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At least 757 records · Page 42

Reconnection and particle acceleration in 3D current sheet evolution in moderately-magnetized astrophysical pair plasma

Magnetic reconnection, a plasma process converting magnetic energy to particle kinetic energy, is often invoked to explain magnetic energy releases powering high-energy flares in astrophysical sources including pulsar wind nebulae and black hole jets. Reconnection is usually seen as the (essentially 2D) nonlinear evolution of the tearing instability disrupting a thin current sheet. To test how this process operates in 3D, we conduct a comprehensive particle-in-cell simulation study comparing 2D and 3D evolution of long, thin current sheets in moderately-magnetized, collisionless, relativistically-hot electron- positron plasma, and find dramatic differences. We first systematically characterize this process in 2D, where classic, hierarchical plasmoid-chain reconnection determines energy release, and explore a wide range of initial configurations, guide magnetic field strengths, and system sizes. We then show that 3D simulations of similar configurations exhibit a diversity of behaviours, including some where energy release is determined by the nonlinear relativistic drift-kink instability. Thus, 3D current-sheet evolution is not always fundamentally classical reconnection with perturbing 3D effects, but, rather, a complex interplay of multiple linear and nonlinear instabilities whose relative importance depends sensitively on the ambient plasma, minor configuration details, and even stochastic events. It often yields slower but longer-lasting and ultimately greater magnetic energy release than in 2D. Intriguingly, nonthermal particle acceleration is astonishingly robust, depending on the upstream magnetization and guide field, but otherwise yielding similar particle energy spectra in 2D and 3D. Though the variety of underlying current-sheet behaviours is interesting, the similarities in overall energy release and particle spectra may be more remarkable.

Gregory R. Werner↗

SKS Polarization Anomalies Due to the Coriolis Force

The Earth’s Coriolis force has been well–known to impact surface waves and normal modes, which is essential to accurately interpret these waves. However, the Coriolis force on body waves has been assumed to be negligible and mostly ignored. It has been previously shown that the Coriolis force impacts polarizations of shear waves, whereas the wavefronts remain unaffected. We expand on the potential influences of Earth’s Coriolis force on shear–wave polarization measurements by conducting 3D numerical simulations for elastic waves generated by earthquake and explosive sources in a radially symmetric, and 3D mantle and crustal models. The Coriolis force can produce polarization anomalies of mantle shear waves up to 7° and core phases, such as SKS and SKKS, up to 4°. Uncorrected shear–wave polarizations due to the Coriolis force can cause an additional source of error (5°–10° in fast direction, and 0.2–0.3 s delay time depending on the method and seismic phase), inaccurate interpretation of station misalignments, and imprecise estimates of the core–mantle boundary topography. We show how to correct for the Coriolis force on teleseismic shear waves using 1D ray tracing for well–isolated phases. Here, we recommend the use of full waveform simulations to accurately account for earthquake sources parameters, poorly isolated phases that could include interfering phase arrivals within the measurement time window, and the effect of the Coriolis force on the polarizations of shear waves.

58 GEOSCIENCES↗

Effects of Initial Condition Spectral Content on Shock Driven-Turbulent Mixing

The mixing of materials due to the Richtmyer-Meshkov instability and the ensuing turbulent behavior is of intense interest in a variety of physical systems including inertial confinement fusion, combustion, and the final stages of stellar evolution. Extensive numerical and laboratory studies of shock-driven mixing have demonstrated the rich behavior associated with the onset of turbulence due to the shocks. Here we report on progress in understanding shock-driven mixing at interfaces between fluids of differing densities through three-dimensional (3D) numerical simulations using the RAGE code in the implicit large eddy simulation context. We consider a shock-tube configuration with a band of high density gas (SF 6 ) embedded in low density gas (air). Shocks with a Mach number of 1.26 are passed through SF 6 bands, resulting in transition to turbulence driven by the Richtmyer-Meshkov instability. The system is followed as a rarefaction wave and a reflected secondary shock from the back wall pass through the SF 6 band. We apply a variety of initial perturbations to the interfaces between the two fluids in which the physical standard deviation, wave number range, and the spectral slope of the perturbations are held constant, but the number of modes initially present is varied. By thus decreasing the density of initial spectral modes of the interface, we find that we can achieve as much as 25% less total mixing at late times. This has potential direct implications for the treatment of initial conditions applied to material interfaces in both 3D and reduced dimensionality simulation models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

THREE-DIMENSIONAL MHD MAGNETIC RECONNECTION SIMULATIONS WITH A FINITE GUIDE FIELD: PROPOSAL OF THE SHOCK-EVOKING POSITIVE-FEEDBACK MODEL

Using a three-dimensional (3D) magnetohydrodynamic model, we simulate the magnetic reconnection in a single current sheet. We assume a finite guide field, a random perturbation on the velocity field, and uniform resistivity. Our model enhances the reconnection rate relative to the classical Sweet–Parker model in the same configuration. The efficiency of magnetic energy conversion is increased by interactions between the multiple tearing layers coexisting in the global current sheet. This interaction, which forms a positive-feedback system, arises from coupling of the inflow and outflow regions in different layers across the current sheet. The coupling accelerates the elementary reconnection events, thereby enhancing the global reconnection rate. The reconnection establishes flux tubes along each tearing layer. Slow-mode shocks gradually form along the outer boundaries of these tubes, further accelerating the magnetic energy conversion. Such a positive-feedback system is absent in two-dimensional simulations, 3D reconnection without a guide field, and reconnection under a single perturbation mode. We refer to our model as the “shock-evoking positive-feedback” model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Habitable Moist Atmospheres on Terrestrial Planets near the Inner Edge of the Habitable Zone around M Dwarfs

Terrestrial planets in the habitable zones (HZs) of low-mass stars and cool dwarfs have received significant scrutiny recently. Transit spectroscopy of such planets with the James Webb Space Telescope (JWST) represents our best shot at obtaining the spectrum of a habitable planet within the next decade. As these planets are likely tidally locked, improved 3D numerical simulations of such planetary atmospheres are needed to guide target selection. Here we use a 3D climate system model, updated with new water-vapor absorption coefficients derived from the HITRAN 2012 database, to study ocean-covered planets at the inner edge of the HZ around late M to mid-K stars (2600 K⩽T{sub eff}⩽4500 K). Our results indicate that these updated water-vapor coefficients result in significant warming compared to previous studies, so the inner HZ around M dwarfs is not as close as suggested by earlier work. Assuming synchronously rotating Earth-sized and Earth-mass planets with background 1 bar N{sub 2} atmospheres, we find that planets at the inner HZ of stars with T{sub eff}>3000 K undergo the classical “moist greenhouse” (H{sub 2}O mixing ratio >10{sup −3} in the stratosphere) at significantly lower surface temperature (∼280 K) in our 3D model compared with 1D climate models (∼340 K). This implies that some planets around low-mass stars can simultaneously undergo water loss and remain habitable. However, for stars with T{sub eff}⩽3000 K, planets at the inner HZ may directly transition to a runaway state, while bypassing the moist greenhouse water loss entirely. We analyze transmission spectra of planets in a moist greenhouse regime and find that there are several prominent H{sub 2}O features, including a broad feature between 5 and 8 μm, within JWST MIRI instrument range. Thus, relying only on standard Earth-analog spectra with 24 hr rotation period around M dwarfs for habitability studies will miss the strong H{sub 2}O features that one would expect to see on synchronously rotating planets around M dwarf stars, with JWST.

79 ASTRONOMY AND ASTROPHYSICS↗

A line-source method for aligning on-board and other pinhole SPECT systems

Purpose: In order to achieve functional and molecular imaging as patients are in position for radiation therapy, a robotic multipinhole SPECT system is being developed. Alignment of the SPECT system—to the linear accelerator (LINAC) coordinate frame and to the coordinate frames of other on-board imaging systems such as cone-beam CT (CBCT)—is essential for target localization and image reconstruction. An alignment method that utilizes line sources and one pinhole projection is proposed and investigated to achieve this goal. Potentially, this method could also be applied to the calibration of the other pinhole SPECT systems.Methods: An alignment model consisting of multiple alignment parameters was developed which maps line sources in three-dimensional (3D) space to their two-dimensional (2D) projections on the SPECT detector. In a computer-simulation study, 3D coordinates of line-sources were defined in a reference room coordinate frame, such as the LINAC coordinate frame. Corresponding 2D line-source projections were generated by computer simulation that included SPECT blurring and noise effects. The Radon transform was utilized to detect angles (α) and offsets (ρ) of the line-source projections. Alignment parameters were then estimated by a nonlinear least squares method, based on the α and ρ values and the alignment model. Alignment performance was evaluated as a function of number of line sources, Radon transform accuracy, finite line-source width, intrinsic camera resolution, Poisson noise, and acquisition geometry. Experimental evaluations were performed using a physical line-source phantom and a pinhole-collimated gamma camera attached to a robot.Results: In computer-simulation studies, when there was no error in determining angles (α) and offsets (ρ) of the measured projections, six alignment parameters (three translational and three rotational) were estimated perfectly using three line sources. When angles (α) and offsets (ρ) were provided by the Radon transform, estimation accuracy was reduced. The estimation error was associated with rounding errors of Radon transform, finite line-source width, Poisson noise, number of line sources, intrinsic camera resolution, and detector acquisition geometry. Statistically, the estimation accuracy was significantly improved by using four line sources rather than three and by thinner line-source projections (obtained by better intrinsic detector resolution). With five line sources, median errors were 0.2 mm for the detector translations, 0.7 mm for the detector radius of rotation, and less than 0.5° for detector rotation, tilt, and twist. In experimental evaluations, average errors relative to a different, independent registration technique were about 1.8 mm for detector translations, 1.1 mm for the detector radius of rotation (ROR), 0.5° and 0.4° for detector rotation and tilt, respectively, and 1.2° for detector twist.Conclusions: Alignment parameters can be estimated using one pinhole projection of line sources. Alignment errors are largely associated with limited accuracy of the Radon transform in determining angles (α) and offsets (ρ) of the line-source projections. This alignment method may be important for multipinhole SPECT, where relative pinhole alignment may vary during rotation. For pinhole and multipinhole SPECT imaging on-board radiation therapy machines, the method could provide alignment of SPECT coordinates with those of CBCT and the LINAC.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Bremsstrahlung in GRMHD Models of Accreting Black Holes

Here, the role of bremsstrahlung in the emission from hot accretion flows around slowly accreting supermassive black holes is not thoroughly understood. In order to appraise the importance of bremsstrahlung relative to other radiative processes, we compute spectral energy distributions (SEDs) of accretion disks around slowly accreting supermassive black holes including synchrotron radiation, inverse Compton scattering, and bremsstrahlung. We compute SEDs for (i) four axisymmetric radiative general relativistic magnetohydrodynamics (RadGRMHD) simulations of 10 8 M ⊙ black holes with accretion rates between 10 -8 $\dot{M}$ Edd and 10 -5 $\dot{M}$ Edd , (ii) four axisymmetric RadGRMHD simulations of M87* with varying dimensionless spin a$_*$ and black hole mass, and (iii) a 3D GRMHD simulation scaled for Sgr A*. At 10 -8 $\dot{M}$ Edd , most of the luminosity is synchrotron radiation, while at 10 -5 $\dot{M}$ Edd the three radiative processes have similar luminosities. In most models, bremsstrahlung dominates the SED near 512 keV. In the M87* models, bremsstrahlung dominates this part of the SED if a$_*$ = 0.5, but inverse Compton scattering dominates if a$_*$ = 0.9375. Since scattering is more variable than bremsstrahlung, this result suggests that 512 keV variability could be a diagnostic of black hole spin. In the appendix, we compare some bremsstrahlung formulæ found in the literature.

79 ASTRONOMY AND ASTROPHYSICS↗

Habitable Moist Atmospheres on Terrestrial Planets near the Inner Edge of the Habitable Zone Around M Dwarfs

Terrestrial planets in the habitable zones (HZs) of low-mass stars and cool dwarfs have received significant scrutiny recently. Transit spectroscopy of such planets with the James Webb Space Telescope (JWST) represents our best shot at obtaining the spectrum of a habitable planet within the next decade. As these planets are likely tidally locked, improved 3D numerical simulations of such planetary atmospheres are needed to guide target selection. Here we use a 3D climate system model, updated with new water-vapor absorption coefficients derived from the HITRAN 2012 database, to study ocean-covered planets at the inner edge of the HZ around late M to mid- K stars (2600 K less than or equal to T(sub eff) less than or equal to 4500 K). Our results indicate that these updated water-vapor coefficients result in significant warming compared to previous studies, so the inner HZ around M dwarfs is not as close as suggested by earlier work. Assuming synchronously rotating Earth-sized and Earth-mass planets with background 1 bar N2 atmospheres, we find that planets at the inner HZ of stars with T(sub eff) greater than 3000 K undergo the classical ''moist greenhouse'' (H2O mixing ratio greater than 10(exp -3) in the stratosphere) at significantly lower surface temperature (approx. 280 K) in our 3D model compared with 1D climate models (approx. 340 K). This implies that some planets around low-mass stars can simultaneously undergo water loss and remain habitable. However, for stars with T(sub eff) less than or equal to 3000 K, planets at the inner HZ may directly transition to a runaway state, while bypassing the moist greenhouse water loss entirely. We analyze transmission spectra of planets in a moist greenhouse regime and find that there are several prominent H2O features, including a broad feature between 5 and 8 micron, within JWST MIRI instrument range. Thus, relying only on standard Earth-analog spectra with 24 hr rotation period around M dwarfs for habitability studies will miss the strong H2O features that one would expect to see on synchronously rotating planets around M dwarf stars, with JWST.

Kopparapu, Ravi kumar↗

Multispecies Ion Acceleration in 3D Magnetic Reconnection with Hybrid-Kinetic Simulations

Magnetic reconnection drives multispecies particle acceleration broadly in space and astrophysics. Here we perform the first 3D hybrid simulations (fluid electrons, kinetic ions) that contain sufficient scale separation to produce nonthermal heavy-ion acceleration, with fragmented flux ropes critical for accelerating all species. We demonstrate the acceleration of all ion species (up to Fe) into power-law spectra with similar indices, by a common Fermi acceleration mechanism. The upstream ion velocities influence the first Fermi reflection for injection. The subsequent onsets of Fermi acceleration are delayed for ions with lower charge-mass ratios (Q/M), until growing flux ropes magnetize them. This leads to a species-dependent maximum energy/nucleon ∝(Q/M) α . These findings are consistent with in situ observations in reconnection regions, suggesting Fermi acceleration as the dominant multispecies ion acceleration mechanism.

79 ASTRONOMY AND ASTROPHYSICS↗

Parallel electric fields in a simulation of magnetotail reconnection and plasmoid evolution

Properties of the electric field component parallel to the magnetic field are investigate in a 3D MHD simulation of plasmoid formation and evolution in the magnetotail, in the presence of a net dawn-dusk magnetic field component. The spatial localization of E-parallel, and the concept of a diffusion zone and the role of E-parallel in accelerating electrons are discussed. A localization of the region of enhanced E-parallel in all space directions is found, with a strong concentration in the z direction. This region is identified as the diffusion zone, which plays a crucial role in reconnection theory through the local break-down of magnetic flux conservation.

Hesse, M.↗

Three-dimensional simulations of black hole tori

The global hydrodynamic nonaxisymmetric instabilities in thick constant angular momentum (l) accretion gas tori in orbit around a Schwarzschild black hole are investigated via 2D and 3D numerical simulations. A radially-wide torus is found to develop and m = 1 nonaxisymmetric density perturbation near the pressure maximum and a trailing spiral wave that extends through the outer part of the torus. This global wave transports angular momentum through the torus, causing the average angular momentum distribution to evolve slowly away from l = constant. The unstable mode drives an accretion flow from the torus into the black hole. The role of accretion is investigated by modeling a wide torus with an inner boundary at the cusp of the Schwarzschild effective potential. In such a torus, accretion is present throughout the evolution; only modest unstable mode growth is observed, and saturation occurs at low amplitude. Comparison simulations performed in the torus equatorial plane show qualitative similarities between the 2D and 3D system, although the 3D modes have a function dependence on height.

Hawley, John F.↗

Impact of the Earthquake Rupture on Ground-Motion Variability of the 24 August 2016 M w 6.2 Amatrice, Italy, Earthquake

Here, the devastating 24 August 2016 M w 6.2 earthquake that struck Amatrice, Italy, marked the beginning of a prolonged seismic sequence dominated by three subsequent M w ≥6.0 events in the central Apennines region. The earthquake destroyed Amatrice’s historic center, claiming the lives of 299 individuals and causing widespread damage in the neighboring villages. The severity of the ground shaking, with a recorded maximum acceleration of 850 cm/s 2 on the east–west component at the Amatrice station, was far greater than the predicted acceleration based on the Italian ground-motion model (GMM). As pointed out by several investigations, the observed ground-motion amplitude and its spatial variability during the earthquake can be linked to specific rupture characteristics, including slip distribution and rupture directivity effects revealed by the observed data (Tinti et al., 2016; Pischiutta et al., 2021). In this study, we conducted physics-based 3D numerical simulations of ground motion for the Amatrice earthquake for frequencies up to 3 Hz. We employed a series of kinematic rupture models and a well-constrained local 3D velocity model incorporating surface topography. The kinematic rupture realizations were generated using multiscale hybrid and fully stochastic models, following the technique proposed by Graves and Pitarka (2016). We focused on assessing the sensitivity of near-fault ground-motion amplitudes to earthquake rupture characteristics, in particular, the spatial slip pattern. To evaluate the quality of our simulations, we employed goodness-of-fit measurements performed in comparisons of simulated and recorded ground motions. The simulated ground motions compare well with the recorded data and predictions from GMMs for Italy, ITA18 (Lanzano et al., 2019). However, we found that the simulated interevent ground-motion variability (randomness in the source process) of peak ground velocity, σ (PGV) is higher than the constant σ (PGV) predicted by conventional GMMs. Our simulations using several rupture scenarios demonstrate that the near-fault ground-motion amplification pattern is directly related to the slip distribution pattern.

3D Ground Motions Simulations↗

Spatiotemporal parallelization of an analytical heat conduction model for additive manufacturing via a hybrid OpenMP + MPI approach

The ability to do thermal simulations for entire additive manufacturing builds is a key computational problem facing the additive manufacturing community; however, complex numerical models considering multiple physical phenomena currently do not have the capacity for simulations at this scale. To this end, conduction only analytic models offer a viable approach due to the massive drop in computational expense. In this work, we extend an existing implementation which uses a governing equation which can be evaluated at any point in space and time. This implementation already utilizes OpenMP with a spatial decompositions scheme stemming from a melt pool tracking algorithm. Furthermore, we then combine this with a parallel in time (PinT) approach to make the problem highly parallelizable. The new scheme, which uses MPI for internode communication and OpenMP for intranode communication, is shown to scale very well across multiple computational nodes. This approach results in the ability to simulate the 3D solidification conditions for entire layers of additively manufactured parts in minutes making part scale thermal simulations more practical.

36 MATERIALS SCIENCE↗

Compare low-gain 1D and 3D models toward a storage ring-based X-ray free-electron-laser oscillator

Fourth-generation diffraction-limited synchrotron light sources (DL-SLS) present a compelling platform for advanced light source applications due to their ultra-low emittance (around tens of picometers), sub-micrometer beam stability, and high repetition rates (greater than 1 MHz). Despite these advantages, fundamental limitations, such as long bunch durations (tens of picoseconds), large relative energy spread (~10⁻³), and low peak current (<300 A), have hindered their effectiveness in free-electron laser (FEL) applications. Using a low-gain three-dimensional (3D) model based on NSLS-II upgrade lattice parameters, we demonstrate that a 6% single-pass gain is achievable with an optimized transverse gradient undulator (TGU). Concurrently, recent advances in X-ray optics—specifically, a four-mirror bow-tie resonator utilizing diamond mirrors and beryllium compound refractive lenses (CRLs)—enable total round-trip losses below 4% and an output coupling efficiency near 1%, rendering a Storage Ring based X-ray FEL oscillator (XFELO) a realistic possibility. In the 3D framework, the TGU effectively mitigates the detrimental effects of large energy spread by spatially dispersing the beam, leading to enhanced gain relative to conventional one-dimensional (1D) models. We establish both analytical and numerical connections between the 1D and 3D descriptions, leveraging GENESIS simulations to map equivalent gain conditions. While 1D resonance is defined in the energy domain, the 3D TGU system shifts the resonance dependence to transverse gradient and dispersion parameters. Once optimized, this framework allows predictive modeling using 1D formulas, which can then be validated through full 3D simulations.

43 PARTICLE ACCELERATORS↗

Inverse Compton Cooling in the Coronae of Simulated Black Hole Accretion Flows

We present a formulation for a local cooling function to be employed in the diffuse, hot corona region of 3D GRMHD simulations of accreting black holes. This new cooling function calculates the cooling rate due to inverse Compton scattering by considering the relevant microphysics in each cell in the corona and approximating the radiation energy density and Compton temperature there by integrating over the thermal seed photon flux from the disk surface. The method either assumes ion and electron tem- peratures are equal (1T), or calculates them separately (2T) using an instantaneous equilibrium approach predicated on the actual relevant rate equations (Coulomb and Compton). The method is shown to be consistent with a more detailed ray-tracing calculation where the bulk of the cooling occurs, but is substantially less costly to per- form. As an example, we apply these methods to a harm3d simulation of a 10M⊙, non-spinning black hole, accreting at nominally 1% the Eddington value. Both 1T and 2T approaches lead to increased radiative efficiency and a larger fraction of total cooling in the corona as compared to the original target-temperature cooling function used by harm3d, especially in the 1T case. Time-averaged post-processing reveals that the continuum spectral observations predicted from these simulations are qualitatively similar to actual X-ray binary data, especially so for the 1T approach which yields a harder power-law component (Γ = 2.25) compared to the 2T version (Γ = 2.53).

Brooks E. Kinch↗

Uncertainty analyses of CO2 plume expansion subsequent to wellbore CO2 leakage into aquifers

In this study, we apply an uncertainty quantification (UQ) framework to CO2 sequestration problems. In one scenario, we look at the risk of wellbore leakage of CO2 into a shallow unconfined aquifer in an urban area; in another scenario, we study the effects of reservoir heterogeneity on CO2 migration. We combine various sampling approaches (quasi-Monte Carlo, probabilistic collocation, and adaptive sampling) in order to reduce the number of forward calculations while trying to fully explore the input parameter space and quantify the input uncertainty. The CO2 migration is simulated using the PNNL-developed simulator STOMP-CO2e (the water-salt-CO2 module). For computationally demanding simulations with 3D heterogeneity fields, we combined the framework with a scalable version module, eSTOMP, as the forward modeling simulator. We built response curves and response surfaces of model outputs with respect to input parameters, to look at the individual and combined effects, and identify and rank the significance of the input parameters.

Carbon sequestration, uncertainty quantification, ↗

Extracting the spectrum of a flow by spatial filtering

We show that the spectrum of a flow field can be extracted within a local region by straightforward filtering in physical space. We find that for a flow with a certain level regularity, the filtering kernel must have a sufficient number of vanishing moments in order for the "filtering spectrum" to be meaningful. Our derivation follows a similar analysis by [1] for the wavelet spectrum, where we show that the filtering kernel has to have at least p vanishing moments in order to correctly extract a spectrum k (-alpha) with (alpha) less/equal to p + 2. For example, any ow with a spectrum shallower than k (-3) can be extracted by a straightforward average on grid-cells of a stencil. We construct two new "simple stencil" kernels, MI and MII, with only two and three fixed stencil weight coefficients, respectively, and that have sufficient vanishing moments to allow for extracting spectra steeper than k(-3). We demonstrate our results using synthetic fields, 2D turbulence from a Direct Numerical Simulation, and 3D turbulence from the JHU Database. Our method guarantees energy conservation and can be useful in both simulations and experiments when a straightforward Fourier analysis is not justified, such as within coherent flow structures covering non-rectangular regions or in geophysical flows on Earth's curved surface.

42 ENGINEERING↗

Filament geometry control in extrusion-based additive manufacturing of concrete: The good, the bad and the ugly

Control of filament geometry in extrusion based additive manufacturing is essential to guarantee the desired quality of the printing process and the final product. Depending on the selected process parameters, material strategy and geometrical features, the printing process can however be susceptible to filament tearing or filament buckling. In this work, 2D and 3D CFD simulations have been used to map the influence of all these parameters in the infinite brick regime of 3D concrete printing processes. Analytical derivations of a tearing factor and buckling factor are presented. The use of these analytical tools is then illustrated, by studying variations in the printing process, such as changes in velocities, nozzle height, or material properties. Finally, the risk of both filament tearing and buckling of a single filament when printing sharp turns is discussed.

36 MATERIALS SCIENCE↗