Particle Transport Model Research Articles

A wave-resolving two-dimensional vertical Lagrangian approach to model microplastic transport in nearshore waters based on TrackMPD 3.0

Abstract. Potentially acting as a source or a sink for plastic pollution to the open ocean, nearshore waters remain a challenging context for predicting the transport and deposition of plastic debris. In this study, we present an advanced modeling approach based on the SWASH wave model and the TrackMPD (v3.0) particle transport model to investigate the transport dynamics of floating and sinking microplastics in wave-dominated environments. This approach introduces novel features such as coupling with advanced turbulence models, simulating resuspension and bedload processes, implementing advanced settling and rising velocity formulations, and enabling parallel computation. The wave laboratory experiments conducted by Forsberg et al. (2020) were simulated to validate the model's ability to reproduce the transport of diverse microplastics (varying in density, shape, and size) along a comprehensive beach profile, capturing the whole water column. Our results underscore the robustness of the proposed model, showing good agreement with experimental data. High-density microplastics moved onshore near the bed, accumulating in proximity to the wave-breaking zone, while the distribution of low-density particles varied along the coastal profile depending on the particle properties. The study also sheds light on the primary mechanisms driving microplastic transport, such as Stokes drift, wave asymmetry, and settling/rising velocities. Sensitivity analyses on calibration parameters further confirm the robustness of the model results and the influence of these factors on transport patterns. This research establishes the SWASH–TrackMPD approach as a valuable tool, opening avenues for future studies to contextualize laboratory findings within the complexities of real-world nearshore environments and further refine our comprehension of microplastic dynamics across different beaches and wave-climate conditions.

ANALYSIS OF THEORETICAL STUDIES OF DEVICES FOR DOSING AND MIXING NUTRIENT SOLUTIONS

Fertigation systems play an important role in greenhouse crop production, which allow combining irrigation and fertilization processes, providing optimal plant nutrition. The main task of such systems is accurate dosing and uniform mixing of nutrient solutions, including different types of fertilizers, with water. Fertigation technology makes it possible to significantly reduce the loss of water and fertilizers, as well as to increase the efficiency of their use at various stages of plant growth. However, the effectiveness of these systems depends on the quality of the mixing and dosing devices, which must ensure the uniform distribution of nutrients in the solution. Today, there are different designs of mixers for the preparation of nutrient solutions: mechanical mixers with moving elements and static mixers that use hydraulic flows for mixing. Mechanical mixers are suitable for solid and hard-to-dissolve fertilizers, but their operation is complicated by the presence of moving parts. Static mixers are easier to use and have no moving parts, making them efficient and reliable for fertigation systems. The analysis of theoretical studies of devices for dosing and mixing nutrient solutions, in particular, jet mixers that work according to the static principle, has been carried out. The considered devices for preparing liquid mixtures are of the ejector type, on the basis of which many modern systems are built. The main attention is paid to the calculations of the optimal geometrical parameters of jet dispensers-mixers. The theoretical studies of most scientists are focused on determining the injection coefficient — as a key parameter that determines the efficiency of mixing and dosing. Theoretical approaches also include models of turbulent particle transport and semi-empirical equations to evaluate mixing quality. However, the issue of practical assessment of the quality of multi-component mixer-dispenser mixtures remains insufficiently studied.

Larmor radius effect on the control of chaotic transport in tokamaks

We investigate the influence of the finite Larmor radius on the dynamics of guiding-center test particles subjected to an E×B drift in a large aspect-ratio tokamak. For that, we adopt the drift-wave test particle transport model presented by Horton et al. [Phys. Plasmas 5, 3910 (1998)] and introduce a second-order gyro-averaged extension, which accounts for the finite Larmor radius effect that arises from a spatially varying electric field. Using this extended model, we numerically examine the influence of the finite Larmor radius on chaotic transport and the formation of transport barriers. For non-monotonic plasma profiles, we show that the twist condition of the dynamical system, i.e., KAM theorem's non-degeneracy condition for the Hamiltonian, is violated along a special curve, which, under non-equilibrium conditions, exhibits significant resilience to destruction, thereby inhibiting chaotic transport. This curve acts as a robust barrier to transport and is usually called shearless transport barrier. While varying the amplitude of the electrostatic perturbations, we analyze bifurcation diagrams of the shearless barriers and escape rates of orbits to explore the impact of the finite Larmor radius on controlling chaotic transport. Our findings show that increasing the Larmor radius enhances the robustness of transport barriers, as larger electrostatic perturbation amplitudes are required to disrupt them. Additionally, as the Larmor radius increases, even in the absence of transport barriers, we observe a reduction in the escape rates, indicating a decrease in chaotic transport.

Evaluating the role of sex-related structure-function differences on airway aerosol transport and deposition.

Several experimental studies have found that females have higher particle deposition in the airways than males. This has implications for the delivery of aerosolized therapeutics and for understanding sex differences in respiratory system response to environmental exposures. This study evaluates several factors that potentially contribute to sex differences in particle deposition, using scale-specific structure-function models of one-dimensional (1-D) ventilation distribution, particle transport, and deposition. The impact of gravity, inhalation flow rate, and dead space are evaluated in 12 structure-based models (7 females; 5 males). Females were found to have significantly higher total, bronchial, and alveolar deposition than males across a particle size range from 0.01 to 10 μm. Results suggest that higher deposition fraction in females is due to higher alveolar deposition for smaller particle sizes and higher bronchial deposition for larger particles. Females had higher alveolar deposition in the lower lobes and slightly lower particle concentration in the left upper lobe. Males were found to be more sensitive to changes due to gravity, showing greater reduction in bronchial deposition fraction. Males were also more sensitive to change in inhalation flow rate and to scaling of dead space due to the larger male baseline airway size. Predictions of sex differences in particle deposition-that are consistent with the literature-suggest that sex-based characteristics of lung and airway size interacting with particle size gives rise to differences in regional deposition.NEW & NOTEWORTHY Sex differences in airway tract particle deposition are analyzed using computational models that account for scale-specific structure and function. We show that sex-related differences in lung and airway size can explain experimental observations of increased deposition fraction in females, with females tending toward enhanced fine particle deposition in the alveolar airways and enhanced bronchial deposition for larger particles.

One-dimensional model for vertical hydraulic transport of high-concentration mineral particles

A novel model is proposed for analyzing high-concentration granular flow systems comprising equally sized spherical particles within vertical, long straight pipelines. This model is specifically tailored for simulating the vertical hydraulic transport of ore particles in marine mining projects. The proposed model treats the granular system akin to a pseudo-fluid and operates through three mechanisms. First, fluid characteristics of the granular system are derived from particle–particle collisions. Second, the resistance exerted by the pipe wall on the granular system is calculated based on the momentum loss of particles during particle–wall collisions. Third, the interaction between individual particles and the surrounding fluid is transformed into an interaction between the carrier fluid and the pseudo-fluid. Additionally, the present work develops a dedicated numerical format and iterative method for solving the one-dimensional two-fluid governing equations. The one-dimensional (1D) model notably enhances computational efficiency and facilitates accurate tracking of high-concentration particles over extended distances within straight pipelines. Notably, the proposed 1D model demonstrates a high degree of predictive accuracy when compared against experimental data as well as results from computational fluid dynamics and discrete element method simulations.

Retention of microplastics by biofilms and their ingestion by protists in rivers.

Microplastics (MPs) are released into the environment through human activities and are transported by rivers from land to sea. Biofilms, which are ubiquitous in aquatic ecosystems such as rivers, may play an essential role in the fate of MPs and their ingestion by biofilm protists. To assess this, biofilms were naturally grown on clay tiles in the River Rhine, Germany, and analysed in a combined field and laboratory study. Compared to the ambient river water, biofilms grown for 6, 12, and 18 months in the River Rhine contained up to 10 times more MPs. Between 70% and 78% of all MPs were smaller than 50 μm. In laboratory experiments, clay tiles covered with 1-month-old naturally grown biofilm retained 6-12 times more MPs than clay tiles without biofilm coverage. Furthermore, the ingestion of MPs of 6 and 10 μm by the ciliate Stentor coeruleus was confirmed, and a positive correlation between ingestion rates and ambient MP concentrations was found. The results are relevant for particle transport models in riverine systems, risk assessment of MPs regarding their distribution and fate in the aquatic environment, and the effects of MPs on micro- and macroorganisms.

A Digital Twin of the Trondheim Fjord for Environmental Monitoring—A Pilot Case

Digital Twins of the Ocean (DTO) are a rapidly emerging topic that has attracted significant interest from scientists in recent years. The initiative, strongly driven by the EU, aims to create a digital replica of the ocean to better understand and manage marine environments. The Iliad project, funded under the EU Green Deal call, is developing a framework to support multiple interoperable DTO using a federated systems-of-systems approach across various fields of applications and ocean areas, called pilots. This paper presents the results of a Water Quality DTO pilot located in the Trondheim fjord in Norway. This paper details the building blocks of DTO, specific to this environmental monitoring pilot. A crucial aspect of any DTO is data, which can be sourced internally, externally, or through a hybrid approach utilizing both. To realistically twin ocean processes, the Water Quality pilot acquires data from both surface and benthic observatories, as well as from mobile sensor platforms for on-demand data collection. Data ingested into an InfluxDB are made available to users via an API or an interface for interacting with the DTO and setting up alerts or events to support ’what-if’ scenarios. Grafana, an interactive visualization application, is used to visualize and interact with not only time-series data but also more complex data such as video streams, maps, and embedded applications. An additional visualization approach leverages game technology based on Unity and Cesium, utilizing their advanced rendering capabilities and physical computations to integrate and dynamically render real-time data from the pilot and diverse sources. This paper includes two case studies that illustrate the use of particle sensors to detect microplastics and monitor algae blooms in the fjord. Numerical models for particle fate and transport, OpenDrift and DREAM, are used to forecast the evolution of these events, simulating the distribution of observed plankton and microplastics during the forecasting period.

Severe Electron Environment for Surface Charging at Geostationary and Medium Earth Orbits

Electron radiation environment with keV energies on medium earth orbit (MEO) is investigated around the times when worst-case severe environments for surface charging were detected at Los Alamos National Laboratory (LANL) satellites on geostationary earth orbit (GEO). The Inner Magnetosphere Particle Transport and Acceleration Model (IMPTAM) is employed to model 1–100 keV electron fluxes in the inner Earth’s magnetosphere (inside 10RE) during four representative events selected out of 400 LANL worst-case severe environment events. Modeled fluxes are compared to the observed ones on GEO, and the peak electron fluxes are then extracted at L=4.6 which is considered as approximate MEO environment following the LANL events. IMPTAM generally reproduces the 10–50 keV electron fluxes on GEO but underestimates (of factor of 2 to 5) at energies above. It is found that the maximum electron flux on MEO is reached in about 1.5–2 h after the worst-case environment for surface charging was detected at GEO. Whereas the magnetic local time (MLT) location of the worst-case severe environments on GEO varies from 23 to 05, the maximum electron flux on MEO is located on 6–7.8 MLT. The maximum electron flux values on MEO can be 2 to 10 times higher than those observed on GEO and those estimated using European Cooperation for Space Standardization and National Aeronautics and Space Administration guidelines, which can be a significant increase of the risks in terms of surface charging.

ATEP: an advanced transport model for energetic particles

In this paper we report on the implementation and verification of a phase-space resolved energetic particle (EP) transport model. It is based on a first-principle theoretical framework, i.e. the system of non-linear gyrokinetic equations and the related transport equations. Its focus is primarily directed toward understanding the meso-scale character of EPs and its consequences. Compared to the conventional description of thermal radial transport via a one-dimensional radial diffusion equation, the newly developed model is three-dimensional using canonical constants-of-motion (CoM) variables. The model does not assume diffusive processes to be dominant a priori, instead the EP fluxes are self-consistently calculated and directly evolved in CoM space. We use the EP-Stability workflow and the HAGIS code to determine the phase space fluxes explicitly either in the limit of constant mode amplitudes or an energy-conserving quasi-linear model. As an application of the model the transport of neutral-beam-generated EPs due to a toroidal Alfvén eigenmode in an ITER plasma is investigated. As there are no sources and collisions taken into account so far (for an extension of the model see the companion paper (Meng et al 2024 Nucl. Fusion accepted)), the results cannot be considered as an exhaustive study, but rather as a practical demonstration of the conceptual framework on the way to a comprehensive reduced description of burning plasmas.

Anomalous diffusion of scaled Brownian tracers.

A model for anomalous transport of tracer particles diffusing in complex media in two dimensions is proposed. The model takes into account the characteristics of persistent motion that an active bath transfers to the tracer; thus, the model proposed here extends active Brownian motion, for which the stochastic dynamics of the orientation of the propelling force is described by scaled Brownian motion (sBm), identified by time-dependent diffusivity of the form D_{β}∝t^{β-1},β>0. If β≠1, sBm is highly nonstationary and suitable to describe such nonequilibrium dynamics induced by complex media. In this paper, we provide analytical calculations and computer simulations to show that genuine anomalous diffusion emerges in the long-time regime, with a time scaling of the mean-squared displacement t^{2-β}, while ballistic transport t^{2}, characteristic of persistent motion, is found in the short-time regime. We also analyze the time dependence of the kurtosis, and the intermediate scattering function of the position distribution, as well as the propulsion autocorrelation function, which defines the effective persistence time.

Indicators to assess temporal variability in marine connectivity processes: A semi-theoretical approach.

Oceanographic connectivity in an effective network of protected areas is crucial for restoring and stabilising marine populations. However, temporal variability in connectivity is rarely considered as a criterion in designing and evaluating marine conservation planning. In this study, indicators were defined to characterise the temporal variability in occurrence, flux, and frequency of connectivity in a northwestern Mediterranean Sea area. Indicators were tested on semi-theoretically-estimated connections provided by the runs of a passive particle transport model in a climatological year and in three years between 2006-2020, showing large deviation from the climatological year. The indicators allowed comparing the temporal variability in connectivity of four zones, highlighted differences in connectivity due to their locations and the mesoscale hydrodynamics, and identified areas that require further investigation. The three indicators also showed that the temporal variability in connectivity was influenced by the duration and depth of particle transport, although no consistent pattern was observed in the indicator variations of the compared zones. Provided that specific objectives will be given when parameterising transport models (i.e., selection of focus species and time period), indicators of temporal variability in connectivity have potential to support spatial conservation planning, prioritise the protection of marine resources, and measure the effectiveness of Marine Protected Areas, in line with a long-term vision of ocean management.

MR-PVHEE: A novel magnetic resonance-guided parallel-beam very high-energy electron radiotherapy system

PurposeMR-guided very high-energy electron (VHEE) radiotherapy can combine the imaging advantages of MR with the dosimetry advantages of VHEE radiotherapy, which is of significant clinical value. However, VHEEs are highly susceptible to the Lorentz force generated by the MR magnetic field, and coupling MR and VHEEs is challenging. Here, we present a novel MR-guided parallel-beam VHEE (MR-PVHEE) radiotherapy system and confirm its feasibility and effectiveness. MethodThe proposed MR-PVHEE radiotherapy system includes an ingenious coupling model of MR and VHEEs and an electromagnetic steering parameters commissioning (ESP-COM) method for accurate delivery. First, by generating parallel VHEE (PVHEE) beamlets that point in the same direction as the MR main magnetic field, the coupling model based on triple-stage electromagnetic steering can significantly lessen the twisting and deflecting of the VHEE beamlets' delivery trajectory caused by the MR magnetic field. The dosimetric advantage of VHEEs will be enhanced by delicately utilizing the MR magnetic field to constrain lateral scatter. Then, the ESP-COM method based on Bayesian black-box optimization for the PVHEE beamlets is designed by constructing a cost function using the position and direction information of particles in phase space and optimizing the parameters to deliver the beamlets accurately to the target spots. Finite element electromagnetic modeling and Monte Carlo particle transport simulation are used to validate the MR-PVHEE. ResultsMR-PVHEE can generate the PVHEE beamlets in the same direction as the MR magnetic field and accurately deliver them to the target spots. The average position error is within 0.5 mm, and the average direction error is about 0.5°, which can meet the requirements of clinical treatment accuracy. MR-PVHEE can reduce the VHEE lateral penumbra and increase the dose drop gradient. ConclusionFor the first time, MR and VHEE radiotherapy are successfully coupled in this study, and the innovative MR-PVHEE radiotherapy system can elicit new modalities for MR-guided charged particle radiotherapy and spatially fractionated radiotherapy.

Simplification strategies for a patient-specific CFD model of particle transport during liver radioembolization

BackgroundPatient-specific 3D computational fluid dynamics (CFD) simulations have been used previously to identify the impact of injection parameters (e.g. injection location, velocity, etc.) on the particle distribution and the tumor dose during transarterial injection of radioactive microspheres for treatment of hepatocellular carcinoma. However, these simulations are computationally costly, so we aim to evaluate whether these can be reliably simplified. MethodsWe identified and applied five simplification strategies (i.e. truncation, steady flow modelling, moderate and severe grid coarsening, and reducing the number of cardiac cycles) to a patient-specific CFD setup. Subsequently, we evaluated whether these strategies can be used to (1) accurately predict the CFD output (i.e. particle distribution and tumor dose) and (2) quantify the sensitivity of the model output to a specific injection parameter (injection flow rate). ResultsFor both accuracy and sensitivity purposes, moderate grid coarsening is the most reliable simplification strategy, allowing to predict the tumor dose with only a maximal deviation of 1.4 %, and a similar sensitivity (deviation of 0.7 %). The steady strategy performs the worst, with a maximal deviation in the tumor dose of 20 % and a difference in sensitivity of 10 %. ConclusionThe patient-specific 3D CFD simulations of this study can be reliably simplified by coarsening the grid, decreasing the computational time by roughly 45 %, which works especially well for sensitivity studies.

Modeling the Transport of Solar Energetic Particles in a Corotating Interaction Region

We present a new three-dimensional (3D) magnetohydrodynamic (MHD) model and a new 3D energetic particle transport (EPT) model. The 3D MHD model numerically solves the ideal MHD equations using the relaxing total variation diminishing scheme. In the 3D MHD simulations, we use simple boundary conditions with a high-speed flow, and we can clearly identify a corotating interaction region (CIR) with the characteristics of forward shock and reverse shock. The 3D EPT model solves the Fokker–Planck transport equation for the solar energetic particles (SEPs) using backward stochastic processes, with the magnetic field and solar wind velocity field from MHD results. For comparison, the 3D EPT model results with Parker fields are also obtained. We investigate the transport of SEPs with particle sources and observers in different positions in MHD fields with a CIR, and we compare the results with those in the Parker fields. Our simulation results show that the compression region with local enhancement of the magnetic field, i.e., CIR, can act as a barrier to scatter energetic particles back, and particles can struggle to diffuse through the strong magnetic field regions. Usually, a normal anisotropy profile is commonly present in SEP simulation results with Parker fields, and it is also typically present in that with MHD fields. However, because of the compression region of the magnetic field, energetic particles may exhibit anomalous anisotropy. This result may be used to replicate the spacecraft observation phenomena of the anomalous anisotropy.

Water, dust, and environmental justice: The case of agricultural water diversions

AbstractWater diversions for agriculture reduce ecosystem services provided by saline lakes around the world. Exposed lakebed surfaces are major sources of dust emissions that may exacerbate existing environmental inequities. This paper studies the effects of water diversions and their impacts on particulate pollution arising from reduced inflows to the Salton Sea in California via a spatially explicit particle transport model and changing lakebed exposure. We demonstrate that lakebed dust emissions increased ambient and concentrations and worsened environmental inequalities, with historically disadvantaged communities receiving a disproportionate increase in pollution. Water diversion decisions are often determined by political processes; our findings demonstrate the need for distributional analysis of such decisions to ensure equitable compensation.

Numerical modeling of the fracturing mechanisms of unconsolidated sand reservoirs under water injection

Produced Water Re-Injection is a standard practice in oil and gas operations. When performed at sufficiently high pressures, it can trigger the fracturing of the reservoir, which should be controlled to stimulate the formation without compromising its safety. While the mechanisms of the hydraulic fracturing of brittle rocks are well-understood, this understanding is more challenging in the case of unconsolidated sand reservoirs. Recent experimental studies indicate that pseudofractures in such formations primarily result from shear banding and flow channelization. There is a need for further interpretation of the experimental findings through numerical models that account for the proper physical phenomena. For that, a coupled finite element model of water percolation, particle transport and strain localization is developed to replicate the experiments of radial injection of water in mixtures of sand and fines by Nguyen et al., 2022: An experimental setup with radial injection cell for investigation of fracturing in unconsolidated sand reservoirs under fluid injection. Journal of Petroleum Science and Engineering 213:11036. To simulate shear banding, the model accounts for strain-softening behavior and introduces material imperfections in a few weak elements. Particle mobilization starts once a critical fluid velocity is reached and permeability is assumed to be a function of particle concentration. The numerical models can replicate the geometry of the observed radial pseudofractures, as well as the measured fracturing pressures. They also qualitatively capture the effects of the initial stress state on the fracturing pressure, the fracture length and on the permeability increases during the fracturing regime as observed in the laboratory tests. Notably, the numerical results gave hints on the role of the coupling between strain localization and particle transport on the formation of the pseudofractures. These findings are used to propose an updated conceptual model for the hydraulic fracturing of sand packs.

A variance deconvolution estimator for efficient uncertainty quantification in Monte Carlo radiation transport applications

Monte Carlo simulations are at the heart of many high-fidelity simulations and analyses for radiation transport systems. As is the case with any complex computational model, it is important to propagate sources of input uncertainty and characterize how they affect model output. Unfortunately, uncertainty quantification (UQ) is made difficult by the stochastic variability that Monte Carlo transport solvers introduce. The standard method to avoid corrupting the UQ statistics with the transport solver noise is to increase the number of particle histories, resulting in very high computational costs. In this contribution, we propose and analyze a sampling estimator based on the law of total variance to compute UQ variance even in the presence of residual noise from Monte Carlo transport calculations. We rigorously derive the statistical properties of the new variance estimator, compare its performance to that of the standard method, and demonstrate its use on neutral particle transport model problems involving both attenuation and scattering physics. We illustrate, both analytically and numerically, the estimator’s statistical performance as a function of available computational budget and the distribution of that budget between UQ samples and particle histories. We show analytically and corroborate numerically that the new estimator is unbiased, unlike the standard approach, and is more accurate and precise than the standard estimator for the same computational budget.

Nanoparticles synthesis in microwave plasmas: peculiarities and comprehensive insight

Low-pressure plasma processes are routinely used to grow, functionalize or etch materials, and thanks to some of its unique attributes, plasma has become a major player for some applications such as microelectronics. Plasma processes are however still at a research level when it comes to the synthesis and functionalization of nanoparticles. Yet plasma processes can offer a particularly suitable solution to produce nanoparticles having very peculiar features since they enable to: (i) reach particle with a variety of chemical compositions, (ii) tune the size and density of the particle cloud by acting on the transport dynamics of neutral or charged particles through a convenient setting of the thermal gradients or the electric field topology in the reactor chamber and (iii) manipulate nanoparticles and deposit them directly onto a substrate, or codeposit them along with a continuous film to produce nanocomposites or (iv) use them as a template to produce 1D materials. In this article, we present an experimental investigation of nanoparticles synthesis and dynamics in low-pressure microwave plasmas by combining time-resolved and in-situ laser extinction and scattering diagnostics, QCL absorption spectroscopy, mass spectrometry, optical emission spectroscopy and SEM along with a particle transport model. We showed for the first time the thermophoresis-driven dynamic of particle cloud in electrodless microwave plasmas. We showed that this effect is linked to particular fluctuations in the plasma composition and results in the formation of a void region in the bulk of the plasma surrounded by a particle cloud in the peripherical post-discharge. We also reveals and analyze the kinetics of precursor dissociation and molecular growth that result in the observed nanoparticle nucleation.

A coupled transport model of pollutants-suspended particles in saturated porous media based on granular thermodynamics

A coupled transport model of thermo-hydro-mechanical two-phase flow in saturated porous media was established based on granular thermodynamics and Newton's second law. This model includes the entropy change generated by material entering and exiting the open system, as well as the solid-liquid relative velocity in the dissipative system, to derive the seepage field equation. Furthermore, it accounted for thermal conduction, porosity changes resulting from suspended particle deposition and soil deformation, and the adsorption-desorption of pollutants by soil particles and suspended particles. To evaluate the model, a sensitivity analysis was conducted. Subsequently, the calculated and experimental results are compared by various scenarios, including different types of pollutants, injection concentrations, and initial seepage velocities. The results indicated that this model accurately describes the transport process and residual distribution of pollutants, as well as the continuous injection of coupled two-phase flow, and effectively predicted the coupled transport process of pollutants and suspended particles, which has strong practicality.

Kinetic Theory for the Low-Density Lorentz Gas

The Lorentz gas is one of the simplest and most widely-studied models for particle transport in matter. It describes a cloud of non-interacting gas particles in an infinitely extended array of identical spherical scatterers. The model was introduced by Lorentz in 1905 who, following the pioneering ideas of Maxwell and Boltzmann, postulated that in the limit of low scatterer density, the macroscopic transport properties of the model should be governed by a linear Boltzmann equation. The linear Boltzmann equation has since proved a useful tool in the description of various phenomena, including semiconductor physics and radiative transfer. A rigorous derivation of the linear Boltzmann equation from the underlying particle dynamics was given, for random scatterer configurations, in three seminal papers by Gallavotti, Spohn and Boldrighini-Bunimovich-Sinai. The objective of the present study is to develop an approach for a large class of deterministic scatterer configurations, including various types of quasicrystals. We prove the convergence of the particle dynamics to transport processes that are in general (depending on the scatterer configuration) not described by the linear Boltzmann equation. This was previously understood only in the case of the periodic Lorentz gas through work of Caglioti-Golse and Marklof-Strömbergsson. Our results extend beyond the classical Lorentz gas with hard sphere scatterers, and in particular hold for general classes of spherically symmetric finite-range potentials. We employ a rescaling technique that randomises the point configuration given by the scatterers’ centers. The limiting transport process is then expressed in terms of a point process that arises as the limit of the randomised point configuration under a certain volume-preserving one-parameter linear group action.