@phdthesis{7258,
abstract = {Many flows encountered in nature and applications are characterized by a chaotic motion known as turbulence. Turbulent flows generate intense friction with pipe walls and are responsible for considerable amounts of energy losses at world scale. The nature of turbulent friction and techniques aimed at reducing it have been subject of extensive research over the last century, but no definite answer has been found yet. In this thesis we show that in pipes at moderate turbulent Reynolds numbers friction is better described by the power law first introduced by Blasius and not by the Prandtl–von Kármán formula. At higher Reynolds numbers, large scale motions gradually become more important in the flow and can be related to the change in scaling of friction. Next, we present a series of new techniques that can relaminarize turbulence by suppressing a key mechanism that regenerates it at walls, the lift–up effect. In addition, we investigate the process of turbulence decay in several experiments and discuss the drag reduction potential. Finally, we examine the behavior of friction under pulsating conditions inspired by the human heart cycle and we show that under such circumstances turbulent friction can be reduced to produce energy savings.},
author = {Scarselli, Davide},
issn = {2663-337X},
pages = {174},
publisher = {IST Austria},
title = {{New approaches to reduce friction in turbulent pipe flow}},
doi = {10.15479/AT:ISTA:7258},
year = {2020},
}
@article{7364,
abstract = {We present nsCouette, a highly scalable software tool to solve the Navier–Stokes equations for incompressible fluid flow between differentially heated and independently rotating, concentric cylinders. It is based on a pseudospectral spatial discretization and dynamic time-stepping. It is implemented in modern Fortran with a hybrid MPI-OpenMP parallelization scheme and thus designed to compute turbulent flows at high Reynolds and Rayleigh numbers. An additional GPU implementation (C-CUDA) for intermediate problem sizes and a version for pipe flow (nsPipe) are also provided.},
author = {Lopez Alonso, Jose M and Feldmann, Daniel and Rampp, Markus and Vela-Martín, Alberto and Shi, Liang and Avila, Marc},
issn = {23527110},
journal = {SoftwareX},
publisher = {Elsevier},
title = {{nsCouette – A high-performance code for direct numerical simulations of turbulent Taylor–Couette flow}},
doi = {10.1016/j.softx.2019.100395},
volume = {11},
year = {2020},
}
@article{7534,
abstract = {In the past two decades, our understanding of the transition to turbulence in shear flows with linearly stable laminar solutions has greatly improved. Regarding the susceptibility of the laminar flow, two concepts have been particularly useful: the edge states and the minimal seeds. In this nonlinear picture of the transition, the basin boundary of turbulence is set by the edge state's stable manifold and this manifold comes closest in energy to the laminar equilibrium at the minimal seed. We begin this paper by presenting numerical experiments in which three-dimensional perturbations are too energetic to trigger turbulence in pipe flow but they do lead to turbulence when their amplitude is reduced. We show that this seemingly counterintuitive observation is in fact consistent with the fully nonlinear description of the transition mediated by the edge state. In order to understand the physical mechanisms behind this process, we measure the turbulent kinetic energy production and dissipation rates as a function of the radial coordinate. Our main observation is that the transition to turbulence relies on the energy amplification away from the wall, as opposed to the turbulence itself, whose energy is predominantly produced near the wall. This observation is further supported by the similar analyses on the minimal seeds and the edge states. Furthermore, we show that the time evolution of production-over-dissipation curves provides a clear distinction between the different initial amplification stages of the transition to turbulence from the minimal seed.},
author = {Budanur, Nazmi B and Marensi, Elena and Willis, Ashley P. and Hof, Björn},
issn = {2469-990X},
journal = {Physical Review Fluids},
number = {2},
publisher = {American Physical Society},
title = {{Upper edge of chaos and the energetics of transition in pipe flow}},
doi = {10.1103/physrevfluids.5.023903},
volume = {5},
year = {2020},
}
@article{7563,
abstract = {We introduce “state space persistence analysis” for deducing the symbolic dynamics of time series data obtained from high-dimensional chaotic attractors. To this end, we adapt a topological data analysis technique known as persistent homology for the characterization of state space projections of chaotic trajectories and periodic orbits. By comparing the shapes along a chaotic trajectory to those of the periodic orbits, state space persistence analysis quantifies the shape similarity of chaotic trajectory segments and periodic orbits. We demonstrate the method by applying it to the three-dimensional Rössler system and a 30-dimensional discretization of the Kuramoto–Sivashinsky partial differential equation in (1+1) dimensions.
One way of studying chaotic attractors systematically is through their symbolic dynamics, in which one partitions the state space into qualitatively different regions and assigns a symbol to each such region.1–3 This yields a “coarse-grained” state space of the system, which can then be reduced to a Markov chain encoding all possible transitions between the states of the system. While it is possible to obtain the symbolic dynamics of low-dimensional chaotic systems with standard tools such as Poincaré maps, when applied to high-dimensional systems such as turbulent flows, these tools alone are not sufficient to determine symbolic dynamics.4,5 In this paper, we develop “state space persistence analysis” and demonstrate that it can be utilized to infer the symbolic dynamics in very high-dimensional settings.},
author = {Yalniz, Gökhan and Budanur, Nazmi B},
issn = {1089-7682},
journal = {Chaos},
number = {3},
publisher = {AIP Publishing},
title = {{Inferring symbolic dynamics of chaotic flows from persistence}},
doi = {10.1063/1.5122969},
volume = {30},
year = {2020},
}
@article{7932,
abstract = {Pulsating flows through tubular geometries are laminar provided that velocities are moderate. This in particular is also believed to apply to cardiovascular flows where inertial forces are typically too low to sustain turbulence. On the other hand, flow instabilities and fluctuating shear stresses are held responsible for a variety of cardiovascular diseases. Here we report a nonlinear instability mechanism for pulsating pipe flow that gives rise to bursts of turbulence at low flow rates. Geometrical distortions of small, yet finite, amplitude are found to excite a state consisting of helical vortices during flow deceleration. The resulting flow pattern grows rapidly in magnitude, breaks down into turbulence, and eventually returns to laminar when the flow accelerates. This scenario causes shear stress fluctuations and flow reversal during each pulsation cycle. Such unsteady conditions can adversely affect blood vessels and have been shown to promote inflammation and dysfunction of the shear stress-sensitive endothelial cell layer.},
author = {Xu, Duo and Varshney, Atul and Ma, Xingyu and Song, Baofang and Riedl, Michael and Avila, Marc and Hof, Björn},
issn = {10916490},
journal = {Proceedings of the National Academy of Sciences of the United States of America},
number = {21},
pages = {11233--11239},
publisher = {National Academy of Sciences},
title = {{Nonlinear hydrodynamic instability and turbulence in pulsatile flow}},
doi = {10.1073/pnas.1913716117},
volume = {117},
year = {2020},
}
@article{8043,
abstract = {With decreasing Reynolds number, Re, turbulence in channel flow becomes spatio-temporally intermittent and self-organises into solitary stripes oblique to the mean flow direction. We report here the existence of localised nonlinear travelling wave solutions of the Navier–Stokes equations possessing this obliqueness property. Such solutions are identified numerically using edge tracking coupled with arclength continuation. All solutions emerge in saddle-node bifurcations at values of Re lower than the non-localised solutions. Relative periodic orbit solutions bifurcating from branches of travelling waves have also been computed. A complete parametric study is performed, including their stability, the investigation of their large-scale flow, and the robustness to changes of the numerical domain.},
author = {Paranjape, Chaitanya S and Duguet, Yohann and Hof, Björn},
issn = {14697645},
journal = {Journal of Fluid Mechanics},
publisher = {Cambridge University Press},
title = {{Oblique stripe solutions of channel flow}},
doi = {10.1017/jfm.2020.322},
volume = {897},
year = {2020},
}
@phdthesis{6957,
abstract = {In many shear flows like pipe flow, plane Couette flow, plane Poiseuille flow, etc. turbulence emerges subcritically. Here, when subjected to strong enough perturbations, the flow becomes turbulent in spite of the laminar base flow being linearly stable. The nature of this instability has puzzled the scientific community for decades. At onset, turbulence appears in localized patches and flows are spatio-temporally intermittent. In pipe flow the localized turbulent structures are referred to as puffs and in planar flows like plane Couette and channel flow, patches arise in the form of localized oblique bands. In this thesis, we study the onset of turbulence in channel flow in direct numerical simulations from a dynamical system theory perspective, as well as by performing experiments in a large aspect ratio channel.
The aim of the experimental work is to determine the critical Reynolds number where turbulence first becomes sustained. Recently, the onset of turbulence has been described in analogy to absorbing state phase transition (i.e. directed percolation). In particular, it has been shown that the critical point can be estimated from the competition between spreading and decay processes. Here, by performing experiments, we identify the mechanisms underlying turbulence proliferation in channel flow and find the critical Reynolds number, above which turbulence becomes sustained. Above the critical point, the continuous growth at the tip of the stripes outweighs the stochastic shedding of turbulent patches at the tail and the stripes expand. For growing stripes, the probability to decay decreases while the probability of stripe splitting increases. Consequently, and unlike for the puffs in pipe flow, neither of these two processes is time-independent i.e. memoryless. Coupling between stripe expansion and creation of new stripes via splitting leads to a significantly lower critical point ($Re_c=670+/-10$) than most earlier studies suggest.
While the above approach sheds light on how turbulence first becomes sustained, it provides no insight into the origin of the stripes themselves. In the numerical part of the thesis we investigate how turbulent stripes form from invariant solutions of the Navier-Stokes equations. The origin of these turbulent stripes can be identified by applying concepts from the dynamical system theory. In doing so, we identify the exact coherent structures underlying stripes and their bifurcations and how they give rise to the turbulent attractor in phase space. We first report a family of localized nonlinear traveling wave solutions of the Navier-Stokes equations in channel flow. These solutions show structural similarities with turbulent stripes in experiments like obliqueness, quasi-streamwise streaks and vortices, etc. A parametric study of these traveling wave solution is performed, with parameters like Reynolds number, stripe tilt angle and domain size, including the stability of the solutions. These solutions emerge through saddle-node bifurcations and form a phase space skeleton for the turbulent stripes observed in the experiments. The lower branches of these TW solutions at different tilt angles undergo Hopf bifurcation and new solutions branches of relative periodic orbits emerge. These RPO solutions do not belong to the same family and therefore the routes to chaos for different angles are different.
In shear flows, turbulence at onset is transient in nature. Consequently,turbulence can not be tracked to lower Reynolds numbers, where the dynamics may simplify. Before this happens, turbulence becomes short-lived and laminarizes. In the last part of the thesis, we show that using numerical simulations we can continue turbulent stripes in channel flow past the 'relaminarization barrier' all the way to their origin. Here, turbulent stripe dynamics simplifies and the fluctuations are no longer stochastic and the stripe settles down to a relative periodic orbit. This relative periodic orbit originates from the aforementioned traveling wave solutions. Starting from the relative periodic orbit, a small increase in speed i.e. Reynolds number gives rise to chaos and the attractor dimension sharply increases in contrast to the classical transition scenario where the instabilities affect the flow globally and give rise to much more gradual route to turbulence.},
author = {Paranjape, Chaitanya S},
issn = {2663-337X},
keywords = {Instabilities, Turbulence, Nonlinear dynamics},
pages = {138},
publisher = {IST Austria},
title = {{Onset of turbulence in plane Poiseuille flow}},
doi = {10.15479/AT:ISTA:6957},
year = {2019},
}
@article{5878,
abstract = {We consider the motion of a droplet bouncing on a vibrating bath of the same fluid in the presence of a central potential. We formulate a rotation symmetry-reduced description of this system, which allows for the straightforward application of dynamical systems theory tools. As an illustration of the utility of the symmetry reduction, we apply it to a model of the pilot-wave system with a central harmonic force. We begin our analysis by identifying local bifurcations and the onset of chaos. We then describe the emergence of chaotic regions and their merging bifurcations, which lead to the formation of a global attractor. In this final regime, the droplet’s angular momentum spontaneously changes its sign as observed in the experiments of Perrard et al.},
author = {Budanur, Nazmi B and Fleury, Marc},
issn = {1089-7682},
journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
number = {1},
publisher = {AIP Publishing},
title = {{State space geometry of the chaotic pilot-wave hydrodynamics}},
doi = {10.1063/1.5058279},
volume = {29},
year = {2019},
}
@article{5943,
abstract = {The hairpin instability of a jet in a crossflow (JICF) for a low jet-to-crossflow velocity ratio is investigated experimentally for a velocity ratio range of R ∈ (0.14, 0.75) and crossflow Reynolds numbers ReD ∈ (260, 640). From spectral analysis we characterize the Strouhal number and amplitude of the hairpin instability as a function of R and ReD. We demonstrate that the dynamics of the hairpins is well described by the Landau model, and, hence, that the instability occurs through Hopf bifurcation, similarly to other hydrodynamical oscillators such as wake behind different bluff bodies. Using the Landau model, we determine the precise threshold values of hairpin shedding. We also study the spatial dependence of this hydrodynamical instability, which shows a global behaviour.},
author = {Klotz, Lukasz and Gumowski, Konrad and Wesfreid, José Eduardo},
journal = {Journal of Fluid Mechanics},
pages = {386--406},
publisher = {Cambridge University Press},
title = {{Experiments on a jet in a crossflow in the low-velocity-ratio regime}},
doi = {10.1017/jfm.2018.974},
volume = {863},
year = {2019},
}
@article{6014,
abstract = {Speed of sound waves in gases and liquids are governed by the compressibility of the medium. There exists another type of non-dispersive wave where the wave speed depends on stress instead of elasticity of the medium. A well-known example is the Alfven wave, which propagates through plasma permeated by a magnetic field with the speed determined by magnetic tension. An elastic analogue of Alfven waves has been predicted in a flow of dilute polymer solution where the elastic stress of the stretching polymers determines the elastic wave speed. Here we present quantitative evidence of elastic Alfven waves in elastic turbulence of a viscoelastic creeping flow between two obstacles in channel flow. The key finding in the experimental proof is a nonlinear dependence of the elastic wave speed cel on the Weissenberg number Wi, which deviates from predictions based on a model of linear polymer elasticity.},
author = {Varshney, Atul and Steinberg, Victor},
issn = {2041-1723},
journal = {Nature Communications},
publisher = {Springer Nature},
title = {{Elastic alfven waves in elastic turbulence}},
doi = {10.1038/s41467-019-08551-0},
volume = {10},
year = {2019},
}
@article{6069,
abstract = {Electron transport in two-dimensional conducting materials such as graphene, with dominant electron–electron interaction, exhibits unusual vortex flow that leads to a nonlocal current-field relation (negative resistance), distinct from the classical Ohm’s law. The transport behavior of these materials is best described by low Reynolds number hydrodynamics, where the constitutive pressure–speed relation is Stoke’s law. Here we report evidence of such vortices observed in a viscous flow of Newtonian fluid in a microfluidic device consisting of a rectangular cavity—analogous to the electronic system. We extend our experimental observations to elliptic cavities of different eccentricities, and validate them by numerically solving bi-harmonic equation obtained for the viscous flow with no-slip boundary conditions. We verify the existence of a predicted threshold at which vortices appear. Strikingly, we find that a two-dimensional theoretical model captures the essential features of three-dimensional Stokes flow in experiments.},
author = {Mayzel, Jonathan and Steinberg, Victor and Varshney, Atul},
issn = {2041-1723},
journal = {Nature Communications},
publisher = {Springer Nature},
title = {{Stokes flow analogous to viscous electron current in graphene}},
doi = {10.1038/s41467-019-08916-5},
volume = {10},
year = {2019},
}
@article{6189,
abstract = {Suspended particles can alter the properties of fluids and in particular also affect the transition fromlaminar to turbulent flow. An earlier study [Mataset al.,Phys. Rev. Lett.90, 014501 (2003)] reported howthe subcritical (i.e., hysteretic) transition to turbulent puffs is affected by the addition of particles. Here weshow that in addition to this known transition, with increasing concentration a supercritical (i.e.,continuous) transition to a globally fluctuating state is found. At the same time the Newtonian-typetransition to puffs is delayed to larger Reynolds numbers. At even higher concentration only the globallyfluctuating state is found. The dynamics of particle laden flows are hence determined by two competinginstabilities that give rise to three flow regimes: Newtonian-type turbulence at low, a particle inducedglobally fluctuating state at high, and a coexistence state at intermediate concentrations.},
author = {Agrawal, Nishchal and Choueiri, George H and Hof, Björn},
issn = {10797114},
journal = {Physical Review Letters},
number = {11},
publisher = {APS},
title = {{Transition to turbulence in particle laden flows}},
doi = {10.1103/PhysRevLett.122.114502},
volume = {122},
year = {2019},
}
@article{6228,
abstract = {Following the recent observation that turbulent pipe flow can be relaminarised bya relatively simple modification of the mean velocity profile, we here carry out aquantitative experimental investigation of this phenomenon. Our study confirms thata flat velocity profile leads to a collapse of turbulence and in order to achieve theblunted profile shape, we employ a moving pipe segment that is briefly and rapidlyshifted in the streamwise direction. The relaminarisation threshold and the minimumshift length and speeds are determined as a function of Reynolds number. Althoughturbulence is still active after the acceleration phase, the modulated profile possessesa severely decreased lift-up potential as measured by transient growth. As shown,this results in an exponential decay of fluctuations and the flow relaminarises. Whilethis method can be easily applied at low to moderate flow speeds, the minimumstreamwise length over which the acceleration needs to act increases linearly with theReynolds number.},
author = {Scarselli, Davide and Kühnen, Jakob and Hof, Björn},
issn = {14697645},
journal = {Journal of Fluid Mechanics},
pages = {934--948},
publisher = {Cambridge University Press},
title = {{Relaminarising pipe flow by wall movement}},
doi = {10.1017/jfm.2019.191},
volume = {867},
year = {2019},
}
@article{6413,
abstract = {Phase-field methods have long been used to model the flow of immiscible fluids. Their ability to naturally capture interface topological changes is widely recognized, but their accuracy in simulating flows of real fluids in practical geometries is not established. We here quantitatively investigate the convergence of the phase-field method to the sharp-interface limit with simulations of two-phase pipe flow. We focus on core-annular flows, in which a highly viscous fluid is lubricated by a less viscous fluid, and validate our simulations with an analytic laminar solution, a formal linear stability analysis and also in the fully nonlinear regime. We demonstrate the ability of the phase-field method to accurately deal with non-rectangular geometry, strong advection, unsteady fluctuations and large viscosity contrast. We argue that phase-field methods are very promising for quantitatively studying moderately turbulent flows, especially at high concentrations of the disperse phase.},
author = {Song, Baofang and Plana, Carlos and Lopez Alonso, Jose M and Avila, Marc},
issn = {03019322},
journal = {International Journal of Multiphase Flow},
pages = {14--24},
publisher = {Elsevier},
title = {{Phase-field simulation of core-annular pipe flow}},
doi = {10.1016/j.ijmultiphaseflow.2019.04.027},
volume = {117},
year = {2019},
}
@article{6486,
abstract = {Based on a novel control scheme, where a steady modification of the streamwise velocity profile leads to complete relaminarization of initially fully turbulent pipe flow, we investigate the applicability and usefulness of custom-shaped honeycombs for such control. The custom-shaped honeycombs are used as stationary flow management devices which generate specific modifications of the streamwise velocity profile. Stereoscopic particle image velocimetry and pressure drop measurements are used to investigate and capture the development of the relaminarizing flow downstream these devices. We compare the performance of straight (constant length across the radius of the pipe) honeycombs with custom-shaped ones (variable length across the radius) and try to determine the optimal shape for maximal relaminarization at minimal pressure loss. The optimally modified streamwise velocity profile is found to be M-shaped, and the maximum attainable Reynolds number for total relaminarization is found to be of the order of 10,000. Consequently, the respective reduction in skin friction downstream of the device is almost by a factor of 5. The break-even point, where the additional pressure drop caused by the device is balanced by the savings due to relaminarization and a net gain is obtained, corresponds to a downstream stretch of distances as low as approximately 100 pipe diameters of laminar flow.},
author = {Kühnen, Jakob and Scarselli, Davide and Hof, Björn},
issn = {1528901X},
journal = {Journal of Fluids Engineering},
number = {11},
publisher = {ASME},
title = {{Relaminarization of pipe flow by means of 3D-printed shaped honeycombs}},
doi = {10.1115/1.4043494},
volume = {141},
year = {2019},
}
@article{6508,
author = {Shamipour, Shayan and Kardos, Roland and Xue, Shi-lei and Hof, Björn and Hannezo, Edouard B and Heisenberg, Carl-Philipp J},
issn = {10974172},
journal = {Cell},
number = {6},
pages = {1463--1479.e18},
publisher = {Elsevier},
title = {{Bulk actin dynamics drive phase segregation in zebrafish oocytes}},
doi = {10.1016/j.cell.2019.04.030},
volume = {177},
year = {2019},
}
@article{6779,
abstract = {Recent studies suggest that unstable recurrent solutions of the Navier-Stokes equation provide new insights
into dynamics of turbulent flows. In this study, we compute an extensive network of dynamical connections
between such solutions in a weakly turbulent quasi-two-dimensional Kolmogorov flow that lies in the inversion symmetric subspace. In particular, we find numerous isolated heteroclinic connections between different
types of solutions—equilibria, periodic, and quasiperiodic orbits—as well as continua of connections forming
higher-dimensional connecting manifolds. We also compute a homoclinic connection of a periodic orbit and
provide strong evidence that the associated homoclinic tangle forms the chaotic repeller that underpins transient
turbulence in the symmetric subspace.},
author = {Suri, Balachandra and Pallantla, Ravi Kumar and Schatz, Michael F. and Grigoriev, Roman O.},
issn = {2470-0053},
journal = {Physical Review E},
number = {1},
publisher = {APS},
title = {{Heteroclinic and homoclinic connections in a Kolmogorov-like flow}},
doi = {10.1103/physreve.100.013112},
volume = {100},
year = {2019},
}
@article{6978,
abstract = {In pipes and channels, the onset of turbulence is initially dominated by localizedtransients, which lead to sustained turbulence through their collective dynamics. In thepresent work, we study numerically the localized turbulence in pipe flow and elucidate astate space structure that gives rise to transient chaos. Starting from the basin boundaryseparating laminar and turbulent flow, we identify transverse homoclinic orbits, thepresence of which necessitates a homoclinic tangle and chaos. A direct consequence ofthe homoclinic tangle is the fractal nature of the laminar-turbulent boundary, which wasconjectured in various earlier studies. By mapping the transverse intersections between thestable and unstable manifold of a periodic orbit, we identify the gateways that promote anescape from turbulence.},
author = {Budanur, Nazmi B and Dogra, Akshunna and Hof, Björn},
journal = {Physical Review Fluids},
number = {10},
pages = {102401},
publisher = {American Physical Society},
title = {{Geometry of transient chaos in streamwise-localized pipe flow turbulence}},
doi = {10.1103/PhysRevFluids.4.102401},
volume = {4},
year = {2019},
}
@article{7001,
author = {Schwayer, Cornelia and Shamipour, Shayan and Pranjic-Ferscha, Kornelija and Schauer, Alexandra and Balda, M and Tada, M and Matter, K and Heisenberg, Carl-Philipp J},
issn = {1097-4172},
journal = {Cell},
number = {4},
pages = {937--952.e18},
publisher = {Cell Press},
title = {{Mechanosensation of tight junctions depends on ZO-1 phase separation and flow}},
doi = {10.1016/j.cell.2019.10.006},
volume = {179},
year = {2019},
}
@article{7197,
abstract = {During bacterial cell division, the tubulin-homolog FtsZ forms a ring-like structure at the center of the cell. This Z-ring not only organizes the division machinery, but treadmilling of FtsZ filaments was also found to play a key role in distributing proteins at the division site. What regulates the architecture, dynamics and stability of the Z-ring is currently unknown, but FtsZ-associated proteins are known to play an important role. Here, using an in vitro reconstitution approach, we studied how the well-conserved protein ZapA affects FtsZ treadmilling and filament organization into large-scale patterns. Using high-resolution fluorescence microscopy and quantitative image analysis, we found that ZapA cooperatively increases the spatial order of the filament network, but binds only transiently to FtsZ filaments and has no effect on filament length and treadmilling velocity. Together, our data provides a model for how FtsZ-associated proteins can increase the precision and stability of the bacterial cell division machinery in a switch-like manner.},
author = {Dos Santos Caldas, Paulo R and Lopez Pelegrin, Maria D and Pearce, Daniel J. G. and Budanur, Nazmi B and Brugués, Jan and Loose, Martin},
issn = {2041-1723},
journal = {Nature Communications},
publisher = {Springer Nature},
title = {{Cooperative ordering of treadmilling filaments in cytoskeletal networks of FtsZ and its crosslinker ZapA}},
doi = {10.1038/s41467-019-13702-4},
volume = {10},
year = {2019},
}