mcdust: 2D Dust Evolution Monte Carlo Code

Updated 7 July 2026

mcdust is a 2D Monte Carlo dust-evolution code that simulates collisional growth, fragmentation, and erosion in protoplanetary disks using a Lagrangian representative-particle method.
The code employs an adaptive grid to ensure uniform Monte Carlo sampling of local collisions, enabling detailed studies of sedimentation-driven coagulation and dust-chemistry interactions.
Benchmark results show mcdust reproduces key features of both 1D and 2D dust evolution, while revealing limitations such as low mass resolution in tenuous disk regions.

mcdust most directly denotes a 2D Monte Carlo dust-evolution code for protoplanetary disks, written in FORTRAN90 and parallelized with OpenMP, designed to model the coupled collisional evolution and transport of dust in the radial and vertical directions of a disk (Vaikundaraman et al., 28 Jul 2025). In the current literature, the same string also appears in other contexts—notably as a search term for the Mars Dust Counter on Nozomi and for Magellanic-Cloud dust reddening products—but in disk-evolution work it refers to a representative-particle code intended for the first stages of planet formation, dust redistribution, and dust–chemistry coupling (Krüger et al., 17 Feb 2026, Chen et al., 2022).

1. Scientific role and problem domain

mcdust is built to address a specific modeling problem: dust evolution in protoplanetary disks is physically rich but computationally difficult, especially when one wants to follow both growth and destruction and simultaneous transport through a disk (Vaikundaraman et al., 28 Jul 2025). The code is designed for the regime in which initially small grains evolve through sticking, fragmentation, and erosion while also moving through the gas disk under drift, settling, and turbulence. This is the regime directly relevant to early planet formation, disk substructure, dust redistribution, and dust–chemistry coupling (Vaikundaraman et al., 28 Jul 2025).

The code adopts a Lagrangian Monte Carlo representative-particle method, following the approach of Zsom & Dullemond (2008), rather than a purely Eulerian Smoluchowski solver (Vaikundaraman et al., 28 Jul 2025). In this formulation, a limited set of computational particles stands in for swarms of identical physical grains. The stated advantages are reduced computational cost, retention of particle histories, and the ability to add new particle attributes without introducing extra dimensions into a Smoluchowski solver (Vaikundaraman et al., 28 Jul 2025). Earlier Monte Carlo coagulation work emphasized the same methodological advantage—flexibility in carrying properties such as porosity or composition—but also documented the computational cost and the difficulty of treating regimes in which a few bodies dominate the mass budget (Zsom, 2010).

A further role of mcdust is as a comparatively inexpensive stand-alone or post-processing tool. The code is used in a prescribed gas background rather than a full gas–dust hydrodynamic calculation, allowing exploration of dust evolution under different physical conditions without the cost of fully coupled hydrodynamics (Vaikundaraman et al., 28 Jul 2025).

2. Numerical architecture and modeled processes

The code resolves dust coagulation in 2D $(r,z)$ and bins representative particles into local spatial cells because coagulation depends on local gas properties (Vaikundaraman et al., 28 Jul 2025). A central algorithmic feature is the adaptive grid, whose boundaries are redistributed so that each cell contains the same number of representative particles. The purpose is statistical rather than geometric: equal occupancy ensures that active collision cells retain sufficient Monte Carlo sampling to resolve local collisional physics (Vaikundaraman et al., 28 Jul 2025).

The included collisional outcomes are explicitly limited to growth by sticking, fragmentation, and erosion, the last described as a small particle chipping material from a larger one (Vaikundaraman et al., 28 Jul 2025). The modeled transport processes include radial drift, vertical settling, and turbulent mixing / diffusion; the schematic associated with the code also mentions Brownian motion, turbulence, and azimuthal drift as contributing physical processes (Vaikundaraman et al., 28 Jul 2025). Because the code is Lagrangian, transport is represented as motion of representative particles through the $(r,z)$ domain.

The gas background is simplified. The disk is static, its radial structure follows a power law, and the temperature is vertically isothermal (Vaikundaraman et al., 28 Jul 2025). The only mathematical forms stated explicitly are

$\Sigma_g(r) \propto r^{-p}, \qquad T(r) \propto r^{-q}.$

The JOSS paper does not print the detailed transport equations, collision kernel, stopping-time formulae, or remeshing equations, and instead points readers to earlier physical-method papers for those details (Vaikundaraman et al., 28 Jul 2025).

3. Collision physics, assumptions, and scope

The presently documented collision physics is intentionally narrow. mcdust includes sticking / growth, fragmentation, and erosion, with the benchmark table identifying fragmentation velocity $v_\mathrm{frag}$ and erosion mass ratio as key collisional parameters (Vaikundaraman et al., 28 Jul 2025). This implies a threshold-based collision model, but the paper does not print the exact redistribution laws for fragments or eroded mass.

Several regimes often discussed in dust-evolution literature are not described here as implemented features. The paper explicitly does not present bouncing, mass transfer as a separate explicit regime, porosity evolution, or detailed aggregate restructuring as part of the current implementation (Vaikundaraman et al., 28 Jul 2025). This is important because earlier representative-particle Monte Carlo models of coagulation found that the bouncing barrier could halt growth before catastrophic fragmentation in inner-disk silicate conditions (Zsom, 2010). A plausible implication is that mcdust occupies a different point in the modeling landscape: it is a 2D transport-plus-collision code whose present public description emphasizes a reduced outcome set and algorithmic extensibility rather than a laboratory-derived multi-regime collision map.

The simplifications extend to the ambient medium. The code version described in the JOSS paper uses a static power-law gas disk and assumes the temperature is vertically isothermal (Vaikundaraman et al., 28 Jul 2025). The result is not a full gas–dust hydro solver, nor a model with self-consistent gas evolution or backreaction. Its strength is therefore controlled dust-evolution modeling in a prescribed background, rather than a complete disk simulation.

4. Benchmarking and validation against other dust-evolution approaches

The initial validation reported for mcdust is a benchmark against dustpy, an open-source 1D dust coagulation code, using a static gas background in both models so that differences reflect dust treatment rather than gas evolution (Vaikundaraman et al., 28 Jul 2025). The benchmark parameters explicitly given are

$\Sigma_g(1\,\mathrm{AU}) = 1000\,\mathrm{g\,cm^{-2}}, \qquad T(1\,\mathrm{AU}) = 280\,\mathrm{K},$

$\alpha = 10^{-3}, \qquad v_\mathrm{frag} = 10\,\mathrm{m\,s^{-1}},$

with the simulation evolved for 10,000 years (Vaikundaraman et al., 28 Jul 2025).

The paper reports that mcdust and dustpy show similar overall outcomes, but with notable differences (Vaikundaraman et al., 28 Jul 2025). First, mcdust does not densely populate regions of parameter space that contain only a very small fraction of the total dust mass; this is presented as an inherent limitation of representative-particle Monte Carlo schemes. Second, the paper notes that mcdust does not suffer from the “artificially sped-up growth” that can affect Smoluchowski-based methods such as dustpy. Third, because mcdust resolves the vertical dimension, it can capture sedimentation-driven coagulation and shows larger surface densities at higher masses around $50\,\mathrm{AU}$ , which the paper attributes to vertical-structure effects not usually present in 1D models (Vaikundaraman et al., 28 Jul 2025).

A more recent intercomparison extends the validation to 2D radial–vertical simulations and places mcdust alongside TriPoD and cuDisc (Eriksson et al., 23 Mar 2026). There the dust size distributions are reported to agree well despite the completely different numerical approaches used to model dust coagulation, with the largest discrepancies arising in tenuous upper layers where mcdust suffers from low mass resolution and TriPoD has difficulty when the local size distribution deviates from a power law (Eriksson et al., 23 Mar 2026).

5. Position in recent 2D code intercomparisons

In the 2026 comparison paper, mcdust appears as the Monte Carlo member of the 2D radial–vertical code comparison, contrasting with the fluid-based approaches of cuDisc and TriPoD (Eriksson et al., 23 Mar 2026). In that study, mcdust models coagulation, fragmentation, erosion, radial transport by gas advection and drift, vertical settling, and turbulent diffusion in both radial and vertical directions. Turbulence is implemented as random kicks, and local collisions are handled by grouping Lagrangian particles into grid cells and computing pairwise collision probabilities (Eriksson et al., 23 Mar 2026).

The 2D comparison examines two regimes, with

$\alpha_{\rm t}=10^{-4}, \quad 10^{-3},$

corresponding respectively to a weak-turbulence, sedimentation-driven case and a strong-turbulence, turbulence-dominated case (Eriksson et al., 23 Mar 2026). All 2D simulations are run for

$2\times 10^5 \,\mathrm{yr},$

which the authors state is sufficient to reach an equilibrium between coagulation, fragmentation, sedimentation, and vertical mixing (Eriksson et al., 23 Mar 2026). In these tests, mcdust reproduces both the strong-turbulence growth patterns and the weak-turbulence sedimentation-driven coagulation pattern, including the bimodal vertically integrated size distribution in the dynamical sedimentation-driven regime (Eriksson et al., 23 Mar 2026).

The principal limitation identified is low mass resolution in the upper atmosphere (Eriksson et al., 23 Mar 2026). In low-density regions far from the midplane, the representative-particle sample is too sparse to reconstruct local size distributions accurately, leading to underestimates of high-altitude dust density and poor sampling of small grains aloft. The same paper also describes Monte Carlo methods like mcdust as computationally expensive, which makes them less efficient to couple to hydrodynamic solvers, while also stressing their niche: they are well suited when tracking individual representative particles, and therefore particle histories, chemistry, or composition, is essential (Eriksson et al., 23 Mar 2026).

6. Nomenclature and other uses of the term

Although mcdust most directly names the protoplanetary-disk code in current disk-evolution literature, the same string has other established uses.

Usage	Meaning	Source
mcdust	2D Monte Carlo dust-evolution code for protoplanetary disks	(Vaikundaraman et al., 28 Jul 2025)
“mcdust” search usage	Mars Dust Counter on Nozomi (PLANET-B)	(Krüger et al., 17 Feb 2026)
MCdust	Magellanic Clouds dust reddening maps and catalog products	(Chen et al., 2022)

In planetary-space instrumentation, the Mars Dust Counter (MDC) on Nozomi is described as being “often searched as ‘mcdust’” (Krüger et al., 17 Feb 2026). MDC was an impact-ionisation dust detector on Japan’s Nozomi Mars mission and returned a dust data set spanning the Earth–Moon environment and heliocentric space between roughly $1.0$ and $(r,z)$ 0 AU. The modern consolidation of those results reports 96 accepted impacts, with 20 in Earth orbit and 76 in interplanetary space, and concludes that the detections were predominantly interplanetary rather than Earth-bound dust or debris (Krüger et al., 17 Feb 2026).

In extragalactic dust mapping, the same string is closely associated with Magellanic-Cloud dust resources (Chen et al., 2022). That work released high-resolution reddening maps of the Large and Small Magellanic Clouds, together with a foreground Milky Way dust map and a stellar reddening catalog. The final catalog contains 4,037,497 stars, including approximately 1.9 million LMC stars, 1.5 million SMC stars, and 0.6 million MW stars, and the products are publicly distributed as FITS files and a GitHub querying tool (Chen et al., 2022).

The consequence is terminological rather than conceptual: in arXiv and software-search practice, mcdust is not a unique label. In protoplanetary-disk modeling it denotes a FORTRAN90/OpenMP, 2D $(r,z)$ 1, Lagrangian Monte Carlo code for dust evolution (Vaikundaraman et al., 28 Jul 2025). In other subfields it may instead indicate the Mars Dust Counter or Magellanic-Cloud dust maps (Krüger et al., 17 Feb 2026, Chen et al., 2022).