# Boosting 5G mm-Wave IAB Reliability with Reconfigurable Intelligent Surfaces

Paolo Fiore∗, Eugenio Moro∗, Ilario Filippini∗, Antonio Capone∗, and Danilo De
Donno§
∗ANTLab - Advanced Network Technologies Laboratory, Politecnico di Milano,
Milan, Italy
§Milan Research Center, Huawei Technologies Italia S.r.l, Milan, Italy
Email: $\\{$paolo.fiore, eugenio.moro, antonio.capone,
<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

The introduction of the mm-Wave spectrum into 5G NR promises to bring about
unprecedented data throughput to future mobile wireless networks but comes
with several challenges. Network densification has been proposed as a viable
solution to increase RAN resilience, and the newly introduced Integrated-
Access-and-Backhaul (IAB) is considered a key enabling technology with
compelling cost-reducing opportunities for such dense deployments.
Reconfigurable Intelligent Surfaces (RIS) have recently gained extreme
popularity as they can create Smart Radio Environments by EM wave manipulation
and behave as inexpensive passive relays. However, it is not yet clear what
role this technology can play in a large RAN deployment. With the scope of
filling this gap, we study the blockage resilience of realistic mm-Wave RAN
deployments that use IAB and RIS. The RAN layouts have been optimised by means
of a novel mm-Wave planning tool based on MILP formulation. Numerical results
show how adding RISs to IAB deployments can provide high blockage resistance
levels while significantly reducing the overall network planning cost.

##  I Introduction

Pushed by an increasingly connected society, mobile data demands are
undergoing an unprecedented growth phase that cellular networks based on
sub-6GHz communications are struggling to keep up with [1]. To address this
issue, the relatively untapped millimetre wave (mm-Wave) spectrum portion has
been recently standardized by 3GPP in Release 16. Additionally, given the
larger available bandwidth and the high spectral efficiency of NR, the goal of
multi-gigabit mobile throughput seems to be finally reached. However, mm-wave
communications present a fundamental limitation when applied to the typical
deployment scenarios of Radio Access Networks (RAN). Indeed, given the adverse
propagation due to the increased carrier frequency, opaque objects such as
people, vehicles and foliage interrupting the communication line of sight
(LOS) between base stations and UEs might cause outages. As these objects are
densely distributed in typical urban scenarios, the problem of ensuring RAN
resilience against LOS obstructions becomes critical. When a radio link is
blocked, not much can be done but to connect the UE to a backup base station,
which must be in sight with the terminal. Consequently, the problem of
guaranteeing RAN resilience has to be addressed at the system level by
planning an adequate base station deployment that ensures multiple
connectivity to the UEs. In particular, base station densification can
naturally provide a higher reliability to high-frequency (HF) RAN while also
increasing throughput [2]. However, denser deployments come with additional
challenges, especially in terms of installation and operation costs.
Among the technologies that can potentially address the issues above,
Reconfigurable Intelligent Surfaces (RIS) are gaining vast popularity within
the academic and industrial communities. An RIS is described as a quasi-
passive planar surface that, if properly controlled, can apply several
electromagnetic manipulations to impinging radio waves [3]. In the context of
cost-effective HF RAN reliability, RISs show the capability to redirect and
focus impinging radio waves towards arbitrary directions, effectively behaving
as passive relays. Moreover, prototypal works [4] have shown that realizing
RIS requires inexpensive materials, hinting that such technology can be
exploited to create backup radio paths between base stations and UEs at a
relatively low cost. While the aforementioned passive-relaying behaviour of
RIS has been extensively analyzed at the link level [5], less has been done to
study the integration of RIS at the system level, with a focus on boosting HF
large-scale RAN reliability.
This work aims at filling this research gap by analyzing the resiliency-
boosting potential of RISs when employed in HF RAN. Moreover, we have included
Integrated Access and Backhaul (IAB) in our analysis. IAB is a technology that
minimizes dense mm-wave deployment costs by using in-band backhauling to relay
access traffic. IAB is considered as a critical enabler for a cost-effective
HF RAN [6] and, as such, we argue that a comprehensive analysis cannot refrain
from including this technology. As previously mentioned, RAN reliability is
sensitive to the final position of the installed network equipment. For this
reason, we have developed a network planning model where the IAB nodes and
RISs deployment over a geographic area is optimized to maximize the final RAN
blockage resiliency.

To test the reliability of the planned network during regular operation,
opaque obstacles are randomly dropped into the geographic area. Furthermore, a
self blockage area is added to each UE, which represents the blocking effect
of the human body holding the terminal [7]. For different obstacle densities,
final results are gathered mainly by analyzing the number of UEs still
retaining connectivity after the obstacle drop. This resilience indicator is
evaluated for RIS-enabled IAB networks and for a baseline RAN approach where
only IAB is employed. Results show that while RISs cannot substitute IAB nodes
completely, the two technologies work well together to maintain high levels of
network resilience, with deployment costs lower than those of IAB-only
planning. In particular, we show how RISs are most effective in boosting RAN
reliability under strict budgets, confirming the cost-cutting potential that
this technology is expected to offer.

The remainder of this paper is organized as follows. Section II presents some
works related to IAB, RIS and mm-wave RAN. Section III describes the RAN
system and the planning model. In section IV, we present numerical results
coming from a reliability analysis of RAN layouts produced employing the
planning optimization model. Section V concludes the paper with some final
remarks.

##  II Related Works

Despite the abundant literature on wireless multi-hop network planning started
more than a decade ago [8, 9], a complete planning optimization model for mm-
Wave IAB RANs considering capacity and reliability issues in the presence of
obstacle blockages is still missing.

RISs are a very recent technological outcome [10, 11]. Nevertheless, they are
the main topic of an increasing number of recently published papers. They have
emerged as a more energy-efficient and less costly alternative to traditional
decode-and-forward approaches [12, 13, 14]. Therefore, the main research
direction to date has aimed to evaluate their link-level performances to
establish the best RIS configuration.

Only a few works consider the impact of RISs at a network level, particularly
addressing the fundamental problem of obstacle blockages. Authors in [15]
propose an analysis based on stochastic geometry to study the relationship
between the density of RISs, network devices, obstacles and network
availability. In [16], authors derive the symbol error probability in a mm-
wave wireless mesh network that makes use of RIS. Some of the authors of this
article propose in [17] a first optimization model to plan mm-Wave 5G RANs
considering the RIS placement. This article extends the work by considering a
different network architecture based on the IAB paradigm, the effect of
obstacle blockages, and a new planning approach that leverages multi-
connectivity and guarantees spatial diversity among access links.

To the best of our knowledge, this is the first work proposing a complete
optimization model jointly 1) addressing the network planning of mm-Wave IAB
radio access networks, 2) including the RIS placement and 3) improving the
network reliability in response to sudden obstacles. Thanks to this model we
can shed light on how RISs can be effectively integrated at RAN level, thus
providing several hints on their final design.

##  III RIS-Enhanced Coverage Model

Figure 1: RAN scenario.

In this section, we detail the RAN system, shown in Fig. 1, and planning model
that we employ to generate optimal RAN layouts, which will then be analyzed in
terms of blockage resiliency in Section IV. We consider RISs as passive
beamformers, capable of focusing an impinging radio wave towards arbitrary
directions. This capability can be exploited at a network level to create a
reflected radio path between a transmitter and a receiver, since RISs
effectively behave as passive relays. The tuple comprising a transmitter, a
receiver and a RIS assisting the communications is known as Smart Radio
Connection (SRC) [17] and extends the well-known concept of smart radio
environment [18]. An SRC can naturally provide dual-connectivity, namely
connecting the UE through multiple radio links, which is effective in reducing
outages due to obstacle obstructions in mm-Wave access networks [19]. Indeed,
a RIS can be installed and configured such that it creates an alternative
reflected radio path, which can be exploited to ensure continuity of service
in case of direct link obstructions111Note that, since IAB donors/nodes and
RISs are installed higher than UEs, backhaul and BS-RIS links are
intrinsically more stable. Therefore, we do not consider BS-RIS blockages,
apart from those given by fixed obstacles populating the geographic area.,
thus enhancing the mm-Wave network reliability against blockages. However,
simply deploying enough reconfigurable surfaces and base stations in a
geographic area is not sufficient to guarantee good blockage resilience since
other geometrical factors need to be considered, namely angular separation and
link length [19]. Indeed, a single but sizeable nomadic obstacle could
interrupt both primary and backup links if these were to present low angular
separation, leading to an outage and decreasing the solution’s efficacy.
Moreover, a significant angular separation between primary and reflected links
can mitigate the well-known self-blockage effect caused by the body of the
device holder interrupting the line of sight [7]. Link length represents
another factor influencing the network resilience that can be controlled
during the network planning phase. Indeed, longer radio connections naturally
experience higher probabilities of being blocked by one or more obstacles
[20]. The proposed coverage planning formulation considers both link lengths
and angular separation to maximize the network resilience against nomadic
obstacles and self-blockage events.

We now detail the assumptions and parameters that characterize the proposed
planning formulation. In the following text, parameter indexes are expressed
enclosed in brackets to differentiate them from optimization variables.
Similarly to what has been done in other coverage planning works [8, 19], we
consider a set $\mathcal{C}$ of Candidate Sites (CSs) over a geographic area
covered by a mm-Wave access service. Each candidate site represents the
position where an IAB donor (i.e., a base station with a wired connection to
the core network), an IAB node (i.e., a base station with a wireless backhaul
realy connection) or an RIS can be installed. A set of Test Points (TPs)
$\mathcal{T}$ represents the UE distribution over the same area. Physical
parameters and propagation characteristics, such as transmit power, receiver
sensitivity and attenuation losses, are captured by a binary activation link
parameter $\Delta_{(t,c,r)}^{\text{SRC}}$, which can be pre-computed for all
$(t,c,r)$ tuples. This is equal to 1 only when an SRC can be established
between TP $t\in\mathcal{T}$, a donor or an IAB node installed in CS
$c\in\mathcal{C}$ and an RIS in CS $r\in\mathcal{C}$. Moreover, fixed
obstacles across the geographic area interrupting any line of sight can be
modelled by setting the corresponding link activation parameter to 0.
Similarly, binary parameter $\Delta_{(c,d)}^{\text{BH}}$ indicates whether two
IAB nodes in CSs $c,d\in\mathcal{C}$ can establish a radio backhaul link. TP
and CS are fixed, and thus achievable downlink rates in backhaul and access
can be computed according to radio device characteristics and channel models.
The extreme directivity of mm-Wave downlink transmissions limits the
interference effects, and we assume these achievable rates to be unaffected by
simultaneous transmissions[19]. For each SRC $\left<t,c,r\right>$, parameter
$C_{(t,c,r)}^{\text{DIR}}$ denotes the achievable TP $t$ downlink rate
obtained through the direct link with the IAB node $c$, namely the direct link
capacity. On the other hand, $C_{(t,c,r)}^{\text{REF}}$ indicates the
achievable rate when the RIS-reflected radio path is employed, that is, the
reflected link capacity. Finally, the capacity of a backhaul link established
between two IAB nodes $c$ and $d$ is denoted by the parameter
$C_{(c,d)}^{\text{BH}}$.

We consider each TP as covered when a specific traffic demand can be
guaranteed on both the direct and reflected link. In particular, the parameter
$D$ represents the demand to be guaranteed by the line of sight connection
with the BS. On the RIS-reflected link, a fraction $\xi\in[0,1]$ of the
traffic demand $D$ is guaranteed. This represents the available backup link
throughput, which can be activated when the primary link is experiencing
outages, thanks to the continuous monitoring of the direct link during regular
network operation. Whenever an obstruction is detected, the RIS of the SRC can
be reconfigured to offer the alternative reflected path. In this case, the TP
would experience a throughput degradation given by parameter $\xi$, but the
connectivity would be preserved. As previously mentioned, our model favours
the activation of those SRCs offering high angular separation between the
direct and reflected lines of sight. This is achieved by considering parameter
$\Theta_{(t,c,d)}$, that denotes the smallest angle between CSs $c$ and $d$,
as seen from TP $t$. Parameter $L_{(t,c)}$, representing the distance between
TP $t$ and CS $c$, is used to control the access link length. Instantaneous
reconfiguration of RIS reflecting elements is assumed, such that the surface
can switch to assist different SRCs. However, we allow up to 1 TX-RX pair to
be RIS-assisted at any time, leading to RIS being shared among SRCs on a time
basis. These previous assumptions may result to be technologically challenging
for current RIS hardware manufacturers. However, we believe them to represent
a realistic technological maturity level which should be considered for a
robust investigation of potential RIS benefits. RIS prototypes have presented
a limited array field of view , similar to what happens for uniform planar
antenna arrays [4, 21]. Consequently, the orientation of installed RISs needs
to be such that the lines of sight of the base stations and test points of all
SRCs to which the RIS is assigned fall inside the RIS field of view. In this
work, we define a horizontal field of view angle $F$, and we discard the
vertical222While a vertical field of view usually has a limited impact on the
final network plan, it can be easily included in the model, if needed. field
of view. Finally, the entire network plan is limited to a budget value $B$.
Prices $P^{\text{IAB}},P^{\text{RIS}}$ represent the costs of installing an
IAB and an RIS in any CS, respectively.

Here follow the decision variables on which the proposed planning model is
based:

  * •

$y_{c}^{\text{DON}},y_{c}^{\text{IAB}},y_{c}^{\text{RIS}}\in\\{0,1\\}$:
installation variables equal to 1 if a donor, an IAB node or a RIS is
installed in CS $c\in\mathcal{C}$, 0 otherwise,

  * •

$x_{t,c,r}\in\\{0,1\\}$: SRC activation variable, equal to 1 if RIS in
$r\in\mathcal{C}$ assists the communication between IAB node in
$c\in\mathcal{C}$ and TP $t\in T$, 0 otherwise,

  * •

$z_{c,d}\in\\{0,1\\}$: backhaul link activation equal to 1 if IAB node in
$c\in\mathcal{C}$ is connected to IAB node $d\in\mathcal{C}$, 0 otherwise,

  * •

$f_{c,d}\in\mathbb{R}^{+}$: backhaul traffic flowing from IAB node
$c\in\mathcal{C}$ to IAB node $d\in\mathcal{C}$,

  * •

$t_{c}^{\text{TX}}\in[0,1]$: for any IAB node $c\in\mathcal{C}$, the fraction
of time spent in transmission,

  * •

$\delta_{r}\in[0,2\pi]$: RIS orientation variable, representing the surface
azimuth with respect to a reference direction,

  * •

$l_{t}\in\mathbb{R}^{+}$: average between direct (with IAB node) and secondary
access (with RIS) link lengths covering TP $t\in\mathcal{T}$,

  * •

$\theta_{t}\in[0,\pi]$ angular separation between direct and reflected links
covering TP $t\in\mathcal{T}$.

With the given notation, parameters and decision variables, we now introduce a
MILP (Mixed Linear Linear Programming) formulation of the IAB network planning
problem with RISs:

$\max\sum_{t\in\mathcal{T}}\left\\{\mu\sum_{t\in\mathcal{T}}\frac{\theta_{t}}{\Theta}-(1-\mu)\sum_{t\in\mathcal{T}}\frac{l_{t}}{\hat{L}}\right\\}\\\
$ (1a) s.t.: $\displaystyle y_{c}^{\text{IAB}}+y_{c}^{\text{RIS}}\leq 1$
$\displaystyle\forall c\in\mathcal{C},$ (1b) $\displaystyle
y_{c}^{\text{DON}}\leq y_{c}^{\text{IAB}}$ $\displaystyle\forall
c\in\mathcal{C},$ (1c)
$\displaystyle\sum_{c\in\mathcal{C}}\left(P^{\text{IAB}}y_{c}^{\text{IAB}}+P^{\text{RIS}}y_{c}^{\text{RIS}}\right)\leq
B,$ (1d) $\displaystyle
z_{c,d}\leq\Delta^{\text{BH}}_{(c,d)}\left(y_{c}^{\text{IAB}}+y_{d}^{\text{IAB}}\right)/2,$
$\displaystyle\forall c,d\in\mathcal{C},$ (1e) $\displaystyle
x_{t,d,r}\leq\Delta^{\text{SRC}}_{(t,d,r)}\left(y_{d}^{\text{IAB}}+y_{r}^{\text{RIS}}\right)/2,$
$\displaystyle\forall t\in\mathcal{T},d,r\in\mathcal{C},$ (1f)
$\displaystyle\sum_{d,r\in C}x_{t,d,r}=1,$ $\displaystyle\forall t\in T,$ (1g)
$\displaystyle\sum_{d\in\mathcal{C}}z_{d,c}\leq 1-y_{c}^{\text{DON}},$
$\displaystyle\forall c\in\mathcal{C},$ (1h)
$\displaystyle|\mathcal{T}|Dy_{c}^{\text{DON}}+\sum_{d\in\mathcal{C}}\left(f_{d,c}-f_{c,d}\right)-\sum_{\begin{subarray}{c}t\in\mathcal{T}\\\
r\in\mathcal{C}\end{subarray}}Dx_{t,d,r}=0,$ $\displaystyle\forall c\in C,$
(1i) $\displaystyle f_{c,d}\leq C_{(c,d)}^{\text{BH}}z_{c,d},$
$\displaystyle\forall c,d\in\mathcal{C},$ (1j) $\displaystyle
t_{c}^{\text{TX}}=\sum_{d\in\mathcal{C}}\frac{f_{c,d}}{C_{(c,d)}^{\text{BH}}}+\sum_{\begin{subarray}{c}t\in\mathcal{T}\\\
r\in\mathcal{C}\end{subarray}}\max\left\\{\frac{D}{C_{(t,d,r)}^{\text{DIR}}},\frac{\xi
D}{C_{(t,d,r)}^{\text{REF}}}\right\\}x_{t,d,r}$ $\displaystyle\forall
c\in\mathcal{C}$ (1k)
$\displaystyle\sum_{d\in\mathcal{C}}\frac{f_{d,c}}{C_{(d,c)}^{\text{BH}}}+t_{c}^{\text{TX}}\leq
1$ $\displaystyle\forall c\in\mathcal{C},$ (1l)
$\displaystyle\sum_{\begin{subarray}{c}t\in\mathcal{T}\\\
d\in\mathcal{C}\end{subarray}}x_{t,d,r}\frac{\xi
D}{C_{(t,d,r)}^{\text{REF}}}\leq 1,$ $\displaystyle\forall r\in\mathcal{C},$
(1n) $\displaystyle\phi_{r}\geq\Phi^{\text{A}}_{(r,t)}-F/2-2\pi(1-x_{t,d,r})$
$\displaystyle\forall t\in\mathcal{T},d,r\in\mathcal{C},$ (1o)
$\displaystyle\phi_{r}\leq\Phi^{\text{A}}_{(r,t)}+F/2+2\pi(1-x_{t,d,r})$
$\displaystyle\forall t\in\mathcal{T},d,r\in\mathcal{C},$ (1p)
$\displaystyle\phi_{r}\geq\Phi^{\text{B}}_{(r,d)}-F/2-2\pi(1-x_{t,d,r})$
$\displaystyle\forall t\in\mathcal{T},d,r\in\mathcal{C},$ (1q)
$\displaystyle\phi_{r}\leq\Phi^{\text{B}}_{(r,d)}+F/2+2\pi(1-x_{t,d,r})$
$\displaystyle\forall t\in\mathcal{T},d,r\in\mathcal{C},$ (1r)
$\displaystyle\theta_{t}\leq\Theta_{(t,c,r)}+2\pi(1-x_{t,c,r})$
$\displaystyle\forall t\in\mathcal{T},c,r\in\mathcal{C},$ (1s) $\displaystyle
l_{t}\geq\frac{1}{2}\sum_{c,r\in\mathcal{C},v\in
V}x_{t,c,r}(L_{(t,c)}+L_{(t,r)})$ $\displaystyle\forall t\in\mathcal{T}.$ (1t)

The objective function (1a) maximizes the average angular separation over the
planned network while minimizing the average link length[19]. In particular,
parameters $\Theta$ and $\hat{L}$ are used to normalize the angular separation
sum and link length sum over all TPs, while parameter $\mu\in[0,1]$ can be
used to tune the maximization emphasis toward one of the two objectives.
Constraint (1b) makes sure that IAB nodes and RISs are not installed in the
same CS. From a modelling standpoint, a donor is equivalent to an IAB node
connected to the core network. Consequently, a donor can only be active in a
candidate site populated by an IAB node, as stated by constraint (1c).
Constraint (1d) enforce a budget limit $B$ for the network deployment cost,
which is given by the number of installed IAB nodes and RISs and the
respective costs $P^{\text{IAB}},P^{\text{RIS}}$. Using binary link activation
parameters $\Delta_{(t,c,r)}^{\text{SRC}}$, constraint (1e) allows for an SRC
variable to be active only if the necessary radio connections can be
established and if the IAB node and RIS involved in the SRC are installed.
Similarly, constraint (1f) allows for a backhaul link to be active only if the
two nodes are installed, and a radio connection can be established between the
two. Constraint (1g) makes such that each TP is covered by one SRC.

According to standard specifications, IAB networks are expected to assume
spanning-tree topology [22]. In our model, constraint (1h) enforces the
creation of a spanning tree by allowing for up to one ingress link per IAB
node and none for the donor. For each node, the traffic flow entering from the
core network and the parent IAB node is balanced with the traffic leaving the
node towards the associated UEs and downstream IAB nodes through constraint
(1i). Note that the traffic coming from the core is available only at the
donor, and it is equivalent to the single user demand $D$ times the number of
test points $|\mathcal{T}|$. Additionally, the constraint above forces the
activation of exactly one donor, as the traffic would be unbalanced otherwise.
Constraint (1j) is such that no traffic can flow on backhaul links which have
not been activated; this also limits the flow to the backhaul link capacity
$C_{(c,d)}^{\text{BH}}$.

In constraint (1k) we set variable $t_{c}^{\text{TX}}$ to the fraction of time
that each donor/IAB node spends during transmission. We assume that node
resources are shared on a time-division basis (i.e., a node can transmit
either to another node or to a UE at any moment) as specified by 3GPP Rel. 15.
Consequently, quantity $t_{c}^{\text{TX}}$ is given by the sum of the time-
fraction spent transmitting to downstream IAB nodes and the time-fraction
spent transmitting to all the associated test points. The former is computed
by considering the backhaul transmission airtime, namely the ratio between the
flow $f_{c,d}$ and the link capacity $C_{(c,d)}^{\text{BH}}$. Similarly, the
latter can be computed by considering the access transmission airtime.
However, since the node can transmit to each test point through either the
direct or reflected link, the longer between the direct and the reflected
airtime is considered. Constraint (1l) sums the transmission airtime variable
set in the previous constraint with the time-fraction that the node spends in
reception. The sum is then limited to 1, meaning that no more than 100% of the
node time-sharing resources can be occupied. Additionally, this enforces half-
duplex for each node. While each RIS can be part of multiple SRCs, we allow
only one TX-RX pair to be served at any time by a single RIS. Each
reconfigurable surface is thus shared among different SRCs through a time-
division process, similarly to what is assumed for IAB nodes and donors. In
the proposed planning formulation, this is achieved through constraint (1n),
where the cumulative airtime of TPs associated with a RIS is limited to 1.

Constraints from (1o) to (1r) set each RIS orientation such that the
associated IAB nodes and UEs all fall inside its field of view $F$, which is
achieved by means of parameters $\Phi_{(r,t)}^{\text{A}}$ and
$\Phi_{(r,d)}^{\text{B}}$ [17]. These represent the angles between the line
connecting the RIS $r$ to TP $t$ or to CS $c$, respectively, and the reference
direction. Finally, constraint (1s) sets $\theta_{t}$ to the minimum angular
separation between the line connecting the TP with the associated IAB node and
the line connecting the TP with the associated RIS. Constraint (1t) sets
variable $l_{t}$ to the average between the IAB node-TP link length and the
RIS-TP link length.

##  IV Results

In this section, we give a reliability analysis of HF RAN deployments that
have been optimized employing the planning formulation shown in Section III.
In particular, we compare the results given by RIS-enabled planning against a
baseline approach where only donors and IAB nodes can be installed. This IAB-
only formulation is available in the extended version of this work [23]. In
the baseline case, dual connectivity is still guaranteed by covering each TP
with two different IAB nodes instead of relying on a RIS-reflected path.
However, apart from the different radio link nature, all the planning
assumptions, objectives and parameters remain unchanged.

The considered planning instances are characterized by a deployment area of
$300\text{x}400m$ where 25 CSs can be activated, and 15 TPs need to be
covered. Donors and IAB nodes are modelled as 64-elements uniform linear array
antennas with a transmission power of $30dBm$ and carrier frequency set to
$28GHz$. Receivers are modelled as omnidirectional antennas. RISs are modeled
as planar surfaces of $50\text{x}50cm$ containing $10^{4}$ passive reflecting
elements, which is compatible with a $\lambda/2$ inter-element spacing [3].
The path-loss model of [20] and the received power formulas in [5] were
employed to precompute the average SNR of the links of every SRC combination.
Finally, achievable rates were extracted according to NR modulation and coding
scheme. TP traffic demand over primary links is set to $100Mbps$. The
degradation factor $\xi$ is set to $0.5$, leading to a demand of $50Mbps$
guaranteed on each secondary link. All the results in this section were
obtained by averaging 20 random drops of CS and TP positions. Random instances
were generated though MATLAB and planning optimization was solved by CPLEX.

###  IV-A Budget Sensitivity

(a) Average angular separation

(b) Average SRC link length

Figure 2: Angular separation and link length sensitivity to budget variations.

As RISs are expected to have an impact on deployment costs, we carried out a
budget sensitivity analysis by evaluating the blockage resilience indicators,
i.e. average angular separation and link length, for different budget planning
values. A clear indication of the cost of deploying a RIS has yet to be found
in the literature. However, prototypes have shown how a RIS can be realized
with inexpensive materials and production processes. Thus, an order of
magnitude between the cost of IAB nodes and RIS seems reasonable.
Consequently, we have set to 1 the cost of deploying an IAB node and to 0.1
the price of installing a RIS. In Figures 2a and 2b we plot the blockage
resilience indicators against a planning budget that spans from 3 to 10 units.
In particular, in Figure 2a we compare the average angular separation of RIS-
enabled planning (solid lines) and IAB-only planning (dashed lines). The
comparison is carried out by considering different values of $\mu$ in the
objective function (1a). Namely, we evaluated the results when either only the
maximization of the average angular separation is considered ($\mu=1$), or
when only the minimization of the link length is considered ($\mu=0$).
Furthermore, we have analyzed $\mu=0.5$, which represents a balance between
the two objectives. A similar analysis is shown in Fig. 2b for the average SRC
link length. In both figures and for any considered $\mu$, the dotted lines,
corresponding to the baseline approach, are interrupted for $B<5$. No solution
could be found with these budget values. That is, a traditional HF RAN cannot
guarantee the minimum rates when no RISs are installed. On the other hand,
RIS-enabled planning is still feasible for these values, showing how RIS can
be used to solve planning scenarios with strict budgets. As the budget
increases past 5 units, the baseline approach can be brought to a solution.
However, RIS-enabled planning generally outperforms the IAB-only approach in
terms of both angular separation and link length. Indeed, a budget increase of
approximately 40% is required such that the IAB-only model can reach the same
level of angular separation and link length of RIS-enabled planning. This
behaviour is due to the reduced RIS installation costs that allow more RISs to
be installed even with lower budgets. Indeed, in our results, the average
number of installed IAB nodes for the baseline approach is always 1 to 3 nodes
higher than the case when RIS are available. This suggests that, while the
number of necessary IAB nodes can be reduced by employing RISs, these cannot
be considered a complete substitute of IAB nodes since a considerable number
of them need to be activated. Finally, for very large budget values, both RIS-
enabled and traditional HF RAN approaches reach the same angular separation
and link length level. This is an expected result since such budgets allow the
activation of the optimal set of candidate sites that bring the aforementioned
topological properties to their saturation level, independently on the
technology employed for the backup link. In other words, when the deployment
is not budget-restricted, there is no significant difference between
installing RISs or IAB nodes.

###  IV-B Obstacle Deployment

In the previous subsection, we have numerically evaluated the angular
separation and link length of optimized RAN layouts. These topological
properties, when properly optimized, are expected to give robustness to HF
RAN. In this subsection, we enrich this analysis by evaluating how these
properties impact the resilience of the resulting planned network during
normal operating conditions. To do this, we drop randomly oriented, 5-meter-
long linear obstacles into random positions of the planning area.
Additionally, we have included a self-blockage angular sector, representing
the human body obstruction to each TP. The angle span is either $2\pi/3$ or
$8\pi/9$ with a probability of $0.5$ each, and it is randomly oriented [24].
Any radio link that falls inside the self blockage sector or that is crossed
by a randomly dropped obstacle is considered blocked. Figure 3a shows the
percentage of served TPs (i.e., at least one between primary and secondary
link is not blocked) for an increasing number of dropped obstacles and a
planning budget of 5 units. In general, the baseline approach (dashed lines)
is consistently outperformed by the RIS-enabled (solid lines), confirming the
results of the previous paragraph. Indeed, Figure 3b shows that RIS-enabled
planning results in up to 50% more served TPs with respect to the baseline
approach. Additionally, Figure 3a shows how the link length-minimizing
objective function ($\mu=0$) outperforms the other two objective approaches as
soon as the dropped obstacles increase past 300. This suggests that the
planning objective should be chosen according to the expected obstacle
density.

(a) Percentage of served TPs

(b) Resilience gain

Figure 3: Impact of obstacles on TPs in outage, $B=5$.

(a) Percentage of served TPs

(b) Resilience gain

Figure 4: Impact of obstacles on TPs in outage, $B=10$.

As previously mentioned, higher budget levels allow for the installation of
more IAB nodes, and the objective function values of the baseline converge to
those of the RIS-enabled planning. Consequently, the resilience gain of the
RIS-based approach is shortened for $B=10$, as shown in Figure 4. In
particular, Figure 4a shows a reduced difference between the percentage of
served TPs of the baseline and RIS-enabled approach when the budget value is
set to $10$ units. Similarly, the resilience gain of using RISs with $B=10$,
in Figure 4b, is limited to a maximum of 10%. Finally, these results confirm
again how RISs are better employed in budget-restricted planning scenarios, as
they effectively provide cost-effective blockage resilience through link
densification.

##  V Conclusion

We have analyzed the resilience of optimized mm-Wave IAB RAN deployments with
RISs. To do so, we have developed a novel MILP network planning model that
privileges topological characteristics such as angular separation and link
length, proven to be effective in enhancing RAN reliability against random
obstacles. In our evaluation campaigns, we have compared the results of the
RIS-enabled planning against a baseline approach where no RIS is installed.
Numerical results showed an increase in access resilience and a reduction in
budget expenditure through the usage of RISs, compared to the more traditional
IAB-only RAN.

## Acknowledgment

The research in this paper has been carried out in the framework of Huawei-
Politecnico di Milano Joint Research Lab. The Authors acknowledge Huawei Milan
research center for the collaboration.

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##  VI Additional material

We hereby detail the planning formulation for an HF RAN where each test point
is associated with a primary and secondary IAB node. This formulation was
employed to produce baseline results in Section IV and it is based on the same
assumptions and parameters described in Section III.
In this formulation, parameter $U^{\text{WRD}}$ represents the capacity of the
wired connection between donors and the core network, which is assumed to be
infinite. Parameter $\Delta_{(t,d)}^{\text{ACC}}$ expresses the possibility of
activating an access link between TP $t\in\mathcal{T}$ and CS
$c\in\mathcal{C}$.
The optimization variables are the following:

  * •

$y_{c}^{\text{DON}},y_{c}^{\text{IAB}}\in\\{0,1\\}$: installation variables
equal to 1 if a donor or an IAB node is installed in CS $c\in\mathcal{C}$, 0
otherwise,

  * •

$x_{t,c}\in\\{0,1\\}$: primary access link activation variable, equal to 1 if
test point $t\in\mathcal{T}$ is covered by a primary link with donor/IAB node
in CS $c\in\mathcal{C}$, 0 otherwise,

  * •

$s_{t,c}\in\\{0,1\\}$: backup access link activation variable, equal to 1 if
test point $t\in\mathcal{T}$ is covered by a backup link with donor/IAB node
in CS $c\in\mathcal{C}$, 0 otherwise,

  * •

$z_{c,d}\in\\{0,1\\}$: backhaul link activation equal to 1 if BS in
$c\in\mathcal{C}$ is connected to BS $d\in\mathcal{C}$, 0 otherwise,

  * •

$f_{c,d}\in\mathbb{R}^{+}$: backhaul traffic flowing from BS $c\in\mathcal{C}$
to BS $d\in\mathcal{C}$,

  * •

$w_{c}\in\mathbb{R}^{+}$: traffic flowing from the core network into donor
$c\in\mathcal{C}$ through a wired connection,

  * •

$t_{c}^{\text{TX}}\in[0,1]$: for any BS $c\in\mathcal{C}$, the fraction of
time spent in transmission,

  * •

$l_{t}\in\mathbb{R}^{+}$: average between primary and backup access link
lengths covering TP $t\in\mathcal{T}$,

  * •

$\theta_{t}\in[0,\pi]$ angular separation between primary and backup links
covering TP $t\in\mathcal{T}$.

Here follows the MILP formulation used to optimize HF IAB RAN deployments:

$\max\sum_{t\in\mathcal{T}}\left\\{\mu\sum_{t\in\mathcal{T}}\frac{\theta_{t}}{\Theta}+(1-\mu)\sum_{t\in\mathcal{T}}\frac{l_{t}}{\hat{L}}\right\\}$
(2a) s.t.: $\displaystyle y_{c}^{\text{DON}}\leq y_{c}^{\text{IAB}}$
$\displaystyle\forall c\in\mathcal{C},$ (2b)
$\displaystyle\sum_{c\in\mathcal{C}}y_{c}^{\text{DON}}\leq 1,$ (2c)
$\displaystyle\sum_{c\in\mathcal{C}}P^{\text{IAB}}y_{c}^{\text{IAB}}\leq B,$
(2d) $\displaystyle
z_{c,d}\leq\Delta^{\text{BH}}_{c,d}\left(y_{c}^{\text{IAB}}+y_{d}^{\text{IAB}}\right)/2,$
$\displaystyle\forall c,d\in\mathcal{C},$ (2e) $\displaystyle
x_{t,d}\leq\Delta^{\text{ACC}}_{(t,d)}y_{d}^{\text{IAB}},$
$\displaystyle\forall t\in\mathcal{T},d\in\mathcal{C},$ (2f) $\displaystyle
s_{t,d}\leq\Delta^{\text{ACC}}_{(t,d)}y_{d}^{\text{IAB}},$
$\displaystyle\forall t\in\mathcal{T},d\in\mathcal{C},$ (2g)
$\displaystyle\sum_{d\in C}x_{t,d}=1,$ $\displaystyle\forall t\in T,$ (2h)
$\displaystyle\sum_{d\in C}s_{t,d}=1,$ $\displaystyle\forall t\in T,$ (2i)
$\displaystyle\sum_{d\in\mathcal{C}}z_{d,c}\leq 1-y_{c}^{\text{DON}},$
$\displaystyle\forall c\in\mathcal{C},$ (2j) $\displaystyle
w_{c}+\sum_{d\in\mathcal{C}}\left(f_{d,c}-f_{c,d}\right)-\sum_{t\in\mathcal{T}}(Dx_{t,c}+\xi
Ds_{t,c})=0,$ $\displaystyle\forall c\in C,$ (2k) $\displaystyle w_{c}\leq
U^{\text{WRD}}y_{c}^{\text{DON}},$ $\displaystyle\forall c\in\mathcal{C},$
(2l) $\displaystyle f_{c,d}\leq C_{(c,d)}^{\text{BH}}z_{c,d},$
$\displaystyle\forall c,d\in\mathcal{C},$ (2m) $\displaystyle
t_{c}^{\text{TX}}=\sum_{d\in\mathcal{C}}\frac{f_{c,d}}{C_{(c,d)}^{\text{BH}}}+\sum_{t\in\mathcal{T}}\left(\frac{D}{C_{(t,c)}^{\text{ACC}}}x_{t,c}+\frac{\xi
D}{C_{(t,c)}^{\text{ACC}}}s_{t,c}\right),$ $\displaystyle\forall
c\in\mathcal{C},$ (2n) $\displaystyle
t_{c}^{\text{TX}}+\sum_{d\in\mathcal{C}}\frac{f_{d,c}}{C_{(d,c)}^{\text{BH}}}\leq
1,$ $\displaystyle\forall c\in\mathcal{C},$ (2o)
$\displaystyle\theta_{t}\leq\Theta_{(t,c,r)}+2\pi(2-x_{t,c}-s_{t,r})$
$\displaystyle\forall t\in\mathcal{T},c,r\in\mathcal{C},$ (2p) $\displaystyle
l_{t}\geq\frac{1}{2}\sum_{c,r\in\mathcal{C}}\left(x_{t,c}L_{(t,c)}+s_{t,r}L_{(t,r)}\right)$
$\displaystyle\forall t\in\mathcal{T}.$ (2q)


11institutetext: Max Planck Institute for Dynamics and Self-organization,
Göttingen, Germany

# Oscillation patterns in active emulsion networks

Shashi Thutupalli _Present address:_ Princeton University, Princeton, NJ, USA
Stephan Herminghaus<EMAIL_ADDRESS>
(Received: date / Revised version: date)

###### Abstract

We study water-in-oil emulsion droplets, running the Belousov-Zhabotinsky
reaction, that form a new type of active matter unit. These droplets,
stabilised by surfactants dispersed in the oil medium, are capable of internal
chemical oscillations and also self-propulsion due to dynamic interfacial
instabilities that result from the chemical reactions. The chemical
oscillations can couple via the exchange of activator and inhibitor type of
reaction intermediates across the droplets under precise conditions of
surfactant bilayer formation between the droplets. Here we present the
synchronization behaviour of networks of such chemical oscillators and show
that the resulting dynamics depend on the network topology. Further, we
demonstrate that the motion of droplets can be synchronized with the chemical
oscillations inside the droplets, leading to exciting possibilities in future
studies of active matter.

##  1 Introduction

There has been rapidly growing interest recently in so-called active matter,
which refers to open (soft) matter systems exhibiting complex dynamics and
collective behavior reminiscent of living organisms. Spontaneous oscillations
and self-sustained motion ramaswamy_mechanics_2010 ; kruse_oscillations_2005
represent the simplest examples of such complex dynamics and hence are ideally
suited for a theoretical analysis of the interactions and dynamic properties
of a complex active system. Systems such as those undergoing catalytic
reactions at interfaces, the autocatalytic Belousov-Zhabotinsky (BZ) reaction,
social amoeba under stress, populations of fireflies or the cells of heart
muscle tissue can all display spatio-temporal oscillatory behaviors following
similar patterns, which may be modelled by means of reaction-diffusion
dynamics or suitable mean-field approaches kuramoto ; Strogatz2000 . Self-
propelling entities such as motile bacteria, sperm, birds, and fish, or
analogous physical systems such as active emulsions have been found to exhibit
remarkable similarities in their collective behavior as well dos_santos_free-
running_1995 ; sumino_self-running_2005 ; linke_self-propelled_2006 ;
Howse2007 ; thutupalli_njp_2011 . There has been tremendous theoretical and
experimental progress towards the understanding of such systems in terms of
the dynamics of oscillators and motile particles. However, most of the
treatment of these phenomena has been in isolation ramaswamy_mechanics_2010 ;
kuramoto  and in most of the studies of the collective behavior of active
matter, the individual unit has typically been abstracted to be either a point
like self propelled particle or a simple phase oscillator kuramoto ;
Strogatz2000 ; thutupalli_njp_2011 ; toner_hydrodynamics_2005 ;
bhattacharya_collective_2010 ; Schaller2010 ; guttal_social_2010 ;
romanczuk_collective_2009 .

While these studies have been very successful in understanding a range of
collective phenomena and synchronization, this is clearly not the complete
picture, as is obvious in many biological processes. For instance, during the
chemotactic self-organization of amoeba and in cellular organization during
embryogenesis, the internal dynamics are entwined with the macroscopic order
that emerges due to cell motility. These internal dynamics of an individual
unit, most often, manifest as biochemical oscillations, linked together with
the motility of the unit. Even in simple physical systems, it has been
observed that there is spontaneous symmetry breaking and emergence of
unexpected complex behavior when the internal degrees of freedom of coupled
non-equilibrium entities are taken into account danTanakaPRL ;
abramsChimeraPRL ; chimeraMetronomes ; erikChimerasChaos . Therefore, it may
be expected that a range of rich collective phenomena in active matter might
open up when the internal dynamics such as oscillations are studied together
with the resultant (or already existing) dynamics such as motility.

Here, we introduce a system that can potentially be a simple table-top
experiment to study the interplay between the internal dynamics of an
individual unit and its motion, and hence the collective behavior of the whole
system. Specifically, we enclose the Belousov-Zhabotinsky reaction in emulsion
droplets of a few tens to hundreds of microns in diameter to form chemical
oscillators. These chemical oscillators can also sustain self-propelled motion
with respect to the surrounding medium due to interfacial instabilities and
Marangoni stresses.

##  2 Experimental Techniques

Our chemical oscillators are made from incorporating the BZ reaction mixture
in aqueous droplets in an external oil phase of squalane contaning mono-olein
as surfactant. The droplets for these experiments were generated using a flow
focussing channel geometry in a PDMS microfluidic chip as shown in Fig. 1
RepProgPhys2012 . In order to prevent any pre-reaction and the formation of
unwanted gaseous bubbles of carbon-di-oxide, the BZ reaction mixture is
separated into two parts and they are combined on chip. The two parts are
created in stock with concentrations as follows: (i) 500 mM sulphuric acid
($\rm H_{2}SO_{4}$) and 280 mM sodium bromate ($\rm NaBrO_{3}$) (ii) 300 - 800
mM malonic acid ($\rm C_{3}H_{4}O_{4}$) and 3 mM ferroin
($C_{36}H_{24}FeN_{6}O_{4}S$). The concentration of the mono-olein in the
squalane ranges between 25 - 100 mM.

Figure 1: Production of monodisperse oscillator droplets. Left: The BZ
reaction consists of two loops (i) an autocatalytic and (ii) an inhibitory
cycle. The reaction state can be visualised by the colour of the ferroin
catalyst. In our setting, an additional reaction with the unsaturated mono-
olein surfactant occurs as shown. Right: The contents of the BZ reaction are
mixed on the microfluidic chip to prevent any pre-reaction. Seen through an
optical 480/20 nm notch filter, the transition from red colour to the blue
colour of the BZ reaction is seen by the change in the brightness of the
droplet.

As can be seen from the left panel of Fig. 1, the BZ reaction consists of an
autocatalytic cycle in which $\rm HBrO_{2}$ catalyses its own production via
the reduction of the ferroin catalyst, which changes its colour rapidly from
red to blue in response. This is when the inhibitory cycle proceeds, leading
to a slow production of bromine which quenches the autocatalysis. The effect
of this is a gradual change of the catalyst back from the blue colour to red.
In our case, an additional side-reaction occurs due to the addition of mono-
olein as a surfactant, which is used to stabilize the droplets against
coalescence. Since the surfactant has an unsaturated hydrocarbon chain as
shown, some of the bromine that is produced in the inhibitory cycle rapidly
reacts with the unsaturated bond. As we will discuss in more detail below,
this ’trapping’ of the bromine by the surfactant significantly affects the
coupling between droplet oscillators in our setup.

Figure 2: Storage of droplet oscillations in one and two dimensional
confinement for observation of their dynamics.

The droplet oscillators are stored as a monolayer in either a one-dimensional
(1d) or two-dimensional (2d) arrangement, as shown in Fig. 2. The 1d array is
created within a glass capillary with a square cross-section of inner width
100 $\rm\mu$m and outer width 135 $\rm\mu$m (Hilgenberg GmbH, Germany). The
inner walls of the capillary are hydrophobised using a coat of commerically
available hydrophobising agent ’Nano-protect’ (W5 Carcare). The 2d array is
created between two similarly hydrophobised glass slides with a PDMS spacer.
The reaction dynamics are recorded by video microscopy on an inverted
microscope (Olympus IX 81) through an appropriate optical filter. As described
earlier, the BZ reaction dynamics can be followed by the colour of the
catalyst as it changes from red to blue and vice versa. The optical filter we
chose is therefore a notch filter of 480/20 nm wavelength such that the red
colour of the catalyst has less transmittance through the filter. Droplets are
identified from the recorded images using Image-Pro Plus (Media Cybernetics)
as shown in Fig. 3 (left panel). The BZ oscillations within the droplet are
then identified by measuring the mean intensity value of the droplet. They are
recorded as traces similar to those of a relaxation oscillator as seen in the
right panel of Fig. 3. The sudden rise of intensity corresponds to the
autocatalytic cycle of the BZ reaction with the catalyst changing from red to
blue colour, and the gradual fall in intensity corresponds to the release of
bromine in the reaction, thus changing the catalyst colour back to red.
Further analysis on the obtained data as described in the results section is
done using MATLAB.

Figure 3: Image processing to identify the droplet oscillators and record
their dynamics.

##  3 Results and Discussion

###  3.1 Isolated BZ oscillators

The BZ oscillators described here are a closed reactor system i.e. there is no
cycling of reactants and final products during the course of the experiment.
Therefore all the reactants and the resultant products remain within the
droplet, except some outflux of promoter and inhibitor into the oil phase. As
a result, the nature of the oscillations gradually changes with time. As soon
as the experiment is started, the oscillation is set by the initial reaction
conditions and the amplitude of the oscillations and the frequency change as
time proceeds. This can be seen in Fig. 4. As time proceeds, the amplitude of
the oscillations reduces significantly, until they die out completely. The
frequency of the oscillation, shown in black, is gradually reduced as well. In
a sense, however, the BZ oscillators provide their own clock, and the
oscillators suggest themselves as a time normal of the experiment if
applicable. In any case, we did not observe any qualitative change of the
behaviour of our system as time proceeded and droplet oscillations slowed
down.

Figure 4: BZ oscillations in a closed reactor. The oscillation trace and its
corresponding frequency (black) are plotted as a function of time.

The BZ oscillators are suspended in an oil phase consisting of squalane, with
mono-olein at concentrations well above the critical micelle concentration
(CMC). The mono-olein serves two purposes. First, it forms dense surfactant
layers at the oil/water interface, which readily form bilayer membranes if
brought into close proximity. Second, the C=C double bond in the mono-olein
molecule acts as an efficient scavenger for bromine, since the latter rapidly
reacts with this site. The oil phase is thus expected to efficiently suppress
coupling between neighboring droplets, which is mediated by the exitatory and
the inhibitory species. That this is indeed the case can be seen in Fig. 5
which shows a two dimensional hexagonal packing of BZ oscillators. The
spherical shape of the droplets in the packing clearly shows that there is oil
between the droplets and that bilayer membranes have not yet formed
thutupalli_SM_2011 . The oscillation trace of a single oscillator is shown in
the lower panel of Fig. 5. We note that in our experiments we do not see a
systematic dependance of the oscillation frequency on the droplet size. When
such isolated droplets are close to each other, in spite of the fact that the
diffusion of the excitatory and inhibitory species can indeed cause coupling
between droplet, they are observed to be uncoupled. This is due to the fact
that, as we discussed before, they might be trapped via reaction with the
surfactant molecules.

Figure 5: Droplet oscillators in a hexagonal packing geometry within a PDMS
microchannel. Top: The different intensities of the droplets show the
different BZ reaction states within each droplet for two different droplet
sizes. Each droplet acts like an isolated individual oscillator without any
coupling with its neighbours. Image contrast is enhanced for better
visualization. Scale bar is 150 microns. Bottom: The intensity trace for a
single droplet is shown as a function of time. The constancy of the frequency
and amplitude of the oscillations can be clearly seen.

However, bilayer membranes form spontaneously between the droplets
thutupalli_SM_2011 , and this happens in the case of the droplet oscillators
too. As soon as bilayers form between droplets, their interfaces touch each
other very closely such that the droplets are not perfectly spherical anymore.
Consequently, the packing fraction increases as seen in Fig. 6, where the gaps
between the droplets due to oil that existed before bilayer formation are now
reduced significantly. Once the bilayers are formed, completely different
oscillatory dynamics are seen. Previously, we demonstrated that oscillator
coupling can be initiated by the formation of a bilayer membrane between the
oscillator droplets thutupalli_SM_2011 . Often, waves of synchronised activity
such as travelling waves are seen as in Fig. 6. Therefore we see a switch from
the individual to collective dynamics of the oscillators when bilayer networks
are formed. We discuss this aspect in greater detail in the next section.

Figure 6: The formation of travelling waves when bilayer membranes are formed
between oscillator droplets. Each image is 5 seconds apart. The droplet
diameter is 30 microns.

###  3.2 Synchronization patterns

Patterns such as pacemaker driven target waves, travelling waves and spirals
are most commonly seen in large assemblies of coupled oscillators. The BZ
droplet oscillators, connected by bilayer membranes, also give rise to a rich
variety of collective dynamics. In the present section, we discuss the various
patterns that emerge in connected networks of oscillators and the dependance
on the network topology of the type of behaviour that emerges. The
discreteness of the droplet oscillators allows us to clearly identify trigger
locations within the networks. All the following experiments are done with a
BZ reaction mixture as described in the experimental section, with a malonic
acid concentration of 500 mM.

First, we discuss the formation of target waves. These are characterised by a
pacemaker core which periodically tiggers excitatory waves that spread from
the core center outward. In our system, we observe that pacemakers
spontaneously emerge in the center of connected droplet ’islands’ or
’peninsulas’. An ’island’ is comprised of connected droplets as shown in the
left panel of Fig. 7 with the outer edges of the ’island’ open to the mono-
olein filled oil phase. A ’peninsula’ is a similar structure and is connected
by a narrow bridge of one or two droplets to a neighbouring ’island’. As we
discussed before, the inhibitory (bromine) and the excitatory ($\rm
BrO^{\cdot}_{2}$) components of the BZ reaction readily diffuse into the
external oil phase, where they are trapped by the surfactant. Therefore, at
the edges of the island, the oscillatory droplets lose their inhibitory and
excitatory components to the external oil phase. However, at the center of the
island, the concentration of the BZ coupling species increases since they come
in from all sides. Depending on the relative concentrations of the inbitory
and excitatory components, the center droplet can therefore either ’turn off’
(i.e. oscillations are inhibited) or trigger an oscillation. For a malonic
acid concentration of 500 mM together with the other concentrations as
described in the experimental section, we find that an oscillation is
triggered in the central droplet as can be seen in the right panel of Fig. 7.
This trigger from the central droplet then propagates outward as a target wave
throughout the ’island’. If it is a ’peninsula’ the connecting bridge can
couple the wave to the neighbouring ’island’ as well. This pattern then
repeats periodically. We find that droplets which are not connected via a
bilayer to the synchronously oscillating cluster are quite likely to not
oscillate at all. This represents an instance of quorum sensing, as reported
before in a similar system Showalter_QS_PRL .

Figure 7: Formation of a target pattern in a ’island’ or ’peninsula’ type of
droplet network. Top: A schematic of a hexagonal arrangement of droplets which
form an ’island’. At the outer edges of the structure, the excitatory and the
inhibitory components are lost to the oil phase (shown by the arrows), while
in the center, they are concentrated leading to the formation of pacemaker
center. Bottom: A target pattern develops within a ’peninsula’ of droplet
oscillators. The excitation and wave pattern are shown in blue for easy
visualization. The scale bar is 500 microns.

Next, we sought if we could induce the pacemaker patterns by confining the
oscillator droplets within a channel made of PDMS. In such a scenario as shown
in Fig. 8, the PDMS walls of the channel, in addition to the oil phase, act as
sinks for the BZ reaction species. Therefore, we expect that along the length
of the channel, multiple pacemaker centers form, each triggering target waves.
That this is indeed the case, can be seen in the right panel of Fig. 8. The
triggering of a wave from a core can be seen in the image sequence shown. In
addition, a wave can be seen coming in from the right of the images, clearly
triggered by a pacemaker upstream in the channel. Indeed there were also waves
coming in the from the left side, but are not shown here.

Figure 8: Formation of target waves with multiple pacemaker centers in a
oscillator network confined in a PDMS microchannel. Top: Schematic of the
oscillators in a PDMS channel. PDMS, in addition to the oil phase, absorbs the
excitatory and inhibitory components of the BZ at the edges (shown by the
arrows). Bottom: Two target wave patterns seen in the channel. One target wave
is forming at a pacemaker center clearly visible. The center of target pattern
coming in from the right is not visible.

Next, for the same concentrations, we looked at a very large network of
hexagonally packed droplet oscillators, such that the edges are too far away
from the cores to have a significant impact. This is shown in Fig. 9. In such
a case, we see the spontaneous emergence of travelling waves across the
network. Indeed, it may be expected that since the BZ concentrations are
rather uniform over the network, a random trigger in one of the oscillators
can set off a cascading wave of activity, which repeats periodically. However,
we were not able in this scenario to find the precise conditions and locations
at which the waves were triggered.

Figure 9: Travelling waves are formed in large densely connected oscillator
networks. Each image is spaced 5 seconds apart. The excitation is coloured
blue for easy visualization.

Spiral waves formed in our experiments, when the hexagonal packing was not
perfect such that not every oscillator is coupled to 6 nearest neighbours.
Yet, the networks were not so sparse as to form ’islands’ or peninsulas’,
where target waves were predominant. An instance of a spiral is seen in Fig.
10. A spiral wave can be clearly seen among the oscillator population. A
closer look into the network reveals that the local network of each oscillator
is not complete according to the 2-dimensional hexagonal packing. The lack of
local connections creates a refractory effect on the excitatory wave due to
the different speeds it travels at, in the different directions. This causes
the wave to turn and eventually forms a spiral or other rotary patterns
depending on the exact topology of the network. Such defects are well known to
provide cores for spiral waves also in other systems DictySpiral1974 ;
LutherHeartSpiral2011

Figure 10: Formation of spirals in oscillator networks. Top: A spiral can be
seen clearly in the oscillator population. Bottom: Image of the network at
higher magnification reavealing the lack of perfect local connectivity for
each droplet. Scale bar is 150 microns.

Finally, we note that the effect of the bilayer membrane is not just to easily
pass the various species of the BZ reaction from one oscillator to another,
such that a discrimination of the ’individual oscillator’ is simply lost. In
such a case, the behaviour of the oscillator network can be considered to be
the same as that of the BZ reaction in the bulk, in a 2d homogeneous planar
system. However, more complex relationships between neighbouring oscillators
connected by a bilayer are seen. As we mentioned before, both the excitatory
and inhibitory components of the BZ reaction can traverse the bilayer. The
formation of the target patterns as described before indicated that the BZ
mixture used in our experiments is excitatory i.e. the excitatory coupling
wins over the inhibitory coupling in determining the state of the coupled
oscillators, leading to wave like patterns as we have seen so far. However, it
has been reported in literature Toiya2008 ; Toiya2010  that due to inhibitory
coupling between BZ oscillators, it is possible to generate patterns that
strongly differ from wave-like patterns. We increased the concentration of
malonic acid to 700 mM compared to the 500 mM used for the previous
experiments. It is expected that increasing the concentration of the malonic
acid results in a greater production of the inhibitor, bromine, as shown in
the BZ reaction schematic in Fig. 1, thus possibly leading to an inhibitory
coupling effect. When the coupling is inhibitory i.e. non-excitatory, we
expect that wave like patterns will not result. As anticipated, the increase
in the concentration of Malonic acid resulted in a non-wave-like pattern as
shown in Fig. 11 where every oscillator droplet is found to be in strict anti-
phase with its neighbour. This can be understood to be a complicated interplay
between the inhibitory and excitatory coupling. In fact it has been shown that
the anti-phase state is an attractor for inhibitory coupling Toiya2008 ;
Toiya2010 . However, in such models of inhibitory coupling, the interdroplet
distance is quite large as compared to our experiments where the droplets are
separated only by a nanometric membrane. This illustrates that the membrane
between the oscillator droplets plays an important role in preserving the
individual properties of each oscillator. These studies, though only
demonstrative in the present work, must be performed in greater detail in
order to quantify the various synchronization patterns and their relation to
the network topology. In particular, a knowledge of the permeability of the
membrane to the various coupling intermediates is crucial to have predictive
control over the oscillator behaviour.

Figure 11: Antiphase pattern in a 1 dimensional oscillator network. Top:
Droplet oscillators in a glass microcapillary. Each droplet pair is connected
by bilayer membranes. The droplet diameter is 100 microns Bottom: Time trace
of the droplet oscillations shown for the three droplets in the center of the
top image. The red, blue and green traces correspond to the droplets marked as
shown.

##  4 Summary and Outlook

Active emulsions, consisting of chemical micro-oscillator droplets as
presented here may provide a crucial first step towards the realization of
active soft matter with complex dynamic functions. The Belousov-Zhabotinsky
reaction used here has been studied as a paradigm system for dynamical and
pattern forming systems for many years. In the present setting of using it
within microfluidic emulsion droplets, qualitatively new phenomena emerge due
to the interplay between the droplet network topologies and the type of
coupling between the oscillators. As we have shown, the bilayer membranes,
which form spontaneouly between adjacent droplets, play a crucial role in the
coupling and synchronization dynamics. In combination with our previous
results thutupalli_SM_2011 , this opens up the possibility to construct self-
organizing dynamic soft matter systems.

Figure 12: A self propelled droplet with oscillating BZ chemical reaction
taking place in the droplet. (a) Time snaps of a chemical wave within the
droplet (diameter $\rm\sim 600microns$). The droplet moves in the direction of
the wave propagation. (b) The speed of the above droplet shows roughly
periodic oscillations corresponding to the BZ waves inside the droplet. (c)
When the droplet size is reduced to $\rm\sim 80microns$ in diameter, the waves
inside the droplets are supressed. In this case, the oscillations in the
droplet speed (black trace) are perfectly synchronized with the optical
transmission of the droplet, plotted in red.

Also, we have shown previously thutupalli_njp_2011  that the BZ reaction
intermediates react with the surfactant in the oil phase and also at the
droplet interface creating artificial self propelled droplets. In Fig. 12, we
demonstrate that the internal oscillations of the BZ reaction affect the speed
of a self propelled droplet, similar to numerical predictions before
Kitahata2011 . Consequently, we can expect that the collective motion of
droplets thutupalli_njp_2011  will be strongly affected by their oscillatory
state and mutual coupling. On the other hand, as we have seen, their local
density affects the formation of bilayer membranes, and therefore acts back on
the mutual coupling of individual droplet oscillators. This provides an
exciting link to the rapidly evolving field of developmental evolution, which
considers the possible back-action mechanisms of the emerging phenotype (i.e.,
the collective arrangement of cells) onto the genotype, i.e., the microscopic
(genetic) state of the cell evoDevo2002 . It is an interesting option to use
emulsions containing chemical oscillator droplets such as BZ as a model for
systems with such mutual interaction of different levels of integration.

When mechanisms such as chemotaxis can be engineered into such systems, we
envisage that many exciting possibilities might be opened in the field of
active matter. For example, our results may provide a useful step to
addressing some of the challenges in the design of artificial self organizing
assemblies capable of achieving complex tasks Kolmakov2010 . Finally, we may
develop well controlled experiments to understand how the internal degrees of
freedom of collections of similar nonequilibrium units couple with their self-
emergent mesoscopic order danTanakaPRL ; thutupalliThesis .

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