{"id":"e61750d7-6abd-4301-8b3a-1552dd21671a","arxiv_id":"2509.06590","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"An SPH two-fluid model with Boltzmann-derived collisional exchange and Lie-Trotter splitting reproduces equilibration of density and temperature in binary gas mixtures at cm-scale, low-pressure conditions.","lead":"A numerical method for simulating how two gases mix in confined spaces, using Smoothed Particle Hydrodynamics with collision terms from kinetic theory, is presented. It splits the calculation so the fast collision timescale no longer forces tiny timesteps, and the authors show density and temperature equilibration tests for Ar-Kr and Ne-Xe.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"First-order Lie-Trotter splitting is not validated in the stiff regime: the uncoupled hydrodynamic substep advects densities before the collision correction acts, so mixing transients may be dt-dependent rather than physical.","rationale":"The paper's central claim is that the Lie-Trotter splitting lets the binary-gas SPH scheme run at hydrodynamic timesteps while accurately capturing equilibration. For this to hold, the uncoupled hydrodynamic substep must not introduce physical drift that the collision correction cannot undo. The analysis in Sec. 2.4 derives a CFL-type bound on dt_coll for the explicit scheme, and Sec. 2.5 replaces it with exponential relaxation; however, no error estimate is given for the splitting. In the stiff regime (collision time << hydro dt), Eq. (25) damps the post-hydro relative velocity to roughly exp(-K_mix rho_tot dt), but the densities and positions have already been advanced by a full dt of two independent Euler systems. The subsequent velocity correction changes momenta but does not advect particles back, so the density field carries a first-order splitting error proportional to the commutator of the pressure and collision operators. Appendix A's stiff DUSTYBOX run with K=1e8 is explicitly unresolved during the decay, so it can only confirm the terminal equilibrium. The Ar-Kr and Ne-Xe tests likewise compare only final densities and temperatures, plus an energy conservation integral; they cannot detect an artificial enhancement of the mixing rate. The single comparison against the explicit SPH collision term (Sec. 3.1) is for mean densities and reports at most 6% disagreement, but it is not run as a dt-convergence test, so it does not bound the splitting error. A concrete dt-convergence study would settle the matter. If the relaxation curves shift with dt, the method's efficiency claim is conditional on an unquantified timestep error; if they converge, the concern is resolved. This does not change the reader's CONDITIONAL verdict but sharpens the requested validation.","tokens_in":16542,"tokens_out":11030,"duration_ms":105916,"concrete_test":"Repeat the Ar-Kr test of Sec. 3.2 with the same initial conditions, 2e5 particles, and cubic-spline kernel, but reduce the CFL factor so the hydrodynamic timestep is dt, dt/2, dt/4, and dt/8. Plot the mean densities and mean temperatures of both gases versus time. If the relaxation curves collapse onto a single physical curve, the first-order splitting error is controlled and the efficiency claim holds. If the equilibration time or the initial compression amplitude shifts systematically with dt, the transient mixing is polluted by the uncoupled hydro substep; then compare the dt->0 limit with the explicit collision-resolved integration of Eq. (23) and report an L1 error in densities and velocities at t=5e-4 s. This single experiment determines whether timestep doubling is safe.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 2.5 splits each step into a full hydrodynamic advance followed by an exponential collisional relaxation. In the intended stiff regime dt >> 1/[(rho_alpha+rho_beta)K_mix], the hydro substep evolves both gases for a whole hydrodynamic timestep with no interspecies coupling. During this substep each species is independently accelerated by its own pressure gradient and advected, building up a relative velocity and, more importantly, a partially separated density field. Equation (25) then exponentially damps Delta v, but the damping changes only velocities; it cannot move particles back or undo the density redistribution produced by the uncoupled advection. The splitting error is therefore not small when the collision rate is large; it is set by dt and by the non-commutation of the advection/pressure operators with the collision operator. Appendix A's stiff test with K=1e8 explicitly states the intermediate velocity decay is not temporally resolved, so it validates only the terminal state. The Ar-Kr and Ne-Xe tests compare final mean densities and temperatures to equilibrium values, which are insensitive to transient splitting errors, and the Sec. 3.1 comparison reports a 6% difference in mean densities without a dt-convergence study. Thus the paper's efficiency-accuracy claim, that a hydrodynamic CFL timestep preserves the transient mixing dynamics, rests on an unquantified first-order splitting error.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a two-fluid Smoothed Particle Hydrodynamics (SPH) model for binary monatomic gas mixtures. Each gas is evolved with its own Euler equations, and interspecies momentum and energy exchange are modeled by collisional terms derived from a Boltzmann-based kinetic relaxation model (Gross–Krook) with Lennard-Jones collision integrals. To avoid the small collisional timestep, the authors use first-order Lie–Trotter operator splitting: a pure hydrodynamic SPH step is followed by an exponential relaxation step for the velocity difference and for the energies. The model is tested on (i) a Ne–Xe comparison between the formal SPH drag-like implementation and the splitting scheme, (ii) Ar–Kr and Ne–Xe closed-cylinder mixing tests with temperature and density equilibration, and (iii) DUSTYBOX-style tests in the non-stiff and stiff regimes. The paper claims that the splitting approach allows a hydrodynamic timestep while accurately reproducing density and temperature equilibration, and it outlines extensions to polyatomic gases and gas–dust interactions for ExoMars contexts.","tokens_in":16840,"tokens_out":33188,"duration_ms":255065,"significance":"If the central claims hold, this is a useful and modular SPH method for simulating binary gas mixing in confined geometries, with a clear computational advantage over explicit integration of the stiff collisional terms. The physical modeling is grounded in standard kinetic theory (Chapman–Cowling, Neufeld correlations, Zahmatkesh et al.), and the paper includes several strengths: validation against analytic equilibrium densities and temperatures, DUSTYBOX solutions in both non-stiff and stiff regimes, total-energy conservation to about 1e-5, a thermodynamic-consistency check through entropy production, and a kernel-insensitivity test. The comparison with an independent formal SPH implementation, although limited, is valuable. However, the paper's main efficiency-accuracy claim is not yet fully supported because the splitting error in the stiff regime is not quantified, and the number-weighted SPH interpolation used for the exchange terms is introduced empirically without a precise definition or convergence study.","major_comments":[{"comment":"The central efficiency-accuracy claim rests on the validity of first-order Lie–Trotter splitting in the stiff regime, but no error bound or convergence study is provided. During the uncoupled hydrodynamic substep, each species evolves alone, so the exponential collision correction in Eq. (25) can only damp the relative velocity; it cannot undo the density redistribution produced by that substep. The stiff DUSTYBOX test with K=10^8 explicitly does not temporally resolve the intermediate decay, so it validates only the terminal state. The Ne–Xe comparison in §3.1 reports a 6% difference in mean densities but no dt-convergence test and no comparison of local fields. Please add a systematic dt-convergence study for the Trotter scheme in a stiff case and compare transient density and velocity fields against the formal SPH implementation or an analytic reference.","section":"§2.5 and Appendix A"},{"comment":"The total-energy conservation identity in Eq. (17) is asserted with \"it can be shown\" and is not derived. This identity is the basis for the total-energy conservation claim in Fig. 5 and for the closed-system validation. The identity is not immediate because the target energies in Eq. (16) involve temperature and velocity differences with different mass weightings. Please prove Eq. (17) from Eqs. (6), (8), (15), and (16), or give a specific reference that contains this derivation for the per-mass formulation used here.","section":"§2.3, Eq. (17)"},{"comment":"The number-weighted SPH interpolation introduced for the exchange terms is not defined. The text states that employing number-weighted interpolation \"improves the accuracy of thermal relaxation and energy conservation in high mass ratio mixtures,\" but it does not specify how this differs from the kernel-weighted velocity estimate in Eq. (32), how it is normalized, or whether it preserves the conservation properties of the continuum exchange terms. Please define the number-weighted estimates explicitly and test their consistency (conservation of total momentum and energy, and convergence with particle number) rather than introducing it as an empirical fix.","section":"§2.5, Eqs. (31)-(32) and §3.3"},{"comment":"The persistent 8–9% underestimate of equilibrium mean densities is attributed to boundary effects, but the evidence is indirect. Appendix C shows a similar bias in a no-collision two-gas simulation, and Appendix B shows insensitivity to the kernel, but there is no quantitative demonstration that the boundary treatment is the dominant source of the offset. A single-species hydrostatic SPH test in the same cylindrical geometry, or the same mixing test with an improved boundary treatment, would directly support the attribution. The statement that the error stabilizes at 7–9% even when increasing the particle number from 2×10^5 to 3×10^5 also needs an explanation.","section":"§3.2 and Appendices B-C"}],"minor_comments":[{"comment":"The 'maximum discrepancy of only 6%' refers to mean densities; please state this explicitly and, in addition, report a local error measure such as the L2 norm of the density field.","section":"§3.1"},{"comment":"The displayed formula for the local density of the other species appears garbled: the expression multiplies the SPH sum by N_neigh. Please write the intended SPH estimate unambiguously and define all symbols (N_neigh, h_a, h_i).","section":"§2.5, Eq. (31)"},{"comment":"The regularization parameter is written as η=0.001h^2, which makes the denominator |r|^2 + η^2 dimensionally inconsistent; presumably η^2 = 0.001 h^2 is intended.","section":"§2.5, Eq. (23)"},{"comment":"The phrase 'two-step Euler integrator' (later 'explicit two-steps Euler') is never defined. Please specify the time-integration scheme explicitly, for example whether it is a predictor-corrector or a two-stage Runge–Kutta method.","section":"§2.5 and Conclusions"},{"comment":"The wording 'good accuracy in reproducing the equilibration of density' overstates the reported 8–9% density offset; please temper the wording or state the offset explicitly in the abstract.","section":"Abstract and §4"},{"comment":"The column header 'Ar and kr' should use proper capitalization: 'Ar and Kr'.","section":"Table 1"},{"comment":"The two panels are described in the text, but the figure should include axis labels and legends or panel titles so that the reader can identify which panel corresponds to gas g1 and which to gas g2.","section":"Appendix A, Fig. A2"},{"comment":"The statement 'No data was used for this article' is misleading for a numerical study; please state that simulation data are available on request or provide a link to a code/data repository.","section":"Data availability"}],"recommendation":"major_revision","confidential_remarks":"This is a potentially useful methods paper, but the validation currently overstates what is demonstrated. The main technical risk is the unquantified splitting error in the stiff regime, on which the central efficiency-accuracy trade-off rests; the number-weighted interpolation is also too vaguely specified. The contribution is incremental over existing gas–dust drag SPH formulations, although the adaptation to gas–gas mixing with kinetic-theory coefficients is nontrivial. I would support publication after a major revision that adds convergence studies, clarifies the numerical discretization, and demonstrates that the density offset is indeed a boundary artifact."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This paper does something genuinely new: it adapts the familiar gas–dust SPH drag structure to gas–gas mixtures, using collision frequencies from kinetic theory and a Lie–Trotter splitting so the timestep is set by hydrodynamics rather than the much shorter collisional timescale. The derivation is mostly careful, the coefficients come from standard external sources (Chapman–Cowling, Neufeld, Lennard-Jones tables), and the test suite is reasonable for a first methods paper. The DUSTYBOX checks and the entropy evolution are nice touches. This is not a breakthrough, but it is a legitimate technical advance, and the modular structure makes future polyatomic and dust-coupled extensions plausible.\n\nThe soft spots are real but not fatal. The biggest one is exactly what the stress-test note flags: the splitting error is never quantified in the stiff regime. The Ne–Xe comparison against the full explicit SPH scheme shows only 6% discrepancy, but that is one configuration, with temperature held constant, and no dt-convergence study. The Ar–Kr and Ne–Xe tests only compare final averages to equilibrium, which would match even if the transient path were wrong. The stiff DUSTYBOX case with K=1e8 explicitly admits the intermediate decay is unresolved. So the efficiency-accuracy trade-off is asserted, not demonstrated. I would want to see a convergence test where dt is varied and the splitting result is compared against a resolved explicit integration (or at least against a Strang-split variant) in a stiff case.\n\nThe 8–9% mean-density underestimate in the cylinder tests is attributed to boundary handling, and the no-collision control test in Appendix C supports that explanation. But the error does not go away with resolution, which makes me uncomfortable; a boundary correction or a more honest statement about the achievable accuracy would help. Also, Eq. (17) is asserted with “it can be shown” rather than proven. I have not verified the algebra myself, but a referee should ask for the intermediate steps. No code is released, which for a numerical methods paper is a real limitation.\n\nOverall, the central claim — that you can evolve binary gas mixtures with a hydrodynamic timestep and still get the right equilibrium and a plausible transient — is plausible and supported, but the transient part is the weakest link. This deserves a serious referee and, if it survives, publication with code. I would not cite it in my own work yet, but I would follow a revised version with interest.\n\nRecommendation: send to peer review. Ask for code, a dt-convergence study of the splitting error, and the missing algebra in Eq. (17).","headline":"A useful and honest SPH method paper for binary gas mixing, with a real efficiency advance from operator splitting, but the transient accuracy of the splitting in the stiff regime is not yet demonstrated.","tokens_in":17339,"tokens_out":1608,"would_cite":false,"duration_ms":17598,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A single exponential relaxation step lets SPH gas-mixing simulations advance on the hydrodynamic timestep instead of the collision timescale.","keywords":["smoothed particle hydrodynamics","binary gas mixtures","collisional relaxation","Lie-Trotter splitting","kinetic theory","planetary atmospheres","Chapman-Enskog diffusion","multiphase flow"],"falsifier":"Run the argon–krypton test at increasing resolution with timesteps chosen so that the ratio of the collisional timescale to the hydrodynamic timestep varies from 0.01 to 1; if the final density and temperature errors grow steeply as that ratio approaches 1, or if a fully coupled small-timestep reference solution disagrees with the splitting result by more than the reported 8–9 percent in density and 2 percent in temperature, the central accuracy claim fails.","tokens_in":16325,"feed_emoji":"💨","tokens_out":13203,"duration_ms":95771,"temperature":0.7,"pith_summary":"The paper proposes an SPH scheme for simulating the mixing of two monatomic gases, each evolved as its own inviscid Euler fluid, with interspecies momentum and energy exchange supplied by a kinetic relaxation model built on the Boltzmann equation. Its central move is to separate the fast collisional exchange from the slower hydrodynamics through a first-order Lie–Trotter splitting, so the collisional step is applied as an exact exponential relaxation rather than a stiff explicit update. This lets the simulation advance on the hydrodynamic timestep instead of the much shorter molecular-collision timestep. The paper validates the scheme against a fully coupled SPH implementation and against analytic equilibrium states, reporting agreement within about 6 percent in the splitting comparison, roughly 8–9 percent in final mean density, and about 2 percent in equilibrium temperature for argon–krypton and neon–xenon mixtures, with total energy conserved to order $10^{-5}$ and total entropy increasing. A sympathetic reader would take the contribution to be a computationally efficient, thermodynamically consistent baseline for binary gas mixing in confined planetary settings.","feed_headline":"40-minute SPH run matches 6-hour gas-mixing simulation","feed_subtitle":"Two-fluid SPH with exponential collisional relaxation reproduces density and temperature equilibration for mixtures up to neon-xenon.","key_machinery":"The load-bearing object is the exponential relaxation update for the interspecies velocity difference and energy. The paper reduces the coupled collisional system to $d\\Delta\\mathbf{v}/dt=-(\\rho_{\\alpha}+\\rho_{\\beta})K_{\\mathrm{mix}}\\Delta\\mathbf{v}$, freezes $(\\rho_{\\alpha}+\\rho_{\\beta})K_{\\mathrm{mix}}$ over the hydrodynamic timestep, and applies the exact solution $\\Delta\\mathbf{v}^{n+1}=\\Delta\\mathbf{v}^{*}e^{-(\\rho_{\\alpha}+\\rho_{\\beta})K_{\\mathrm{mix}}\\Delta t}$, then reconstructs each species' velocity from the conserved center-of-mass velocity. Energies relax analogously, $\\epsilon_{\\mathrm{tk}}^{n+1}=\\hat{\\epsilon}+(\\epsilon_{\\mathrm{tk}}^{*}-\\hat{\\epsilon})e^{-f\\Delta t}$, toward collision-target energies $\\hat{\\epsilon}$. Here $K_{\\mathrm{mix}}$ is a mixture coefficient built from Chapman–Cowling collision integrals for a Lennard-Jones potential; in the strong-collision limit the exponential factors drive the gases to a common velocity and temperature, and in the no-collision limit the hydrodynamic values are untouched. Together with the first-order Lie–Trotter split, this object is what lets the scheme advance on the hydrodynamic timestep while still reaching the correct equilibrium.","core_discovery":"The central claim is that binary monatomic gas mixing can be modeled in SPH by giving each species its own continuity, momentum, and energy equations and coupling them through the collision terms of a Gross–Krook relaxation model, and that the resulting stiff coupling can be handled without an implicit solver. The paper claims that after the hydrodynamic step, the velocity difference between the two gases relaxes according to $\\Delta\\mathbf{v}^{n+1}=\\Delta\\mathbf{v}^{*}\\exp[-(\\rho_{\\alpha}+\\rho_{\\beta})K_{\\mathrm{mix}}\\Delta t]$, with individual velocities reconstructed from the center-of-mass velocity, and that the thermokinetic energies relax with the analogous exponential factors toward the collision-target energies. With this splitting, the timestep is set by hydrodynamics rather than by the collisional timescale, and the method reproduces the equilibration of density and temperature over a range of molecular mass ratios, including the high-ratio neon–xenon case, while conserving total momentum and energy and increasing entropy.","pith_inferences":["Inference: the same exponential-closure machinery should extend directly to polyatomic mixtures by replacing the monatomic target energies with values that include rotational and vibrational contributions; the paper names this extension but does not test it, and the argon–krypton mass-ratio test gives a ready proxy for a water-vapor/carbon-dioxide system.","Inference: the persistent 8–9 percent density underestimate, which the paper attributes to boundary mirroring and kernel truncation, can be tested by repeating the same tests in a periodic domain; if the underestimate persists there, the collisional closure itself would be implicated.","Inference: the paper's use of Taylor–Aris dispersion to estimate effective diffusion suggests a testable corollary: in the drill-hole geometry, measured species concentration profiles over time should be consistent with the model's effective diffusion coefficient, which the paper currently validates only through equilibrium values and relaxation times."],"forward_implications":["The validation runs reproduce equilibrium densities to within about 8–9 percent and equilibrium temperatures to within about 2 percent for argon–krypton and neon–xenon, so the scheme is accurate enough for order-of-magnitude mixing studies in similar confined geometries.","Because the collisional correction is an exponential closure rather than an explicit stiff step, the simulation timestep is set by the hydrodynamic CFL condition, which in the reported comparison reduced wall-clock time from about six hours to about forty minutes at the same particle count.","Each species keeps its own density, velocity, and energy fields, so the model can represent transient non-equilibrium states in which the lighter gas is compressed before redistributing, rather than forcing instantaneous mixing.","The modular two-fluid structure gives a direct path to adding polyatomic degrees of freedom and gas–solid drag with dust or ice, which the paper identifies as the next step toward Mars-relevant volatile-release scenarios.","The scheme conserves total momentum and energy and produces positive entropy production during mixing, so its equilibrium states are thermodynamically consistent."],"supporting_citations":[{"why":"Supplies the kinetic-theory foundation: the Boltzmann collision operator, Lennard-Jones collision integrals, and the Chapman–Enskog diffusion coefficient used for the mixing-time estimate.","marker":"Chapman & Cowling 1970"},{"why":"Provides the relaxation approximation to the elastic collision integral from which the collisional exchange terms and target distributions are built.","marker":"Gross & Krook 1956"},{"why":"Introduces the gas–dust drag form that the collisional momentum terms mimic, including the SPH discretization and regularization parameter used in Eq. (23).","marker":"Monaghan & Kocharyan 1995"},{"why":"Basis for the multi-fluid SPH density and velocity interpolation and for the Von Neumann stability analysis that yields the collisional timestep constraint.","marker":"Laibe & Price 2012a,b"},{"why":"Source for the macroscopic collisional energy-exchange terms and the target temperature and velocity parameters in Eq. (6).","marker":"Zahmatkesh et al. 2013"},{"why":"Establishes the Gaussian target distribution and the constraints on the collisional temperature and velocity that make the kinetic model reproduce Boltzmann collisional moments.","marker":"Vega Reyes et al. 2007"},{"why":"Gives the empirical expression for the reduced collision integral that determines the mixture coefficient $K_{\\mathrm{mix}}$.","marker":"Neufeld et al. 1972"},{"why":"Supplies the operator-splitting theorem used to separate hydrodynamic evolution from collisional relaxation.","marker":"Trotter 1959"},{"why":"Provides the DUSTYBOX analytical test used to validate both the explicit SPH drag form and the stiff-regime splitting behavior.","marker":"Laibe & Price 2011"},{"why":"Supplies the Lennard-Jones potential parameters for argon, krypton, neon, and xenon used in the validation runs.","marker":"Oh 2013"}],"fun_headline_variants":["SPH gas mixing: hydro timestep, not collisional","Two-fluid SPH mixes gases without implicit solver","Exponential relaxation speeds SPH gas mixing","Neon-xenon mixing in SPH at hydro timescales","40-min SPH run matches 6-hour gas mixing"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that during one hydrodynamic timestep the total density and the mixing coefficient stay nearly constant while the gases relax exponentially; if densities or collision rates change substantially within that timestep, the correction is only first-order accurate and the reported speed-versus-accuracy tradeoff may not hold.","fun_headline_variants_meta":{"raw":{"variants":["SPH gas mixing: hydro timestep, not collisional","Two-fluid SPH mixes gases without implicit solver","Exponential relaxation speeds SPH gas mixing","Neon-xenon mixing in SPH at hydro timescales","40-min SPH run matches 6-hour gas mixing"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000335,"raw_usage":{"total_tokens":1877,"prompt_tokens":984,"completion_tokens":893,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":600,"completion_tokens_details":{"reasoning_tokens":812}},"tokens_in":600,"tokens_out":893,"duration_ms":7853,"temperature":1.0,"reasoning_tokens":812,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T16:15:13.499646+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the argon–krypton test at increasing resolution with timesteps chosen so that the ratio of the collisional timescale to the hydrodynamic timestep varies from 0.01 to 1; if the final density and temperature errors grow steeply as that ratio approaches 1, or if a fully coupled small-timestep reference solution disagrees with the splitting result by more than the reported 8–9 percent in density and 2 percent in temperature, the central accuracy claim fails.","supporting_citations":[{"cited_title":"G., 1970, The mathematical theory of non-uniform gases","cited_arxiv_id":null,"evidence_quote":"Supplies the kinetic-theory foundation: the Boltzmann collision operator, Lennard-Jones collision integrals, and the Chapman–Enskog diffusion coefficient used for the mixing-time estimate."},{"cited_title":"P., Krook M., 1956, @doi [Phys","cited_arxiv_id":null,"evidence_quote":"Provides the relaxation approximation to the elastic collision integral from which the collisional exchange terms and target distributions are built."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Source for the macroscopic collisional energy-exchange terms and the target temperature and velocity parameters in Eq. (6)."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the Gaussian target distribution and the constraints on the collisional temperature and velocity that make the kinetic model reproduce Boltzmann collisional moments."},{"cited_title":"F., 1959, Proceedings of the American Mathematical Society, 10, 545","cited_arxiv_id":null,"evidence_quote":"Supplies the operator-splitting theorem used to separate hydrodynamic evolution from collisional relaxation."}],"review_version":2}