---
title: 'mcdust: 2D Dust Evolution Monte Carlo Code'
url: https://www.emergentmind.com/topics/mcdust
type: topic
---

# mcdust: 2D Dust Evolution Monte Carlo Code

*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 [2507.21239]. 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 [2602.15576] [2201.03152].

## 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 [2507.21239]. 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 [2507.21239].

The code adopts a **Lagrangian Monte Carlo representative-particle method**, following the approach of **Zsom & Dullemond (2008)**, rather than a purely Eulerian Smoluchowski solver [2507.21239]. 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 [2507.21239]. 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 [1011.0194].

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 [2507.21239].

## 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 [2507.21239]. 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 [2507.21239].

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 [2507.21239]. 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 [2507.21239]. 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** [2507.21239]. 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 [2507.21239].

## 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 [2507.21239]. 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 [2507.21239]. 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 [1011.0194]. 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** [2507.21239]. 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 [2507.21239]. 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** [2507.21239].

The paper reports that mcdust and dustpy show **similar overall outcomes**, but with notable differences [2507.21239]. 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 [2507.21239].

A more recent intercomparison extends the validation to **2D radial–vertical** simulations and places mcdust alongside **TriPoD** and **cuDisc** [2603.22550]. 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 [2603.22550].

## 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 [2603.22550]. 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 [2603.22550].

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 [2603.22550]. 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 [2603.22550]. 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 [2603.22550].

The principal limitation identified is **low mass resolution in the upper atmosphere** [2603.22550]. 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 [2603.22550].

## 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 | [2507.21239] |
| **“mcdust” search usage** | Mars Dust Counter on Nozomi (PLANET-B) | [2602.15576] |
| **MCdust** | Magellanic Clouds dust reddening maps and catalog products | [2201.03152] |

In planetary-space instrumentation, the **Mars Dust Counter (MDC)** on Nozomi is described as being “often searched as ‘mcdust’” [2602.15576]. 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 \(1.44\) 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 [2602.15576].

In extragalactic dust mapping, the same string is closely associated with **Magellanic-Cloud dust** resources [2201.03152]. 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 [2201.03152].

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 \((r,z)\), Lagrangian Monte Carlo code** for dust evolution [2507.21239]. In other subfields it may instead indicate the **Mars Dust Counter** or **Magellanic-Cloud dust maps** [2602.15576] [2201.03152].

Source: https://www.emergentmind.com/topics/mcdust