arXiv subjects

Bruno Eckhardt

Publications and source records attributed to Bruno Eckhardt.

At least 91 records · Page 5Linked to original sources

arXiv2002

Stretching of polymers in a turbulent environment

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 turbulence with an Oldroyd-B model for the polymer. In the coiled state the lengths of polymers are distributed algebraically with an exponent alpha=2 gamma-1/De, where gamma is a characteristic stretching rate of the flow and De the Deborah number. In the stretched state we demonstrate that the length distribution of the polymers is limited by the feedback to the flow.

nlin.CD↗

arXiv2001

Wannier threshold law for two electron escape in the presence of an external electric field

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 near threshold is dominated by a saddle. With a field the saddle lies in a subspace of symmetrically escaping electrons. Near threshold the classical cross section scales with excess energy E like sigma=E^alpha, where the exponent alpha can be determined from the stability of the saddle and does not depend on the field strength. For example, if the remaining ion has charge Z=2, the exponent is 1.292, significantly different from the 1.056 without the field.

quant-ph↗

arXiv2001

Non-sequential triple ionization in strong fields

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 dominated by the simultaneous escape of three electrons from a highly excited intermediate complex. We identify within a classical model two pathways to triple ionization, one with a triangular configuration of electrons and one with a more linear one. Both are saddles in phase space. A stability analysis indicates that the triangular configuration has the larger cross sections and should be the dominant one. Trajectory simulations within the dominant symmetry subspace reproduce the experimentally observed distribution of ion momenta parallel to the polarization axis.

quant-ph↗

arXiv2001

Turbulence and passive scalar transport in a free-slip surface

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 in the surface are neither compressible nor incompressible but strongly influenced by the 3D flow underneath the surface. The velocity correlation functions in the 2D surface and in the 3D volume scale with the same exponents. In the viscous subrange the amplitudes are the same, but in the inertial subrange the 2D one is reduced to 2/3 of the 3D amplitude. The surface flow is more strongly intermittent than the 3D volume flow. Geometric scaling theory is used to derive a relation between the scaling of the velocity field and the density fluctuations of a passive scalar advected on the surface.

nlin.CD↗

arXiv2001

Evolution of turbulent spots in a parallel shear flow

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 regions in the spanwise spot cross-section can be identified: a turbulent interior, an interface layer with prominent streamwise streaks and vortices and a laminar exterior region with a large scale flow induced by the presence of the spot. The lift-up of streamwise streaks which is caused by non-normal amplification is clearly detected in the region adjacent to the spot interface. The spot can be characterized by an exponentially decaying front that moves with a speed different from that of the cross-stream outflow or the spanwise phase velocity of the streamwise roll pattern. Growth of the spots seems to be intimately connected to the large scale outside flow, for a turbulent ribbon extending across the box in downstream direction does not show the large scale flow and does not grow. Quantitatively, the large scale flow induces a linear instability in the neighborhood of the spot, but the associated front velocity is too small to explain the spot spreading.

nlin.CD↗

arXiv2001

Pathways to double ionization of atoms in strong fields

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 ionization pass close to a saddle in phase space which we identify and characterize. The saddle lies in a two degree of freedom subspace of symmetrically escaping electrons. The distribution of longitudinal momenta of ions as calculated within the subspace shows the double hump structure observed in experiments. Including a symmetric bending mode of the electrons allows us to reproduce the transverse ion momenta. We discuss also a path to sequential ionization and show that it does not lead to the observed momentum distributions.

physics.atom-ph↗

arXiv2000

On statistically stationary homogeneous shear turbulence

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 stress free surfaces in the normal direction. Except for small layers near the surfaces the flow is homogeneous. The fluctuations in turbulent energy are less violent than in the simulations using remeshing, but the anisotropy on small scales as measured by the skewness of derivatives is similar and decays weakly with increasing Reynolds number.

nlin.CD↗

arXiv2000

Stroboscopic quantization of autonomous systems

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 interested in extracting the energy spectrum within a prescribed and finite energy interval. The resulting semiclassical expression involves a finite number of periodic orbits whose energies are in the considered interval. Higher order corrections which reflect the sharp restriction of the spectrum to an interval are explicitely given. The relation to Fourier methods for extracting semiclassical spectra, such as harmonic inversion, is worked out. The constraints due to the finite dimension of the Hilbert space and the unitarity of the restricted quantum evolution operator are important ingredients in this context.

nlin.CD↗

arXiv2000

Classical analysis of correlated multiple ionization in strong fields

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 non-sequential escape has the electrons escaping in a symmetric arrangement. Classical trajectory models within and near to this symmetry subspace support the theoretical considerations and give final momentum distributions in close agreement with experiments.

quant-ph↗

arXiv2000

Scaling of global momentum transport in Taylor-Couette and pipe flow

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 Zagarola, [Phys. Fluids 10, 1045 (1998)] within the scaling theory of Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000)], developed in the context of thermal convection. The main idea is to split the energy dissipation into contributions from a boundary layer and the turbulent bulk. This ansatz can account for the observed scaling in both cases if it is assumed that the internal wind velocity $U_w$ introduced through the rotational or pressure forcing is related to the the external (imposed) velocity U, by $U_w/U \propto Re^ξ$ with xi = -0.051 and xi = -0.041 for the Taylor-Couette (U inner cylinder velocity) and pipe flow (U mean flow velocity) case, respectively. In contrast to the Rayleigh-Benard case the scaling exponents cannot (yet) be derived from the dynamical equations.

nlin.CD↗

arXiv2000

Correlations and fluctuations of matrix elements and cross sections

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 within a statistical analysis and tested in calculations for a damped quantum kicked rotator. We briefly comment on the modifications expected for systems with slowly decaying correlations, a typical feature in mixed phase spaces.

nlin.CD↗

arXiv2000

Semiclassical cross section correlations

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. For general operators with a smooth classical limit the autocorrelation function of such matrix elements has two contributions with relative weights determined by classical dynamics. We show how the random matrix result can be obtained if the operator approaches a projector onto a single initial state. The expressions are verified in calculations for the kicked rotor.

nlin.CD↗

arXiv2000

Classical fluctuations and semiclassical matrix elements

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, both classical and quantal distributions are Gaussian. If the observable is a projection onto a single state or an incoherent projection onto several states classical and quantal distribution differ, but the mean and the variance are still obtainable from classical considerations.

nlin.CD↗

arXiv2000

Multielectron ionization of atoms in strong fields: Classical analysis in symmetric subspace

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 symmetric escape from a highly excited intermediate complex. For a configuration of N electrons with C_Nv symmetry in a plane perpendicular to the electric field we analyze the classical motion in phase space and discuss the final momentum distribution parallel and perpendicular to the polarization axis. The results are in good agreement with recent experiment of multiple ionization in Ne.

physics.atom-ph↗

arXiv2000

Classical double ionization of atoms in strong fields

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 be ejected in the same direction along the field. We discuss the final stages of this process in a classical model in the spirit of Wanniers approach to double ionization after electron impact. Starting from an intermediate state of high but negative energy the field opens up a channel through which both electrons can escape. Near the threshold for this process Coulomb repulsion favors an escape with the electron momenta and positions symmetric with respect to the electric field axis. Classical trajectory simulations within this symmetry subspace account for most features of the observed momentum distribution.

physics.atom-ph↗

arXiv2000

Transition from the Couette-Taylor system to the plane Couette system

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 the formation of Taylor vortices is lost and how the character of the transition approaches that of planar shear flows. In particular, a parameter regime is identified where fractal distributions of life times and spatiotemporal intermittency occur. Experiments in this regime should allow to study the characteristics of shear flow turbulence in a closed flow geometry.

physics.flu-dyn↗

arXiv1999

Magnetic field correlations in kinematic two-dimensional magnetohydrodynamic turbulence

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 magnetohydrodynamic turbulence in the kinematic regime where the ratio of kinetic energy to magnetic energy is much larger than one. In this regime the magnetic flux function $ψ$ can be treated as a passive scalar advected in a two-dimensional turbulent flow. Its structure function $D_2^{(ψ)}(r)$ and the one for the magnetic field D_2^{(B)}(r) are connected by an exact relation. We calculate D_2^{(ψ)}(r) and thus D_2^{(B)}(r) within geometric measure theory over a wide range of scales r and magnetic Prandtl numbers Pr_m. The magnetic field correlations follow a r^{-4/3} - scaling law and show an anticorrelation at the beginning of the Batchelor regime indicative of the formation of strongly filamented current sheets. Differences to the full dynamic regime, where the ratio of kinetic to magnetic energies is smaller than in the kinematic case, are discussed.

chao-dyn↗

arXiv1999

Structure function of passive scalars in two-dimensional turbulence

The structure function of a scalar $θ({\bf x},t)$, passively advected in a two-dimensional turbulent flow ${\bf u}({\bf x},t)$, is discussed by means of the fractal dimension $δ^{(1)}_g$ of the passive scalar graph. A relation between $δ^{(1)}_g$, the scaling exponent $ζ_1^{(θ)}$ of the scalar structure function $D_1^{(θ)}(r)$, and the structure function D_2(r) of the underlying flow field is derived. Different from the 3-d case, the 2-d structure function also depends on an additional parameter, characteristic of the driving of the passive scalar. In the enstrophy inertial subrange a mean field approximation for the velocity structure function gives a scaling of the passive scalar graph with $δ^{(1)}_g<2$ for intermediate and large values of the Prandtl number Pr. In the energy inertial subrange a model for the energy spectrum and thus D_2(r) gives a passive scalar graph scaling with exponent $δ^{(1)}_g={5/3}$. Finally, we discuss an application to recent observations of scalar dispersion in non-universal 2-d flows.

chao-dyn↗