Journal articles: 'Coherent structures dynamics'

1

Sirovich, Lawrence. "Turbulence and the dynamics of coherent structures. I. Coherent structures." Quarterly of Applied Mathematics 45, no. 3 (October 1, 1987): 561–71. http://dx.doi.org/10.1090/qam/910462.

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Sirovich, L. "Chaotic dynamics of coherent structures." Physica D: Nonlinear Phenomena 37, no. 1-3 (July 1989): 126–45. http://dx.doi.org/10.1016/0167-2789(89)90123-1.

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Belotserkovskii, O. M., N. N. Fimin, and V. M. Chechetkin. "Coherent hydrodynamic structures and vortex dynamics." Mathematical Models and Computer Simulations 8, no. 2 (March 2016): 135–48. http://dx.doi.org/10.1134/s2070048216020034.

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Colocci, M., F. Bogani, S. Ceccherini, and M. Gurioli. "Coherent Exciton Dynamics in GaAs-Based Semiconductor Structures." Journal of Nonlinear Optical Physics & Materials 07, no. 02 (June 1998): 215–26. http://dx.doi.org/10.1142/s0218863598000181.

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We show that a very powerful tool in the investigation of the coherent exciton dynamics in semiconductors is provided by the study of the emitted light after resonant excitation from pairs of phase-locked femtosecond pulses. Under these conditions, not only the full dynamics of the coherent transients (dephasing times, quantum beat periods, etc.) can be obtained from linear experiments, but it can also be obtained a straightforward discrimination between the coherent or incoherent character of the emission by means of spectral filtering.

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Belotserkovskii, O. M., N. N. Fimin, and V. M. Chechetkin. "Coherent structures in fluid dynamics and kinetic equations." Computational Mathematics and Mathematical Physics 50, no. 9 (September 2010): 1536–45. http://dx.doi.org/10.1134/s096554251009006x.

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Qian, Yuehong, Hudong Chen, and Da-Hsuan Feng. "Diffusive Lorenz dynamics: Coherent structures and spatiotemporal chaos." Communications in Nonlinear Science and Numerical Simulation 5, no. 2 (June 2000): 49–57. http://dx.doi.org/10.1016/s1007-5704(00)90001-7.

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Abdurakipov, Sergey, Vladimir Dulin, and Dmitriy Markovich. "Experimental Investigation of Coherent Structure Dynamics in a Submerged Forced Jet." Siberian Journal of Physics 8, no. 1 (March 1, 2013): 56–64. http://dx.doi.org/10.54362/1818-7919-2013-8-1-56-64.

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The present work investigates the dynamics of coherent structures, including their scales and intensity, in an initial region of a submerged round forced jet by a Particle Image Velocimetry (PIV) technique for measurements of instantaneous velocity fields and statistical analysis tool Dynamic Mode Decomposition (DMD). The PIV measurements were carried out with 1,1 kHz acquisition rate. Application of DMD to the measured set of the velocity fields provided information about dominant frequencies, contained in DMD spectrum, of velocity fluctuations in different flow regions and about scales of the corresponding spatial coherent structures, contained in DMD modes. Additional calculations of time-spectra from turbulent fluctuations showed good agreement between frequencies of the main harmonics and characteristic frequencies of the dominant dynamic modes. Superposition of relevant DMD modes approximately described nonlinear interaction of coherent structures: vortex formation, their quasi-periodic pairing with modulation amplitude of generated harmonics

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Loiseau, Jean-Christophe, Bernd R. Noack, and Steven L. Brunton. "Sparse reduced-order modelling: sensor-based dynamics to full-state estimation." Journal of Fluid Mechanics 844 (April 6, 2018): 459–90. http://dx.doi.org/10.1017/jfm.2018.147.

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We propose a general dynamic reduced-order modelling framework for typical experimental data: time-resolved sensor data and optional non-time-resolved particle image velocimetry (PIV) snapshots. This framework can be decomposed into four building blocks. First, the sensor signals are lifted to a dynamic feature space without false neighbours. Second, we identify a sparse human-interpretable nonlinear dynamical system for the feature state based on the sparse identification of nonlinear dynamics (SINDy). Third, if PIV snapshots are available, a local linear mapping from the feature state to the velocity field is performed to reconstruct the full state of the system. Fourth, a generalized feature-based modal decomposition identifies coherent structures that are most dynamically correlated with the linear and nonlinear interaction terms in the sparse model, adding interpretability. Steps 1 and 2 define a black-box model. Optional steps 3 and 4 lift the black-box dynamics to a grey-box model in terms of the identified coherent structures, if non-time-resolved full-state data are available. This grey-box modelling strategy is successfully applied to the transient and post-transient laminar cylinder wake, and compares favourably with a proper orthogonal decomposition model. We foresee numerous applications of this highly flexible modelling strategy, including estimation, prediction and control. Moreover, the feature space may be based on intrinsic coordinates, which are unaffected by a key challenge of modal expansion: the slow change of low-dimensional coherent structures with changing geometry and varying parameters.

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Sirovich, Lawrence. "Turbulence and the dynamics of coherent structures. III. Dynamics and scaling." Quarterly of Applied Mathematics 45, no. 3 (October 1, 1987): 583–90. http://dx.doi.org/10.1090/qam/910464.

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Sánchez-Martín, P., J. J. Masdemont, and M. Romero-Gómez. "From manifolds to Lagrangian coherent structures in galactic bar models." Astronomy & Astrophysics 618 (October 2018): A72. http://dx.doi.org/10.1051/0004-6361/201833451.

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We study the dynamics near the unstable Lagrangian points in galactic bar models using dynamical system tools in order to determine the global morphology of a barred galaxy. We aim at the case of non-autonomous models, in particular with secular evolution, by allowing the bar pattern speed to decrease with time. We have extended the concept of manifolds widely used in the autonomous problem to the Lagrangian coherent structures (LCS), widely used in fluid dynamics, which behave similar to the invariant manifolds driving the motion. After adapting the LCS computation code to the galactic dynamics problem, we apply it to both the autonomous and non-autonomous problems, relating the results with the manifolds and identifying the objects that best describe the motion in the non-autonomous case. We see that the strainlines coincide with the first intersection of the stable manifold when applied to the autonomous case, while, when the secular model is used, the strainlines still show the regions of maximal repulsion associated to both the corresponding stable manifolds and regions with a steep change of energy. The global morphology of the galaxy predicted by the autonomous problem remains unchanged.

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11

Williamson, J. Charles, and Ahmed H. Zewail. "Ultrafast Electron Diffraction. 4. Molecular Structures and Coherent Dynamics." Journal of Physical Chemistry 98, no. 11 (March 1994): 2766–81. http://dx.doi.org/10.1021/j100062a010.

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Husain, Hyder S., and Fazle Hussain. "Elliptic jets. Part 2. Dynamics of coherent structures: pairing." Journal of Fluid Mechanics 233 (December 1991): 439–82. http://dx.doi.org/10.1017/s0022112091000551.

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The dynamics of coherent structure interactions, in particular the jet column mode of vortex pairing, in the near field of an elliptic jet have been investigated using hotwire measurements and flow visualization. A 2:1 aspect-ratio jet with an initially laminar boundary layer and a constant momentum thickness all around the nozzle exit perimeter is used for this study. While detailed hot-wire measurements were made in air at a Reynolds number ReDe (≡UeDe/ν) = 3.2 × 104, flow visualization was performed in water at a lower ReDe = 1.7 × 104; here Ue is the exit speed and De is the equivalent diameter of the nozzle exit cross-section. Excitation at the stable pairing mode induced successive pairings to occur periodically at the same location, allowing phase-locked measurements using a local trigger sensor. Coherent structures were educed at different phases of pairing in the planes of both the major and minor axes. These are compared with corresponding data in a circular jet, educed similarly.Pairing interactions are found to be quite different from those in a circular jet. Owing to non-planar and non-uniform self-induction of elliptical vortical structures and the consequent effect on mutual induction, pairing of elliptic vortices in the jet column does not occur uniformly around the entire perimeter, unlike in a circular jet. Merger occurs only in the initial major-axis plane through an entanglement process, while in the initial minor-axis plane, the trailing vortex rushes through the leading vortex without pairing and then breaks down violently. These motions produce considerably greater entrainment and mixing than in circular or plane jets. From distributions of dynamical properties over the extent of coherent structures, the production mechanism is explained in terms of the longitudinal vortices (or ribs) connecting the elliptic structures. Time-average measures and their modification by controlled excitation are also discussed in terms of coherent structure dynamics. A significant space in this paper is devoted to documenting phase-dependent and time-average flow measures; these new results should serve as target data for numerical simulations. Further details are given in Husain (1984).

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Sambelashvili, Nicholas, A. W. C. Lau, and David Cai. "Dynamics of bacterial flow: Emergence of spatiotemporal coherent structures." Physics Letters A 360, no. 4-5 (January 2007): 507–11. http://dx.doi.org/10.1016/j.physleta.2006.08.064.

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Califano, F., L. Galeotti, and C. Briand. "Electrostatic coherent structures: The role of the ions dynamics." Physics of Plasmas 14, no. 5 (May 2007): 052306. http://dx.doi.org/10.1063/1.2724807.

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Khan, Hamid Hassan, Syed Fahad Anwer, Nadeem Hasan, and Sanjeev Sanghi. "Dynamics of coherent structures in turbulent square duct flow." Physics of Fluids 32, no. 4 (April 1, 2020): 045106. http://dx.doi.org/10.1063/5.0001977.

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Fedorova, A., and M. Zeitlin. "Localization and Coherent Structures in Wave Dynamics via Multiresolution." PAMM 1, no. 1 (March 2002): 399. http://dx.doi.org/10.1002/1617-7061(200203)1:1<399::aid-pamm399>3.0.co;2-8.

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Cliff, Oliver M., Joseph T. Lizier, X. Rosalind Wang, Peter Wang, Oliver Obst, and Mikhail Prokopenko. "Quantifying Long-Range Interactions and Coherent Structure in Multi-Agent Dynamics." Artificial Life 23, no. 1 (February 2017): 34–57. http://dx.doi.org/10.1162/artl_a_00221.

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We develop and apply several novel methods quantifying dynamic multi-agent team interactions. These interactions are detected information-theoretically and captured in two ways: via (i) directed networks (interaction diagrams) representing significant coupled dynamics between pairs of agents, and (ii) state-space plots (coherence diagrams) showing coherent structures in Shannon information dynamics. This model-free analysis relates, on the one hand, the information transfer to responsiveness of the agents and the team, and, on the other hand, the information storage within the team to the team's rigidity and lack of tactical flexibility. The resultant interaction and coherence diagrams reveal implicit interactions, across teams, that may be spatially long-range. The analysis was verified with a statistically significant number of experiments (using simulated football games, produced during RoboCup 2D Simulation League matches), identifying the zones of the most intense competition, the extent and types of interactions, and the correlation between the strength of specific interactions and the results of the matches.

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FROYLAND, GARY, SIMON LLOYD, and ANTHONY QUAS. "Coherent structures and isolated spectrum for Perron–Frobenius cocycles." Ergodic Theory and Dynamical Systems 30, no. 3 (September 4, 2009): 729–56. http://dx.doi.org/10.1017/s0143385709000339.

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AbstractWe present an analysis of one-dimensional models of dynamical systems that possess ‘coherent structures’: global structures that disperse more slowly than local trajectory separation. We study cocycles generated by expanding interval maps and the rates of decay for functions of bounded variation under the action of the associated Perron–Frobenius cocycles. We prove that when the generators are piecewise affine and share a common Markov partition, the Lyapunov spectrum of the Perron–Frobenius cocycle has at most finitely many isolated points. Moreover, we develop a strengthened version of the Multiplicative Ergodic Theorem for non-invertible matrices and construct an invariant splitting into Oseledets subspaces. We detail examples of cocycles of expanding maps with isolated Lyapunov spectrum and calculate the Oseledets subspaces, which lead to an identification of the underlying coherent structures. Our constructions generalize the notions of almost-invariant and almost-cyclic sets to non-autonomous dynamical systems and provide a new ensemble-based formalism for coherent structures in one-dimensional non-autonomous dynamics.

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Schmid, P. J., and T. Sayadi. "Low-dimensional representation of near-wall dynamics in shear flows, with implications to wall-models." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 375, no. 2089 (March 13, 2017): 20160082. http://dx.doi.org/10.1098/rsta.2016.0082.

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The dynamics of coherent structures near the wall of a turbulent boundary layer is investigated with the aim of a low-dimensional representation of its essential features. Based on a triple decomposition into mean, coherent and incoherent motion and a dynamic mode decomposition to recover statistical information about the incoherent part of the flow field, a driven linear system coupling first- and second-order moments of the coherent structures is derived and analysed. The transfer function for this system, evaluated for a wall-parallel plane, confirms a strong bias towards streamwise elongated structures, and is proposed as an ‘impedance’ boundary condition which replaces the bulk of the transport between the coherent velocity field and the coherent Reynolds stresses, thus acting as a wall model for large-eddy simulations (LES). It is interesting to note that the boundary condition is non-local in space and time. The extracted model is capable of reproducing the principal Reynolds stress components for the pretransitional, transitional and fully turbulent boundary layer. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

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Rempfer, Dietmar, and Hermann F. Fasel. "Dynamics of three-dimensional coherent structures in a flat-plate boundary layer." Journal of Fluid Mechanics 275 (September 25, 1994): 257–83. http://dx.doi.org/10.1017/s0022112094002351.

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An investigation is presented that analyses the energy flows that are connected to the dynamical behaviour of coherent structures in a transitional flat-plate boundary layer. Based on a mathematical description of the three-dimensional coherent structures of this flow as provided by the Karhunen–Loève procedure, energy equations for the coherent structures are derived by Galerkin projection of the Navier–Stokes equations in vorticity transport formulation onto the corresponding basis of eigenfunctions. In a first step, the time-averaged energy balance – showing the energy flows that support the different coherent structures and thus maintain the fluctuations of the velocity field – is considered. In a second step, the instantaneous power budget is investigated for the particularly interesting case of a coherent structure providing a prime contribution to the characteristic spike events of the transitional boundary layer. As this structure shows a strong variation in energy, the question about which mechanisms cause these variations is addressed. Our results show that the occurrence of a spike must be attributed to an autonomous event and cannot be interpreted as just an epiphenomenon of the passage of a Λ-vortex.

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COSTAMAGNA, PAOLA, GIOVANNA VITTORI, and PAOLO BLONDEAUX. "Coherent structures in oscillatory boundary layers." Journal of Fluid Mechanics 474 (January 10, 2003): 1–33. http://dx.doi.org/10.1017/s0022112002002665.

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The dynamics of the vortex structures appearing in an oscillatory boundary layer (Stokes boundary layer), when the flow departs from the laminar regime, is investigated by means of flow visualizations and a quantitative analysis of the velocity and vorticity fields. The data are obtained by means of direct numerical simulations of the Navier–Stokes and continuity equations. The wall is flat but characterized by small imperfections. The analysis is aimed at identifying points in common and differences between wall turbulence in unsteady flows and the well-investigated turbulence structure in the steady case. As in Jimenez & Moin (1991), the goal is to isolate the basic flow unit and to study its morphology and dynamics. Therefore, the computational domain is kept as small as possible.The elementary process which maintains turbulence in oscillatory boundary layers is found to be similar to that of steady flows. Indeed, when turbulence is generated, a sequence of events similar to those observed in steady boundary layers is observed. However, these events do not occur randomly in time but with a repetition time scale which is about half the period of fluid oscillations. At the end of the accelerating phases of the cycle, low-speed streaks appear close to the wall. During the early part of the decelerating phases the strength of the low-speed streaks grows. Then the streaks twist, oscillate and eventually break, originating small-scale vortices. Far from the wall, the analysis of the vorticity field has revealed the existence of a sequence of streamwise vortices of alternating circulation pumping low-speed fluid far from the wall as suggested by Sendstad & Moin (1992) for steady flows. The vortex structures observed far from the wall disappear when too small a computational domain is used, even though turbulence is self-sustaining. The present results suggest that the streak instability mechanism is the dominant mechanism generating and maintaining turbulence; no evidence of the well-known parent vortex structures spawning offspring vortices is found. Although wall imperfections are necessary to trigger transition to turbulence, the characteristics of the coherent vortex structures, for example the spacing of the low-speed streaks, are found to be independent of wall imperfections.

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Graham, Michael D., and Daniel Floryan. "Exact Coherent States and the Nonlinear Dynamics of Wall-Bounded Turbulent Flows." Annual Review of Fluid Mechanics 53, no. 1 (January 5, 2021): 227–53. http://dx.doi.org/10.1146/annurev-fluid-051820-020223.

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Wall-bounded turbulence exhibits patterns that persist in time and space: coherent structures. These are important for transport processes and form a conceptual framework for important theoretical approaches. Key observed structures include quasi-streamwise and hairpin vortices, as well as the localized spots and puffs of turbulence observed during transition. This review describes recent research on so-called exact coherent states (ECS) in wall-bounded parallel flows at Reynolds numbers Re [Formula: see text] 104; these are nonturbulent, nonlinear solutions to the Navier–Stokes equations that in many cases resemble coherent structures in turbulence. That is, idealized versions of many of these structures exist as distinct, self-sustaining entities. ECS are saddle points in state space and form, at least in part, the state space skeleton of the turbulent dynamics. While most work on ECS focuses on Newtonian flow, some advances have been made on the role of ECS in turbulent drag reduction in polymer solutions. Emerging directions include applications to control and connections to large-scale structures and the attached eddy model.

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Alfonsi, Giancarlo. "Coherent Structures of Turbulence: Methods of Eduction and Results." Applied Mechanics Reviews 59, no. 6 (November 1, 2006): 307–23. http://dx.doi.org/10.1115/1.2345370.

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In this paper the issue of the coherent structures of turbulence developing in wall-bounded flows is addressed. After a short historical synthesis, some basic concepts are reviewed and the idea of coherent structure is introduced. The phenomena occurring in the inner and outer regions of the turbulent boundary layer in conjunction with the most widely used event-detection techniques are considered, with reference to the large amount of mainly experimental results existing on the subject. The flow phenomena are described in terms of events occurring in the inner region, large-scale motions developing in the outer layer and dynamics of vortical structures. In the second part of the paper, methods for the eduction of the coherent structures of turbulence from the background flow and results obtained in the framework of each method are presented. The techniques involving the invariants of the velocity gradient tensor, the analysis of the Hessian of the pressure and the proper orthogonal decomposition are considered. Each procedure involves a particular definition of coherent structure that is supported by an appropriate mathematical framework and permits the analysis of a turbulent-flow database in terms of dynamics of coherent structures. This work may contribute to the dissemination of the most recent concepts and techniques now in use in turbulence research among fluid dynamicists.

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Tabi, Conrad Bertrand, Alidou Mohamadou, and Timoléon Crépin Kofané. "Formation and Interaction of Localized Coherent Structures for DNA Dynamics." Journal of Bionanoscience 2, no. 1 (June 1, 2008): 1–8. http://dx.doi.org/10.1166/jbns.2008.020.

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Hlina, J., Z. Sekeresova, and J. Sonsky. "Spatial Dynamics of Coherent Structures in a Thermal Plasma Jet." IEEE Transactions on Plasma Science 36, no. 4 (August 2008): 1066–67. http://dx.doi.org/10.1109/tps.2008.924610.

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Chang, Hsueh-Chia, Evgeny A. Demekhin, and Evgeny Kalaidin. "Coherent structures, self-similarity, and universal roll wave coarsening dynamics." Physics of Fluids 12, no. 9 (September 2000): 2268–78. http://dx.doi.org/10.1063/1.1287659.

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Fontán, C. Ferro, and A. Verga. "Dynamics of coherent structures and turbulence of plasma drift waves." Physical Review E 52, no. 6 (December 1, 1995): 6717–35. http://dx.doi.org/10.1103/physreve.52.6717.

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Smaoui, Nejib. "A hybrid neural network model for the dynamics of the Kuramoto-Sivashinsky equation." Mathematical Problems in Engineering 2004, no. 3 (2004): 305–21. http://dx.doi.org/10.1155/s1024123x0440101x.

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A hybrid approach consisting of two neural networks is used to model the oscillatory dynamical behavior of the Kuramoto-Sivashinsky (KS) equation at a bifurcation parameterα=84.25. This oscillatory behavior results from a fixed point that occurs atα=72having a shape of two-humped curve that becomes unstable and undergoes a Hopf bifurcation atα=83.75. First, Karhunen-Loève (KL) decomposition was used to extract five coherent structures of the oscillatory behavior capturing almost 100% of the energy. Based on the five coherent structures, a system offive ordinary differential equations (ODEs) whose dynamics is similar to the original dynamics of the KS equation was derived via KL Galerkin projection. Then, an autoassociative neural network was utilized on the amplitudes of the ODEs system with the task of reducing the dimension of the dynamical behavior to its intrinsic dimension, and a feedforward neural network was usedto model the dynamics at a future time. We show that by combining KL decomposition and neural networks, a reduced dynamical model of the KS equation is obtained.

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Wang, Wei, Jia-Zhong Zhang, Zhi-Yu Chen, and Zhi-Hui Li. "Quantitative analysis of fluid transport in dynamic stall of a pitching airfoil using variational Lagrangian coherent structures and lobe dynamics." Physics of Fluids 34, no. 7 (July 2022): 075112. http://dx.doi.org/10.1063/5.0096622.

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The evolution of flow structures during dynamic stall of a two-dimensional pitching National Advisory Committee for Aeronautics 0012 airfoil is studied using the variational Lagrangian coherent structures (LCSs), and the mass transport and vorticity transport are precisely analyzed using LCSs and lobe dynamics for further understanding the nature of flow phenomena in dynamic stall. First, the variational LCS algorithm is improved to be efficiently used in the accurate extraction of flow structures. Then, both the hyperbolic LCSs and elliptic LCSs are computed numerically in the whole process of dynamic stall to analyze the evolution of flow structures in detail. Further, a high-accuracy LCS-advection method is used in the advection of LCSs to quantitatively analyze the mass transport and vorticity transport in the evolution of LCSs utilizing lobe dynamics based on nonlinear dynamics. Finally, the evolution and motion of primary leading edge vortex (LEV) and trailing edge vortex (TEV) identified by elliptic LCSs are analyzed in depth. The results obtained can provide a deeper insight into the nature of flow phenomena in dynamic stall from the viewpoint of nonlinear dynamics. Specifically, the nature of evolution of primary LEV and the TEV and the reasons for the changes of lift coefficients are clarified from the viewpoint of fluid transport. To explain it briefly, the variational LCSs and lobe dynamics are powerful tools to quantitatively analyze the evolution of flow structures and fluid transport.

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Wu, Xuesong, and Xiuling Zhuang. "Nonlinear dynamics of large-scale coherent structures in turbulent free shear layers." Journal of Fluid Mechanics 787 (December 16, 2015): 396–439. http://dx.doi.org/10.1017/jfm.2015.646.

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Fully developed turbulent free shear layers exhibit a high degree of order, characterized by large-scale coherent structures in the form of spanwise vortex rollers. Extensive experimental investigations show that such organized motions bear remarkable resemblance to instability waves, and their main characteristics, including the length scales, propagation speeds and transverse structures, are reasonably well predicted by linear stability analysis of the mean flow. In this paper, we present a mathematical theory to describe the nonlinear dynamics of coherent structures. The formulation is based on the triple decomposition of the instantaneous flow into a mean field, coherent fluctuations and small-scale turbulence but with the mean-flow distortion induced by nonlinear interactions of coherent fluctuations being treated as part of the organized motion. The system is closed by employing a gradient type of model for the time- and phase-averaged Reynolds stresses of fine-scale turbulence. In the high-Reynolds-number limit, the nonlinear non-equilibrium critical-layer theory for laminar-flow instabilities is adapted to turbulent shear layers by accounting for (1) the enhanced non-parallelism associated with fast spreading of the mean flow, and (2) the influence of small-scale turbulence on coherent structures. The combination of these factors with nonlinearity leads to an interesting evolution system, consisting of coupled amplitude and vorticity equations, in which non-parallelism contributes the so-called translating critical-layer effect. Numerical solutions of the evolution system capture vortex roll-up, which is the hallmark of a turbulent mixing layer, and the predicted amplitude development mimics the qualitative feature of oscillatory saturation that has been observed in a number of experiments. A fair degree of quantitative agreement is obtained with one set of experimental data.

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ZHANG, H., D. NOBLE, M. CANNELL, C. H. ORCHARD, M. LANCASTER, S. A. JONES, M. R. BOYETT, et al. "DYNAMICS OF CARDIAC INTRACELLULAR Ca2+ HANDLING — FROM EXPERIMENTS TO VIRTUAL CELLS." International Journal of Bifurcation and Chaos 13, no. 12 (December 2003): 3535–60. http://dx.doi.org/10.1142/s0218127403008843.

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Intracellular cardiac Ca 2+ handling involves interactions of numerous distinct cellular and macromolecular structures. Such interactions coordinate the complicated behaviors of individual processes into spatial and temporal coherent patterns of Ca 2+ sparks, oscillations and traveling waves. Understanding the dynamical behaviors and functional roles of intracellular Ca 2+ handling requires not only detailed experimental information about subcellular structures and dynamics, but also useful tools to integrate and analyze this information. This requires interactions between experimental and simulation results within a virtual cell.

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Qu, Qingyu, Mingpei Lin, and Ming Xu. "Lagrangian coherent structures in the planar parabolic/hyperbolic restricted three-body problem." Monthly Notices of the Royal Astronomical Society 493, no. 2 (January 24, 2020): 1574–86. http://dx.doi.org/10.1093/mnras/staa199.

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ABSTRACT It is clarified that the parabolic/hyperbolic restricted three-body problem (PRTBP/HRTBP) can be adopted to provide a simple description of the dynamics of fly-by asteroids or the close encounters between different galaxies. For these reasons, PRTBP and HRTBP have been investigated for long intervals of time. However, they are quite different from the circular restricted three-body problem due to the time-dependent and non-periodic dynamics. The Lagrangian coherent structures (LCSs), as a useful tool to analyse the time-dependent dynamical system, could be applied to explain some mechanics of the PRTBP and HRTBP. In this paper, we verify the invariant manifolds on the boundary manifolds of PRTBP by analysing the LCSs in proper Poincaré sections, which shows that it works in such a non-periodic problem. One of the contributions is to investigate the LCSs in the complete phase space of PRTBP, and then some natural escape and capture trajectories from or to the two main bodies can be obtained in this way. Another contribution is to establish and study the dynamics of HRTBP and its boundary. The LCSs can be introduced into this system, reasonably, to work as the analogues of the invariant manifolds, and the similar natural escape and capture trajectories corresponding to the two main bodies can also be obtained in the complete phase space of HRTBP. As a typical technique applied to fluid, flows to identify transport barriers in the time-dependent system, the LCSs provide an effective way to determine the time-dependent analogues of invariant manifolds for the PRTBP/HRTBP.

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Priymak, V. G. "Splitting dynamics of coherent structures in a transitional round-pipe flow." Doklady Physics 58, no. 10 (October 2013): 457–63. http://dx.doi.org/10.1134/s102833581310008x.

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L. "Dynamics of Coherent Structures in the Coupled Complex Ginzburg-Landau Equations." Journal of Mathematics and Statistics 8, no. 3 (March 1, 2012): 413–18. http://dx.doi.org/10.3844/jmssp.2012.413.418.

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Epureanu, Bogdan I., Liaosha S. Tang, and Michael P. Paı̈doussis. "Coherent structures and their influence on the dynamics of aeroelastic panels." International Journal of Non-Linear Mechanics 39, no. 6 (August 2004): 977–91. http://dx.doi.org/10.1016/s0020-7462(03)00090-8.

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Taraskin, S. N., Y. L. Loh, G. Natarajan, and S. R. Elliott. "Vibrational dynamics in disordered structures studied by the coherent potential approximation." Journal of Non-Crystalline Solids 293-295 (November 2001): 333–38. http://dx.doi.org/10.1016/s0022-3093(01)00834-1.

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Rempfer, D., and H. Fasel. "The dynamics of coherent structures in a flat-plate boundary layer." Applied Scientific Research 51, no. 1-2 (June 1993): 73–77. http://dx.doi.org/10.1007/bf01082517.

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Huerre, Patrick. "Evolution of coherent structures in shear flows: A phase dynamics approach." Nuclear Physics B - Proceedings Supplements 2 (November 1987): 159–77. http://dx.doi.org/10.1016/0920-5632(87)90015-6.

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39

Sirovich, Lawrence. "Turbulence and the dynamics of coherent structures. II. Symmetries and transformations." Quarterly of Applied Mathematics 45, no. 3 (October 1, 1987): 573–82. http://dx.doi.org/10.1090/qam/910463.

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40

Assoum, Hassan H., Jana Hamdi, Marwan Alkheir, Kamel Abed Meraim, Anas Sakout, Bachar Obeid, and Mouhammad El Hassan. "Tomographic Particle Image Velocimetry and Dynamic Mode Decomposition (DMD) in a Rectangular Impinging Jet: Vortex Dynamics and Acoustic Generation." Fluids 6, no. 12 (November 27, 2021): 429. http://dx.doi.org/10.3390/fluids6120429.

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Impinging jets are encountered in ventilation systems and many other industrial applications. Their flows are three-dimensional, time-dependent, and turbulent. These jets can generate a high level of noise and often present a source of discomfort in closed areas. In order to reduce and control such mechanisms, one should investigate the flow dynamics that generate the acoustic field. The purpose of this study is to investigate the flow dynamics and, more specifically, the coherent structures involved in the acoustic generation of these jets. Model reduction techniques are commonly used to study the underlying mechanisms by decomposing the flow into coherent structures. The dynamic mode decomposition (DMD) is an equation-free method that relies only on the system’s data taken either through experiments or through numerical simulations. In this paper, the DMD technique is applied, and the spatial modes and their frequencies are presented. The temporal content of the DMD’s modes is then correlated with the acoustic signal. The flow is generated by a rectangular jet impinging on a slotted plate (for a Reynolds number Re = 4458) and its kinematic field is obtained via the tomographic particle image velocimetry technique (TPIV). The findings of this research highlight the coherent structures signature in the DMD’s spectral content and show the cross correlations between the DMD’s modes and the acoustic field.

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41

Moffatt, H. Keith. "Helicity and singular structures in fluid dynamics." Proceedings of the National Academy of Sciences 111, no. 10 (February 11, 2014): 3663–70. http://dx.doi.org/10.1073/pnas.1400277111.

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Helicity is, like energy, a quadratic invariant of the Euler equations of ideal fluid flow, although, unlike energy, it is not sign definite. In physical terms, it represents the degree of linkage of the vortex lines of a flow, conserved when conditions are such that these vortex lines are frozen in the fluid. Some basic properties of helicity are reviewed, with particular reference to (i) its crucial role in the dynamo excitation of magnetic fields in cosmic systems; (ii) its bearing on the existence of Euler flows of arbitrarily complex streamline topology; (iii) the constraining role of the analogous magnetic helicity in the determination of stable knotted minimum-energy magnetostatic structures; and (iv) its role in depleting nonlinearity in the Navier-Stokes equations, with implications for the coherent structures and energy cascade of turbulence. In a final section, some singular phenomena in low Reynolds number flows are briefly described.

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Phillips, W. R. C. "Coherent Structures and the Generalized Lagrangian Mean Equation." Applied Mechanics Reviews 43, no. 5S (May 1, 1990): S227—S231. http://dx.doi.org/10.1115/1.3120812.

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The Generalized Lagrangian mean equations are used to derive evolution equations for the perturbation flow about a turbulent mean base flow which is homogeneous in the streamwise and spanwise directions. The equations expose the mechanism which leads to the formation of streamwise vortices in the wall region of turbulent bounded flows and may be solved numerically. The advantage of this formulation is that the form of the coupling terms in the equations is known precisely; moreover, they can be expressed in terms of space time correlations, most of which have been measured. The result is a set of partial differential equations for the rectified flow field with the fluctuations filtered out. The rectified flow field then provides a way to represent the underlying coherent structures in the flow. It also permits the determination of their dynamics, which may be chaotic.

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Dawes, J. H. P. "The emergence of a coherent structure for coherent structures: localized states in nonlinear systems." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1924 (August 13, 2010): 3519–34. http://dx.doi.org/10.1098/rsta.2010.0057.

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Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific subclass of such problems, in which a pattern-forming, or ‘Turing’, instability occurs, rapid progress has been made recently in our understanding of the formation of localized states: patches of regular pattern surrounded by the unpatterned homogeneous background state. This short review article surveys the progress that has been made for localized states and proposes three areas of application for these ideas that would take the theory in new directions and ultimately be of substantial benefit to areas of applied science. Finally, I offer speculations for future work, based on localized states, that may help researchers to understand coherent structures more generally.

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Linden, Nathaniel J., Dennis R. Tabuena, Nicholas A. Steinmetz, William J. Moody, Steven L. Brunton, and Bingni W. Brunton. "Go with the FLOW: visualizing spatiotemporal dynamics in optical widefield calcium imaging." Journal of The Royal Society Interface 18, no. 181 (August 2021): 20210523. http://dx.doi.org/10.1098/rsif.2021.0523.

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Widefield calcium imaging has recently emerged as a powerful experimental technique to record coordinated large-scale brain activity. These measurements present a unique opportunity to characterize spatiotemporally coherent structures that underlie neural activity across many regions of the brain. In this work, we leverage analytic techniques from fluid dynamics to develop a visualization framework that highlights features of flow across the cortex, mapping wavefronts that may be correlated with behavioural events. First, we transform the time series of widefield calcium images into time-varying vector fields using optic flow. Next, we extract concise diagrams summarizing the dynamics, which we refer to as FLOW (flow lines in optical widefield imaging) portraits . These FLOW portraits provide an intuitive map of dynamic calcium activity, including regions of initiation and termination, as well as the direction and extent of activity spread. To extract these structures, we use the finite-time Lyapunov exponent technique developed to analyse time-varying manifolds in unsteady fluids. Importantly, our approach captures coherent structures that are poorly represented by traditional modal decomposition techniques. We demonstrate the application of FLOW portraits on three simple synthetic datasets and two widefield calcium imaging datasets, including cortical waves in the developing mouse and spontaneous cortical activity in an adult mouse.

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Manzalini, Antonio, and Bruno Galeazzi. "Explaining Homeopathy with Quantum Electrodynamics." Homeopathy 108, no. 03 (March 22, 2019): 169–76. http://dx.doi.org/10.1055/s-0039-1681037.

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Background Every living organism is an open system operating far from thermodynamic equilibrium and exchanging energy, matter and information with an external environment. These exchanges are performed through non-linear interactions of billions of different biological components, at different levels, from the quantum to the macro-dimensional. The concept of quantum coherence is an inherent property of living cells, used for long-range interactions such as synchronization of cell division processes. There is support from recent advances in quantum biology, which demonstrate that coherence, as a state of order of matter coupled with electromagnetic (EM) fields, is one of the key quantum phenomena supporting life dynamics. Coherent phenomena are well explained by quantum field theory (QFT), a well-established theoretical framework in quantum physics. Water is essential for life, being the medium used by living organisms to carry out various biochemical reactions and playing a fundamental role in coherent phenomena. Methods Quantum electrodynamics (QED), which is the relativistic QFT of electrodynamics, deals with the interactions between EM fields and matter. QED provides theoretical models and experimental frameworks for the emergence and dynamics of coherent structures, even in living organisms. This article provides a model of multi-level coherence for living organisms in which fractal phase oscillations of water are able to link and regulate a biochemical reaction. A mathematical approach, based on the eigenfunctions of Laplace operator in hyper-structures, is explored as a valuable framework to simulate and explain the oneness dynamics of multi-level coherence in life. The preparation process of a homeopathic medicine is analyzed according to QED principles, thus providing a scientific explanation for the theoretical model of “information transfer” from the substance to the water solution. A subsequent step explores the action of a homeopathic medicine in a living organism according to QED principles and the phase-space attractor's dynamics. Results According to the developed model, all levels of a living organism—organelles, cells, tissues, organs, organ systems, whole organism—are characterized by their own specific wave functions, whose phases are perfectly orchestrated in a multi-level coherence oneness. When this multi-level coherence is broken, a disease emerges. An example shows how a homeopathic medicine can bring back a patient from a disease state to a healthy one. In particular, by adopting QED, it is argued that in the preparation of homeopathic medicines, the progressive dilution/succussion processes create the conditions for the emergence of coherence domains (CDs) in the aqueous solution. Those domains code the original substance information (in terms of phase oscillations) and therefore they can transfer said information (by phase resonance) to the multi-level coherent structures of the living organism. Conclusions We encourage that QED principles and explanations become embodied in the fundamental teachings of the homeopathic method, thus providing the homeopath with a firm grounding in the practice of rational medicine. Systematic efforts in this direction should include multiple disciplines, such as quantum physics, quantum biology, conventional and homeopathic medicine and psychology.

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Kachulin, D. I., A. A. Gelash, A. I. Dyachenko, and V. E. Zakharov. "PAIRWISE INTERACTIONS OF COHERENT STRUCTURES ON THE SURFACE OF DEEP WATER." XXII workshop of the Council of nonlinear dynamics of the Russian Academy of Sciences 47, no. 1 (April 30, 2019): 66–68. http://dx.doi.org/10.29006/1564-2291.jor-2019.47(1).18.

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The interactions of coherent structures (different types of solitary wave groups) on the surface of deep water is an important nonlinear wave process, which has been studied both theoretically and experimentally (Dyachenko et al., 2013a, b; Slunyaev et al., 2017). At the moment, a complete theoretical description of such interactions is known only for the simplest model – the nonlinear Schrödinger equation (NSE) where exact multi-soliton solutions are found. In the work (Kachulin, Gelash, 2018), the dynamics of pairwise interactions of coherent structures (breathers) on the surface of deep water were numerically investigated in the framework of the Dyachenko-Zakharov model. Significant differences were found in the collision dynamics of breathers of the compact Dyachenko-Zakharov equation when compared to the behavior of the NLSE solitons. It was found that in a more precise model of gravitational surface waves, in contrast to the NLSE, the maximum amplification of the wave field amplitude during the collision process of coherent structures can exceed the sum of the initial amplitudes of the breathers. In addition, the maximum amplification of the wave field amplitude increases with increasing steepness of the interacting breathers and exceeds unity by 20% at the value of the wave steepness m ≈ 0.2. It was revealed that an important parameter determining the dynamics of pairwise collisions of breathers is the relative phase of these objects at the moment of interaction. The interaction of breathers in the non-integrable Dyachenko-Zakharov model leads to the appearance of small radiation, which was discovered earlier in 2013 (Dyachenko et al., 2013a, b). In the work (Kachulin, Gelash, 2018) we demonstrate that the magnitude of the energy losses of the colliding solitons to radiation also depends on their relative phase. Maximum of the energy losses is observed at the same relative phase, at which the amplitude amplification maximum is observed. In addition, depending on the value of the relative phase, solitons can both gain and lose the energy, which results in increase or decrease of their amplitude after a collision. It was found that, in contrast to the NSE model, the spatial shifts of solitons in a more precise model can be both positive and negative. We use the exact breather solutions of the Dyachenko-Zakharov model and the canonical transformation to physical variables (the free surface profile and the potential on the liquid surface) to find approximate solutions in the form of breathers within the framework of exact nonlinear equations for potential incompressible fluid flows. The preliminary results of our numerical experiments in the exact model demonstrate similar dynamics of the interaction of breathers, which indicates that the theoretical picture of the interaction of coherent structures presented here is universal and can be observed in laboratory experiments. The study of the dynamics of breather interactions in the exact model performed by D.I. Kachulin was supported by the Russian Science Foundation (Grant No. 18-71-00079). The work of V.E. Zakharov and A.I. Dyachenko on the dynamics of breather interactions in approximate models was supported by the state assignment “Dynamics of the complex materials”.

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Constantinou, Navid C., Brian F. Farrell, and Petros J. Ioannou. "Statistical State Dynamics of Jet–Wave Coexistence in Barotropic Beta-Plane Turbulence." Journal of the Atmospheric Sciences 73, no. 5 (May 1, 2016): 2229–53. http://dx.doi.org/10.1175/jas-d-15-0288.1.

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Abstract Jets coexist with planetary-scale waves in the turbulence of planetary atmospheres. The coherent component of these structures arises from cooperative interaction between the coherent structures and the incoherent small-scale turbulence in which they are embedded. It follows that theoretical understanding of the dynamics of jets and planetary-scale waves requires adopting the perspective of statistical state dynamics (SSD), which comprises the dynamics of the interaction between coherent and incoherent components in the turbulent state. In this work, the stochastic structural stability theory (S3T) implementation of SSD for barotropic beta-plane turbulence is used to develop a theory for the jet–wave coexistence regime by separating the coherent motions consisting of the zonal jets together with a selection of large-scale waves from the smaller-scale motions that constitute the incoherent component. It is found that mean flow–turbulence interaction gives rise to jets that coexist with large-scale coherent waves in a synergistic manner. Large-scale waves that would exist only as damped modes in the laminar jet are found to be transformed into exponentially growing waves by interaction with the incoherent small-scale turbulence, which results in a change in the mode structure, allowing the mode to tap the energy of the mean jet. This mechanism of destabilization differs fundamentally and serves to augment the more familiar S3T instabilities in which jets and waves arise from homogeneous turbulence with the energy source exclusively from the incoherent eddy field and provides further insight into the cooperative dynamics of the jet–wave coexistence regime in planetary turbulence.

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Romanò, Francesco. "Particle Coherent Structures in Confined Oscillatory Switching Centrifugation." Crystals 11, no. 2 (February 12, 2021): 183. http://dx.doi.org/10.3390/cryst11020183.

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A small spherical rigid particle in a cylindrical cavity is considered. The harmonic rotation of the cavity wall drives the background flow characterized by the Strouhal number Str, assumed as the first parameter of our investigation. The particle immersed in the flow (assumed Stokesian) has a Stokes number St=1 and a particle-to-fluid density ratio ϱ which is assumed as the second parameter of this study. Building on the theoretical understanding of the recently discovered oscillatory switching centrifugation for inertial particles in unbounded flows, we investigate the effect of a confinement. For the first time we study how the presence of a wall affects the particle trajectory in oscillatory switching centrifugation dynamics. The emergence of two qualitatively different particle attractors is characterized for particles centrifuged towards the cavity wall. The implication of two such classes of attractors is discussed focusing on the application to microfluidics. We propose some strategies for exploiting the confined oscillatory switching centrifugation for selective particle segregation and for the enhancement of particle interaction events.

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Yu. ROMANENKO, E., A. N. SHARKOVSKY, and M. B. VEREIKINA. "SELF-STRUCTURING AND SELF-SIMILARITY IN BOUNDARY VALUE PROBLEMS." International Journal of Bifurcation and Chaos 05, no. 05 (October 1995): 1407–18. http://dx.doi.org/10.1142/s0218127495001083.

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This paper aims at understanding the mathematical features of self-structuring in distributive media. We suggest a mathematical formalism for the description of structures and their dynamics in time and in space; in particular, the notions of coherent and self-similar structures are covered. A specific class of nonlinear boundary value problems presenting the evolution of some ideal medium is studied. Some regularities of structures appearing in its solutions with time increasing are established, The mathematical formulation is accompanied by computer pictures which visualize various properties of structures, in particular, the cascade process of appearance of coherent spatial-temporal structures and the process of forming spatially self-similar structures which become fractal as t → ∞.

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Debnath, M., C. Santoni, S. Leonardi, and G. V. Iungo. "Towards reduced order modelling for predicting the dynamics of coherent vorticity structures within wind turbine wakes." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 375, no. 2091 (March 6, 2017): 20160108. http://dx.doi.org/10.1098/rsta.2016.0108.

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The dynamics of the velocity field resulting from the interaction between the atmospheric boundary layer and a wind turbine array can affect significantly the performance of a wind power plant and the durability of wind turbines. In this work, dynamics in wind turbine wakes and instabilities of helicoidal tip vortices are detected and characterized through modal decomposition techniques. The dataset under examination consists of snapshots of the velocity field obtained from large-eddy simulations (LES) of an isolated wind turbine, for which aerodynamic forcing exerted by the turbine blades on the atmospheric boundary layer is mimicked through the actuator line model. Particular attention is paid to the interaction between the downstream evolution of the helicoidal tip vortices and the alternate vortex shedding from the turbine tower. The LES dataset is interrogated through different modal decomposition techniques, such as proper orthogonal decomposition and dynamic mode decomposition. The dominant wake dynamics are selected for the formulation of a reduced order model, which consists in a linear time-marching algorithm where temporal evolution of flow dynamics is obtained from the previous temporal realization multiplied by a time-invariant operator. This article is part of the themed issue ‘Wind energy in complex terrains’.

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Journal articles on the topic 'Coherent structures dynamics'

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