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Wounds in epithelial tissues compromise their vital role in homeostasis. A rapid and efficient wound healing encompasses different mechanisms, which includes the formation of a contractile actin-myosin cable around its edge, known as the purse-string mechanism. We combine mean-field calculations and numerical simulations of the Vertex model to study the interplay between tissue properties and the purse-string mechanism and its impact on the healing process. We find different regimes, where the wound opens, closes partially or completely. We also derive an analytic expression for the closure time which is validated by numerical simulations. This study establishes under which conditions the purse-string mechanism suffices for closure, providing an analytical mean-field expression for the respective thresholds.

Identifying the necessary conditions for the onset of rigidity in a gel remains a challenge. It has been suggested that local particle coordination could be used to establish such conditions, but rigid gels occur for various coordination numbers. Combining simulations, oscillatory rheology, and a percolation analysis, for particles where the valence can be controlled, we find that the onset of rigidity coincides with the percolation of particles with three or more bonds, which arises after the connectivity percolation. We show that the rigidity results from an interplay of bonding and non-bonding interactions, providing insight into low-valence colloidal gel rigidity.

We generalize to three dimensions (3D) a recently developed improved multi-component pseudopotential lattice Boltzmann method and analyze its applicability to simulate flows through realistic porous media. The model is validated and characterized via benchmarks, and we investigate its performance by simulating the displacement of immiscible fluids in 3D geometries. Two samples are considered, namely, a pack of spheres obtained numerically, and a Bentheimer sandstone rock sample obtained experimentally. We show that, with this model it is possible to simulate realistic viscosity ratios, to tune surface tension independently and, most importantly, to preserve the volume of trapped fluid. We also evaluate the computational performance of the model on the Graphical Processing Unit (GPU) and mention the implemented optimizations to increase the computational speed and reduce the memory requirements., Comment: arXiv admin note: text overlap with arXiv:2111.08666

We propose a minimal model, based on active Brownian particles, for the dynamics of cells confined in a two-state micropattern, composed of two rectangular boxes connected by a bridge, and investigate the transition statistics. A transition between boxes occurs when the active particle crosses the center of the bridge, and the time between subsequent transitions is the dwell time. By assuming that the rotational diffusion time $\tau$ is a function of the position, the main features of the transition statistics observed experimentally are recovered. $\tau$ controls the transition from a ballistic regime at short time scales to a diffusive regime at long time scales, with an effective diffusion coefficient proportional to $\tau$. For small values of $\tau$, the dwell time is determined by the characteristic diffusion timescale which decays with $\tau$. For large values of $\tau$, the interaction with the walls dominates and the particle stays mostly at the corners of the boxes increasing the dwell time. We find that there is an optimal $\tau$ for which the dwell time is minimal and its value can be tuned by changing the geometry of the pattern.

The Voronoi model is a popular tool for studying confluent living tissues. It exhibits an anomalous glassy behavior even at very low temperatures or weak active self-propulsion, and at zero temperature the model exhibits a disordered solid structure with no evidence of a rigidity transition. Here we investigate the properties of the energy landscape in this limit. We find two disordered solid phases that have similar structural features but that differ in the ultrametricity of their energy landscapes; the crossover between these two states shares phenomenological properties with a Gardner transition. We further highlight how the metric used to calculate distances between configurations influences the ability to detect hierarchical arrangements of basins in the energy landscape.

We develop a model to investigate analytically and numerically the mechanics of wound opening made in a viscoelastic, isotropic, homogeneous, and incompressive thin tissue. This process occurs just immediately after the wound infliction. Before any active biological action has taken place, the tissue relaxes, and the wound opens mostly due to the initial homeostatic tension of the tissue, its elastic and viscous properties, and the existing friction between the tissue and its substrate. We find that for a circular wound the regimes of deformation are defined by a single adimensional parameter $\lambda$, which characterizes the relative importance of viscosity over friction., Comment: 7 pages, 4 figures

Three-dimensional shell-like structures can be obtained spontaneously at the microscale from the self-folding of 2D templates of rigid panels. At least for simple structures, the motion of each panel is consistent with a Brownian process and folding occurs through a sequence of binding events, where pairs of panels meet at a specific closing angle. Here, we propose a lattice model to describe the dynamics of self-folding. As an example, we study the folding of a pyramid of N lateral faces. We combine analytical and numerical Monte Carlo simulations to find how the folding time depends on the number of faces, closing angle, and initial configuration. Implications for the study of more complex structures are discussed.

Assessing the resilience of a road network is instrumental to improve existing infrastructures and design new ones. Here we apply the optimal path crack model (OPC) to investigate the mobility of road networks and propose a new proxy for resilience of urban mobility. In contrast to static approaches, the OPC accounts for the dynamics of rerouting as a response to traffic jams. Precisely, one simulates a sequence of failures (cracks) at the most vulnerable segments of the optimal origin-destination paths that are capable to collapse the system. Our results with synthetic and real road networks reveal that their levels of disorder, fractions of unidirectional segments and spatial correlations can drastically affect the vulnerability to traffic congestion. By applying the OPC to downtown Boston and Manhattan, we found that Boston is significantly more vulnerable than Manhattan. This is compatible with the fact that Boston heads the list of American metropolitan areas with the highest average time waste in traffic. Moreover, our analysis discloses that the origin of this difference comes from the intrinsic spatial correlations of each road network. Finally, we argue that, due to their global influence, the most important cracks identified with OPC can be used to pinpoint potential small rerouting and structural changes in road networks that are capable to substantially improve urban mobility., Comment: 7 pages, 9 figures

Without a vaccine, the fight against the spreading of the coronavirus has focused on maintaining physical distance. To study the impact of such measures on inter-municipality traffic, we analyze a mobile dataset with the daily flow of people in Portugal in March and April 2020. We find that the reduction in inter-municipality traffic depends strongly on its initial outflow. In municipalities where the mobility is low, the outflow reduced by $10-20\%$ and this decrease was independent of the population size. Whereas, for municipalities of high mobility, the reduction was a monotonic increasing function of the population size and it even exceeded $60\%$ for the largest municipalities. As a consequence of such heterogeneities, there were significant structural changes on the most probable paths for the spreading of the virus, which must be considered when modeling the impact of control measures.

A critical step in tissue engineering is the design and synthesis of 3D biocompatible matrices (scaffolds) to support and guide the proliferation of cells and tissue growth. Most existing techniques rely on the processing of scaffolds under controlled conditions and then implanting them \textit{in vivo}, with questions related to biocompatibility and the implantation process that are still challenging. As an alternative, it was proposed to assemble the scaffolds \textit{in loco} through the self-organization of colloidal particles mediated by cells. In this study, we combine experiments, particle-based simulations, and mean-field calculations to show that, in general, the size of the self-assembled scaffold scales with the cell-to-particle ratio. However, we found an optimal value of this ratio, for which the size of the scaffold is maximal when cell-cell adhesion is suppressed. These results suggest that the size and structure of the self-assembled scaffolds may be designed by tuning the adhesion between cells in the colloidal suspension.

We study the spontaneous folding of a 2D template of microscopic panels into a 3D pyramid, driven by thermal fluctuations. Combining numerical simulations and analytical calculations, we find that the total folding time is a non-monotonic function of the number of faces, with a minimum for five faces. The motion of each face is consistent with a Brownian process and folding occurs through a sequence of irreversible binding events that close edges between pairs of faces. The first edge closing is well-described by a first-passage process in 2D, with a characteristic time that decays with the number of faces. By contrast, the subsequent edge closings are all first-passage processes in 1D and so the time of the last one grows logarithmically with the number of faces. It is the interplay between these two different sets of events that explains the non-monotonic behavior. Implications in the self-folding of more complex structures are discussed.

In order to study linker-mediated aggregation of colloidal particles with limited valence, we combine kinetic Monte Carlo simulations and an approximate theory based on the Smoluchowski equations. We found that aggregation depends strongly on two parameters, the ratio of the number of linkers and particles and the ratio of their diffusion coefficients. These control parameters are absent in single-species aggregation and provide a much greater variety and control of the resulting structures. We show that aggregation is non-trivial when two time scales of aggregation are present. Our aggregation dynamics theory is in qualitative and quantitative agreement with kinetic Monte Carlo simulations. Our results show how the optimal aggregation may be tuned through the ratio of the linkers and particles and that of the diffusion coefficients.

Tourism is a worldwide practice with international tourism revenues increasing from US\$495 billion in 2000 to US\$1340 billion in 2017. Its relevance to the economy of many countries is obvious. Even though the World Airline Network (WAN) is global and has a peculiar construction, the International Tourism Network (ITN) is very similar to a random network and barely global in its reach. To understand the impact of global distances on local flows, we map the flow of tourists around the world onto a complex network and study its topological and dynamical balance. We find that although the WAN serves as infrastructural support for the ITN, the flow of tourism does not correlate strongly with the extent of flight connections worldwide. Instead, unidirectional flows appear locally forming communities that shed light on global travelling behaviour inasmuch as there is only a 15% probability of finding bidirectional tourism between a pair of countries. We conjecture that this is a consequence of one-way cyclic tourism by analyzing the triangles that are formed by the network of flows in the ITN. Finally, we find that most tourists travel to neighbouring countries and mainly cover larger distances when there is a direct flight, irrespective of the time it takes.

Contact charging between insulators is one of the most basic, yet least well understood, of physical processes. For example we have no clear theory for how insulators recruit enough charge carriers to deposit charge but not enough to discharge. In this letter we note that charging and discharging kinetics may be distinct, and from this observation we develop a mathematical model. The model surprisingly predicts that charging can decrease as contact frequency increases: we confirm this prediction experimentally and propose future steps.

We study the dynamics of diffusion-limited irreversible aggregation of monomers, where bonds are mediated by linkers. We combine kinetic Monte Carlo simulations of a lattice model with a mean-field theory to study the dynamics when the diffusion of aggregates is negligible and only monomers diffuse. We find two values of the number of linkers per monomer which maximize the size of the largest aggregate. We explain the existence of the two maxima based on the distribution of linkers per monomer. This observation is well described by a simple mean-field model. We also show that a relevant parameter is the ratio of the diffusion coefficients of monomers and linkers. In particular, when this ratio is close to ten, the two maxima merge at a single maximum.

The number of votes correlates strongly with the money spent in a campaign, but the relation between the two is not straightforward. Among other factors, the output of a ballot depends on the number of candidates, voters, and available resources. Here, we develop a conceptual framework based on Shannon entropy maximization and Superstatistics to establish a relation between the distributions of money spent by candidates and their votes. By establishing such a relation, we provide a tool to predict the outcome of a ballot and to alert for possible misconduct either in the report of fundraising and spending of campaigns or on vote counting. As an example, we consider real data from a proportional election with $6323$ candidates, where a detailed data verification is virtually impossible, and show that the number of potential misconducting candidates to audit can be reduced to only nine.

At sufficiently low temperatures and high densities, repulsive spherical particles in two-dimensions (2d) form close-packed structures with six-fold symmetry. By contrast, when the interparticle interaction has an attractive anisotropic component, the structure may exhibit the symmetry of the interaction. We consider a suspension of spherical particles interacting through an isotropic repulsive potential and a three-fold symmetric attractive interaction, confined in circular potential traps in 2d. We find that, due to the competition between the interparticle and the external potentials, the particles self-organize into structures with three- or six-fold symmetry, depending on the width of the traps. For intermediate trap widths, a core-shell structure is formed, where the core has six-fold symmetry and the shell is three-fold symmetric. When the width of the trap changes periodically in time, the symmetry of the colloidal structure also changes, but it does not necessarily follow that of the corresponding static trap.

Industrial as well as natural aggregation of fine particles is believed to be associated with electrostatics. Yet like charges repel, so it is unclear how similarly treated particles aggregate. To resolve this apparent contradiction, we analyze conditions necessary to hold aggregates together with electrostatic forces. We find that aggregates of particles charged with the same sign can be held together due to dielectric polarization, we evaluate the effect of aggregate size, and we briefly summarize consequences for practical aggregation.

We investigate the sedimentation dynamics of a binary mixture, the species of which differ by their Stokes coefficients but are identical otherwise. We analyze the sedimentation dynamics and the morphology of the final deposits using Brownian dynamics simulations for mixtures with a range of sedimentation velocities of both species. In addition, we use the lattice Boltzmann method to study hydrodynamic effects. We found a threshold in the difference of the sedimentation velocities above which the species in the final deposit are segregated. The degree of segregation increases with the difference in the Stokes coefficients or the sedimentation velocities above the threshold. We propose a simple analytical model that captures the main features of the simulated deposits.

We performed Monte Carlo simulations of the symbiotic contact process on different spatial dimensions ($d$). On the complete and random graphs (infinite dimension), we observe hysteresis cycles and bistable regions, what is consistent with the discontinuous absorbing-state phase transition predicted by mean-field theory. By contrast, on a regular square lattice, we find no signs of bistability or hysteretic behavior. This result suggests that the transition in two dimensions is rather continuous. Based on our numerical observations, we conjecture that the nature of the transition changes at the upper critical dimension ($d_c$), from continuous ($dd_c$)., Comment: 6 pages, 6 figures

We study the contact process on spatially embedded networks, consisting of a regular square lattice with long-range connections. To generate the networks, a long-range connection is randomly added to each node $i$ of a square lattice, following the probability, $P_{ij}\sim{r_{ij}^{-\alpha}}$ , where $r_{ij}$ is the Manhattan distance between nodes $i$ and $j$, and the exponent $\alpha$ is a tunable parameter. Extensive Monte Carlo simulations and a finite-size scaling analysis for different values of $\alpha$ reveal a crossover from the mean-field to $2d$ Directed Percolation universality class with increasing $\alpha$, in the range $3<\alpha<4$., Comment: 5 pages, 7 figures

We combine particle-based simulations, mean-field rate equations, and Wertheim's theory to study the dynamics of patchy particles in and out of equilibrium, at different temperatures and densities. We consider an initial random distribution of non-overlapping three-patch particles, with no bonds, and analyze the time evolution of the breaking and bonding rates of a single bond. We find that the asymptotic (equilibrium) dynamics differs from the initial (out of equilibrium) one. These differences are expected to depend on the initial conditions, temperature, and density.

Three-dimensional shells can be synthesized from the spontaneous self-folding of two-dimensional templates of interconnected panels, called nets. However, some nets are more likely to self-fold into the desired shell under random movements. The optimal nets are the ones that maximize the number of vertex connections, i.e., vertices that have only two of its faces cut away from each other in the net. Previous methods for finding such nets are based on random search and thus do not guarantee the optimal solution. Here, we propose a deterministic procedure. We map the connectivity of the shell into a shell graph, where the nodes and links of the graph represent the vertices and edges of the shell, respectively. Identifying the nets that maximize the number of vertex connections corresponds to finding the set of maximum leaf spanning trees of the shell graph. This method allows not only to design the self-assembly of much larger shell structures but also to apply additional design criteria, as a complete catalog of the maximum leaf spanning trees is obtained., Comment: 6 pages, 5 figures, Supplemental Material, Source Code

We study the collective dynamics of colloidal suspensions in the presence of a time-dependent potential, by means of dynamical density functional theory. We consider a non-linear diffusion equation for the density and show that spatial patterns emerge from a sinusoidal external potential with a time-dependent wavelength. These patterns are characterized by a sinusoidal density with the average wavelength and a Bessel-function envelope with an induced wavelength that depends only on the amplitude of the temporal oscillations. As a generalization of this result, we propose a design strategy to obtain a family of spatial patterns using time-dependent potentials of practically arbitrary shape.

We study the rectification of a two-dimensional thermal gas in a channel of asymmetric dissipative walls. For an ensemble of smooth Lennard-Jones particles, our numerical simulations reveal a non-monotonic dependence of the flux on the thermostat temperature, channel asymmetry, and particle density, with three distinct regimes. Theoretical arguments are developed to shed light on the functional dependence of the flux on the model parameters.

We study segregation of a binary mixture of similarly charged particles under shear using particle-based simulations. We simulate particle dynamics using a discrete-element model including electrostatic interactions and find that particles segregate according to their net charge. Particles that are charged twice as strong as other particles of the same electrical sign are seen more at insulating boundaries with which we shear the system. Weakly charged particles, on the other hand, stay more in the center of the sheared bed. We propose a simple model based on electrostatic potential energy to understand this segregation. The model shows that the segregated system we observe in our simulations is indeed the most favorable configuration in terms of electrostatic potential energy. Our simulations further show that for a given packing fraction there is an optimal shear velocity where the segregation maximally intensifies. We show that this maximum results from a competition between diffusional and Coulomb fluxes. For a larger shear velocity, diffusion suppresses segregation.

Network fluids are structured fluids consisting of chains and branches. They are characterized by unusual physical properties, such as, exotic bulk phase diagrams, interfacial roughening and wetting transitions, and equilibrium and nonequilibrium gels. Here, we provide an overview of a selection of their equilibrium and dynamical properties. Recent research efforts towards bridging equilibrium and non-equilibrium studies are discussed, as well as several open questions.

Capillary rise plays a crucial role in the construction of road embankments in flood zones, where hydrophobic compounds are added to the soil to suppress the rising of water and avoid possible damage of the pavement. Water rises through liquid bridges, menisci and trimers, whose width and connectivity depends on the maximal half-length {\lambda} of the capillary bridges among grains. Low {\lambda} generate a disconnect structure, with small clusters everywhere. On the contrary, for high {\lambda}, create a percolating cluster of trimers and enclosed volumes that form a natural path for capillary rise. Hereby, we study the percolation transition of this geometric structure as a function of {\lambda} on a granular media of monodisperse spheres in a random close packing. We determine both the percolating threshold {\lambda}_{c} = (0.049 \pm 0.004)R (with R the radius of the granular spheres), and the critical exponent of the correlation length {\nu} = (0.830 \pm 0.051), suggesting that the percolation transition falls into the universality class of ordinary percolation.

Colloidal particles are considered ideal building blocks to produce materials with enhanced physical properties. The state-of-the-art techniques for synthesizing these particles provide control over shape, size, and directionality of the interactions. In spite of these advances, there is still a huge gap between the synthesis of individual components and the management of their spontaneous organization towards the desired structures. The main challenge is the control over the dynamics of self-organization. In their kinetic route towards thermodynamically stable structures, colloidal particles self-organize into intermediate (mesoscopic) structures that are much larger than the individual particles and become the relevant units for the dynamics. To follow the dynamics and identify kinetically trapped structures, one needs to develop new theoretical and numerical tools. Here we discuss the self-organization of functionalized colloids (also known as patchy colloids) on attractive substrates. We review our recent results on the adsorption and relaxation and explore the use of annealing cycles to overcome kinetic barriers and drive the relaxation towards the targeted structures.

We investigate the effect of the node degree and energy $E$ on the electronic wave function for regular and irregular structures, namely, regular lattices, disordered percolation clusters, and complex networks. We evaluate the dependence of the quantum probability for each site on its degree. For bi-regular structures, we prove analytically that the probability $P_k(E)$ of finding the particle on any site with $k$ neighbors is independent of $E$. For more general structures, the dependency of $P_k(E)$ on $E$ is discussed by taking into account exact results on a one-dimensional semi-regular chain: $P_k(E)$ is large for small values of $E$ when $k$ is also small, and its maximum values shift towards large values of $|E|$ with increasing $k$. Numerical evaluations of $P_k(E)$ for two different types of percolation clusters and the Apollonian network suggest that this feature might be generally valid, Comment: 19 pages, 6 figures, original article

Low-density networks of molecules or colloids are formed at low temperatures when the interparticle interactions are valence limited. Prototypical examples are networks of patchy particles, where the limited valence results from highly directional pairwise interactions. We combine extensive Langevin simulations and Wertheim's theory of association to study these networks. We find a scale-free (relaxation) dynamics within the liquid-gas coexistence region, which differs from that usually observed for isotropic particles. While for isotropic particles the relaxation dynamics is driven by surface tension (coarsening), when the valence is limited, the slow relaxation proceeds through the formation of an intermediate non-equilibrium gel via a geometrical percolation transition in the Random Percolation universality class.

A simplified model has previously described the inductive charging of colliding identical grains in the presence of an external electric field. Here we extend that model by including heterogeneous surface charge distributions, grain rotations and electrostatic interactions between grains. We find from this more realistic model that strong heterogeneities in charging can occur in agitated granular beds, and we predict that shielding due to these heterogeneities can dramatically alter the charging rate in such beds.

Studying abroad has become very popular among students. The ERASMUS mobility program is one of the largest international student exchange programs in the world, which has supported already more than three million participants since 1987. We analyzed the mobility pattern within this program in 2011-12 and found a gender gap across countries and subject areas. Namely, for almost all participating countries, female students are over-represented in the ERASMUS program when compared to the entire population of tertiary students. The same tendency is observed across different subject areas. We also found a gender asymmetry in the geographical distribution of hosting institutions, with a bias of male students in Scandinavian countries. However, a detailed analysis reveals that this latter asymmetry is rather driven by subject and consistent with the distribution of gender ratios among subject areas.

A number of important transport networks, such as the airline and trade networks of the world, exhibit a characteristic core-periphery structure, wherein a few nodes are highly interconnected and the rest of the network frays into a tree. Mechanisms underlying the emergence of core-peripheries, however, remain elusive. Here, we demonstrate that a simple pruning process based on removal of underutilized links and redistribution of loads can lead to the emergence of core-peripheries. Links are assumed beneficial if they either carry a sufficiently large load or are essential for global connectivity. This incentivized redistribution process is controlled by a single parameter which balances connectivity and profit. The obtained networks exhibit a highly resilient and connected core with a frayed periphery. The balanced network shows a higher resilience than the World Airline Network or the World Trade Network, revealing a pathway towards robust structural features through pruning.

We propose a probabilistic growth model for transport networks which employs a balance between popularity of nodes and the physical distance between nodes. By comparing the degree of each node in the model network and the WAN, we observe that the difference between the two is minimized for $\alpha\approx 2$. Interestingly, this is the value obtained for the node-node correlation function in the WAN. This suggests that our model explains quite well the growth of airline networks., Comment: 4 pages, 3 figures

A solid wooden cube fragments into pieces as we sequentially drill holes through it randomly. This seemingly straightforward observation encompasses deep and nontrivial geometrical and probabilistic behavior that is discussed here. Combining numerical simulations and rigorous results, we find off-critical scale-free behavior and a continuous transition at a critical density of holes that significantly differs from classical percolation.

Particle-based simulations are performed to study the post-relaxation dynamics of functionalized (patchy) colloids adsorbed on an attractive substrate. Kinetically arrested structures that depend on the number of adsorbed particles and the strength of the particle-particle and particle-substrate interactions are identified. The radial distribution function is characterized by a sequence of peaks, with relative intensities that depend on the number of adsorbed particles. The first-layer coverage is a non-monotonic function of the number of particles, with an optimal value around one layer of adsorbed particles. The initial relaxation towards these structures is characterized by a fast (exponential) and a slow (power-law) dynamics. The fast relaxation timescale is a linearly increasing function of the number of adsorbed particles in the submonolayer regime, but it saturates for more than one adsorbed layer. The slow dynamics exhibits two characteristic exponents, depending on the surface coverage.

Real landscapes are usually characterized by long-range height-height correlations, which are quantified by the Hurst exponent $H$. We analyze the statistical properties of the isoheight lines for correlated landscapes of $H\in [-1,1]$. We show numerically that, for $H\leq 0$ the statistics of these lines is compatible with $SLE$ and that established analytic results are recovered for $H=-1$ and $H=0$. This result suggests that for negative $H$, in spite of the long-range nature of correlations, the statistics of isolines is fully encoded in a Brownian motion with a single parameter in the continuum limit. By contrast, for positive $H$ we find that the one-dimensional time series encoding the isoheight lines is not Markovian and therefore not consistent with $SLE$.

We study the formation of bands of colloidal particles driven by periodic external fields. Using Brownian dynamics, we determine the dependence of the band width on the strength of the particle interactions and on the intensity and periodicity of the field. We also investigate the switching (field-on) dynamics and the relaxation times as a function of the system parameters. The observed scaling relations were analyzed using a simple dynamic density-functional theory of fluids.

We study fixed assemblies of touching spheres that can individually rotate. From any initial state, sliding friction drives an assembly toward a slip-free rotation state. For bipartite assemblies, which have only even loops, this state has at least four degrees of freedom. For exactly four degrees of freedom, we analytically predict the final state, which we prove to be independent of the strength of sliding friction, from an arbitrary initial one. With a tabletop experiment, we show how to impose any slip-free rotation state by only controlling two spheres, regardless of the total number.

Two dimensional space-filling bearings are dense packings of disks that can rotate without slip. We consider the entire first family of bearings for loops of size four and propose a hierarchical construction of their contact network. We provide analytic expressions for the clustering coefficient and degree distribution, revealing bipartite scale-free behavior with tunable degree exponent depending on the bearing parameters. We also analyze their average shortest path and percolation properties.

What is the best way to divide a rugged landscape? Since ancient times, watersheds separating adjacent water systems that flow, for example, toward different seas, have been used to delimit boundaries. Interestingly, serious and even tense border disputes between countries have relied on the subtle geometrical properties of these tortuous lines. For instance, slight and even anthropogenic modifications of landscapes can produce large changes in a watershed, and the effects can be highly nonlocal. Although the watershed concept arises naturally in geomorphology, where it plays a fundamental role in water management, landslide, and flood prevention, it also has important applications in seemingly unrelated fields such as image processing and medicine. Despite the far-reaching consequences of the scaling properties on watershed-related hydrological and political issues, it was only recently that a more profound and revealing connection has been disclosed between the concept of watershed and statistical physics of disordered systems. This review initially surveys the origin and definition of a watershed line in a geomorphological framework to subsequently introduce its basic geometrical and physical properties. Results on statistical properties of watersheds obtained from artificial model landscapes generated with long-range correlations are presented and shown to be in good qualitative and quantitative agreement with real landscapes.

We investigate numerically the irreversible aggregation of patchy spherical colloids on a flat substrate. We consider $n$-patch particles and characterize the dependence of the irreversible aggregation kinetics on $n$. For all values of $n$, considered in this study, the growing interface of the aggregate is in the Kardar-Parisi-Zhang universality class, although the bulk structure exhibits a rich dependence on $n$. In particular, the bulk density varies with $n$ and the network is more ordered for particles with fewer patches. Preferred orientations of the bonds are also observed for networks of particles with low $n$.

We study the irreversible adsorption of patchy particles on substrates in the limit of advective mass transport. Recent numerical results show that the interface roughening depends strongly on the particle attributes, such as, patch-patch correlations, bond flexibility, and strength of the interactions, uncovering new absorbing phase transitions. Here, we revisit these results and discuss in detail the transitions. In particular, we present new evidence that the tricritical point, observed in systems of particles with flexible patches, is in the tricritical directed percolation universality class. A scaling analysis of the time evolution of the correlation length for the aggregation of patchy particles with distinct bonding energies confirms that the critical regime is in the Kardar-Parisi-Zhang with quenched disorder universality class.

We study the irreversible aggregation of films of patchy spherical colloids with directional and selective interactions. We report a crossover of the interfacial roughening from the Kardar-Parisi-Zhang (KPZ) to the KPZ with quenched disorder (KPZQ) universality class when the difference between the strong and weak bonds is sufficiently large. We calculate the critical exponents and identify the crossover between the two regimes.

We investigate numerically the role of spatial arrangement of the patches on the irreversible adsorption of patchy colloids on a substrate. We consider spherical three-patch colloids and study the dependence of the kinetics on the opening angle between patches. We show that growth is suppressed below and above minimum and maximum opening angles, revealing two absorbing phase transitions between thick and thin film regimes. While the transition at the minimum angle is continuous, in the Directed Percolation class, that at the maximum angle is clearly discontinuous. For intermediate values of the opening angle, a rough colloidal network in the Kardar-Parisi-Zhang universality class grows indefinitely. The nature of the transitions was analyzed in detail by considering bond flexibility, defined as the dispersion of the angle between the bond and the center of the patch. For the range of flexibilities considered we always observe two phase transitions. However, the range of opening angles where growth is sustained increases with flexibility. At a tricritical flexibility, the discontinuous transition becomes continuous. The practical implications of our findings and the relation to other nonequilibrium transitions are discussed.

Percolation is the paradigm for random connectivity and has been one of the most applied statistical models. With simple geometrical rules a transition is obtained which is related to magnetic models. This transition is, in all dimensions, one of the most robust continuous transitions known. We present a very brief overview of more than 60 years of work in this area and discuss several open questions for a variety of models, including classical, explosive, invasion, bootstrap, and correlated percolation.

This study investigates flood avalanches in a dense reservoir network in the semiarid north-eastern Brazil. The population living in this area strongly depends on the availability of the water from this network. Water is stored during intense wet-season rainfall events and evaporates from the reservoir surface during the dry season. These seasonal changes are the driving forces behind the water dynamics in the network. The reservoir network and its connectivity properties during flood avalanches are investigated with a model called ResNetM, which simulates each reservoir explicitly. It runs on the basis of daily calculated water balances for each reservoir. A spilling reservoir contributes with water to the reservoir downstream, which can trigger avalanches affecting, in some cases, large fractions of the network. The main focus is on the study of the relation between the total amount of water stored and the largest observable cluster of connected reservoirs that overspill in the same day. It is shown that the thousands of small and middle-sized reservoirs are eminent for the retention of water upstream the large ones. Therefore, they prevent large clusters at a low level of water. Concerning connectivity measures, the actual reservoir network, which evolved without an integrated plan, performed better (i.e., generated smaller avalanches for similar amount of stored water) than numerous stochastically generated artificial reservoir networks on the same river network.

A robust worldwide air-transportation network (WAN) is one that minimizes the number of stranded passengers under a sequence of airport closures. Building on top of this realistic example, here we address how spatial network robustness can profit from cooperation between local actors. We swap a series of links within a certain distance, a cooperation range, while following typical constraints of spatially embedded networks. We find that the network robustness is only improved above a critical cooperation range. Such improvement can be described in the framework of a continuum transition, where the critical exponents depend on the spatial correlation of connected nodes. For the WAN we show that, except for Australia, all continental networks fall into the same universality class. Practical implications of this result are also discussed.

Network infrastructures are essential for the distribution of resources such as electricity and water. Typical strategies to assess their resilience focus on the impact of a sequence of random or targeted failures of network nodes or links. Here we consider a more realistic scenario, where elements fail based on their usage. We propose a dynamic model of transport based on the Bak-Tang-Wiesenfeld sandpile model where links fail after they have transported more than an amount $\mu$ (threshold) of the resource and we investigate it on the square lattice. As we deal with a new model, we provide insight on its fundamental behavior and dependence on parameters. We observe that for low values of the threshold due to a positive feedback of link failure, an avalanche develops that leads to an abrupt collapse of the lattice. By contrast, for high thresholds the lattice breaks down in an uncorrelated fashion. We determine the critical threshold $\mu^*$ separating these two regimes and show how it depends on the toppling threshold of the nodes and the mass increment added stepwise to the system. We find that the time of major disconnection is well described with a linear dependence on $\mu$. Furthermore, we propose a lower bound for $\mu^*$ by measuring the strength of the dynamics leading to abrupt collapses., Comment: 9 pages, 12 figures