@article{1087,
abstract = {Using extensive direct numerical simulations, the dynamics of laminar-turbulent fronts in pipe flow is investigated for Reynolds numbers between and 5500. We here investigate the physical distinction between the fronts of weak and strong slugs both by analysing the turbulent kinetic energy budget and by comparing the downstream front motion to the advection speed of bulk turbulent structures. Our study shows that weak downstream fronts travel slower than turbulent structures in the bulk and correspond to decaying turbulence at the front. At the downstream front speed becomes faster than the advection speed, marking the onset of strong fronts. In contrast to weak fronts, turbulent eddies are generated at strong fronts by feeding on the downstream laminar flow. Our study also suggests that temporal fluctuations of production and dissipation at the downstream laminar-turbulent front drive the dynamical switches between the two types of front observed up to.},
author = {Song, Baofang and Barkley, Dwight and Hof, Björn and Avila, Marc},
issn = {00221120},
journal = {Journal of Fluid Mechanics},
pages = {1045 -- 1059},
publisher = {Cambridge University Press},
title = {{Speed and structure of turbulent fronts in pipe flow}},
doi = {10.1017/jfm.2017.14},
volume = {813},
year = {2017},
}
@article{1160,
abstract = {We investigate fundamental nonlinear dynamics of ferrofluidic Taylor-Couette flow - flow confined be-tween two concentric independently rotating cylinders - consider small aspect ratio by solving the ferro-hydrodynamical equations, carrying out systematic bifurcation analysis. Without magnetic field, we find steady flow patterns, previously observed with a simple fluid, such as those containing normal one- or two vortex cells, as well as anomalous one-cell and twin-cell flow states. However, when a symmetry-breaking transverse magnetic field is present, all flow states exhibit stimulated, finite two-fold mode. Various bifurcations between steady and unsteady states can occur, corresponding to the transitions between the two-cell and one-cell states. While unsteady, axially oscillating flow states can arise, we also detect the emergence of new unsteady flow states. In particular, we uncover two new states: one contains only the azimuthally oscillating solution in the configuration of the twin-cell flow state, and an-other a rotating flow state. Topologically, these flow states are a limit cycle and a quasiperiodic solution on a two-torus, respectively. Emergence of new flow states in addition to observed ones with classical fluid, indicates that richer but potentially more controllable dynamics in ferrofluidic flows, as such flow states depend on the external magnetic field.},
author = {Altmeyer, Sebastian and Do, Younghae and Lai, Ying},
issn = {20452322},
journal = {Scientific Reports},
publisher = {Nature Publishing Group},
title = {{Dynamics of ferrofluidic flow in the Taylor-Couette system with a small aspect ratio}},
doi = {10.1038/srep40012},
volume = {7},
year = {2017},
}
@article{1211,
abstract = {Systems such as fluid flows in channels and pipes or the complex Ginzburg–Landau system, defined over periodic domains, exhibit both continuous symmetries, translational and rotational, as well as discrete symmetries under spatial reflections or complex conjugation. The simplest, and very common symmetry of this type is the equivariance of the defining equations under the orthogonal group O(2). We formulate a novel symmetry reduction scheme for such systems by combining the method of slices with invariant polynomial methods, and show how it works by applying it to the Kuramoto–Sivashinsky system in one spatial dimension. As an example, we track a relative periodic orbit through a sequence of bifurcations to the onset of chaos. Within the symmetry-reduced state space we are able to compute and visualize the unstable manifolds of relative periodic orbits, their torus bifurcations, a transition to chaos via torus breakdown, and heteroclinic connections between various relative periodic orbits. It would be very hard to carry through such analysis in the full state space, without a symmetry reduction such as the one we present here.},
author = {Budanur, Nazmi B and Cvitanović, Predrag},
journal = {Journal of Statistical Physics},
number = {3-4},
pages = {636--655},
publisher = {Springer},
title = {{Unstable manifolds of relative periodic orbits in the symmetry reduced state space of the Kuramoto–Sivashinsky system}},
doi = {10.1007/s10955-016-1672-z},
volume = {167},
year = {2017},
}
@article{1494,
abstract = {Turbulence is one of the most frequently encountered non-equilibrium phenomena in nature, yet characterizing the transition that gives rise to turbulence in basic shear flows has remained an elusive task. Although, in recent studies, critical points marking the onset of sustained turbulence have been determined for several such flows, the physical nature of the transition could not be fully explained. In extensive experimental and computational studies we show for the example of Couette flow that the onset of turbulence is a second-order phase transition and falls into the directed percolation universality class. Consequently, the complex laminar–turbulent patterns distinctive for the onset of turbulence in shear flows result from short-range interactions of turbulent domains and are characterized by universal critical exponents. More generally, our study demonstrates that even high-dimensional systems far from equilibrium such as turbulence exhibit universality at onset and that here the collective dynamics obeys simple rules.},
author = {Lemoult, Grégoire M and Shi, Liang and Avila, Kerstin and Jalikop, Shreyas V and Avila, Marc and Hof, Björn},
journal = {Nature Physics},
number = {3},
pages = {254 -- 258},
publisher = {Nature Publishing Group},
title = {{Directed percolation phase transition to sustained turbulence in Couette flow}},
doi = {10.1038/nphys3675},
volume = {12},
year = {2016},
}
@article{1664,
abstract = {Over a century of research into the origin of turbulence in wall-bounded shear flows has resulted in a puzzling picture in which turbulence appears in a variety of different states competing with laminar background flow. At moderate flow speeds, turbulence is confined to localized patches; it is only at higher speeds that the entire flow becomes turbulent. The origin of the different states encountered during this transition, the front dynamics of the turbulent regions and the transformation to full turbulence have yet to be explained. By combining experiments, theory and computer simulations, here we uncover a bifurcation scenario that explains the transformation to fully turbulent pipe flow and describe the front dynamics of the different states encountered in the process. Key to resolving this problem is the interpretation of the flow as a bistable system with nonlinear propagation (advection) of turbulent fronts. These findings bridge the gap between our understanding of the onset of turbulence and fully turbulent flows.},
author = {Barkley, Dwight and Song, Baofang and Vasudevan, Mukund and Lemoult, Grégoire M and Avila, Marc and Hof, Björn},
journal = {Nature},
number = {7574},
pages = {550 -- 553},
publisher = {Nature Publishing Group},
title = {{The rise of fully turbulent flow}},
doi = {10.1038/nature15701},
volume = {526},
year = {2015},
}
@article{1679,
author = {Lemoult, Grégoire M and Maier, Philipp and Hof, Björn},
journal = {Physics of Fluids},
number = {9},
publisher = {American Institute of Physics},
title = {{Taylor's Forest}},
doi = {10.1063/1.4930850},
volume = {27},
year = {2015},
}
@article{1804,
abstract = {It is known that in classical fluids turbulence typically occurs at high Reynolds numbers. But can turbulence occur at low Reynolds numbers? Here we investigate the transition to turbulence in the classic Taylor-Couette system in which the rotating fluids are manufactured ferrofluids with magnetized nanoparticles embedded in liquid carriers. We find that, in the presence of a magnetic field transverse to the symmetry axis of the system, turbulence can occur at Reynolds numbers that are at least one order of magnitude smaller than those in conventional fluids. This is established by extensive computational ferrohydrodynamics through a detailed investigation of transitions in the flow structure, and characterization of behaviors of physical quantities such as the energy, the wave number, and the angular momentum through the bifurcations. A finding is that, as the magnetic field is increased, onset of turbulence can be determined accurately and reliably. Our results imply that experimental investigation of turbulence may be feasible by using ferrofluids. Our study of transition to and evolution of turbulence in the Taylor-Couette ferrofluidic flow system provides insights into the challenging problem of turbulence control.},
author = {Altmeyer, Sebastian and Do, Younghae and Lai, Ying},
journal = {Scientific Reports},
publisher = {Nature Publishing Group},
title = {{Transition to turbulence in Taylor-Couette ferrofluidic flow}},
doi = {10.1038/srep10781},
volume = {5},
year = {2015},
}
@article{1837,
abstract = {Transition to turbulence in straight pipes occurs in spite of the linear stability of the laminar Hagen-Poiseuille flow if both the amplitude of flow perturbations and the Reynolds number Re exceed a minimum threshold (subcritical transition). As the pipe curvature increases, centrifugal effects become important, modifying the basic flow as well as the most unstable linear modes. If the curvature (tube-to-coiling diameter d/D) is sufficiently large, a Hopf bifurcation (supercritical instability) is encountered before turbulence can be excited (subcritical instability). We trace the instability thresholds in the Re - d/D parameter space in the range 0.01 ≤ d/D\ ≤ 0.1 by means of laser-Doppler velocimetry and determine the point where the subcritical and supercritical instabilities meet. Two different experimental set-ups are used: a closed system where the pipe forms an axisymmetric torus and an open system employing a helical pipe. Implications for the measurement of friction factors in curved pipes are discussed.},
author = {Kühnen, Jakob and Braunshier, P and Schwegel, M and Kuhlmann, Hendrik and Hof, Björn},
journal = {Journal of Fluid Mechanics},
number = {5},
publisher = {Cambridge University Press},
title = {{Subcritical versus supercritical transition to turbulence in curved pipes}},
doi = {10.1017/jfm.2015.184},
volume = {770},
year = {2015},
}
@article{1868,
abstract = {We investigate high-dimensional nonlinear dynamical systems exhibiting multiple resonances under adiabatic parameter variations. Our motivations come from experimental considerations where time-dependent sweeping of parameters is a practical approach to probing and characterizing the bifurcations of the system. The question is whether bifurcations so detected are faithful representations of the bifurcations intrinsic to the original stationary system. Utilizing a harmonically forced, closed fluid flow system that possesses multiple resonances and solving the Navier-Stokes equation under proper boundary conditions, we uncover the phenomenon of the early effect. Specifically, as a control parameter, e.g., the driving frequency, is adiabatically increased from an initial value, resonances emerge at frequency values that are lower than those in the corresponding stationary system. The phenomenon is established by numerical characterization of physical quantities through the resonances, which include the kinetic energy and the vorticity field, and a heuristic analysis based on the concept of instantaneous frequency. A simple formula is obtained which relates the resonance points in the time-dependent and time-independent systems. Our findings suggest that, in general, any true bifurcation of a nonlinear dynamical system can be unequivocally uncovered through adiabatic parameter sweeping, in spite of a shift in the bifurcation point, which is of value to experimental studies of nonlinear dynamical systems.},
author = {Park, Youngyong and Do, Younghae and Altmeyer, Sebastian and Lai, Yingcheng and Lee, Gyuwon},
issn = {1539-3755},
journal = {Physical Review E},
number = {2},
publisher = {American Physical Society},
title = {{Early effect in time-dependent, high-dimensional nonlinear dynamical systems with multiple resonances}},
doi = {10.1103/PhysRevE.91.022906},
volume = {91},
year = {2015},
}
@article{2030,
abstract = {A hybrid-parallel direct-numerical-simulation method with application to turbulent Taylor-Couette flow is presented. The Navier-Stokes equations are discretized in cylindrical coordinates with the spectral Fourier-Galerkin method in the axial and azimuthal directions, and high-order finite differences in the radial direction. Time is advanced by a second-order, semi-implicit projection scheme, which requires the solution of five Helmholtz/Poisson equations, avoids staggered grids and renders very small slip velocities. Nonlinear terms are evaluated with the pseudospectral method. The code is parallelized using a hybrid MPI-OpenMP strategy, which, compared with a flat MPI parallelization, is simpler to implement, allows to reduce inter-node communications and MPI overhead that become relevant at high processor-core counts, and helps to contain the memory footprint. A strong scaling study shows that the hybrid code maintains scalability up to more than 20,000 processor cores and thus allows to perform simulations at higher resolutions than previously feasible. In particular, it opens up the possibility to simulate turbulent Taylor-Couette flows at Reynolds numbers up to O(105). This enables to probe hydrodynamic turbulence in Keplerian flows in experimentally relevant regimes.},
author = {Shi, Liang and Rampp, Markus and Hof, Björn and Avila, Marc},
journal = {Computers and Fluids},
number = {1},
pages = {1 -- 11},
publisher = {Elsevier},
title = {{A hybrid MPI-OpenMP parallel implementation for pseudospectral simulations with application to Taylor-Couette flow}},
doi = {10.1016/j.compfluid.2014.09.021},
volume = {106},
year = {2015},
}
@article{1588,
abstract = {We investigate the Taylor-Couette system where the radius ratio is close to unity. Systematically increasing the Reynolds number, we observe a number of previously known transitions, such as one from the classical Taylor vortex flow (TVF) to wavy vortex flow (WVF) and the transition to fully developed turbulence. Prior to the onset of turbulence, we observe intermittent bursting patterns of localized turbulent patches, confirming the experimentally observed pattern of very short wavelength bursts (VSWBs). A striking finding is that, for a Reynolds number larger than that for the onset of VSWBs, a new type of intermittently bursting behavior emerges: patterns of azimuthally closed rings of various orders. We call them ring-bursting patterns, which surround the cylinder completely but remain localized and separated in the axial direction through nonturbulent wavy structures. We employ a number of quantitative measures including the cross-flow energy to characterize the ring-bursting patterns and to distinguish them from the background flow. These patterns are interesting because they do not occur in the wide-gap Taylor-Couette flow systems. The narrow-gap regime is less studied but certainly deserves further attention to gain deeper insights into complex flow dynamics in fluids.},
author = {Altmeyer, Sebastian and Do, Younghae and Lai, Ying},
journal = {Physical Review E},
number = {5},
publisher = {American Physical Society},
title = {{Ring-bursting behavior en route to turbulence in narrow-gap Taylor-Couette flows}},
doi = {10.1103/PhysRevE.92.053018},
volume = {92},
year = {2015},
}
@article{1589,
abstract = {We investigate the dynamics of ferrofluidic wavy vortex flows in the counter-rotating Taylor-Couette system, with a focus on wavy flows with a mixture of the dominant azimuthal modes. Without external magnetic field flows are stable and pro-grade with respect to the rotation of the inner cylinder. More complex behaviors can arise when an axial or a transverse magnetic field is applied. Depending on the direction and strength of the field, multi-stable wavy states and bifurcations can occur. We uncover the phenomenon of flow pattern reversal as the strength of the magnetic field is increased through a critical value. In between the regimes of pro-grade and retrograde flow rotations, standing waves with zero angular velocities can emerge. A striking finding is that, under a transverse magnetic field, a second reversal in the flow pattern direction can occur, where the flow pattern evolves into pro-grade rotation again from a retrograde state. Flow reversal is relevant to intriguing phenomena in nature such as geomagnetic reversal. Our results suggest that, in ferrofluids, flow pattern reversal can be induced by varying a magnetic field in a controlled manner, which can be realized in laboratory experiments with potential applications in the development of modern fluid devices.},
author = {Altmeyer, Sebastian and Do, Younghae and Lai, Ying},
journal = {Scientific Reports},
publisher = {Nature Publishing Group},
title = {{Magnetic field induced flow pattern reversal in a ferrofluidic Taylor-Couette system}},
doi = {10.1038/srep18589},
volume = {5},
year = {2015},
}
@article{2050,
abstract = {The flow instability and further transition to turbulence in a toroidal pipe (torus) with curvature ratio (tube-to-coiling diameter) 0.049 is investigated experimentally. The flow inside the toroidal pipe is driven by a steel sphere fitted to the inner pipe diameter. The sphere is moved with constant azimuthal velocity from outside the torus by a moving magnet. The experiment is designed to investigate curved pipe flow by optical measurement techniques. Using stereoscopic particle image velocimetry, laser Doppler velocimetry and pressure drop measurements, the flow is measured for Reynolds numbers ranging from 1000 to 15 000. Time- and space-resolved velocity fields are obtained and analysed. The steady axisymmetric basic flow is strongly influenced by centrifugal effects. On an increase of the Reynolds number we find a sequence of bifurcations. For Re=4075±2% a supercritical bifurcation to an oscillatory flow is found in which waves travel in the streamwise direction with a phase velocity slightly faster than the mean flow. The oscillatory flow is superseded by a presumably quasi-periodic flow at a further increase of the Reynolds number before turbulence sets in. The results are found to be compatible, in general, with earlier experimental and numerical investigations on transition to turbulence in helical and curved pipes. However, important aspects of the bifurcation scenario differ considerably.},
author = {Kühnen, Jakob and Holzner, Markus and Hof, Björn and Kuhlmann, Hendrik},
journal = {Journal of Fluid Mechanics},
pages = {463 -- 491},
publisher = {Cambridge University Press},
title = {{Experimental investigation of transitional flow in a toroidal pipe}},
doi = {10.1017/jfm.2013.603 },
volume = {738},
year = {2014},
}
@article{2224,
abstract = {This work investigates the transition between different traveling helical waves (spirals, SPIs) in the setup of differentially independent rotating cylinders. We use direct numerical simulations to consider an infinite long and periodic Taylor-Couette apparatus with fixed axial periodicity length. We find so-called mixed-cross-spirals (MCSs), that can be seen as nonlinear superpositions of SPIs, to establish stable footbridges connecting SPI states. While bridging the bifurcation branches of SPIs, the corresponding contributions within the MCS vary continuously with the control parameters. Here discussed MCSs presenting footbridge solutions start and end in different SPI branches. Therefore they differ significantly from the already known MCSs that present bypass solutions (Altmeyer and Hoffmann 2010 New J. Phys. 12 113035). The latter start and end in the same SPI branch, while they always bifurcate out of those SPI branches with the larger mode amplitude. Meanwhile, these only appear within the coexisting region of both SPIs. In contrast, the footbridge solutions can also bifurcate out of the minor SPI contribution. We also find they exist in regions where only one of the SPIs contributions exists. In addition, MCS as footbridge solution can appear either stable or unstable. The latter detected transient solutions offer similar spatio-temporal characteristics to the flow establishing stable footbridges. Such transition processes are interesting for pattern-forming systems in general because they accomplish transitions between traveling waves of different azimuthal wave numbers and have not been described in the literature yet.},
author = {Altmeyer, Sebastian},
issn = {01695983},
journal = {Fluid Dynamics Research},
number = {2},
publisher = {IOP Publishing Ltd.},
title = {{On secondary instabilities generating footbridges between spiral vortex flow}},
doi = {10.1088/0169-5983/46/2/025503},
volume = {46},
year = {2014},
}
@article{2226,
abstract = {Coriolis force effects on shear flows are important in geophysical and astrophysical contexts. We report a study on the linear stability and the transient energy growth of the plane Couette flow with system rotation perpendicular to the shear direction. External rotation causes linear instability. At small rotation rates, the onset of linear instability scales inversely with the rotation rate and the optimal transient growth in the linearly stable region is slightly enhanced ∼Re2. The corresponding optimal initial perturbations are characterized by roll structures inclined in the streamwise direction and are twisted under external rotation. At large rotation rates, the transient growth is significantly inhibited and hence linear stability analysis is a reliable indicator for instability.},
author = {Shi, Liang and Hof, Björn and Tilgner, Andreas},
issn = {15393755},
journal = {Physical Review E Statistical Nonlinear and Soft Matter Physics},
number = {1},
publisher = {American Institute of Physics},
title = {{Transient growth of Ekman-Couette flow}},
doi = {10.1103/PhysRevE.89.013001},
volume = {89},
year = {2014},
}
@article{2232,
abstract = {The purpose of this contribution is to summarize and discuss recent advances regarding the onset of turbulence in shear flows. The absence of a clear-cut instability mechanism, the spatio-temporal intermittent character and extremely long lived transients are some of the major difficulties encountered in these flows and have hindered progress towards understanding the transition process. We will show for the case of pipe flow that concepts from nonlinear dynamics and statistical physics can help to explain the onset of turbulence. In particular, the turbulent structures (puffs) observed close to onset are spatially localized chaotic transients and their lifetimes increase super-exponentially with Reynolds number. At the same time fluctuations of individual turbulent puffs can (although very rarely) lead to the nucleation of new puffs. The competition between these two stochastic processes gives rise to a non-equilibrium phase transition where turbulence changes from a super-transient to a sustained state.},
author = {Song, Baofang and Hof, Björn},
issn = {17425468},
journal = {Journal of Statistical Mechanics Theory and Experiment},
number = {2},
publisher = {IOP Publishing Ltd.},
title = {{Deterministic and stochastic aspects of the transition to turbulence}},
doi = {10.1088/1742-5468/2014/02/P02001},
volume = {2014},
year = {2014},
}
@article{2806,
abstract = {A novel Taylor-Couette system has been constructed for investigations of transitional as well as high Reynolds number turbulent flows in very large aspect ratios. The flexibility of the setup enables studies of a variety of problems regarding hydrodynamic instabilities and turbulence in rotating flows. The inner and outer cylinders and the top and bottom endplates can be rotated independently with rotation rates of up to 30 Hz, thereby covering five orders of magnitude in Reynolds numbers (Re = 101-106). The radius ratio can be easily changed, the highest realized one is η = 0.98 corresponding to an aspect ratio of 260 gap width in the vertical and 300 in the azimuthal direction. For η < 0.98 the aspect ratio can be dynamically changed during measurements and complete transparency in the radial direction over the full length of the cylinders is provided by the usage of a precision glass inner cylinder. The temperatures of both cylinders are controlled independently. Overall this apparatus combines an unmatched variety in geometry, rotation rates, and temperatures, which is provided by a sophisticated high-precision bearing system. Possible applications are accurate studies of the onset of turbulence and spatio-temporal intermittent flow patterns in very large domains, transport processes of turbulence at high Re, the stability of Keplerian flows for different boundary conditions, and studies of baroclinic instabilities.},
author = {Avila, Kerstin and Hof, Björn},
journal = {Review of Scientific Instruments},
number = {6},
publisher = {American Institute of Physics},
title = {{High-precision Taylor-Couette experiment to study subcritical transitions and the role of boundary conditions and size effects}},
doi = {10.1063/1.4807704},
volume = {84},
year = {2013},
}
@article{2811,
abstract = {In pipe, channel, and boundary layer flows turbulence first occurs intermittently in space and time: at moderate Reynolds numbers domains of disordered turbulent motion are separated by quiescent laminar regions. Based on direct numerical simulations of pipe flow we argue here that the spatial intermittency has its origin in a nearest neighbor interaction between turbulent regions. We further show that in this regime turbulent flows are intrinsically intermittent with a well-defined equilibrium turbulent fraction but without ever assuming a steady pattern. This transition scenario is analogous to that found in simple models such as coupled map lattices. The scaling observed implies that laminar intermissions of the turbulent flow will persist to arbitrarily large Reynolds numbers.},
author = {Avila, Marc and Hof, Björn},
journal = {Physical Review E},
number = {6},
publisher = {American Institute of Physics},
title = {{Nature of laminar-turbulence intermittency in shear flows}},
doi = {10.1103/PhysRevE.87.063012},
volume = {87},
year = {2013},
}
@article{2813,
abstract = {Turbulence is ubiquitous in nature, yet even for the case of ordinary Newtonian fluids like water, our understanding of this phenomenon is limited. Many liquids of practical importance are more complicated (e.g., blood, polymer melts, paints), however; they exhibit elastic as well as viscous characteristics, and the relation between stress and strain is nonlinear. We demonstrate here for a model system of such complex fluids that at high shear rates, turbulence is not simply modified as previously believed but is suppressed and replaced by a different type of disordered motion, elasto-inertial turbulence. Elasto-inertial turbulence is found to occur at much lower Reynolds numbers than Newtonian turbulence, and the dynamical properties differ significantly. The friction scaling observed coincides with the so-called "maximum drag reduction" asymptote, which is exhibited by a wide range of viscoelastic fluids.},
author = {Samanta, Devranjan and Dubief, Yves and Holzner, Markus and Schäfer, Christof and Morozov, Alexander and Wagner, Christian and Hof, Björn},
journal = {PNAS},
number = {26},
pages = {10557 -- 10562},
publisher = {National Academy of Sciences},
title = {{Elasto-inertial turbulence}},
doi = {10.1073/pnas.1219666110},
volume = {110},
year = {2013},
}
@article{2829,
abstract = {Laminar-turbulent intermittency is intrinsic to the transitional regime of a wide range of fluid flows including pipe, channel, boundary layer, and Couette flow. In the latter turbulent spots can grow and form continuous stripes, yet in the stripe-normal direction they remain interspersed by laminar fluid. We carry out direct numerical simulations in a long narrow domain and observe that individual turbulent stripes are transient. In agreement with recent observations in pipe flow, we find that turbulence becomes sustained at a distinct critical point once the spatial proliferation outweighs the inherent decaying process. By resolving the asymptotic size distributions close to criticality we can for the first time demonstrate scale invariance at the onset of turbulence.},
author = {Shi, Liang and Avila, Marc and Hof, Björn},
journal = {Physical Review Letters},
number = {20},
publisher = {American Physical Society},
title = {{Scale invariance at the onset of turbulence in couette flow}},
doi = {10.1103/PhysRevLett.110.204502},
volume = {110},
year = {2013},
}