paper: minor cosmentic suggestions

paper/paper.md

@@ -31,54 +31,54 @@ bibliography: paper.bib
 # Summary
 
 Dynamical systems such as those derived from models of fluid flows show transition behavior associated with fluid flow instabilities [@wubs:23].
-Examples are dynamical systems from ocean models which show transition behavior due to slow changes in parameters representing the surface forcing [@westen:24].
+Examples are dynamical systems from ocean models in which transition behavior is caused by slow changes in parameters representing the surface forcing [@westen:24].
 Such changes in the stability of the fluid flow can be studied by performing numerical simulations with a model and observing its transient behavior after a certain time.
 This is, however, computationally very expensive, and in many cases infeasible.
-Instead, so called continuation methods exist, that are able to trace stable and unstable steady states in parameter space, without having to perform the expensive transient simulations [@dijkstra:05].
+Instead, so called continuation methods are able to trace stable and unstable steady states in parameter space, obviating expensive transient simulations [@dijkstra:05].
 The `TransiFlow` Python package implements a continuation framework in which fluid flow problems can be studied with the help of several computational back-ends that can, based on the needs of the user, easily be switched between.
 
 One motivation behind `TransiFlow` is that writing research software that works efficiently on a parallel computer is a challenging task.
-Therefore, numerical models are often developed as a sequential code with parallelization as an afterthought, which makes them very difficult to parallelize, or as a parallel code from the start, which makes them complicated to work with for researchers .
+Therefore, numerical models are often developed as a sequential code with parallelization as an afterthought, which makes them very difficult to parallelize, or as a parallel code from the start, which makes them complicated to work with for researchers.
 This is especially problematic since people that work with these codes generally only work with them for the duration of their project.
 If there is insufficient continuity between the projects, knowledge of how to use the codes or work on them may get lost, which renders the developed software useless.
 
-In climate modelling, this is a prominent issue, since the models are complex, are usually intercoupled with other models (e.g. ocean, atmosphere, ice), take a very long time to run (i.e. multiple months) and require large amounts of parallelism to reach a sufficient resolution (i.e. using thousands of cores for a single run) [@thies:09; @mulder:21].
+In climate modelling, this is a prominent issue, since the models are complex, are usually intercoupled with other models (e.g., ocean, atmosphere, ice), take a very long time to run (i.e., multiple months) and require large amounts of parallelism to reach a sufficient resolution (i.e., using thousands of cores for a single run) [@thies:09; @mulder:21].
 Therefore, ease of developing and using the parallel software is crucial.
 
-By abstracting away the computational back-end from the user, the user can develop their model on their own machine (e.g. a laptop) in Python using the SciPy back-end, and once the model works, run a large scale simulation on a supercomputer e.g. using the `Trilinos` back-end, which can use a combination of OpenMP, MPI and potentially GPUs, without requiring any changes to the code.
+By abstracting away the computational back-end from the user, the user can develop their model on their own machine (e.g., a laptop) in Python using the SciPy back-end, and once the model works, run a large scale simulation on a supercomputer, e.g., using the `Trilinos` back-end, which can use a combination of OpenMP, MPI and potentially GPUs, without requiring any changes to the code.
 The computationally expensive parts of the program are implemented by these libraries, so one does not have to worry about the efficiency of the Python implementation of the model.
-Initial tests show us that the overhead of using Python is less than 1% of the total computational cost.
+Initial tests indicate that the overhead of using Python is less than 1% of the total computational cost.
 
-![Bifurcation diagram of the double-gyre wind-driven circulation configuration that is present in `TransiFlow`.
+![Bifurcation diagram of the double-gyre wind-driven circulation configuration that is included in `TransiFlow`.
 The markers indicate pitchfork and saddle-node bifurcations that were automatically detected by the software.
-Solid lines indicate stable steady states of the system, dashed lines indicate unstable steady states](qg-bif.pdf){height=250pt}
+Solid lines indicate stable steady states of the system, dashed lines indicate unstable steady states.](qg-bif.pdf){height=250pt}
 
 # Statement of need
 
 `TransiFlow` aims to be an easy to use tool for performing bifurcation analysis on fluid flow problems that can be used in combination with fast parallel solvers without any additional effort.
-Moreover, since `TransiFlow` is focussed on fluid flow problems, it already includes discretizations of the governing equations for several canonical fluid flow problems, which is something none of the competitiors have.
+Moreover, `TransiFlow` includes discretizations of the governing equations for several canonical fluid flow problems, a feature none of its competitors provides.
 
 The main competitors are [`AUTO`](http://indy.cs.concordia.ca/auto/) [@doedel:07], [`MatCont`](https://sourceforge.net/projects/matcont/) [@dhooge:08] and [`pde2path`](https://www.staff.uni-oldenburg.de/hannes.uecker/pde2path/) [@uecker:14].
 These packages are widely used, and they are much more feature complete in terms of bifurcation analysis.
-They do, however, lack the aforementioned discretized fluid flow models and parallel solver interfaces that make `TransiFlow` easy to use.
+They do, however, lack the discretized fluid flow models and parallel solver interfaces that make `TransiFlow` easy to use.
 
 A continuation package that does allow for easy coupling with parallel solvers is the [`LOCA`](https://trilinos.github.io/nox_and_loca.html) package in `Trilinos` [@trilinos].
 Using `LOCA`, however, requires a vast knowledge of C++ and any change to the continuation algorithm requires a full stack of C++ templates to be reimplemented.
 Moreover, `LOCA` has not seen any active development in over 10 years.
 
 An alternative Python package for performing bifurcation analysis is [`PyNCT`](https://pypi.org/project/PyNCT/) [@draelants:15].
-It is, however, difficult to extend, the latest version of the software is not freely available, and it can not be used for systems that are not symmetric positive-definite.
+It is, however, difficult to extend, the latest version of the software is not freely available, and it cannot be used for systems that are not symmetric positive-definite.
 
 # Past and ongoing research
 
 `TransiFlow` has been used to generate results in [@wubs:23]  and [@bernuzzi:24] and has been used in courses at Utrecht University and the University of Groningen (NL).
 Earlier versions have also been used to generate results in [@song:19] and [@baars:20].
-The code is currently being used in various projects at Utrecht University and is also used by several external researchers.
+The code is currently being used in various projects at Utrecht University and by several external researchers.
 
 # Acknowledgements
 
 H.A.D. and S.B. are funded by the European Research Council through the ERC-AdG project TAOC (project 101055096).
 S.B. and F.W.W. were supported by funding from the SMCM project of the Netherlands eScience Center (NLeSC) with project number 027.017.G02.
 We would like to thank Lourens Veen for his contributions in providing guidance in setting up the documentation and continuous deployment.
 
-# References
+# References