the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 27 Feb 2023
Partial melting in polycrystalline ice: Pathways identified in 3D neutron tomographic images
Abstract. In frozen cylinders composed of deuterium ice (Tm+3.8 ºC) and 10 % water ice (Tm 0 ºC) it is possible to track melt pathways produced by increasing the temperature during deformation. Raising the temperature to +2 ºC produces water (H2O) which combines with the D2O ice to form mixtures of HDO. As a consequence of deformation, HDO and H2O meltwater are expelled along conjugate shear bands and as compactional melt segregations. Melt segregations are also associated with high porosity networks related to the location of transient reaction fronts where the passage of melt-enriched fluids is controlled by the localized ductile yielding and lowering of the effective viscosity. Accompanying the softening, the meltwater also changes and weakens the crystallographic fabric development of the ice. Our observations suggest meltwater-enriched compaction and shear band initiation provides instabilities and the driving force for an enhancement of permeability in terrestrial ice sheets and glaciers.
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RC1: 'Comment on egusphere-2023-70', Anonymous Referee #1, 03 Apr 2023
Review of Christopher, Wilson et al.’s: “Partial melting in polycrystalline ice: Pathways identified in 3D neutron tomographic images.”
General comment on the manuscript:The preprint article by Wilson et al. presents an innovative approach for characterizing the microstructure of polycrystalline ice using small-angle neutron scattering (SANS) measurements. The authors successfully obtained high-resolution images of the 3D ice microstructure, providing valuable insights into the crystallographic structure of the ice, the distribution of pores, and the connectivity of the pore network. Notably, this study is unique in its use of deuterium ice, which allowed the authors to obtain higher-quality data than previously possible. They explore the role of crystal orientation and pore geometry on the deformation of polycrystalline ice and investigate the effect of stress and strain rate on the microstructural pore evolution of ice resulting from deformation. The paper is well-written and presents a clear and concise overview of the methodology and results. However, there are some sections that may benefit from further clarification or expansion, as outlined below.
Specific comments for the authors’ consideration:
- I’m curious why 90% deuterium ice was chosen. Does this suggest 10% liquid water content when samples deform above the H2O melting temperature? If so, why not use a higher fraction of deuterium solid to produce water contents more in the range expected of glacier ice? (< 3% liquid water i.e., Vallon et al., 1976). Moreover, assuming liquid water contents are high, I would be hesitant to infer known ice deformation mechanisms in unexplored water-content regimes.
- It remains unclear why calcite powder was used in some layered samples (or at all). Consider including the objective/ relevance of the calcite layer with regard to the overarching research questions.
- When labeling “pores” (i.e., Line 161), consider being explicit as to whether you refer to liquid water interstices (i.e., veins) or bubble inclusions. Further, are you able to get a sense of the volumetric air content in the samples using tomography?
- Following Nye and Mae (1972), the authors may consider clarifying the differences between their deuterium–H2O samples and pure ice with regard to textural and thermo-mechanical equilibrium at the melting temperature. My (perhaps limited) understanding is that melt evolution, migration, and distribution during compression will be driven by grain-scale stress heterogeneity and a tendency for liquid in a polycrystal to be drawn from warm to cold temperatures as a result. In a system with two distinct melting temperatures, I’m unsure how applicable this paper’s results on molten phase migration will be to glacier ice systems.
- I didn’t catch how the textural characteristics (including grain size) were measured and what the errors were. Perhaps you could elaborate? I apologize if I overlooked it.
- It remains unclear to me how the coordination number was measured (and what the errors are) in the mean CNs (Table 1). Could you elaborate? And do you think the resolution is sufficient to adequately characterize the connectivity of pores in the samples? (i.e., if your voxel resolution is 20 microns, are melt channels smaller than 20 microns overlooked and/or deemed insignificant?)
- Were you able to examine the general melt channel shape in your samples? I’m curious whether the mean dihedral angle is greater for deuterium ice (possibly producing more spherical pores), causing the pore connectivity and melt migration rates to be lower than pure polycrystalline ice.
- I think the conclusion could be strengthened by summarizing the main findings of this study and their significance in a more succinct way, as well as highlighting the key areas for future work that emerge from the study.
Overall, this paper presents original, high-quality data on the deformation behavior of laboratory-made ice samples under uniaxial compression tests. The novel use of neutron imaging allows for non-destructive 3D visualization of the internal ice structure during and after the deformation, providing unique insights into the deformation mechanisms of ice. The results have implications for a range of applications, including ice mechanics, ice sheet modeling, glacier dynamics, and englacial hydrology. Therefore, I believe this paper is well-suited for publication in The Cryosphere.
Editorial comments keyed to line numbers:
28 – Insert the word “to” before “suggest”
43–44 – Consider adding a comma after “masses” and some rephrasing, as the meaning in this sentence I find unclear.
59 – Change the word “occurs” to “occur”
149 – Consider changing adopting to “as they adopt” as it reads a bit awkward otherwise.
154 – Missing first parenthesis in “Supplementary Fig. 3).
164–166 – This reads a bit awkward. Consider changing “its correlation” to “correlating it” perhaps?
172 – Consider adding a comma after “sample” for clarity
174–175 – “Mix-3 occurs as a fine rim (Fig. 1d-e) and Mix-2 and Mix-3 at the outer rims of the sample (Fig. 2a-c)” reads a bit awkwardly; consider rephrasing for clarity.
193 – Change “concentration” to “concentrations” (for agreement with “are”)
194 – Consider adding comma after “(Fig. 2e, Supplementary Fig. 3a)“
211 – Add “and” before “blind”
219 – Change “relative” to “relatively”
220 – Add a comma after “samples”
224 – Change the word “was” to “were”
232 – Consider adding a comma after “(Kronenberg et al., 2020)”
233 – Add a hyphen between “meltwater” and “free”
243 – Move the hyphen position to be between “dry” and “compacted”
250 – Hyphenate “quasi steady”
266 – Add the word “and” after “boundaries,”
276 – Change the word “are” to “is”
278 – Consider changing the word "shears" to "shear bands" for consistency with later usage
281 – Hyphenate “dry compacted”; this is a bit inconsistent throughout the paper, so check occurrences elsewhere for consistency.
283 – Add the word “and” after “shapes,”
292 – Consider changing “which preceded” to “that precede” for grammatical correctness.
312 – Add a comma after “stresses”
330 – Add a comma after viscosity, or change “reaching” to “reaches.” With the current phrasing, the meaning of the sentence is unclear.
356 – Add a comma after “(Fig. 10e)”.
389 – Remove the hyphen in “ice-sheet”
392 – Remove the comma and change “is” to “are.” Otherwise, I think it reads awkwardly.
405 – Change the word “control” to “controls” and change “on” to “of.”
423 – Consider bracketing “more commonly” with commas on either side.
559 – I would suggest explaining what is meant by “pore fluid factor” and, additionally, consider adding a hyphen between “pore” and “fluid” here.
655 – Consider explaining what is meant by a “capped yield surface” as I, and perhaps others, will be unfamiliar with that terminology.
References:
Vallon, M., Petit, J., & Fabre, B. (1976). Study of an Ice Core to the Bedrock in the Accumulation zone of an Alpine Glacier. Journal of Glaciology, 17(75), 13-28. doi: 10.3189/S0022143000030677
Nye, J., & Mae, S. (1972). The Effect of Non-Hydrostatic Stress on Intergranular Water Veins and Lenses in Ice. Journal of Glaciology, 11(61), 81-101. doi:10.3189/S0022143000022528
Citation: https://doi.org/10.5194/egusphere-2023-70-RC1 -
AC1: 'Reply on RC1', Chris Wilson, 14 Jul 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-70/egusphere-2023-70-AC1-supplement.pdf
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RC2: 'Comment on egusphere-2023-70', Anonymous Referee #2, 12 Jul 2023
This paper deals with the effect of melt on the rheology and permeability of ice sheets and glaciers ices. The authors make use of ice specimens made of a mixture of deuterium and water ices. This is a very interesting idea as both have different melting point, and neutron scattering can distinguish between both allowing neutron tomography to be carried out.
The topic of the paper is relevant and very interesting, however I am asking for a rejection of this contribution as the authors largely over-interpret the experimental results that are shown. Many times in the paper, the figures do not provide any support to the text and interpretation, and therefore, after completing the reading, I am not convinced at all by the robustness of the results. Sometimes, the text is completely disconnected with the figures (experimental evidences) provided.
- The paper severely lacks of a quantitative analysis. For example, the sample porosity and its evolution with strain, which has a central position in the paper, is never given quantitatively, although it can be estimated from neutron tomography. Porosity might affect the effective behaviour even more than the melt content (the melt content is also never quantify !). ex. line 193 state an ‘increase in porosity’, but no evaluation is provided.
- It is not clear to me how the author can distinguish between water ice and melt water with tomography… Is this possible ? How much of the specimen really melts during the experiment ?
- Line 179 is a typical example of over-interpretation of the results, occurring too many times in the paper : “The frozen-in melt-enriched regions or segregations predominantly occupy conjugate shear bands (Fig. 1)”. First of all, the strain field has not been measured (eg. with DIC or DVC) so that I don’t understand how the author can decide whether a specific feature is a shear band or not. Second, the ellipse show ‘concentration of Mix-2’, not really aligned at 35° as indicated; this could be due to the sample preparation, or simply due to some random process, etc… this really needs to check and quantify further.
- Legend fig 1, at point A and B it is said that there is an increase in porosity, but one do not see anything in the figure and no quantitative estimation is provided !
- Line 185 ‘low pressure regions or non-deforming region’ : pressure and deformation field have not been measured, so how can the authors estimated that some regions do not deform, and that some are at lower pressure ? One even don’t know whether the porosity is open or closed (althrougth this might be accessible by tomography).
- Line 203 : “This bimodal distribution into shear and compaction bands are all part of a connected network”. No proof for bimodal distribution, nor shear band / compaction band, nor proof of a connected porosity network in the data …
- Line 205 “increasd porosity” but the porosity is not quantified…
- Line 223 “(fig 2d). the network consists of pores situated on grain boundaries” => grain structure (and thus grain boundaries) are not indicated in figure 2…
- Line 231 why should quartz (not deforming by basal glide) should be a good analog for ice (deforming mostly by basal glide) ?
- Line 251 I find really strange that the stress increases as the temperature is increased up to +2°C, as part of the specimen melts and ice should become softer. What is the reason for this stress increase ?
- Line 252-255 “This stress drop we attribute to the softening of the ice with the onset of melting, grain boundary migration and initiation of the deformation bands. This ductile to shear transition can be explained by the competition between different time scales corresponding to the relatively slow melting of the H2O ice, and broken bonds as the HDO mixes were generated” => not clear at all. Has gbm been observed (not shown in the figures) ? initiation of deformation bands => strain localization into deformation bands starts at the very beginning of the deformation (before 1% strain), see the paper of Grennerat et al. Acta Mater 2012. What is a ‘ductile to shear transition’ ? shear deformation is not in the ductile regime ? ’different time scales’ => could you explain what is meant here ? ‘broken bonds’ => do you mean atomic bonds ?? any evidences ?
- Line 256-260 : in fig 6, one do not see as written in the text, for LDH-20, a transition from hardening to weakening within the -7°C regime. And one do not see, for LDH-35, a decrease of the flow stress at +2°C (even modest)
- I really don’t understand paragraph 278-284 and what are the supporting informations. One do not see ‘white lines’ in fig 8c. What do you mean with ‘refraction of shear bands’ (line 280) ??
- Line 287 what is meant with ‘evaluated through statistical analysis of particular angular positions and hkl reflections’ ?? I guess this is related with the neutron diffraction experiment, but this is really not clear
- Line 294 : one do see, as stated in the text, ‘a strain dependent increase in grain nucleation up to 14.6% strain’ for both DH29, LDH20, and DHC06 (grain size clearly decreases before this strain level). Same for ‘a variable but decreasing number of grains in the final deformation stage (15.4 – 20% strain)’, not observed for dhc06, dh29, dhc23…
- Line 310 ‘as these experiments have shown, the movement of meltwater’ As far I understand, the meltwater movement has not been observed here. Only few static tomographic images have been acquired
- Line 315 ‘shear induced failure mode’ => do you have observed any cracks in the specimen (not shown/discussed in the figures) ? why invoking suddenly failure modes ?
- I find really weird that the word “recrystallization” does not appear even once in such a paper dealing with microstructure evolution at the melting temperature…
- Etc…
Citation: https://doi.org/10.5194/egusphere-2023-70-RC2 -
AC2: 'Reply on RC2', Chris Wilson, 14 Jul 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-70/egusphere-2023-70-AC2-supplement.pdf
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2023-70', Anonymous Referee #1, 03 Apr 2023
Review of Christopher, Wilson et al.’s: “Partial melting in polycrystalline ice: Pathways identified in 3D neutron tomographic images.”
General comment on the manuscript:The preprint article by Wilson et al. presents an innovative approach for characterizing the microstructure of polycrystalline ice using small-angle neutron scattering (SANS) measurements. The authors successfully obtained high-resolution images of the 3D ice microstructure, providing valuable insights into the crystallographic structure of the ice, the distribution of pores, and the connectivity of the pore network. Notably, this study is unique in its use of deuterium ice, which allowed the authors to obtain higher-quality data than previously possible. They explore the role of crystal orientation and pore geometry on the deformation of polycrystalline ice and investigate the effect of stress and strain rate on the microstructural pore evolution of ice resulting from deformation. The paper is well-written and presents a clear and concise overview of the methodology and results. However, there are some sections that may benefit from further clarification or expansion, as outlined below.
Specific comments for the authors’ consideration:
- I’m curious why 90% deuterium ice was chosen. Does this suggest 10% liquid water content when samples deform above the H2O melting temperature? If so, why not use a higher fraction of deuterium solid to produce water contents more in the range expected of glacier ice? (< 3% liquid water i.e., Vallon et al., 1976). Moreover, assuming liquid water contents are high, I would be hesitant to infer known ice deformation mechanisms in unexplored water-content regimes.
- It remains unclear why calcite powder was used in some layered samples (or at all). Consider including the objective/ relevance of the calcite layer with regard to the overarching research questions.
- When labeling “pores” (i.e., Line 161), consider being explicit as to whether you refer to liquid water interstices (i.e., veins) or bubble inclusions. Further, are you able to get a sense of the volumetric air content in the samples using tomography?
- Following Nye and Mae (1972), the authors may consider clarifying the differences between their deuterium–H2O samples and pure ice with regard to textural and thermo-mechanical equilibrium at the melting temperature. My (perhaps limited) understanding is that melt evolution, migration, and distribution during compression will be driven by grain-scale stress heterogeneity and a tendency for liquid in a polycrystal to be drawn from warm to cold temperatures as a result. In a system with two distinct melting temperatures, I’m unsure how applicable this paper’s results on molten phase migration will be to glacier ice systems.
- I didn’t catch how the textural characteristics (including grain size) were measured and what the errors were. Perhaps you could elaborate? I apologize if I overlooked it.
- It remains unclear to me how the coordination number was measured (and what the errors are) in the mean CNs (Table 1). Could you elaborate? And do you think the resolution is sufficient to adequately characterize the connectivity of pores in the samples? (i.e., if your voxel resolution is 20 microns, are melt channels smaller than 20 microns overlooked and/or deemed insignificant?)
- Were you able to examine the general melt channel shape in your samples? I’m curious whether the mean dihedral angle is greater for deuterium ice (possibly producing more spherical pores), causing the pore connectivity and melt migration rates to be lower than pure polycrystalline ice.
- I think the conclusion could be strengthened by summarizing the main findings of this study and their significance in a more succinct way, as well as highlighting the key areas for future work that emerge from the study.
Overall, this paper presents original, high-quality data on the deformation behavior of laboratory-made ice samples under uniaxial compression tests. The novel use of neutron imaging allows for non-destructive 3D visualization of the internal ice structure during and after the deformation, providing unique insights into the deformation mechanisms of ice. The results have implications for a range of applications, including ice mechanics, ice sheet modeling, glacier dynamics, and englacial hydrology. Therefore, I believe this paper is well-suited for publication in The Cryosphere.
Editorial comments keyed to line numbers:
28 – Insert the word “to” before “suggest”
43–44 – Consider adding a comma after “masses” and some rephrasing, as the meaning in this sentence I find unclear.
59 – Change the word “occurs” to “occur”
149 – Consider changing adopting to “as they adopt” as it reads a bit awkward otherwise.
154 – Missing first parenthesis in “Supplementary Fig. 3).
164–166 – This reads a bit awkward. Consider changing “its correlation” to “correlating it” perhaps?
172 – Consider adding a comma after “sample” for clarity
174–175 – “Mix-3 occurs as a fine rim (Fig. 1d-e) and Mix-2 and Mix-3 at the outer rims of the sample (Fig. 2a-c)” reads a bit awkwardly; consider rephrasing for clarity.
193 – Change “concentration” to “concentrations” (for agreement with “are”)
194 – Consider adding comma after “(Fig. 2e, Supplementary Fig. 3a)“
211 – Add “and” before “blind”
219 – Change “relative” to “relatively”
220 – Add a comma after “samples”
224 – Change the word “was” to “were”
232 – Consider adding a comma after “(Kronenberg et al., 2020)”
233 – Add a hyphen between “meltwater” and “free”
243 – Move the hyphen position to be between “dry” and “compacted”
250 – Hyphenate “quasi steady”
266 – Add the word “and” after “boundaries,”
276 – Change the word “are” to “is”
278 – Consider changing the word "shears" to "shear bands" for consistency with later usage
281 – Hyphenate “dry compacted”; this is a bit inconsistent throughout the paper, so check occurrences elsewhere for consistency.
283 – Add the word “and” after “shapes,”
292 – Consider changing “which preceded” to “that precede” for grammatical correctness.
312 – Add a comma after “stresses”
330 – Add a comma after viscosity, or change “reaching” to “reaches.” With the current phrasing, the meaning of the sentence is unclear.
356 – Add a comma after “(Fig. 10e)”.
389 – Remove the hyphen in “ice-sheet”
392 – Remove the comma and change “is” to “are.” Otherwise, I think it reads awkwardly.
405 – Change the word “control” to “controls” and change “on” to “of.”
423 – Consider bracketing “more commonly” with commas on either side.
559 – I would suggest explaining what is meant by “pore fluid factor” and, additionally, consider adding a hyphen between “pore” and “fluid” here.
655 – Consider explaining what is meant by a “capped yield surface” as I, and perhaps others, will be unfamiliar with that terminology.
References:
Vallon, M., Petit, J., & Fabre, B. (1976). Study of an Ice Core to the Bedrock in the Accumulation zone of an Alpine Glacier. Journal of Glaciology, 17(75), 13-28. doi: 10.3189/S0022143000030677
Nye, J., & Mae, S. (1972). The Effect of Non-Hydrostatic Stress on Intergranular Water Veins and Lenses in Ice. Journal of Glaciology, 11(61), 81-101. doi:10.3189/S0022143000022528
Citation: https://doi.org/10.5194/egusphere-2023-70-RC1 -
AC1: 'Reply on RC1', Chris Wilson, 14 Jul 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-70/egusphere-2023-70-AC1-supplement.pdf
-
RC2: 'Comment on egusphere-2023-70', Anonymous Referee #2, 12 Jul 2023
This paper deals with the effect of melt on the rheology and permeability of ice sheets and glaciers ices. The authors make use of ice specimens made of a mixture of deuterium and water ices. This is a very interesting idea as both have different melting point, and neutron scattering can distinguish between both allowing neutron tomography to be carried out.
The topic of the paper is relevant and very interesting, however I am asking for a rejection of this contribution as the authors largely over-interpret the experimental results that are shown. Many times in the paper, the figures do not provide any support to the text and interpretation, and therefore, after completing the reading, I am not convinced at all by the robustness of the results. Sometimes, the text is completely disconnected with the figures (experimental evidences) provided.
- The paper severely lacks of a quantitative analysis. For example, the sample porosity and its evolution with strain, which has a central position in the paper, is never given quantitatively, although it can be estimated from neutron tomography. Porosity might affect the effective behaviour even more than the melt content (the melt content is also never quantify !). ex. line 193 state an ‘increase in porosity’, but no evaluation is provided.
- It is not clear to me how the author can distinguish between water ice and melt water with tomography… Is this possible ? How much of the specimen really melts during the experiment ?
- Line 179 is a typical example of over-interpretation of the results, occurring too many times in the paper : “The frozen-in melt-enriched regions or segregations predominantly occupy conjugate shear bands (Fig. 1)”. First of all, the strain field has not been measured (eg. with DIC or DVC) so that I don’t understand how the author can decide whether a specific feature is a shear band or not. Second, the ellipse show ‘concentration of Mix-2’, not really aligned at 35° as indicated; this could be due to the sample preparation, or simply due to some random process, etc… this really needs to check and quantify further.
- Legend fig 1, at point A and B it is said that there is an increase in porosity, but one do not see anything in the figure and no quantitative estimation is provided !
- Line 185 ‘low pressure regions or non-deforming region’ : pressure and deformation field have not been measured, so how can the authors estimated that some regions do not deform, and that some are at lower pressure ? One even don’t know whether the porosity is open or closed (althrougth this might be accessible by tomography).
- Line 203 : “This bimodal distribution into shear and compaction bands are all part of a connected network”. No proof for bimodal distribution, nor shear band / compaction band, nor proof of a connected porosity network in the data …
- Line 205 “increasd porosity” but the porosity is not quantified…
- Line 223 “(fig 2d). the network consists of pores situated on grain boundaries” => grain structure (and thus grain boundaries) are not indicated in figure 2…
- Line 231 why should quartz (not deforming by basal glide) should be a good analog for ice (deforming mostly by basal glide) ?
- Line 251 I find really strange that the stress increases as the temperature is increased up to +2°C, as part of the specimen melts and ice should become softer. What is the reason for this stress increase ?
- Line 252-255 “This stress drop we attribute to the softening of the ice with the onset of melting, grain boundary migration and initiation of the deformation bands. This ductile to shear transition can be explained by the competition between different time scales corresponding to the relatively slow melting of the H2O ice, and broken bonds as the HDO mixes were generated” => not clear at all. Has gbm been observed (not shown in the figures) ? initiation of deformation bands => strain localization into deformation bands starts at the very beginning of the deformation (before 1% strain), see the paper of Grennerat et al. Acta Mater 2012. What is a ‘ductile to shear transition’ ? shear deformation is not in the ductile regime ? ’different time scales’ => could you explain what is meant here ? ‘broken bonds’ => do you mean atomic bonds ?? any evidences ?
- Line 256-260 : in fig 6, one do not see as written in the text, for LDH-20, a transition from hardening to weakening within the -7°C regime. And one do not see, for LDH-35, a decrease of the flow stress at +2°C (even modest)
- I really don’t understand paragraph 278-284 and what are the supporting informations. One do not see ‘white lines’ in fig 8c. What do you mean with ‘refraction of shear bands’ (line 280) ??
- Line 287 what is meant with ‘evaluated through statistical analysis of particular angular positions and hkl reflections’ ?? I guess this is related with the neutron diffraction experiment, but this is really not clear
- Line 294 : one do see, as stated in the text, ‘a strain dependent increase in grain nucleation up to 14.6% strain’ for both DH29, LDH20, and DHC06 (grain size clearly decreases before this strain level). Same for ‘a variable but decreasing number of grains in the final deformation stage (15.4 – 20% strain)’, not observed for dhc06, dh29, dhc23…
- Line 310 ‘as these experiments have shown, the movement of meltwater’ As far I understand, the meltwater movement has not been observed here. Only few static tomographic images have been acquired
- Line 315 ‘shear induced failure mode’ => do you have observed any cracks in the specimen (not shown/discussed in the figures) ? why invoking suddenly failure modes ?
- I find really weird that the word “recrystallization” does not appear even once in such a paper dealing with microstructure evolution at the melting temperature…
- Etc…
Citation: https://doi.org/10.5194/egusphere-2023-70-RC2 -
AC2: 'Reply on RC2', Chris Wilson, 14 Jul 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-70/egusphere-2023-70-AC2-supplement.pdf
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Christopher Wilson
Mark Peternell
Filomena Salvemini
Vladimir Luzin
Frieder Enzmann
Olga Moravcova
Nicholas Hunter
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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