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	diff --git a/paper.md b/paper.md
	index 696604c..ea5d90f 100644
	--- a/paper.md
	+++ b/paper.md
	@@ -1,122 +1,122 @@
	---
	title: 'Tamaas: a library for elastic-plastic contact of rough surfaces'
	tags:
	- C++
	- Python
	- contact
	- rough surface
	- plasticity
	authors:
	- name: Lucas Frérot
	orcid: 0000-0002-4138-1052
	affiliation: 1
	- name: Guillaume Anciaux
	orcid: 0000-0002-9624-5621
	affiliation: 1
	- name: Jean-François Molinari
	orcid: 0000-0002-1728-1844
	affiliation: 1
	affiliations:
	- name: Civil Engineering Institute, École Polytechnique Fédérale de Lausanne, Switzerland
	index: 1
	date: 13 December 2019
	bibliography: paper.bibtex
	---

	# Summary

	Physical phenomena that happen at solid contact interfaces, such as
	friction and wear, are largely entwined with the roughness of the
	surfaces in contact. For example, the fact that the friction force
	between two solids in contact is independent of their apparent contact
	area is due to roughness, as the solids are only in contact over a
	smaller "true contact area" which only depends on the normal force.
	Roughness occurs on most man-made and natural surfaces alike
	[@persson_nature_2005] and can span many orders of magnitude, from the
	nanometer scale to the kilometer scale [@renard_constant_2013]. This
	poses a serious challenge to conventional numerical approaches in
	solid mechanics such as the finite-element method (FEM).

	Boundary integral methods [@bonnet_boundary_1995] are commonly
	employed in place of the FEM in rough elastic contact because of an
	inherent dimensionality reduction: the computational effort is focused
	on the contact interface whereas the FEM requires discretization of
	the volume of the solids in contact. In addition, the use of a
	half-space geometry provides a translational invariance: the
	computation of equilibrium solutions can then be accelerated with the
	fast-Fourier Transform.

	However, because of the roughness, the total contact load is
	distributed over a small area and local contact pressures are expected
	to cause non-linear material behavior, such as plasticity. In such a
	case, volume integral methods can be employed to account for plastic
	deformation. These enjoy properties analogous to boundary integral
	methods and can be accelerated with a Fourier approach
	[@frerot_fourieraccelerated_2019].

	Taking plasticity into account is necessary in the accurate
	description of contact interfaces for the understanding of friction
	and wear. Moreover, high performance implementations are needed to
	model realistic rough surfaces.

	``Tamaas`` is a C++ library with a Python interface, developed in the
	[Solid Mechanics Simulation Lab](https://www.epfl.ch/labs/lsms) at
	EPFL, that implements a unique Fourier-accelerated volume integral
	formulation of equilibrium [@frerot_fourieraccelerated_2019] for the
	solution of elastic-plastic rough contact problems. The use of C++
	allows for a particular focus on performance: most loops are
	paralelized using ``Thrust/OpenMP`` and the fast-Fourier transforms
	are computed with ``FFTW3/OpenMP``. Thanks to this, it can handle
	simulations with upwards of 100 million degrees of freedom on a single
	compute node [@frerot_fourieraccelerated_2019].

	# Features and Performance

	``Tamaas`` provides access in its Python API to random rough surface
	generation procedures (e.g. @hu_simulation_1992), statistical tools
	(e.g. autocorrelation and power spectrum computations) and a variety
	of contact algorithms:

	- Normal and adhesive contact schemes based on the conjugate gradient
	[@polonsky_numerical_1999; @rey_normal_2017];
	- Frictional contact;
	- Elastic-plastic contact [@frerot_fourieraccelerated_2019].

	``Tamaas`` also exposes in its Python API the accelerated linear
	operators it uses to compute equilibrium solutions, making prototyping
	new algorithms convenient.

	We compare in figure 1 the scaling properties of Tamaas to a reference
	high-performance C++ FEM implementation named
	[Akantu](https://akantu.ch/) [@richart_implementation_2015] which uses
	the direct solver [MUMPS](http://mumps.enseeiht.fr/). The reference
	problem is the elastic equilibrium of a half-space with an isotropic
	spherical inclusion [@mindlin_thermoelastic_1950]. $N$ represents the
	number of points in the computational domain.

	![Scaling comparison between the acclerated volume integral method
	implemented in ``Tamaas`` and a finite-element method with a direct
	solver for the solution of the equilibrium of a half-space with a
	spherical isotropic inclusion. $N$ is the number of points in the
	-computational domain. When $N=2^18$ ``Tamaas`` is 200 times faster
	-than the FEM implementation Akantu.](complexity.svg)
	+computational domain. When $N=2^{18}$ ``Tamaas`` is 200 times faster
	+than the FEM implementation Akantu.](complexity.pdf)

	The following publications have been made possible with ``Tamaas``:

	- @yastrebov_contact_2012
	- @yastrebov_contact_2014
	- @yastrebov_infinitesimal_2015
	- @yastrebov_accurate_2017
	- @yastrebov_role_2017
	- @rey_normal_2017
	- @rey_stability_2018
	- @rey_quantifying_2019
	- @frerot_mechanistic_2018
	- @frerot_fourieraccelerated_2019
	- @frerot_crack_2019

	# Acknowledgements

	We acknowledge the financial support of the Swiss National Science Foundation (grant #162569 "Contact mechanics of rough surfaces").

	# References

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