We thank the reviewers for their repeated evaluation of our manuscript. We have addressed all points, as detailed below. The resulting changes in the manuscript are marked in blue. > Reviewer #1 > Review of "Collision fluctuations of lucky droplets with superdroplets" > by Xiang-Yu Li et al. In response to my previous comments, the poor > narrative of the manuscript has been improved a little bit, but not > satisfactory yet. In addition, there is a growing concern regarding > the numerical setup of this study, which could substantially affect > the main conclusions; that is, the height of the domain for approach IV > (both 1-D and 3-D) could be too small. In this revised manuscript, the > authors provide more detail about their numerical setup, and as a result, > the issue has come to the surface. I would suggest the authors rerun all > the simulations with a much taller domain. If not, the authors have to > clearly justify that it is not crucial for this study. I acknowledge > that this is a cutting edge study. It is worth publishing, but after > all these issues are resolved. We have now modified the code so that we can run many realizations in one run. In this way, we have now demonstrated that the results are insensitive to the domain size and also the density of background droplets; see our changes to the paper in section 4.a. > Major Comments > 1) [request] P. 8, Eq. (7) > It is still unclear whether multiplicity \xi_i is an integer or a > real number in this study. Please clarify how you calculate \xi_i/2 > and \xi_j/2 in Eq. (7) when \xi_i/2=\xi_j/2 is an odd number. In the paragraph below that of Eq.(7), we have now added the following to clarify that \xi is a real number in our study: "We emphasize that Eq. (5) does not require \xi to be an integer. Since we usually specify the initial number density of physical particles, \xi may well be fractional from the beginning. This is different from the integer treatment of \xi in Shima et al 2009." > 2) [request] P. 8, ll. 159--161, "It is then assumed that, ..." > I do not understand. Does "two superdroplets with less than > one physical droplet" mean \xi_i<1 \wedge \xi_j<1? How can such > superdroplets be created from Eqs. (5) and (7)? Could you elaborate? We have now explained that \xi can be any fractional number already initially, thus Eq.(5) does not pose any constraint on this. > 3) [question] P. 11, ll. 213--215, 1-D setup I have several questions > regarding the setup. You explain that n_0=3e8 m^{-3}. Please clarify if > n_0 includes the lucky droplet or not. You distributed 256 droplets > in the domain. Then, the number concentration including the lucky > droplets is 256/8.56\times10^{-7}\unit{m^{3}}\approx2.99\unit{m^{-3}, > and the number concentration of background droplets is > 255/8.56\times10^{-7}\unit{m^{3}}\approx2.98\unit{m^{-3}; both are > slightly smaller than n_0. Is this difference acceptable? We have now written "initial number density of background droplets of...". Instead of giving both the volume and the side lengths, we give just the side lengths of the domain. We now see that we were not accurate enough in specifying those, but we judge that this <1% error does not affect our results in any visible way. > 4) [question] P. 11, ll. 216 and 218, time step Please add the units. > Here, you show a fixed time step, but on p. 7, l. 134, you said that > it is adaptively determined. Which is correct? We have now rephrased our statement as the following, "...are integrated with an adaptive time step, the mean value of which delta t = 2.94 x 10^{-4} s. > 5) [request] P. 11, ll. 219, "Ngrid=64" > Please clarify the shape of the grid used for the 3-D simulations. > 4x4x4, 2x2x16, or anything else? We now write that "we use a cubic mesh with 4^3 points". > 6) [request] P. 12, l. 221, "125 collisions are required" This is > not correct. 123 collisions are required for a lucky droplet with > an initial radius 12.6 um grow to 50 um. We agree with the referee and have now corrected this. This mistake was also done in the earlier papers, which we have now emphasized in the text. > 7) [suggestion] P. 11, ll. 221, "This justifies our use of Ns(t0)>=128" > In both 1-D and 3-D, the vertical extent of the domains are too small > and not appropriate for the purpose of the study. > In 1-D, you have only 255 background droplets in the domain. Then, at > the time when the lucky droplet grows to 50 um, the number of background > droplets reduces from 255 to 132. Therefore, the number concentration of > the background droplets reduces from 2.98 m^{-3} to 1.54 m^{-3}, i.e., > almost halved! However, in the original LDM (approach I) it is assumed > that is constant in time. Considering that the lucky droplet falls > about 100 m or much more, we can expect that the substantial decrease > of n^{back} has a strong impact on the results. The number of superdroplets is kept approximately constant, i.e., for this experiment, only a negligible fraction of background droplets are removed from the simulations. We say this now in the middle of paragraph 6 of Sec.4.a. Whether or not this compromises the statistical accuracy is now being addressed in the new Figure 8, where we also address other potential shortcomings pointed out by the referee below. We have now also conducted simulations with larger sizes (2L, 8L, and 64L) and showed in Fig.8(c) that P(T) is insensitive to the domain size. Therefore, the size we chose is appropriate for this study. Also, we demonstrated that P(T) is insensitive to xi, as discussed in section A2, "The most practical application of the superdroplet algorithm is the case when xi^i > 1. Thus, we investigate how xi affects fluctuations by performing the same 1-D simulation as described in section 2.b with different values of xi^i(t0). Fig.A1(b) shows that P(T) is insensitive to xi^i(t0), which suggests that the superdroplet algorithm can capture the effects of fluctuations regardless of the value of xi^i(t0)." > In 3-D, the setup is more confusing to me. I assumed that the shape of > the grid is 2x2x16. Then, in the column where the lucky superdroplet > is located, you have only 64 droplets (32 superdroplets) in it on > average. This is not at all sufficient for the lucky droplet to grow > to 50 um, because 64 is much less than 123x2 (x2 is for the two lucky > droplets). Am I missing something? We recall that the boundary condition for the superdroplets is periodic and that the number of droplets is approximately constant. This is how 50 um is reached in our simulations. We have clarified this now in the text in the 5th paragraph of Section 4.a. > All in all, I strongly suggest the authors rerun all the simulations > in much taller domains, say 100m, to obtain reliable statistics. For > taller domains, I consider the difference between 1-D and 3-D will > become negligible. If the authors stick to their original numerical > setup, they at least have to provide some clear justification of their > numerical setup. We have now added a new Figure 8 to clarify quantitatively the shortcomings of different tallness of the domain and different densities. We hope that the discussion around our new Figure 8 clarifies these questions. In our approach II, our domain is actually large enough and background particles are not recycled. In approach IV, we show that there is no marked difference compared with a 64 times larger domain. > 8) [request] P. 12, l. 230, "After the kth collision step ..." This > is not correct, because the initial size of the lucky droplet is . You > may say "After (k-2)th collision step ..." or add a note "For > convenience, we consider k starts from 3.". Please make it rigorous. We have corrected it to (k-1)th, because after the first collision means after r2 has collided with r1, so k-1=1=first. > 9) [request] P. 12, Eq. (9) > This must be a summation from k=3 to 125, not k=2 to 125. Please correct. We agree that there is a problem, but according to our counting, the first collision must happen with the lucky droplet of radius r2=12.6um, so the first mean waiting time is t2 = ...*(r2+r1)^2 (v2-v1). The first collision leads to r3. The target radius 50um is r_125, and it is achieved by colliding with a droplet of radius r_124, so the sum should go from k=2 to 124. > 10) [request] P. 12, l. 124, "124 collisions" Not "124 collisions" > but "123 collisions". We have corrected this now. > 11) [request] P. 12, Eq. (10) > This is something that I already pointed out in (9) of my previous > review comments, but this equation and the explanation that follows > are incorrect. Here is my suggestion how to introduce lambda_k: The collision > rate at the (k+1)th collision of the lucky droplet r_k obeys lambda_k=..., > where E_k=..., and v_k and v_1 are given by their terminal velocities. > Note here that lambda_k is the collision rate between the lucky droplets > and ALL the background droplets, therefore lambda_k /= lambda_k1. To > avoid this confusion, I suggest you not use the greek letter lambda > for lambda_k. In relation to the above note, how do you evaluate the > velocities of the droplets in approach I? I assume that you use their > terminal velocity. Please clarify this point. Yes, we do use the terminal velocities here. (We have checked at one point that the inclusion of the acceleration phase made virtually no difference.) We have now included the formulation suggested by the referee. > 12) [request] P. 13, ll. 251--252, "Given that the variance of ..." > This is again what I already pointed out in my previous comment (10). You > should explicitly mention that the variance of the mean collision time > is lambda_k^{-2}. Otherwise, readers cannot tell if the variance is > large for smaller k. We have adopted this formulation in the revised text after Eq.(11). > 13) [comment] P. 13, Eq. (12) > Here you assumed the terminal velocity. Yes, and this is now explained in our response to your earlier point above. We made this assumption in Sect.3d (page 17) when we solve a dynamical model, but we felt it would be confusing to make a corresponding remark at this point, where we just state the cross section as a function of a given velocity difference. > 14) [request] P. 13, l. 261, "... would correspond to the expression > equation (4) used in the superdroplet algorithm" Eq. (12) does not > correspond to Eq. (4), but corresponds to Eq. (10). Please correct. We have now corrected this. > 15) [request and suggestions] P. 14, l. 277, "In Figure 4 ..." In > Figure 4, you are comparing not P(T) but the normalized probability > density, P(T/). Please explicitly mention this here. As you show in > Table 2, differs very much among the three cases. is an important > quantity that characterizes the behavior of the lucky droplet. Why do you > compare not P(T) but P(T/)? Please explain. I do not say comparing > P(T/) is pointless, but I strongly suggest that you should discuss > the difference of as well. We have now added an extra paragraph emphasizing this; see the penultimate paragraph of Section 3.b. > 16) [request] P. 15, l. 288, "In Figure 5, ..." The same as the above > applies here. According to Table 2, differs very much among the three > cases. Please explain why you compare not P(T) but P(T/). Please also > discuss the difference of . This applies actually to all our plots of distribution times, and was also done in the work of Kostinski and Shaw. > 17) [comment] P. 15, l. 302, "it does not result in any significant > error to assume r_k >> r_1" I do not agree. According to Table 2, > are different among the three cases in Fig. 4. Please discuss this point. We agree with the referee and have now inserted "as far as the shapes of the different curves is concerned" in that sentence; see the first sentence of the third paragraph after Eq.(16). Regarding the changes of , we have now added an additional paragraph after the present paragraph. > 18) [request] P. 15, l. 306, "T_125^MFT". > Based on the definition (14), =T_124^MFT. Please show this relation > to the readers and provide the values of T_124^MFT", not T_125^MFT". We agree with the referee, so we have now added the sentence "We normally compute as an average over all realizations, but these averages also agree with T_124^MFT." Regarding the variation, we have now added "On the other hand, the actual averages such as $ ~ T_124^MFT vary by almost 50%." > 19) [request] P. 18, l. 351, approach III > You have to explain explicitly that you will use only two superdroplets in > approach III; one for the lucky droplet and the other for the background > droplets. Please also clarify whether you remove the background droplet > (i.e., decrease the multiplicity) after coalescence or not. This is > important information because lambda_k is proportional to the multiplicity of > the background superdroplet, and hence lambda_k changes in time if you remove > the background droplet. Please also specify the size of the domain you > use for approach III. If you do not remove background droplets and the > background droplet number concentration is unchanged, I understand that > the domain size does not matter to approach III. If it is the case, please > explain this explicitly in the manuscript to increase the readability. We have done this now added the sentence "We note that in this approach, n is kept constant, i.e., no background droplet is being removed after a collision." > 20) [request] P. 19, l. 393, "We see examples in Figure 8 ..." > Is this approach IV in 1-D? Please clarify. Yes. We have added this now to the caption of Figure 6, but not to that of Figure 8, because it says "same as Figure 6". In addition, in the caption to Figure 11 we have now added that it is done with approach III. > 21) [request and question] P. 20, l. 403, "approach III" > Please explicitly explain that you have one superdroplet that represents > the background droplets. When the collision-coalescence of two lucky > droplets takes place, do you remove one of the lucky droplets? Please > clarify. To clarify this, we have now added the parenthetic sentence "(As always in approach III, the background particles are still represented by only one superdroplet, and n is kept constant.)" > 22) [question] P. 20, Eq. (19) > Is epsilon only for approach III? In approach III, are all N_d^luck, > N_d^back, xi_i, N_s^luck, and N_d^back constant in time? If not, please > declare that you define epsilon by their initial value. Yes, epsilon is an input parameter only for approach III, but we also estimate its effective value for approach IV, when we discuss Figure 6. We have now also clarified this by adding the parenthetic sentence "(In that approach, all quantities in Eq.(19) are kept constant.)" > 23) [request] P. 20, l. 413, "in the full superdroplet model studied > above, ..." Do you mean "in the full superdroplet model studied in > Fig. 8, ..."? Please clarify where you are pointing. We have now added "(see Figures 6 and 9)" in parentheses. > 24) [request] P. 21, l. 426, "As shown in section 4.b, ..." We are > still in Sec. 4.b. Please clarify. We have now removed "As shown in section 4.b", because we do already refer to Figure 11 in this sentence. > 25) [request] P. 21, l. 431, "Figure 11" > Is this a result of approach III? Please clarify. Yes, this have now been added in the caption. > 26) [question] P. 22, l. 450, "..., thus containing on average 700 > droplets." Because the number concentration of the background droplets > is 3e8 m^{-3}, is it not 2100 droplets on average? Anyway, the domain is much > taller than that in approach IV. I believe you should test approach IV > (1-D and 3-D) in a similarly sized domain. We agree with the referee regarding 2100 droplets on average and have now corrected this. The results for taller domains are shown in our new Figure 8. > 27) [question] P. 22, l. 459, "..., we could only run 10^3 > realizations." I do not understand why the computational cost of > approach IV is much larger than other approaches. Could you provide some > explanation why? This is because we solve the momentum equation (Eq.1) of all the superdroplets and detect their collision. So the time step is determined by the smallest value between the Stokes time and the collision time, which is often quite small and therefore the time step is small. Also, in the original calculation, every single simulation was treated as a separate run, and poor usage of the parallelization was made. We have now added an option to the Pencil Code to run independent realizations all in one go, which allowed us now to present results for the 8192 realizations in our new Figure 8. > 28) [request] P. 23, l. 466, "4-d. The effect of fluctuations in 3-D > simulations" I think the fluctuations in 3-D in your simulation is very > much exaggerated because the domain is not tall enough. Please rerun the > simulations with a much taller domain or provide some concrete evidence > that the domain height for 1-D and 3-D is not crucial. The effect of fluctuations agrees with what we expect theoretically. While we agree that the domain was not tall enough for accurate results, especially for the correct representation of rare events, we emphasize that effect of lateral fluctuations has the opposite trend and that therefore, these two effects compensate each other. > 29) [request] P. 4, ll. 79--80, "The ratio of droplets per > superdroplet is called the multiplicity." This explanation is not > precise enough. I would suggest the following: "The number of droplets > in each superdroplet is called the multiplicity." We have now changed it to "The number of droplets in each superdroplet is called the multiplicity." > 30) [typo] P. 5, l. 104, "Third" > I could not find any "First" or "Second". We have now removed the "Third" and rephrased the sentence, "As the small ..." > 31) [request] P. 7, ll. 131--132, "To avoid a probability larger than > unity, we limit the integration step through the condition ..." Shima > et al. (2009) introduced the multiple coalescence trick to relax this > condition. Unterstrasser et al. (2020) confirmed that this technique > works efficiently. Please explicitly mention that this is not adopted > in this study. We explicitly explained this at the end of section 2.a in the first revised version. We have now elaborated more on it as the following, "To reduce the computational cost and make it linear in the number of superdroplets per mesh point, n_s(t), Shima et al. (2009) assumed that each droplet interacts at most with one other one, which is referred to as random permutation technique. This technique was also adopted in Dziekan and Pawlowska (2017) and Unterstrasser et al. (2020) but is not used in the Pencil Code ..." > 32) [request] P. 9, ll. 163--164, "..., Shima et al. (2009) assumed > that ..." This is not precise because it is not an assumption. I would > suggest the following: "..., Shima et al. (2009) imposed that ..." We have now replaced "assumed" by "imposed". > 33) [typo] P. 9, ll. 165--166, "This technique was also..." > Repetition. Please delete the second "Dziekan and Pawlowska (2017)". We have now removed it. > 34) [request] P. 9, ll. 175--176, "Since the flow is not disturbed > by the particles, we neglect two-way coupling" This is a misleading > statement. I understand that the flow is assumed to be quiescent and > the time evolution of the flow is not calculated in this study. If I am > correct, please remove the sentence. We have now removed it. > 35) [request] P. 10, l. 186, "... lucky and background droplets > ..." This has to be "... lucky and background superdroplets ..." We have now changed it to "superdroplets". > 36) [typo] P. 12, l. 245, "collision rate (4)" Collision rate (10) We have corrected this now. > 37) [typo] P.14, l. 274, "In the right hand panel" Perhaps "In > Fig. 2"? We have now changed it to Fig.2. > 38) [request] P. 14, l. 277 > Please explicitly explain that you are using the Approach I here. We have now added "...using approach I". > 39) [typo] P. 14, Eq. (16) Do you mean min(1,(r_k/r*)^2)? If so, > please correct the following: "late in the evolution" -> "early in > the evolution" (P. 14, l.285), "r_k>=r*" -> "r_k<=r*" (P. 14, > l. 286). No, the text is correct as it is; we really meant the late evolution. We wanted to say that P(T) is not only sensitive to the first few collisions, but *also* later collisions, (albeit to a lesser extent. To show this, we have used a modified form of E(r) such that E=const for r 0, but to prevent this and to have a constant value, we clip it by using the max function. > 40) [typo] P. 14, l. 286, "To ensure that E_k<=1, ... to ensure > E_k<=1" Remove one of the two "to ensure that E_k<=1". We have now removed one of them. > 41) [typo] P. 15, l. 306 "Table 3" -> "Table 2" We have now corrected it. > 42) [request] P. 19, l. 378, "\int P(T) dT = 1" Ambiguous > explanation. In Figure 7, are you showing P(T/)=P(T), > the probability density of T/? Please clarify. We agree with the referee and have now omitted this. The P(T) or P(T/) are of course normalized as earlier in the paper. > 43) [typo] P. 52, Fig. 7. N_p/s is not defined. We have corrected this and have replaced N_p/s by xi. ----------------------------------------------------------------------------- Reviewer #2 > Review of a revised manuscript "Collision fluctuations of lucky > droplets with superdroplets" by Li at al. Recommendation: accept > after additional revisions General comments: The revised manuscript has > been improved. I like the expanded and now very comprehensive list of > references to previous studies in both communities (i.e., astrophysics > and cloud physics). However, I feel the lead author run simulations > described in the paper by custom-adopting the DNS code he is using in > other publications, the Pencil code. As far as I can tell there is no > flow dynamics in the simulations (see line 516) and thus references to > the Pencil code (and other related comments, see below) only provide > confusion. I think this has to change to improve readability. Overall, > the results are of interest and should be eventually published. > Line-by-line comments: It is true that there is no fluid dynamics in the present paper, but the superdroplet algorithm is part of the Pencil Code and this part has been used when working with approach IV. Any changes or improvements that we have made are publicly available in the default version of the code. > 1. L. 116: Replace "in terms of" by "by". It is now replaced. > 2. L. 126-128: The following text is unclear: "When two superdroplets > collide, a Monte-Carlo scheme is used to determine which pairs of > superdroplets collide. All pairs of superdroplets within the volume > around one mesh point may collide.". I suggest revising the description > of the collision algorithm. Please see how other describe collisions of > real droplets as represented by superdroplets. We have now revised this text; see the blue part in the text above Equation (3). > 3. L. 129: as above. What do you mean by "two droplets in either of > the superdroplets"? I do not think separate droplet collisions are > considered, superdroplet collisions are. We have now changed it to "Superdroplet $i$ and $j$ residing in the same grid cell collide with a probability of ...". >4. L. 133: Why does the speed of sound (and other factors) limit the > time step? I think you mean in the dynamic model, but it is not used > in simulations discussed in this paper. I suggest removal. We have now removed it. > 5. L. 168: What is the PENCIL CODE? If this is a dynamic model (like > the DNS code), why it is referred to in this paper? As far as I can > understand, there is no fluid flow in the simulations. See my general > comment above. We have now rephrased that part to explain that the Pencil Code comes with many different modules, many of which are not invoked in the present studies. The particle modules are part of the code, and that part is used in the present studies. > 6. L. 193: "(One time step...". Why? I do not think this is > correct. Maybe because of the coupling with the dynamic model, but the > dynamic model is not used in the simulations. We solve the momentum equation of particles (Eq.1 and Eq.2 ), where the Stokes time in Eq.(2) need to be resolved. Also the collision time scale, which is the inverse of Eq.(4) should be resolved. We have now explained it as follows: "The simulation time step must be less than the time for a superdroplet to fall from one mesh point to the next (Stokes time expressed in equation (2)) and the collision time scale (inverse of the collision rate expressed in equation (4))" > 7. Paragraph starting at L. 211. I do not understand why the reference > to the Pencil code is needed as there is no flow dynamics. The problem > of droplet collisions can be solved without any grid. I think I miss > something from the very beginning (see general comments). The 2 mm grid > in x and y is unclear. Why only about 20 cm in the vertical? Similar > comment for the 3D simulations. 3D does not have flow dynamics either, > just nonuniform spatial droplet distribution, correct? We already explained that the Pencil Code is not just a DNS code. The particle modules are part of it. It is true that droplet collisions can be solved without a mesh, and this is done in approach II. The connection with a mesh is an essential aspect of the superdroplet approach and is explained in paragraph 3 of Section 2.a. It avoids the problem of searching for possible collision partners. As we emphasize in the paper, the superdroplet approach (which we also refer to as approach IV) is a combination between approaches II and III, and in approach III there are only two superdroplets. Those are at the same mesh point, so a mesh is needed even then, even though we only need one! We hope that our paper clarifies this aspect of the superdroplet approach of Shima et al, which was not discussed previously. > 8. L. 242: what is "stopping time" for the collision? We have now rephrased it and write: "Here we use the subscript $k$ to represent the time until the $k$th collision." > 9. Please use the same scales and labels on the axes in Fig.6 and 8. > Please check other figures that the text calls to compare. We have now applied the same scales and labels on the axes in Fig.6 and 8 and other figures. ----------------------------------------------------------------------------- Reviewer #3: > Following up on the review of the JAS-D-20-0371, let me confirm that > several updates carried out by the Authors made the paper read much > better. I'm providing below a list of several minor issues still worth > addressing in my opinion: We thank the referee for the repeated review of our manuscript. > 1. Earlier references on the lucky droplet model and related discussion > worth citing, e.g.: Twomey 1964: "Statistical Effects in the Evolution > of a Distribution of Cloud Droplets by Coalescence" Madival 2018: > "Stochastic growth of cloud droplets by collisions during settling" We have now cited these papers; see the third-to-last paragraph of the introduction. > 2. On page 7/l138, the Authors rightly point out that superdroplets > of the same size can never collide with a geometric kernel (4); it would > be worth to elaborate as well on the issue of lack of representation of > self-collisions within a single superdroplet. The point is that even with > a collision kernel allowing collisions among droplets of the same size, > the superdroplet algorithm does not feature collision of same-sized > droplets within a single superdroplet. We have now added the following below Eq.(4), "Moreover, no collision is allowed in a single superdroplet" > 3. p8/l159: in Shima et al., the multiplicities are represented with > integer numbers, worth pointing out this difference. We have now added the following below Eq.(7) "Since we usually specify the initial number density of physical particles, \xi may well be fractional from the beginning. This is different from the integer treatment of \xi in Shima et al. (2009)." > 4. p9/l168: the linearity of computational cost is worth elaborating on: > as the Authors hint, it is the number of super-droplets per collision > volume that has either quadratic or linear scaling; however, as the > pair-sampling method can always be balanced by introducing substeps to > obtain matching statistics, what is likely of greater importance is the > lack of data dependence across candidate pairs in the Shima approach > which paves the way for parallel evaluation. For discussion, see e.g., > section 2.3.3 in Unterstrasser et al. 2020, also Bartman & Arabas 2021) The text in this paragraph, which was not well written, has now improved. In addition, we have added the following text to the end of the paragraph in order to be explicit about the parallelization: "For the Pencil Code, collisions between particles residing within a given grid cell are evaluated by the same processor which is also evaluating the fluid equations of that grid cell. Due to this, together with the domain decomposition used in the code, the particle collisions are automatically efficiently parallelized as long as the particles are more or less uniformly distributed over the domain." > 5. p15/l307 "four approaches" are mentioned before being defined. We have now removed it. > 6. Technical issues with references I have pointed out in previous > iteration were not addressed: > - some reference entries include DOIs, some not; > - several include doubled URLs (i.e., DOI and DOI-URL); > - acronyms and proper names have bogus spelling (Mcsnow, > lagrangian, kuiper, slams, neptunian, lcm1d, warsaw, uwlcm, monte carlo); > - capitalisation is not consistent; > - some journal names are abbreviated, some not. We have now made all the references consistent. We apologize for overlooking this issue in the previous iteration.