
[267]

2003 , keywords =

Term rewriting systems , isbn =. 2003 , keywords =

2003
[268]

, year =

Birkhoff, Garrett and Lynch, Robert E. , year =. Numerical solution of elliptic problems , isbn =
[269]

and Safko, John L

Goldstein, Herbert and Poole, Charles P. and Safko, John L. , year =. Classical mechanics , isbn =
[270]

, month = mar, year =

Lemos, Nivaldo A. , month = mar, year =. Mecanica
[271]

, year =

Glatzmaier, Gary A. , year =. Introduction to modeling convection in planets and stars: magnetic field, density stratification, rotation , isbn =
[272]

Physics , isbn =

Halliday, David and Resnick, Robert , year =. Physics , isbn =
[273]

2015 , file =

Fundamentos de física: mecânica: volume. 2015 , file =

2015
[274]

International Journal for Numerical Methods in Fluids , author =

Eddy resolving simulations of turbulent solar convection , volume =. International Journal for Numerical Methods in Fluids , author =. 2002 , note =. doi:10.1002/fld.333 , abstract =

2002 doi
[275]

Crowley, W. P. , month = jan, year =. Monthly Weather Review , publisher =. doi:10.1175/1520-0493(1968)096<0001:NAE>2.0.CO;2 , abstract =

1968 doi
[276]

Journal of Computational Physics , author =

The multidimensional positive definite advection transport algorithm:. Journal of Computational Physics , author =. 1986 , pages =. doi:10.1016/0021-9991(86)90270-6 , abstract =

1986 doi
[277]

Shewchuk, Jonathan R , year =. An
[278]

Applied Numerical Mathematics , author =

Review of preconditioning methods for fluid dynamics , volume =. Applied Numerical Mathematics , author =. 1993 , pages =. doi:10.1016/0168-9274(93)90122-8 , abstract =

1993 doi
[279]

and Haase, Gundolf and Langer, Ulrich , year =

Douglas, Craig C. and Haase, Gundolf and Langer, Ulrich , year =. A tutorial on elliptic
[280]

, month = mar, year =

Smolarkiewicz, Piotr K. , month = mar, year =. A. Monthly Weather Review , publisher =. doi:10.1175/1520-0493(1983)111<0479:ASPDAS>2.0.CO;2 , abstract =

1983 doi
[281]

Third and

Zwas, Gideon and Abarbanel, Saul , year =. Third and. Mathematics of Computation , publisher =. doi:10.2307/2004918 , abstract =

doi
[282]

and Richtmyer, Robert Davis , year =

Richtmyer, Robert Davis and Morton, Keith W. and Richtmyer, Robert Davis , year =. Difference methods for initial-value problems , isbn =
[283]

The Physics of Fluids , author =

Numerical. The Physics of Fluids , author =. 1965 , pages =. doi:10.1063/1.1761178 , abstract =

1965 doi
[284]

Computational physics , isbn =

Potter, David , year =. Computational physics , isbn =
[285]

2006 , note =

International Journal for Numerical Methods in Fluids , author =. 2006 , note =. doi:10.1002/fld.1118 , abstract =

2006 doi
[286]

Landau, L. D. and Lifshitz, E. M. , month = sep, year =. Fluid
[287]

and Julien, Keith and Marti, Philippe , month = jul, year =

Calkins, Michael A. and Julien, Keith and Marti, Philippe , month = jul, year =. Onset of rotating and non-rotating convection in compressible and anelastic ideal gases , volume =. Geophysical & Astrophysical Fluid Dynamics , publisher =. doi:10.1080/03091929.2014.987670 , abstract =

2014
[288]

The atmosphere and ocean: a physical introduction , isbn =

Wells, Neil , year =. The atmosphere and ocean: a physical introduction , isbn =
[289]

Alan , year =

Marshall, John and Plumb, R. Alan , year =. Atmosphere, ocean, and climate dynamics: an introductory text , isbn =
[290]

and Held, Hermann and Kriegler, Elmar and Hall, Jim W

Lenton, Timothy M. and Held, Hermann and Kriegler, Elmar and Hall, Jim W. and Lucht, Wolfgang and Rahmstorf, Stefan and Schellnhuber, Hans Joachim , month = feb, year =. Tipping elements in the. Proceedings of the National Academy of Sciences , publisher =. doi:10.1073/pnas.07...

doi
[291]

and Folke, Carl and Liverman, Diana and Summerhayes, Colin P

Steffen, Will and Rockström, Johan and Richardson, Katherine and Lenton, Timothy M. and Folke, Carl and Liverman, Diana and Summerhayes, Colin P. and Barnosky, Anthony D. and Cornell, Sarah E. and Crucifix, Michel and Donges, Jonathan F. and Fetzer, Ingo and Lade, Steven J. an...

doi
[292]

and Frame, David J

Allen, Myles R. and Frame, David J. and Huntingford, Chris and Jones, Chris D. and Lowe, Jason A. and Meinshausen, Malte and Meinshausen, Nicolai , month = apr, year =. Warming caused by cumulative carbon emissions towards the trillionth tonne , volume =. Nature , publisher =....

doi
[293]

American Journal of Physics , author =

Simple model to estimate the contribution of atmospheric. American Journal of Physics , author =. 2012 , pages =. doi:10.1119/1.3681188 , abstract =

2012 doi
[294]

Damon and Gillett, Nathan P

Matthews, H. Damon and Gillett, Nathan P. and Stott, Peter A. and Zickfeld, Kirsten , month = jun, year =. The proportionality of global warming to cumulative carbon emissions , volume =. Nature , publisher =. doi:10.1038/nature08047 , abstract =

doi
[295]

Quarterly Journal of the Royal Meteorological Society , author =

A very simple model for the water vapour feedback on climate change , volume =. Quarterly Journal of the Royal Meteorological Society , author =. 2010 , note =. doi:10.1002/qj.546 , abstract =

2010 doi
[296]

, month = nov, year =

Ingersoll, Andrew P. , month = nov, year =. The. Journal of the Atmospheric Sciences , publisher =. doi:10.1175/1520-0469(1969)026<1191:TRGAHO>2.0.CO;2 , abstract =

1969 doi
[297]

Living Reviews in Solar Physics , author =

Large-. Living Reviews in Solar Physics , author =. doi:10.12942/lrsp-2005-1 , language =

2005 doi
[298]

, month = jan, year =

Verhoeven, Jan and Glatzmaier, Gary A. , month = jan, year =. Validity of sound-proof approaches in rapidly-rotating compressible convection: marginal stability versus turbulence , volume =. Geophysical & Astrophysical Fluid Dynamics , publisher =. doi:10.1080/03091929.2017.13...

2017
[299]

Physica D: Nonlinear Phenomena , author =

Large-eddy simulations of convective boundary layers using nonoscillatory differencing , volume =. Physica D: Nonlinear Phenomena , author =. 1999 , keywords =. doi:10.1016/S0167-2789(99)00083-4 , abstract =

1999 doi
[300]

Pope, S. B. , year =. Turbulent flows , isbn =

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.

[1] [1]

New Journal of Physics , author =

A quantum information processor with trapped ions , volume =. New Journal of Physics , author =. 2013 , note =. doi:10.1088/1367-2630/15/12/123012 , abstract =

work page doi:10.1088/1367-2630/15/12/123012 2013

[2] [2]

Nature , author =

Experimental realization of. Nature , author =. 2001 , pages =. doi:10.1038/414883a , language =

work page doi:10.1038/414883a 2001

[3] [3]

Science China Information Sciences , author =

Superconducting quantum computing: a review , volume =. Science China Information Sciences , author =. 2020 , pages =. doi:10.1007/s11432-020-2881-9 , abstract =

doi:10.1007/s11432-020-2881-9 2020

[4] [4]

SIAM Journal on Computing , author =

Strengths and. SIAM Journal on Computing , author =. 1997 , note =. doi:10.1137/S0097539796300933 , abstract =

doi:10.1137/s0097539796300933 1997

[5] [5]

Proceedings of the National Academy of Sciences , author =

Ensemble quantum computing by. Proceedings of the National Academy of Sciences , author =. 1997 , keywords =. doi:10.1073/pnas.94.5.1634 , abstract =

work page doi:10.1073/pnas.94.5.1634 1997

[6] [6]

Advances in Physics , author =

The. Advances in Physics , author =. 2003 , note =. doi:10.1080/0001873021000049195 , abstract =

work page doi:10.1080/0001873021000049195 2003

[7] [7]

Physical Review B , author =

Stochastic series expansion method with operator-loop update , volume =. Physical Review B , author =. 1999 , pages =. doi:10.1103/PhysRevB.59.R14157 , language =

doi:10.1103/physrevb.59.r14157 1999

[8] [8]

Physical Review , author =

Residual. Physical Review , author =. 1967 , pages =. doi:10.1103/PhysRev.162.162 , language =

doi:10.1103/physrev.162.162 1967