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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Quasi-static MHD processes in earth's magnetosphere

An attempt is made to use the MHD equilibrium theory to describe the global magnetic field configuration of earth's magnetosphere and its time evolution under the influence of magnetospheric convection. To circumvent the difficulties inherent in today's MHD codes, use is made of a restriction to slowly time-dependent convection processes with convective velocities well below the typical Alfven speed. This restriction leads to a quasi-static MHD theory. The two-dimensional theory is outlined, and it is shown how sequences of two-dimensional equilibria evolve into a steady state configuration that is likely to become tearing mode unstable. It is then concluded that magnetospheric substorms occur periodically in earth's magnetosphere, thus being an integral part of the entire convection cycle.

Voigt, Gerd-Hannes↗
NASA NTRS1990

On the choice of boundary conditions in continuum models of continental deformation

Recent studies of continental deformation have treated the lithosphere as a viscous medium and investigated the time evolution of the deformation caused by tectonic and buoyancy forces. This paper examines the differences between (1) continuum models that keep velocity boundary conditions constant with time and (2) models that keep stress boundary conditions constant with time. These differences are demonstrated by using a simple example of a continental lithosphere that is subjected to horizontal compression. The results show that in (2) the indentation velocity decreases with time, while in (1) the indentation velocity remains constant with time.

Wdowinski, Shimon↗
NASA NTRS2020

X-Ray Spectral and Flux Variability of the Microquasar GRS 1758-258 on Timescales from Weeks to Years

We present the spectral and timing evolution of the persistent black hole X-ray binary GRS 1758-258 based on almost 12 years of observations using the Rossi X-ray Timing Explorer Proportional Counter Array. While the source was predominantly found in the hard state during this time, it entered the thermally dominated soft state seven times. In the soft state GRS 1758-258 shows a strong decline in flux above 3 keV rather than the pivoting flux around 10 keV more commonly shown by black hole transients. In its 3-20 keV hardness intensity diagram, GRS 1758-258 shows a hysteresis of hard and soft state fluxes typical for transient sources in outburst. The RXTE-PCA and RXTE-ASM long-term light curves do not show any orbital modulations in the range of 2 to 30 d. However, in the dynamic power spectra significant peaks drift between 18.47d and 18.04d for the PCA data, while less significant signatures between 19d and 20d are seen for the ASM data as well as for the Swift/BAT data. We discuss different models for the hysteresis behavior during state transitions as well as possibilities for the origin of the long term variation in the context of a warped accretion disk.

Maria Hirsch↗
DOE OSTI2025

Efficient Simulation of Open Quantum Systems on NISQ Trapped‐Ion Hardware

Abstract Simulating open quantum systems, which interact with external environments, presents significant challenges on noisy intermediate‐scale quantum (NISQ) devices due to limited qubit resources and noise. In this study, an efficient framework is proposed for simulating open quantum systems on NISQ hardware by leveraging a time‐perturbative Kraus operator representation of the system's dynamics. This approach avoids the computationally expensive Trotterization method and exploits the Lindblad master equation to represent time evolution in a compact form, particularly for systems satisfying specific commutation relations. The efficiency of this method is demonstrated by simulating quantum channels, such as the continuous‐time Pauli channel and damped harmonic oscillators, on NISQ trapped‐ion hardware, including IonQ Harmony and Quantinuum H1‐1. Additionally, hardware‐agnostic error mitigation techniques are introduced, including Pauli channel fitting and quantum depolarizing channel inversion, to enhance the fidelity of quantum simulations. These results show strong agreement between the simulations on real quantum hardware and exact solutions, highlighting the potential of Kraus‐based methods for scalable and accurate simulation of open quantum systems on NISQ devices. This framework opens pathways for simulating more complex systems under realistic conditions in the near term.

Burdine, Colin [Department of Electrical and Compu↗
DOE OSTI2021

Exciton-driven antiferromagnetic metal in a correlated van der Waals insulator

Abstract Collective excitations of bound electron-hole pairs—known as excitons—are ubiquitous in condensed matter, emerging in systems as diverse as band semiconductors, molecular crystals, and proteins. Recently, their existence in strongly correlated electron materials has attracted increasing interest due to the excitons’ unique coupling to spin and orbital degrees of freedom. The non-equilibrium driving of such dressed quasiparticles offers a promising platform for realizing unconventional many-body phenomena and phases beyond thermodynamic equilibrium. Here, we achieve this in the van der Waals correlated insulator NiPS 3 by photoexciting its newly discovered spin–orbit-entangled excitons that arise from Zhang-Rice states. By monitoring the time evolution of the terahertz conductivity, we observe the coexistence of itinerant carriers produced by exciton dissociation and a long-wavelength antiferromagnetic magnon that coherently precesses in time. These results demonstrate the emergence of a transient metallic state that preserves long-range antiferromagnetism, a phase that cannot be reached by simply tuning the temperature. More broadly, our findings open an avenue toward the exciton-mediated optical manipulation of magnetism.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Phase and Morphology of Water-ice Grains Formed in a Cryogenic Laboratory Plasma

Abstract Grains of ice are formed spontaneously when water vapor is injected into a weakly ionized laboratory plasma in which the background gas has been cooled to cryogenic temperatures comparable to those of deep space. These ice grains are levitated indefinitely within the plasma so that their time evolution can be observed under free-floating conditions. Using microscope imaging, ice grains are shown to have a spindle-like fractal structure and grow over time. Both crystalline and amorphous phases of ice are observed using Fourier transform infrared spectroscopy. A mix of crystalline and amorphous grains coexists under certain thermal conditions, and a linear mixing model is used on the ice absorption band surrounding 3.2 μ m to examine the ice phase composition and its temporal stability. The extinction spectrum is also affected by inelastic scattering as grains grow, and characteristic grain radii are obtained from Mie scattering theory and compared to size measurements from direct imaging. Observations are used to compare possible ice nucleation mechanisms, and it is concluded that nucleation is likely catalyzed by ions, as ice does not nucleate in the absence of plasma and impurities are not detected. Ice grain properties and infrared extinction spectra show similarity to observations of some astrophysical ices observed in protoplanetary disks, implying that the fractal morphology of the ice and observed processes of homogeneous ice nucleation could occur as well in such astrophysical environments with weakly ionized conditions.

Astronomy & Astrophysics↗
NASA NTRSDate not supplied

Temporal and Spatial Dynamics of Nitric Oxide Production at High Latitudes During an ICME-driven Storm on Dec. 14, 2006

During geomagnetic storms driven by interplanetary coronal mass ejections (ICMEs), Earth’s upper atmosphere neutral mass density is directly driven by the geomagnetic storm cycle from intense driving and subsequent recovery. The neutral density heating and cooling times are shorter for stronger storms and longer for weaker storms. The influx of energy (Joule Heating and precipitation) into Earth’s upper atmosphere during the storm main phase allows for the enhanced production of nitric oxide (NO) at high latitudes, which in turn cools the thermosphere by radiating away excess energy. As a result, greater NO production results in quicker thermospheric cooling. Yet while the production of NO on a global scale has been examined in detail, the space and time evolution of NO is not well-known. In this study, we investigate the effects of a particular ICME-driven storm, which occurred on Dec. 14th, 2006, on the production of NO at high latitudes. We compare NO measurements from the Thermosphere, Ionosphere, Mesosphere Dynamics (TIMED) spacecraft to neutral mass density measurements from the Challenging Minisatellite Payload (CHAMP) spacecraft and find that the impact of the shock prior to the storm, not just the onset of the storm itself, is responsible for an increase in NO production. We also observe a dawn-dusk asymmetry in high-latitude NO production and discuss how the geometry of the solar wind driver may play a role in creating this asymmetry. Finally, we discuss how the improved hemispheric and local time coverage provided by the GDC and DYNAMIC missions will enable more robust studies of the spatiotemporal evolution of NO during storms. Since NO is an important factor in regulating the neutral density of the thermosphere, such studies will be relevant for more accurate orbital drag calculations.

Kevin Delano↗
DOE OSTI2023

Topological terms with qubit regularization and relativistic quantum circuits

Qubit regularization provides a rich framework to explore quantum field theories. The freedom to choose how the important symmetries of the theory are embedded in the qubit regularization scheme allows us to construct new lattice models with rich phase diagrams. Some of the phases can contain topological terms which lead to critical phases. In this work we introduce and study the SU(3)-F qubit regularization scheme to embed the SO(3) spin-symmetry. We argue that qubit models in this regularization scheme contain several phases including a critical phase which describes the k = 1 Wess-Zumino-Witten (WZW) conformal field theory (CFT) at long distances, and two massive phases one of which is trvially gapped and the other which breaks the lattice translation symmetry. We construct a simple space-time Euclidean lattice model with a single coupling U and study it using the Monte Carlo method. We show the model has a critical phase at small U and a trivially massive phase at large U with a first order transition separating the two. Another feature of our model is that it is symmetric under space-time rotations, which means the temporal and spatial lattice spacing are connected to each other. The unitary time evolution operator obtained by a Wick rotation of the transfer matrix of our model can help us compute the physics of the k = 1 WZW CFT in real time without the need for tuning the temporal lattice spacing to zero. We use this idea to introduce the concept of a relativistic quantum circuit on a discrete space-time lattice.

Bhattacharya, Tanmoy↗
DOE OSTI2021

Large scale multi-node simulations of $\mathbb{Z}_2$ gauge theory quantum circuits using Google Cloud Platform

Simulating quantum field theories on a quantum computer is one of the most exciting fundamental physics applications of quantum information science. Dynamical time evolution of quantum fields is a challenge that is beyond the capabilities of classical computing, but it can teach us important lessons about the fundamental fabric of space and time. Whether we may answer scientific questions of interest using near-term quantum computing hardware is an open question that requires a detailed simulation study of quantum noise. Here we present a large scale simulation study powered by a multi-node implementation of qsim using the Google Cloud Platform. We additionally employ newly-developed GPU capabilities in qsim and show how Tensor Processing Units -- Application-specific Integrated Circuits (ASICs) specialized for Machine Learning -- may be used to dramatically speed up the simulation of large quantum circuits. We demonstrate the use of high performance cloud computing for simulating $\mathbb{Z}_2$ quantum field theories on system sizes up to 36 qubits. We find this lattice size is not able to simulate our problem and observable combination with sufficient accuracy, implying more challenging observables of interest for this theory are likely beyond the reach of classical computation using exact circuit simulation.

Gustafson, Erik↗
DOE OSTI2021

A second order yield-temperature relation for accurate inference of burn-averaged quantities in multi-species plasmas

Measured yields and ion temperatures inferred from the fusion product energy spectra can be used as metrics for the performance of an ICF implosion. This can be used to infer species separation, thermal decoupling, flows, or other effects that can cause the inferred ion temperatures to deviate from the true underlying thermal temperature and the yield ratio to deviate from the expected value. Direct inference of the impact of these effects on observed temperatures and yields can be difficult to uncover due to the underlying dependence on the shape and time evolution of the temperature and density profiles of the fusing plasma. Due to differences in the temperature dependence of the reactivities, different fusion products are emitted from different regions and times within the implosion. In order to properly account for this, a second-order analytical expression relating the apparent temperatures and yield ratios is developed. This expression can be coupled to models of yield and/or temperature altering effects to infer their burn-averaged impact on an implosion. The second-order expression shows significant improvement over lower-order expressions in synthetic data studies. Demonstrations of its applications to synthetic data coupled with models of ion thermal decoupling and radial flows are presented. In the case of thermal decoupling, both first and second-order expressions show reasonable levels of accuracy. To consistently infer the amplitude of radial flow with a <10% error, the second-order equation is required.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Unraveling the Wrinkle in Time-Variable Sources with Lunes and Synthetic Seismic Data

In this report, we describe how to estimate the time-variable components of the seismic moment tensor and compare these estimates to the more conventional analysis that incorporates an assumption of the source time function (STF) across all components of the seismic moment tensor. The advantage of our method is that we are able to independently estimate the time-evolution of each component of the seismic moment tensor, which may help to resolve the complex source phenomena associated with buried explosions. By performing an eigen decomposition of the time-evolving seismic moment tensor components, we are able to plot the seismic mechanism as a trajectory on a lune diagram. This technique enables interpretation of the seismic mechanism as a function of time, as opposed to the more conventional analysis which assumes that the seismic mechanism is time invariant. Finally, we describe the differences between the seismic moment and the seismic moment rate STFs, how to implement each one in inversion schemes, and the relative strengths/weaknesses of each. Our key take-away is that we are able to distinguish nearly-overlapping sources with highly different mechanisms, such as an explosion immediately following an earthquake, by estimating moment rate from seismic data through a STF-invariant inversion for the full time-variable moment tensor.

58 GEOSCIENCES↗
DOE OSTI2021

A second order yield-temperature relation for accurate inference of burn-averaged quantities in multi-species plasmas

Measured yields and ion temperatures inferred from the fusion product energy spectra can be used as metrics for the performance of an ICF implosion. This can be to infer species separation, thermal decoupling, flows or other effects that can cause the inferred ion temperatures to deviate from the true underlying thermal temperature and the yield ratio to deviate from the expected value. Direct inference of the impact of these effects on observed temperatures and yields can be difficult to uncover due to underlying dependence on the shape and time evolution of the temperature and density proles of the fusing plasma. Due to differences in the temperature dependence of the reactivities, different fusion products are emitted from different regions and times within the implosion. In order to properly account for this, a second order analytic expression relating the apparent temperatures and yield ratios is developed. This expression can be coupled to models of yield and/or temperature altering effects to infer their burn-averaged impact on an implosion. The second order expression shows significant improvement over lower order expressions in synthetic data studies. Demonstrations of its applications to synthetic data coupled with models of ion thermal decoupling and radial flows are presented. In the case of thermal decoupling both first and second order expressions show reasonable levels of accuracy. To consistently infer the amplitude of radial flow with <10% error the second order equation is required.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2019

Detailed Infrared Study of Amorphous to Crystalline Propionitrile Ices Relevant to Observed Spectra of Titan's Stratospheric Ice Clouds

We have conducted a comprehensive study of propionitrile (C2H5CN) ice from the amorphous to crystalline phase in order to provide detailed information on this specific cyanide, which may potentially contribute to the chemical composition of the Haystack ice cloud observed in Titan’s stratosphere by the Cassini Composite InfraRed Spectrometer (CIRS). Infrared transmission spectra of thin films of pure propionitrile ices deposited at low temperature (30 – 160 K) were collected from 50 cm(exp -1) to 11700 cm(exp -1) (200 – 0.85 μm). The far-infrared spectral region was specifically targeted to compare with CIRS far-infrared limb spectra. The temperature and time evolution of C2H5CN ice was thoroughly investigated to better understand discrepancies reported in previously published laboratory studies on the crystalline phase of C2H5CN. Specifically, we observe peculiar temperature and time-driven ice phase transitions, revealed by significant spectral variations in the ice, which stabilizes once a complete crystalline phase is achieved. From these results, the crystalline phase of propionitrile ice was identified at deposition temperatures greater than or equal to 135 K and less than 140 K. Our findings corroborate previous studies that ruled out pure propionitrile ice as the sole chemical identity of Titan’s observed Haystack emission feature. As a result, we have initiated co-deposition experiments that incorporate mixtures of Titan relevant organics, many of which have corresponding vapors that are abundantly present in Titan's stratosphere. In this paper, we present the result of one example of a co-deposited trinary ice mixture containing 16% hydrogen cyanide (HCN), 23% C2H5CN, and 61% benzene (C6H6). Although this co-condensed ice mixture is the best fit thus far obtained to match the broad width of the Haystack, it is still not the appropriate chemical candidate. However, it reveals an intriguing result: the strong lattice mode of pure C2H5CN ice is drastically altered by the surrounding molecules as a result of mixing in a co-condensed phase. The laboratory results reported here on propionitrile ice may help to further constrain the chemical identification of Titan’s stratospheric Haystack ice cloud, as well as improve on the current state of knowledge of Titan's stratospheric ice cloud chemistry.

Delphine Nna-Mvondo↗
NASA NTRS2019

Detailed Infrared Study of Amorphous to Crystalline Propionitrile Ices Relevant to Observed Spectra of Titan's Stratospheric Ice Clouds

We have conducted a comprehensive study of propionitrile (C2H5CN) ice from the amorphous to crystalline phase in order to provide detailed information on this specific cyanide, which may potentially contribute to the chemical composition of the Haystack ice cloud observed in Titan's stratosphere by the Cassini Composite InfraRed spectrometer (CIRS). Infrared transmission spectra of thin films of pure propionitrile ices deposited at low temperature (30–160 K) were collected from 50 cm(exp −1) to 11,700 cm(exp −1) (200–0.85 μm). The far-infrared spectral region was specifically targeted to compare with CIRS far-infrared limb spectra. The temperature and time evolution of C2H5CN ice was thoroughly investigated to better understand discrepancies reported in previously published laboratory studies on the crystalline phase of C2H5CN. Specifically, we observe peculiar temperature and time-driven ice phase transitions, revealed by significant spectral variations in the ice, which stabilizes once a complete crystalline phase is achieved. From these results, the crystalline phase of propionitrile ice was identified at deposition temperatures greater than or equal to 135 K and <140 K. Our findings corroborate previous studies that ruled out pure propionitrile ice as the sole chemical identity of Titan's observed Haystack emission feature. In order to understand and identify the Haystack cloud, we have initiated co-deposition experiments that incorporate mixtures of Titan-relevant organics, many of which have corresponding vapors that are abundantly present in Titan's stratosphere. In this paper, we present the result of one example of a co-deposited ternary ice mixture containing 16% hydrogen cyanide (HCN), 23% C2H5CN, and 61% benzene (C6H6). Although this co-condensed ice mixture is the best fit thus far obtained to match the broad width of the Haystack, it is still not the appropriate chemical candidate. However, it reveals an intriguing result: the strong lattice mode of pure C2H5CN ice is drastically altered by the surrounding molecules as a result of mixing in a co-condensed phase. The laboratory results reported here on propionitrile ice may help to further constrain the chemical identification of Titan's stratospheric Haystack ice cloud, as well as improve on the current state of knowledge of Titan's stratospheric ice cloud chemistry.

Delphine Nna-Mvondo↗
NASA NTRS2019

Detailed infrared study of amorphous to crystalline propionitrile ices relevant to observed spectra of Titan's stratospheric ice clouds

We have conducted a comprehensive study of propionitrile (C2H5CN) ice from the amorphous to crystalline phase in order to provide detailed information on this specific cyanide, which may potentially contribute to the chemical composition of the Haystack ice cloud observed in Titan’s stratosphere by the Cassini Composite InfraRed Spectrometer (CIRS). Infrared transmission spectra of thin films of pure propionitrile ices deposited at low temperature (30 – 160 K) were collected from 50 cm-1 to 11,700 cm-1 (200 – 0.85 μm). The far-infrared spectral region was specifically targeted to compare with CIRS far-infrared limb spectra. The temperature and time evolution of C2H5CN ice was thoroughly investigated to better understand discrepancies reported in previously published laboratory studies on the crystalline phase of C2H5CN. Specifically, we observe peculiar temperature and time-driven ice phase transitions, revealed by significant spectral variations in the ice, which stabilizes once a complete crystalline phase is achieved. From these results, the crystalline phase of propionitrile ice was identified at deposition temperatures greater than or equal to 135 K and less than 140 K. Our findings corroborate previous studies that ruled out pure propionitrile ice as the sole chemical identity of Titan’s observed Haystack emission feature. As a result, we have initiated co-deposition experiments that incorporate mixtures of Titan-relevant organics, many of which have corresponding vapors that are abundantly present in Titan's stratosphere. In this paper, we present one example of a co-deposited trinary ice mixture containing 16% hydrogen cyanide (HCN), 23% C2H5CN, and 61% benzene (C6H6). Although this co-condensed ice mixture is a poor spectral match for the Haystack, it reveals an intriguing result: the strong lattice mode of pure C2H5CN ice is drastically altered by the surrounding molecules as a result of mixing in a co-condensed phase. The laboratory results reported here on propionitrile ice may help to further constrain the chemical identification of Titan’s stratospheric Haystack ice cloud, as well as improve on the current state of knowledge of Titan's stratospheric ice cloud chemistry.

Ices↗
NASA NTRS2019

Detailed Infrared Study of Amorphous to Crystalline Propionitrile Ices Relevant to Observed Spectra of Titan's Stratospheric Ice Clouds

We have conducted a comprehensive study of propionitrile (C2H5CN) ice from the amorphous to crystalline phase in order to provide detailed information on this specific cyanide, which may potentially contribute to the chemical composition of the Haystack ice cloud observed in Titan's stratosphere by the Cassini Composite InfraRed Spectrometer (CIRS). Infrared transmission spectra of thin films of pure propionitrile ices deposited at low temperature (30-160 K) were collected from 50 cm1 to 11,700 cm1 (200-0.85 m). The far-infrared spectral region was specifically targeted to compare with CIRS far-infrared limb spectra. The temperature and time evolution of C2H5CN ice was thoroughly investigated to better understand discrepancies reported in pre- viously published laboratory studies on the crystalline phase of C2H5CN. Specifically, we observe peculiar temperature and time-driven ice phase transitions, revealed by significant spectral variations in the ice, which stabilizes once a complete crystalline phase is achieved. From these results, the crystalline phase of propionitrile ice was identified at deposition temperatures greater than or equal to 135 K and < 140 K. Our findings corro- borate previous studies that ruled out pure propionitrile ice as the sole chemical identity of Titan's observed Haystack emission feature. In order to understand and identify the Haystack cloud, we have initiated co-de- position experiments that incorporate mixtures of Titan-relevant organics, many of which have corresponding vapors that are abundantly present in Titan's stratosphere. In this paper, we present the result of one example of a co-deposited ternary ice mixture containing 16% hydrogen cyanide (HCN), 23% C2H5CN, and 61% benzene (C6H6). Although this co-condensed ice mixture is the best fit thus far obtained to match the broad width of the Haystack, it is still not the appropriate chemical candidate. However, it reveals an intriguing result: the strong lattice mode of pure C2H5CN ice is drastically altered by the surrounding molecules as a result of mixing in a co- condensed phase. The laboratory results reported here on propionitrile ice may help to further constrain the chemical identification of Titan's stratospheric Haystack ice cloud, as well as improve on the current state of knowledge of Titan's stratospheric ice cloud chemistry.

Nna-Mvondo, Delphine↗
NASA NTRS2020

Progress in Interferometric Rayleigh Scattering to Measure Fluctuations Spectra of Velocity and Temperature in High Speed Flows

A new, spectrally-resolved, Rayleigh scattering setup at NASA Ames is further developed to measure fluctuations in velocity and temperature. Using a combination of a continuous-wave laser, a stabilized Fabry-Perot interferometer (FPI), an EMCCD camera, and a photo-multiplier tube, the setup was demonstrated to provide fairly accurate measurements of time-averaged velocity, temperature, density and spectrum of density fluctuations in a high-speed free jet (Panda & White, 2018). This paper describes further progress in fast measurement of the Rayleigh-Brillouin spectrum via a 16-anode linear-array of photo-multiplier tube and a multi-channel, photo-electron counter. Rayleigh scattered light from a 0.4mm long probe volume was directly imaged through the FPI and was imaged on the linear array. Synchronous photo-electron counting over a series of short, contiguous gates provided time-evolution of the fringes at a 10 kHz sampling rate. Sample spectra collected from a Mach 0.98 jet show spectral content floating on high noise-floor. Efforts to collect longer time series of data and different schemes of extracting velocity and temperature information are now in progress.

Panda, J.↗
NASA NTRSDate not supplied

Characterization of Dendritic Spatially Extended 3D Patterns in Directional Solidification: Microgravity Experiments in DECLIC-DSI onboard ISS and 3D Phase-field Simulations

To clarify and characterize the fundamental physical mechanisms active in the dynamical formation of three-dimensional (3D) arrays of dendrites under diffusive growth conditions, in situ monitoring of series of experiments on transparent model alloy succinonitrile – 0.46 wt% camphor was carried out under low gravity in the DECLIC Directional Solidification Insert onboard the International Space Station. These experiments offer the very unique opportunity to observe in situ and characterize the dynamics of the microstructure formation and evolution in extended 3D patterns under microgravity environment. The analyses of the dendritic patterns for a broad range of growth velocities displaying different levels of sidebranching will be presented. Especially, the time evolution of primary spacing, in case of solidifications at constant pulling rate as well as for experiments with pulling rate jump, will be compared to 3D phase-field simulations, and the results will be discussed in terms of stable spacing range.

Kaihua Ji↗