1889
Stick–slip boundary friction mode as a second-order phase
transition with an inhomogeneous distribution of elastic
stress in the contact area
Iakov A. Lyashenko *1,2 , Vadym N. Borysiuk 1,2 and Valentin L. Popov 1,3,4
Full Research Paper Open Access
Address:
1 Technische Universität Berlin, 10623 Berlin, Germany, 2 Sumy State
University, 40007 Sumy, Ukraine, 3 National Research Tomsk State
University, 634050 Tomsk, Russia, and 4 National Research Tomsk
Polytechnic University, 634050 Tomsk, Russia
Email:
Iakov A. Lyashenko * - [email protected]
* Corresponding author
Keywords:
boundary friction; dimensionality reduction; numerical simulation;
shear stress and strain; stick–slip motion; tribology
Beilstein J. Nanotechnol. 2017, 8, 1889–1896.
doi:10.3762/bjnano.8.189
Received: 23 April 2017
Accepted: 16 August 2017
Published: 08 September 2017
This article is part of the Thematic Series "Nanotribology".
Guest Editor: E. Gnecco
© 2017 Lyashenko et al.; licensee Beilstein-Institut.
License and terms: see end of document.
Abstract
This article presents an investigation of the dynamical contact between two atomically flat surfaces separated by an ultrathin lubri-
cant film. Using a thermodynamic approach we describe the second-order phase transition between two structural states of the
lubricant which leads to the stick–slip mode of boundary friction. An analytical description and numerical simulation with radial
distributions of the order parameter, stress and strain were performed to investigate the spatial inhomogeneity. It is shown that in
the case when the driving device is connected to the upper part of the friction block through an elastic spring, the frequency of the
melting/solidification phase transitions increases with time.
1889
Introduction
The boundary friction mode occurs in tribological systems
when the thickness of the lubricant layer separating two
contacting surfaces is significantly smaller than the typical size
of the surface roughness. At such a system configuration, the
lateral motion of the friction surface is followed by a contact
interaction between the asperities. A specific case of boundary
friction is friction between two atomically flat surfaces separat-
ed by a layer of lubricant with thickness of a few atomic diame-
ters [1,2], or even monolayers [3]. Such type of friction mode
plays an important role in applied mechanics as it often occurs
in nanometer-sized tribological systems that are commonly used
in aerospace technologies, computer memory devices and elec-
tronic positioning systems [4]. Various experimental research
has shown that in the boundary friction mode, the lubricant can
undergo periodic phase transitions between the structure states
which may lead to the stick–slip motion with non-monotonic
time dependence of the friction force [1,2,4,5]. Stick–slip
motion is known to cause fast destruction of the contact parts of
microscopic devices, which is why it receives significant atten-
tion from the scientists and engineers.

Beilstein J. Nanotechnol. 2017, 8, 1889–1896.
1890
The boundary friction mode can be described within the frame-
work of several theoretical models [6-12] where lubricant
melting is described either as a first-order [8,9], or a second-
order [10,11] phase transition. It is worth mentioning that in
three-dimensional systems, melting always appears as a first-
order phase transition [13], while in the systems with confined
lubricant, second-order phase transitions were observed in both
numerical [14-16] and theoretical [10] studies. Moreover, recent
experimental investigations [5] have shown that melting as a
first-order phase transition is not possible for boundary lubri-
cants consisting of spherically shaped molecules. However for
the polymeric lubricant materials, first-order phase transition
may occur [17].
In our previous work [18] we studied the stick–slip boundary
friction mode considering lubricant melting as both first and
second-order phase transitions with an inhomogeneous distribu-
tion of elastic stress in a contact area. This obtained results have
shown that the melting begins at the edge of a contact area and
propagates to its center, and the wave of melting is followed by
a wave of recrystallization. Such inhomogeneous behavior was
also observed in experiments [19,20]. However, in [18] we con-
sider the motion of the friction surfaces with constant relative
velocity, while in the real experiments, the driving device is
applied to the upper surface through the elastic spring [1,4,6]. In
such an experimental configuration, the velocities of the fric-
tion surface and driving device are not equal, which significant-
ly affects the friction mode. In the present paper, we study this
situation using a previously developed technique [18]. In our
research we use a thermodynamic approach, as proposed in
[10], which gives relevant physical results. The dependence of
the order parameter on elastic strain in the lubricant layer, ob-
tained using the above-mentioned thermodynamic approach,
agrees with the similar data obtained from computational
studies [14-16]. Moreover, strain–stress curves obtained in [10]
are confirmed by experimental data [21].
Results and Discussion
We consider a simplified case where the properties of the lubri-
cant are independent of pressure and its behavior can be de-
scribed within a thermodynamic approach [10]. Assuming that
the melting of the lubricant develops as a second-order phase
transition (which follows from the computer simulations [14,15]
and experimental investigations [5]), the free-energy density
can be written in the form [10]:
(1)
where T is the temperature of the lubricant; T c is the critical
temperature; ε el is the shear component of the elastic stress; α , a
and b are positive constants. The order parameter φ is a peri-
odic component of the microscopic density of the material: in a
solid-like state of the lubricant φ > 0, while in a liquid-like state
φ = 0.
Using Equation 1 and the definition τ = ∂ f / ∂ε el [10,22] shear
stresses that appear in the lubricant can be written in the form:
(2)
where we have introduced the shear modulus of the lubricant μ ,
that takes nonzero values only in solid-like states. The station-
ary values of the order parameter φ 0 can be estimated from the
condition ∂ f / ∂φ = 0 in the following form:
(3)
According to Equation 3, the stationary value of the order pa-
rameter φ 0 decreases with the growth of both temperature T and
elastic strain ε el . When the strain exceeds a critical value
(4)
stationary values of the order parameter φ 0 and shear modulus
μ 0 (according to Equation 2) equal to zero and the lubricant
melts. In the case ε el < ε el,c as defined by Equation 4, the sta-
tionary stress in the lubricant can be expressed as
(5)
Equation 5 describes the strain–stress curve defined by the
expansion parameters. However, it is more convenient to use
experimentally observable values of the maximum stress τ max
and strain . The relation between the expansion parameters
α , a and b and values of τ max and can be estimated from
Equation 5 in the following form [18]:
(6)
To study the kinetics of the lubricant we employed the
Ginzburg–Landau–Khalatnikov evolutionary equation for the
order parameter in the form:

Beilstein J. Nanotechnol. 2017, 8, 1889–1896.
1891
Figure 1: Geometrical scheme of the system under investigation. Stamp of a cylindrical shape with radius a 0 , made of material with shear modulus of
G 2 and Poisson ratio v 2 , placed over the material with elastic parameters G 1 , v 1 . Upper and lower friction blocks are separated by a layer of lubricant
with thickness h 0 .
(7)
where γ is the kinetic parameter that defines the inertial proper-
ties of the system, ξ ( t ) represents random processes in the heat
fluctuation of a small amplitude which cannot significantly
affect the system behavior. Nevertheless, it is necessary to take
them into account due to the peculiarities of the further numeri-
cal calculations [23]. In explicit form, Equation 7 can be written
as
(8)
The thermodynamic approach described above can be used to
investigate the boundary friction mode with different geomet-
rical shapes of the contact area. In the present work we consider
a tribological system as shown in Figure 1.
As can be seen from Figure 1, a cylindrically shaped flat-ended
stamp with radius a 0 is in contact with a lower surface through
the lubricant layer with thickness h 0 . The materials of the top
and bottom surfaces have the shear moduli G 1 , G 2 and Poisson
ratios v 1 , v 2 , respectively. This configuration can be reduced to
the contact of a rigid stamp with half-space characterized by an
effective shear modulus [24]
(9)
Assuming that the upper stamp has mass m , and the coordinate
of the stamp center is X , let us consider the situation where the
stamp is driven by a spring with the constant stiffness K . The
free end of the spring moves with a constant velocity V 0 . Thus,
the equation of motion for the upper friction block with mass m
has the following form [4]:
(10)
where t is the time, and F x is the friction force between two
contacting surfaces. The magnitude of the friction force F x
depends on the properties of the system shown in Figure 1.
As the upper stamp moves, local displacements of its surface in
the contact area with a lubricant are defined by a radial distribu-
tion , where r is the radial coordinate. Denoting the cor-
responding local displacements of a bottom surface as ,
we can define the local shear strain in the lubricant layer as a
function of the radial coordinate r :
(11)
Knowing the distribution of strain ε ( r ) and order parameter φ ( r )
we can obtain the distribution of the stress in the lubricant ac-
cording to Equation 2:
(12)
The distribution of the displacements in Equation 11 is
defined by shear stress. In our further investigations we will use
the method of dimensionality reduction (MDR) [24-26], which
allows us to reduce the three-dimensional problem (with general
coordinate r ) to an equivalent one-dimensional (coordinate x )
with a possible reverse transition.

Beilstein J. Nanotechnol. 2017, 8, 1889–1896.
1892
Figure 2: (a) Kinetic dependence of the friction force F x ( t ), calculated at parameters τ max = 10 6 Pa, = 1.0, a = 10 6 Pa, h 0 = 10 − 7 m,
γ = 10 (Pa·s) − 1 , a 0 = 2·10 − 5 m, G * = 10 9 Pa, K = 500 N/m, m = 0.1 kg, V 0 = 1 m/s. (b) Spatial distribution of the order parameter φ ( r ) in the moment of
time t = 1.3 ms, related to final point of the dependence shown in Figure 2a. (c) Time dependence of the mean values of the order parameter < φ >
(solid line) and elastic strain < ε el > (dashed line). (d) Spatial distribution of the elastic strain ε el ( r ) at t = 1.3 ms.
Within the MDR technique, a one-dimensional distribution of
the force density can be defined from the known distribution
τ ( r ) as:
(13)
From the obtained q ( x ), the one-dimensional distribution of the
displacements can be calculated as:
(14)
and the distribution can be obtained from the equation:
(15)
The elastic component of the friction force in the system can be
defined in two ways (in one-dimensional and three-dimensional
interpretations):
(16)
The aim of the present work is to take into account the elastic
properties of the contacting materials in simulation of the
kinetics of the boundary friction in the system shown in
Figure 1. Let us introduce the brief algorithm of the simulation
scheme. First, we need to set the initial distributions
and . After that, the procedure described in Equa-
tion 11–Equation 15 is repeated in loops and for every value of
ε ( r ) a related value of the order parameter is calculated from
Equation 8.
The displacement of upper stamp X can be estimated from the
numerical solution of Equation 10 with friction force F x calcu-
lated from Equation 16. With incremental growth of the upper
friction block, coordinate X values of the distribution
are also incremented by the same magnitude. Thus, at the begin-
ning of motion, . However, is set to
zero when the lubricant melts (in numerical scheme
when φ ( r i ) < 0.01 [18]).
In numerical calculations integrals of Equation 13, Equation 15
and Equation 16 were replaced by corresponding sums,
while coordinates x and r were divided into N segments. All
calculated distributions depending on radius r (or coordinate x ),
were computed at the points r i = ia 0 / N ( x i = ia 0 / N ), where
. In our simulation we set the time step to be
Δ t = 10 − 8 s and number of segments N = 2000.
Figure 2 shows the results of a numerical simulation of the
shifting of the free end of the spring with constant velocity V 0 at
constant system parameters.
An analogous dependence was described in [18], where the
motion of a stamp with constant velocity was considered. Such
configuration relates to the case where the spring, shown in
Figure 1, is replaced by the rigid coupler. However, in real ex-

Beilstein J. Nanotechnol. 2017, 8, 1889–1896.
1893
periments, the spring (finite stiffness) between the stamp and
the driving device always exists.
The dependence shown in Figure 2 allows us to conclude
that the stick–slip mode, with increasing frequency of the
melting/solidification phase transitions, is established in the
system. The growth of the frequency is caused by the increas-
ing tension of the driving spring Δ X = V 0 t − X and the elastic
force F u = K ( V 0 t − X ). The shear velocity of the upper stamp
also increases according to Equation 10, while the time
interval, during which the elastic stress ε el exceeds the critical
value, is reduced.
As it is follows from Figure 2b,d, melting of the lubricant
occurs at the edge of the contact area and propagates to the
center; this situation was observed earlier in theoretical [18,27]
and experimental [19] research. It is worth mentioning that
before the first melting, the dependencies F x ( t ), < φ >( t ) and
< ε el >( t ) show the transition mode where monotonic growth of
the friction force F x and mean value of elastic strain < ε el > as
well as < φ > are significantly slower. The corresponding time
interval from the beginning of motion to the first melting is the
largest due to the presence of the spring between the stamp and
driving device [4]. Such a transition mode was not observed in
[18] as the stamp was moving with constant velocity V from the
very beginning of motion.
Additional time dependence of the order parameter φ ( t ) ob-
tained for different values of the radial coordinate r is shown in
Figure 3.
Figure 3: (a) Time dependence of the order parameter φ ( t ), calculated
using the same parameters as in Figure 2 and corresponding to the
melting process (arrow 1) before the first dashed line and to the recrys-
tallization process (arrow 2) after the first dashed line for different
values of the radial coordinate r . Arrows show the increment of a radial
coordinate r from 2 to 18 μ m, with a step of 2 μ m. Inset shows the time
interval between two dashed lines.
As it can be seen from Figure 3, melting begins at the edge of
the contact area and is immediately followed by recrystalliza-
tion. We also conclude that the inhomogeneous distribution of
the parameters weakly affects the behavior of the considered
tribological system in contrast to the case of a first-order phase
transition, where the influence of inhomogeneity is significant-
ly stronger [18].
The developed theoretical model of the boundary friction allows
investigating of the influence of the temperature of the lubri-
cant on the melting process. It is worth mentioning that the in-
fluence of the temperature was studied in a previous work [18]
for the case where the stamp was moving with a constant
velocity, and here we will discuss an analogous investigation
for the system with the spring. As the coefficient
(17)
is the only parameter in the model that depends on the tempera-
ture T , the variations of this coefficient can be considered as
variations of the temperature of the lubricant. As it follows from
the definition, the coefficient A decreases with temperature
increase. The dependence in Figure 2 is obtained using the pa-
rameters τ max = 10 6 Pa and = 1.0, which corresponds to
the value of A = 1.5·10 6 Pa according to Equation 6. Figure 4
shows the time dependence of the friction force with monotoni-
cally decreasing coefficient A according to the relaxation law
(18)
where A 0 is the initial value of coefficient A at time t = 0, while
is the relaxation time. Equation 18 relates to the increase of
the lubricant temperature.
The temperature of the lubricant can vary during the natural
heat exchange with the environment (friction surfaces are
considered as a thermostat) [28]. As it follows from Figure 4,
the higher temperature of the lubricant leads to the reduced
amplitude of the friction force, elastic stress and order
parameter, which was previously observed in [18]. However, in
the considered case, the frequency of the phase transitions
increase with time due to the presence of the spring, as shown
in Figure 1. Complete melting of the lubricant occurs at
A = 2 α ( T c − T ) a / b ≤ 0 (not shown in the figure) and is followed
by a sliding mode with zero friction force F x = 0 (only the
elastic component of the friction force is considered within the
proposed model).

Beilstein J. Nanotechnol. 2017, 8, 1889–1896.
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Figure 4: (a) Time dependence of the friction force F x (Equation 16)
using the parameters of Figure 2 and an increasing temperature ac-
cording to Equation 18 using the parameters A 0 = 1.5·10 6 Pa and
s. (b) Mean values of the order parameter < φ > and elastic
strain < ε el > are according to the parameters of Figure 4a.
Let us note that all presented dependencies relate to the particu-
lar situation where elastic stress increases according to Equa-
tion 11. However, in various experimental and theoretical
studies, the boundary friction mode develops through an alter-
native mechanism where elastic stress, which cause the melting
of a lubricant, can also exist in a liquid-like state [4,9,23]. At
these conditions of time dependence, the friction force has a
saw-like form and melting of the lubricant occurs when the
shear velocity V exceeds some critical value. After the lubricant
is melted, the elastic friction force becomes equal to zero, i.e.
F x = 0.
In the proposed model, we consider a quasi-static case where
the elastic strain is defined by the displacement of the friction
surfaces (see Equation 11) instead of the shear velocity V .
Moreover, in the case of quasi-static contact, the viscous fric-
tion force is not considered, while in the standard dynamic
model, it plays significant role [9]. Note however, that in most
cases, the boundary lubricant layers will exhibit non-Newtonian
behavior, so obtaining the dependence of viscous friction force
on shear velocity may represent another difficult challenge [29].
Thus, in our model, the increase in the shear velocity V causes
the increase in the frequency of phase transitions, and a critical
value of V related to the complete melting of the lubricant is not
observed. However, it is worth mentioning that the developed
approach allows us to investigate the physical processes directly
in the contact area, which is not possible within standard
models.
The dependence of the friction force F x on the coordinate of the
upper friction block X as shown in Figure 5 corresponds to the
data from Figure 2a and Figure 4a.
Figure 5: (a) Dependence of the friction force F x on the stamp coordi-
nate X (upper friction surface), corresponding to Figure 2a. (b) Depen-
dence of the friction force F x on the stamp coordinate X , correspond-
ing to Figure 4a.
As it can be seen from Figure 5, F x ( X ) is periodical (with
damping oscillations in the second case, as the amplitude of the
friction force decreases in time due to the heating of the lubri-
cant). The presented dependencies have a regular form in
contrast to the data in Figure 2 and Figure 4, where the frequen-
cy of the phase transitions increases with time. Different forms
of the obtained dependencies can be explained as follows. Let
us recall that in our simulations we introduced the constant
velocity of the free edge of the spring V 0 (see Figure 1). The
velocity of the stamp center is calculated from
Equation 10 and does not coincide with the velocity V 0 mostly
due to the presence of the friction force F x (Equation 16). After
the motion has begun, the tension of the spring and related
growth of the elastic force causes the growth of the upper stamp
velocity V . The lubricant melts in certain regions of the contact
area where elastic stress, ε el ( r ), exceed a critical value, ε el,c
(Equation 4). As the velocity of the upper stamp V grows, the
time needed for the elastic stress to reach the critical value ε el,c
decreases. Thus, the frequency of the phase transitions in
Figure 2 and Figure 4 increases in time. However, strains
(Equation 11) are determined by the magnitude of the displace-
ment of the upper stamp over the bottom surface after another
melting and subsequent solidification (when the lubricant solid-
ifies after melting, strain is equal to zero for the subsequent
growth according to Equation 11). Thus, the upper stamp, after
another solidification of the lubricant, must pass approximately
the same distance before the next melting, as is depicted in

Beilstein J. Nanotechnol. 2017, 8, 1889–1896.
1895
Figure 5. This situation confirms the assumption that the fre-
quency of the phase transitions increases (as it is shown in
Figure 2 and Figure 4) due to the increase in the strain rate.
Conclusion
We have presented the dynamical simulation of the boundary
friction between a cylindrically shaped stamp and a flat surface.
Using the method of dimensionality reduction (MDR) we have
studied the stick–slip friction mode that occurs in the tribolog-
ical system under shear deformation. The MDR approach
allowed us to describe the situation in which elastic stress,
strain and order parameter are spatially distributed within con-
tact area. The established stick–slip mode is characterized by
continuous phase transitions between solid-like and liquid-like
states of the lubricant, which were described as the second-
order phase transitions between kinetic states of friction. Within
the performed numerical simulation it is shown that an increase
of the lubricant temperature leads to smaller amplitudes of the
friction force, elastic stress and order parameter, while the fre-
quency of phase transitions increases due to the presence of the
spring. It is worth mentioning that the spatial distribution of
elastic stress considered in the presented study will always
occur in tribological systems with analogous geometrical shape
of the contact area; thus, the developed approach can be an ad-
ditional tool in various experimental investigations for contact
problems of this type.
Acknowledgements
This work was supported in part by Tomsk State University,
Academic D.I. Mendeleev Fund Program and the Deutsche
Forschungsgemeinschaft. I.A.L. and V.N.B. are grateful to the
Ministry of Education and Science of Ukraine for financial
support under the project for young scientists “Thermodynamic
theory of the phase transitions between structural states of
the boundary lubricant with spatial inhomogeneity” (Project
No. 0116U006818).
References
1. Zhang, J.; Meng, Y. Friction 2015, 3, 115–147.
doi:10.1007/s40544-015-0084-4
2. Krim, J. Adv. Phys. 2012, 61, 155–323.
doi:10.1080/00018732.2012.706401
3. Bruschi, L.; Fois, G.; Pontarollo, A.; Mistura, G.; Torre, F.;
Buatier de Mongeot, C.; Borango, R.; Buzio, R.; Valbusa, U.
Phys. Rev. Lett. 2006, 96, No. 216101.
doi:10.1103/PhysRevLett.96.216101
4. Yoshizawa, H.; Israelachvili, J. J. Phys. Chem. 1993, 97,
11300–11313. doi:10.1021/j100145a031
5. Kienle, D. F.; Kuhl, T. L. Phys. Rev. Lett. 2016, 117, No. 036101.
doi:10.1103/PhysRevLett.117.036101
6. Carlson, J. M.; Batista, A. A. Phys. Rev. E 1996, 53, 4153–4165.
doi:10.1103/PhysRevE.53.4153
7. Filippov, A. E.; Klafter, J.; Urbakh, M. Phys. Rev. Lett. 2004, 92,
No. 135503. doi:10.1103/PhysRevLett.92.135503
8. Aranson, I. S.; Tsimring, L. S.; Vinokur, V. M. Phys. Rev. B 2002, 65,
No. 125402. doi:10.1103/PhysRevB.65.125402
9. Lyashenko, I. A.; Khomenko, A. V. Tribol. Lett. 2012, 48, 63–75.
doi:10.1007/s11249-012-9939-2
10. Popov, V. L. Tech. Phys. 2001, 46, 605–615. doi:10.1134/1.1372955
11. Popov, V. L. Solid State Commun. 2000, 115, 369–373.
doi:10.1016/S0038-1098(00)00179-4
12. Persson, B. N. J. Phys. Rev. B 1994, 50, 4771–4786.
doi:10.1103/PhysRevB.50.4771
13. Landau, L. D. Sov. Phys. – JETP 1937, 7, 627.
14. Bock, H.; Schoen, M. J. Phys.: Condens. Matter 2000, 12, 1545–1568.
doi:10.1088/0953-8984/12/8/301
15. Schoen, M.; Hess, S.; Diestler, D. J. Phys. Rev. E 1995, 52,
2587–2602. doi:10.1103/PhysRevE.52.2587
16. Bordarier, P.; Schoen, M.; Fuchs, A. H. Phys. Rev. E 1998, 57,
1621–1635. doi:10.1103/PhysRevE.57.1621
17. Braun, O. M.; Naumovets, A. G. Surf. Sci. Rep. 2006, 60, 79–158.
doi:10.1016/j.surfrep.2005.10.004
18. Lyashenko, I. A.; Filippov, A. E.; Popov, M.; Popov, V. L. Phys. Rev. E
2016, 94, No. 053002. doi:10.1103/PhysRevE.94.053002
19. Bayart, E.; Svetlizky, I.; Fineberg, J. Phys. Rev. Lett. 2016, 116,
No. 194301. doi:10.1103/PhysRevLett.116.194301
20. Pierno, M.; Bruschi, L.; Mistura, G.; Paolicelli, G.; di Bona, A.;
Valeri, S.; Guerra, R.; Vanossi, A.; Tosatti, E. Nat. Nanotechnol. 2015,
10, 714–718. doi:10.1038/nnano.2015.106
21. Reiter, G.; Demirel, A. L.; Peanasky, J.; Cai, L.; Granick, S. In Physics
of Sliding Friction; Persson, B. N. J.; Tosatti, E., Eds.; NATO Advanced
Studies Institute, Series E: Applied Science, Vol. 311; Kluwer:
Dordrecht, Netherlands, 1996; pp 119 ff.
22. Pogrebnjak, A. D.; Bratushka, S. N.; Beresnev, V. M.;
Levintant-Zayonts, N. Russ. Chem. Rev. 2013, 82, 1135–1159.
doi:10.1070/RC2013v082n12ABEH004344
23. Lyashenko, I. A. Tech. Phys. 2011, 56, 869–876.
doi:10.1134/S1063784211060168
24. Popov, V. L.; Heß, M. Method of dimensionality reduction in contact
mechanics and friction; Springer: Berlin, Germany, 2015.
doi:10.1007/978-3-642-53876-6
25. Popov, V. L.; Hess, M. Facta Univ., Ser.: Mech. Eng. 2014, 12, 1–14.
26. Hess, M.; Popov, V. L. Facta Univ., Ser.: Mech. Eng. 2016, 14,
251–268.
27. Slutsker, J.; Thornton, K.; Roytburd, A. L.; Warren, J. A.;
McFadden, G. B. Phys. Rev. B 2006, 74, No. 014103.
doi:10.1103/PhysRevB.74.014103
28. Kisiel, M.; Pellegrini, F.; Santoro, G. E.; Samadashvili, M.; Pawlak, R.;
Benassi, A.; Gysin, U.; Buzio, R.; Gerbi, A.; Meyer, E.; Tosatti, E.
Phys. Rev. Lett. 2015, 115, No. 046101.
doi:10.1103/PhysRevLett.115.046101
29. Vågberg, D.; Olsson, P.; Teitel, S. Phys. Rev. E 2017, 95, No. 052903.
doi:10.1103/PhysRevE.95.052903

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