Localised edge states nucleate turbulence in extended plane Couette cells (2009)
Schneider, TM, Marinc, D, Eckhardt, Bruno
We study the turbulence transition of plane Couette flow in large domains where localised perturbations are observed to generate growing turbulent spots. Extending previous studies on the boundary...
John von Neumann Institute for Computing Homogeneous Shear Turbulence (2009)
Bruno Eckhardt, Andreas Dietrich, Arne Jachens, Jörg Schumacher, Bruno Eckhardt, Andreas Dietrich, ...
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State Space Properties of Transitional Pipe Flow (2008)
Dem Fachbereich Physik, Tobias M. Schneider, Vom Fachbereich, Erstgutachter Prof, Bruno Eckhardt, Zweitgutachter Prof, ...
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Lifetime statistics in transitional pipe flow (2008)
Schneider, Tobias M., Eckhardt, Bruno
Several experimental and numerical studies have shown that turbulent motions in circular pipe flow near transitional Reynolds numbers may not persist forever, but may decay. We study the properties...
Laminar-turbulent boundary in plane Couette flow (2008)
Schneider, Tobias M, Gibson, John F, Lagha, Maher, De Lillo, Filippo, Eckhardt, Bruno
We apply the iterated edge state tracking algorithm to study the boundary between laminar and turbulent dynamics in plane Couette flow at Re=400. Perturbations that are not strong enough to become...
Mixing effectiveness depends on the source-sink structure: Simulation results (2008)
Okabe, Takahide, Eckhardt, Bruno, Thiffeault, Jean-Luc, Doering, Charles R.
The mixing effectiveness, i.e., the enhancement of molecular diffusion, of a flow can be quantified in terms of the suppression of concentration variance of a passive scalar sustained by steady...
Mixing effectiveness depends on the source ndash sink structure: simulation results (2008)
Okabe, Takahide, Eckhardt, Bruno, Thiffeault, Jean-Luc, Doering, Charles R
"Mixing refers to the homogenization of concentrations of passive scalars in fluids. On small scales it is dominated by diffusion and on large scales it is assisted by stirring. In the presence of...
Quantum model for double ionization of atoms in strong laser fields (2007)
Prauzner-Bechcicki, Jakub S., Sacha, Krzysztof, Eckhardt, Bruno, Zakrzewski, Jakub
We discuss double ionization of atoms in strong laser pulses using a reduced dimensionality model. Following the insights obtained from an analysis of the classical mechanics of the process, we...
Periodic Orbit Expansions for Classical Smooth Flows (2007)
Predrag Cvitanovic, Bruno Eckhardt
We derive a generalized Selberg-type zeta function for a smooth deterministic flow which relates the spectrum of an evolution operator to the periodic orbits of the flow. This relation is a classical...
Periodic Orbit Quantization of Chaotic Systems (2007)
Predrag Cvitanovic, Bruno Eckhardt
We demonstrate the utility of the periodic orbit description of chaotic motion by computing from a few periodic orbits highly accurate estimates of a large number of quantum resonances for the...
How does flow in a pipe become turbulent? (2007)
Eckhardt, Bruno, Schneider, Tobias M.
The transition to turbulence in pipe flow does not follow the scenario familiar from Rayleigh-Benard or Taylor-Couette flow since the laminar profile is stable against infinitesimal perturbations for...
Comment on 'Critical behaviour in the relaminarization of localized turbulence in pipe flow' (2007)
Hof, Bjorn, Westerweel, Jerry, Schneider, Tobias M., Eckhardt, Bruno
This is a comment on arXiv:physics/0608292, subsequently published in Phys Rev Lett, 98, 014501 (2007), in which Willis and Kerswell study in direct numerical simulations the statistics of turbulent...
Suppression of correlated electron escape in double ionization in strong laser fields (2007)
Eckhardt, Bruno, Prauzner-Bechcicki, Jakub S., Sacha, Krzysztof, Zakrzewski, Jakub
The effect of the Pauli exclusion principle on double ionization of He atoms by strong, linearly polarized laser pulses is analyzed. We show that correlated electron escape, with electron momenta...
Turbulence transition and the edge of chaos in pipe flow (2007)
Schneider, Tobias M, Eckhardt, Bruno, Yorke, James A
The linear stability of pipe flow implies that only perturbations of sufficient strength will trigger the transition to turbulence. In order to determine this threshold in perturbation amplitude we...
Turbulence Transition in Pipe flow (2007)
Eckhardt, Bruno, Schneider, Tobias, Hof, Bjoern, Westerweel, Jerry
Statistical analysis of coherent structures in transitional pipe flow (2006)
Schneider, Tobias M., Eckhardt, Bruno, Vollmer, Juergen
Numerical and experimental studies of transitional pipe flow have shown the prevalence of coherent flow structures that are dominated by downstream vortices. They attract special attention because...
Fluxes and energy dissipation in thermal convection and shear flows (2006)
Eckhardt, Bruno, Grossmann, Siegfried, Lohse, Detlef
We expose analogies between turbulence in a fluid heated from below (Rayleigh-Bénard (RB) flow) and shear flows: The unifying theory for RB flow (S.Grossmann and D.Lohse, J.Fluid Mech. 407, 27-56...
Time resolved quantum dynamics of double ionization in strong laser fields (2006)
Prauzner-Bechcicki, Jakub S., Sacha, Krzysztof, Eckhardt, Bruno, Zakrzewski, Jakub
Quantum calculations of a 1+1-dimensional model for double ionization in strong laser fields are used to trace the time evolution from the ground state through ionization and rescattering to the two...
Eckhardt, Bruno, Sacha, Krzysztof
Building on insights about the classical pathways to double ionization in strong laser fields we here propose a 1+1-dimensional model that captures essentials of the 3-d potential landscape and...
Links between dissipation, intermittency, and helicity in the GOY model revisited (2005)
Bowman, John C., Doering, Charles R., Eckhardt, Bruno, Davoudi, Jahanshah, Roberts, Malcolm, Schumacher, Joerg
High-resolution simulations within the GOY shell model are used to study various scaling relations for turbulence. A power-law relation between the second-order intermittency correction and the...
Non-sequential double ionization of molecules in a strong laser field (2004)
Prauzner-Bechcicki, Jakub S., Sacha, Krzysztof, Eckhardt, Bruno
We consider the final stage of double ionization of $\rm O_2$ molecules by short linearly polarized laser pulses. The saddles of the effective adiabatic potential energy close to which simultaneous...
Lagrangian tracers on a surface flow: the role of time correlations (2004)
Boffetta, Guido, Davoudi, Jahanshah, Eckhardt, Bruno, Schumacher, Joerg
Finite time correlations of the velocity in a surface flow are found to be important for the formation of clusters of Lagrangian tracers. The degree of clustering characterized by the Lyapunov...
Non-sequential double ionization of molecules (2004)
Prauzner-Bechcicki, Jakub S., Sacha, Krzysztof, Eckhardt, Bruno, Zakrzewski, Jakub
Double ionization of diatomic molecules by short linearly polarized laser pulses is analyzed. We consider the final stage of the ionization process, that is the decay of a highly excited two electron...
Homogeneous shear turbulence (2004)
Eckhardt, Bruno, Dietrich, Andreas, Jachens, Arne, Schumacher, Joerg
The addition of suitable volume forces to the Navier-Stokes equation allows to simulate flows in the presence of a homogeneous shear. Because of the explicit form of the driving the flows are...
Sensitive dependence on initial conditions in transition to turbulence in pipe flow (2003)
Faisst, Holger, Eckhardt, Bruno
The experiments by Darbyshire and Mullin (J. Fluid Mech. 289, 83 (1995)) on the transition to turbulence in pipe flow show that there is no sharp border between initial conditions that trigger...
Energy dissipation in body-forced plane shear flow (2003)
Doering, Charles R., Eckhardt, Bruno, Schumacher, Joerg
We study the problem of body-force driven shear flows in a plane channel of width l with free-slip boundaries. A mini-max variational problem for upper bounds on the bulk time averaged energy...
Asymmetric time correlations in turbulent shear flows (2003)
Eckhardt, Bruno, Jachens, Arne, Schumacher, Jörg
Cross correlations between normal and downstream velocity fluctuations in a turbulent shear flow are shown to carry information about the non-normal amplification process. The creation of spanwise...
Noise Correlations in Shear Flows (2003)
Eckhardt, Bruno, Pandit, Rahul
We consider the effects of a shear on velocity fluctuations in a flow. The shear gives rise to a transient amplification that not only influences the amplitude of perturbations but also their time...
Pathways to non-sequential multiple ionization in strong laser fields (2003)
Sacha, Krzysztof, Eckhardt, Bruno
The outgoing electrons in non-sequential multiple ionization in intense laser fields are strongly correlated. The correlations can be explained within a classical model for interacting electrons in...
Fluctuations of energy injection rate in a shear flow (2003)
Schumacher, Joerg, Eckhardt, Bruno
We study the instantaneous and local energy injection in a turbulent shear flow driven by volume forces. The energy injection can be both positive and negative. Extremal events are related to...
Passive fields and particles in chaotic flows (2003)
Eckhardt, Bruno, Hascoet, Erwan, Braun, Wolfgang
Two examples for the interplay between chaotic dynamics and stochastic forces within hydrodynamical systems are considered. The first case concerns the relaxation to equilibrium of a concentration...
Echoes in classical dynamical systems (2002)
Echoes arise when external manipulations to a system induce a reversal of its time evolution that leads to a more or less perfect recovery of the initial state. We discuss the accuracy with which a...
Clustering dynamics of Lagrangian tracers in free-surface flows (2002)
Schumacher, Joerg, Eckhardt, Bruno
We study the formation of clusters of passive Lagrangian tracers in a non-smooth turbulent flow in a flat free-slip surface as a model for particle dynamics on free surfaces. Single particle and pair...
Stretching of polymers in a turbulent environment (2002)
Eckhardt, Bruno, Kronjaeger, Jochen, Schumacher, Joerg
The interaction of polymers with small-scale velocity gradients can trigger a coil-stretch transition in the polymers. We analyze this transition within a direct numerical simulation of shear...
Wannier threshold law for two electron escape in the presence of an external electric field (2001)
Eckhardt, Bruno, Sacha, Krzysztof
We consider double ionization of atoms or ions by electron impact in the presence of a static electric field. As in Wanniers analysis of the analogous situation without external field the dynamics...
Non-sequential triple ionization in strong fields (2001)
Sacha, Krzysztof, Eckhardt, Bruno
We consider the final stage of triple ionization of atoms in a strong linearly polarized laser field. We propose that for intensities below the saturation value for triple ionization the process is...
Turbulence and passive scalar transport in a free-slip surface (2001)
Eckhardt, Bruno, Schumacher, Joerg
We consider the two-dimensional (2D) flow in a flat free-slip surface that bounds a three-dimensional (3D) volume in which the flow is turbulent. The equations of motion for the two-dimensional flow...
Evolution of turbulent spots in a parallel shear flow (2001)
Schumacher, Joerg, Eckhardt, Bruno
The evolution of turbulent spots in a parallel shear flow is studied by means of full three-dimensional numerical simulations. The flow is bounded by free surfaces and driven by a volume force. Three...
Stroboscopic quantization of autonomous systems (2000)
Eckhardt, Bruno, Smilansky, Uzy
We introduce a semiclassical quantization method which is based on a stroboscopic description of the classical and the quantum flows. We show that this approach emerges naturally when one is...
Classical analysis of correlated multiple ionization in strong fields (2000)
Eckhardt, Bruno, Sacha, Krzysztof
We discuss the final stages of the simultaneous ionization of two or more electrons due to a strong laser pulse. An analysis of the classical dynamics suggests that the dominant pathway for...
Pathways to double ionization of atoms in strong fields (2000)
Sacha, Krzysztof, Eckhardt, Bruno
We discuss the final stages of double ionization of atoms in a strong linearly polarized laser field within a classical model. We propose that all trajectories leading to non-sequential double...
Scaling of global momentum transport in Taylor-Couette and pipe flow (2000)
Eckhardt, Bruno, Grossmann, Siegfried, Lohse, Detlef
We interpret measurements of the Reynolds number dependence of the torque in Taylor-Couette flow by Lewis and Swinney [Phys. Rev. E 59, 5457 (1999)] and of the pressure drop in pipe flow by Smits and...
Correlations and fluctuations of matrix elements and cross sections (2000)
Eckhardt, Bruno, Varga, Imre, Pollner, Peter
The fluctuations and correlations of matrix elements of cross sections are investigated in open systems that are chaotic in the classical limit. The form of the correlation functions is discussed...
Semiclassical cross section correlations (2000)
Eckhardt, Bruno, Fishman, Shmuel, Varga, Imre
We calculate within a semiclassical approximation the autocorrelation function of cross sections. The starting point is the semiclassical expression for the diagonal matrix elements of an operator....
Classical fluctuations and semiclassical matrix elements (2000)
Eckhardt, Bruno, Varga, Imre, Pollner, Peter
We discuss the fluctuation properties of diagonal matrix elements in the semiclassical limit in chaotic systems. For extended observables, covering a phase space area of many times Planck's constant,...
Multielectron ionization of atoms in strong fields: Classical analysis in symmetric subspace (2000)
Sacha, Krzysztof, Eckhardt, Bruno
We consider the final stage of multiple ionization of atoms in a strong linearly polarized laser field within a classical model. We propose that non-sequential multiple ionization is dominated by...
Classical double ionization of atoms in strong fields (2000)
Eckhardt, Bruno, Sacha, Krzysztof
Recent high resolution measurements of the momenta of two electrons emitted from Argon atoms in a strong laser field show a strong preference for the outgoing electrons to have similar momenta and to...
On statistically stationary homogeneous shear turbulence (2000)
Schumacher, Joerg, Eckhardt, Bruno
A statistically stationary turbulence with a mean shear gradient is realized in a flow driven by suitable body forces. The flow domain is periodic in downstream and spanwise directions and bounded by...
Transition from the Couette-Taylor system to the plane Couette system (2000)
Faisst, Holger, Eckhardt, Bruno
We discuss the flow between concentric rotating cylinders in the limit of large radii where the system approaches plane Couette flow. We discuss how in this limit the linear instability that leads to...
Transition to turbulence in a shear flow (1999)
Eckhardt, Bruno, Mersmann, Alois
We analyze the properties of a 19 dimensional Galerkin approximation to a parallel shear flow. The laminar flow with a sinusoidal shape is stable for all Reynolds numbers Re. For sufficiently large...
Structure function of passive scalars in two-dimensional turbulence (1999)
Eckhardt, Bruno, Schumacher, Joerg
The structure function of a scalar $\theta({\bf x},t)$, passively advected in a two-dimensional turbulent flow ${\bf u}({\bf x},t)$, is discussed by means of the fractal dimension $\delta^{(1)}_g$ of...
Magnetic field correlations in kinematic two-dimensional magnetohydrodynamic turbulence (1999)
Schumacher, Joerg, Eckhardt, Bruno
The scaling properties of the second order magnetic structure function D_2^{(B)}(r) and the corresponding magnetic correlation function C_2^{(B)}(r) are derived for two-dimensional...
Fractal Stability Border in Plane Couette Flow (1997)
Schmiegel, Armin, Eckhardt, Bruno
We study the dynamics of localised perturbations in plane Couette flow with periodic lateral boundary conditions. For small Reynolds number and small amplitude of the initial state the perturbation...
Approach to ergodicity in quantum wave functions (1995)
Eckhardt, Bruno, Fishman, Shmuel, Keating, Jonathan, Agam, Oded, Main, Jörg, Müller, Kirsten
According to theorems of Shnirelman and followers, in the semiclassical limit the quantum wavefunctions of classically ergodic systems tend to the microcanonical density on the energy shell. We here...
Semiclassical form factor of matrix element fluctuations (1995)
We analyze within a semiclassical approximation the form factor for the fluctuations of quantum matrix elements around their classical average. We find two contributions: one is proportional to the...
Symmetry Decomposition of Chaotic Dynamics (1993)
Cvitanović, Predrag, Eckhardt, Bruno
Discrete symmetries of dynamical flows give rise to relations between periodic orbits, reduce the dynamics to a fundamental domain, and lead to factorizations of zeta functions. These factorizations...
[[ RM: A review paper on cycle expansions. I quote the introduction: in section (2) ]] I will summarize Gutzwiller's theory for the spectrum of eigenenergies and extend it to diagonal matrix elements...
Order and chaos in quantum irregular scattering: Wigner's time delay (1993)
Recent developments in the semiclassical analysis of chaotic systems are reviewed and illustrated for Wigner's time delay in elastic scattering of a point particle from three disks in the plane. The...
Resummation of classical and semiclassical periodic orbit formulas (1993)
Eckhardt, Bruno, Russberg, Gunnar
The convergence properties of cycle expanded periodic orbit expressions for the spectra of classical and semiclassical time evolution operators have been studied for the open three disk billiard. We...
Symmetry Decomposition of Chaotic Dynamics (1993)
Predrag Cvitanovic, Bruno Eckhardt
Discrete symmetries of dynamical flows give rise to relations between periodic orbits, reduce the dynamics to a fundamental domain, and lead to factorizations of zeta functions. These factorizations...
Bruno Eckhardt, Gunnar Russberg, Predrag Cvitanovic, Per E. Rosenqvist, ...
Classical and semiclassical periodic orbit expansions are applied to the dynamics of a point particle scattering elastically off several disks in a plane. Fredholm determinants, zeta functions, and...
Exact eigenfunctions for a quantised map (1985)
Abstract. Exact eigenfunctions for quantised linear maps on a torus are constructed. A