262 research outputs found
Chaotic saddles in nonlinear modulational interactions in a plasma
A nonlinear model of modulational processes in the subsonic regime involving
a linearly unstable wave and two linearly damped waves with different damping
rates in a plasma is studied numerically. We compute the maximum Lyapunov
exponent as a function of the damping rates in a two-parameter space, and
identify shrimp-shaped self-similar structures in the parameter space. By
varying the damping rate of the low-frequency wave, we construct bifurcation
diagrams and focus on a saddle-node bifurcation and an interior crisis
associated with a periodic window. We detect chaotic saddles and their stable
and unstable manifolds, and demonstrate how the connection between two chaotic
saddles via coupling unstable periodic orbits can result in a crisis-induced
intermittency. The relevance of this work for the understanding of modulational
processes observed in plasmas and fluids is discussed.Comment: Physics of Plasmas, in pres
Relativistic ponderomotive force, uphill acceleration, and transition to chaos
Starting from a covariant cycle-averaged Lagrangian the relativistic
oscillation center equation of motion of a point charge is deduced and
analytical formulae for the ponderomotive force in a travelling wave of
arbitrary strength are presented. It is further shown that the ponderomotive
forces for transverse and longitudinal waves are different; in the latter,
uphill acceleration can occur. In a standing wave there exists a threshold
intensity above which, owing to transition to chaos, the secular motion can no
longer be described by a regular ponderomotive force.
PACS number(s): 52.20.Dq,05.45.+b,52.35.Mw,52.60.+hComment: 8 pages, RevTeX, 3 figures in PostScript, see also
http://www.physik.th-darmstadt.de/tqe
A Geometrical Method of Decoupling
The computation of tunes and matched beam distributions are essential steps
in the analysis of circular accelerators. If certain symmetries - like midplane
symmetrie - are present, then it is possible to treat the betatron motion in
the horizontal, the vertical plane and (under certain circumstances) the
longitudinal motion separately using the well-known Courant-Snyder theory, or
to apply transformations that have been described previously as for instance
the method of Teng and Edwards. In a preceeding paper it has been shown that
this method requires a modification for the treatment of isochronous cyclotrons
with non-negligible space charge forces. Unfortunately the modification was
numerically not as stable as desired and it was still unclear, if the extension
would work for all thinkable cases. Hence a systematic derivation of a more
general treatment seemed advisable.
In a second paper the author suggested the use of real Dirac matrices as
basic tools to coupled linear optics and gave a straightforward recipe to
decouple positive definite Hamiltonians with imaginary eigenvalues. In this
article this method is generalized and simplified in order to formulate a
straightforward method to decouple Hamiltonian matrices with eigenvalues on the
real and the imaginary axis. It is shown that this algebraic decoupling is
closely related to a geometric "decoupling" by the orthogonalization of the
vectors , and , that were introduced with the
so-called "electromechanical equivalence". We present a structure-preserving
block-diagonalization of symplectic or Hamiltonian matrices, respectively. When
used iteratively, the decoupling algorithm can also be applied to n-dimensional
systems and requires iterations to converge to a given
precision.Comment: 13 pages, 1 figur
Numerical estimation of Carbonate properties using a digital rock physics workflow
Digital rock physics combines modern imaging with advanced numerical simulations to analyze the physical properties of rocks -- In this paper we suggest a special segmentation procedure which is applied to a carbonate rock from Switzerland -- Starting point is a CTscan of a specimen of Hauptmuschelkalk -- The first step applied to the raw image data is a nonlocal mean filter -- We then apply different thresholds to identify pores and solid phases -- Because we are aware of a nonneglectable amount of unresolved microporosity we also define intermediate phases -- Based on this segmentation determine porositydependent values for the pwave velocity and for the permeability -- The porosity measured in the laboratory is then used to compare our numerical data with experimental data -- We observe a good agreement -- Future work includes an analytic validation to the numerical results of the pwave velocity upper bound, employing different filters for the image segmentation and using data with higher resolutio
Digital carbonate rock physics
Modern estimation of rock properties combines imaging with advanced numerical simulations, an approach known as digital rock physics (DRP). In this paper we suggest a specific segmentation procedure of X-ray micro-computed tomography data with two different resolutions in the µm range for two sets of carbonate rock samples. These carbonates were already characterized in detail in a previous laboratory study which we complement with nanoindentation experiments (for local elastic properties). In a first step a non-local mean filter is applied to the raw image data. We then apply different thresholds to identify pores and solid phases. Because of a non-neglectable amount of unresolved microporosity (micritic phase) we also define intermediate threshold values for distinct phases. Based on this segmentation we determine porosity-dependent values for effective P- and S-wave velocities as well as for the intrinsic permeability. For effective velocities we confirm an observed two-phase trend reported in another study using a different carbonate data set. As an upscaling approach we use this two-phase trend as an effective medium approach to estimate the porosity-dependent elastic properties of the micritic phase for the low-resolution images. The porosity measured in the laboratory is then used to predict the effective rock properties from the observed trends for a comparison with experimental data.The two-phase trend can be regarded as an upper bound for elastic properties; the use of the two-phase trend for low-resolution images led to a good estimate for a lower bound of effective elastic properties. Anisotropy is observed for some of the considered subvolumes, but seems to be insignificant for the analysed rocks at the DRP scale. Because of the complexity of carbonates we suggest using DRP as a complementary tool for rock characterization in addition to classical experimental methods
Non-abelian plane waves and stochastic regimes for (2+1)-dimensional gauge field models with Chern-Simons term
An exact time-dependent solution of field equations for the 3-d gauge field
model with a Chern-Simons (CS) topological mass is found. Limiting cases of
constant solution and solution with vanishing topological mass are considered.
After Lorentz boost, the found solution describes a massive nonlinear
non-abelian plane wave. For the more complicate case of gauge fields with CS
mass interacting with a Higgs field, the stochastic character of motion is
demonstrated.Comment: LaTeX 2.09, 13 pages, 11 eps figure
Digital material laboratory: Wave propagation effects in open-cell aluminium foams
This paper is concerned with numerical wave propagation effects in highly porous media using digitized images of aluminum foam -- Starting point is a virtual material laboratory approach -- The Aluminum foam microstructure is imaged by 3D X-ray tomography -- Effective velocities for the fluid-saturated media are derived by dynamic wave propagation simulations -- We apply a displacement-stress rotated staggered fnite-difference grid technique to solve the elastodynamic wave equation -- The used setup is similar to laboratory ultrasound measurements and the computed results are in agreement with our experimental data -- Theoretical investigations allow to quantify the influence of the interaction of foam and fluid during wave propagation – Together with simulations using an artificial dense foam we are able to determine the tortuosity of aluminum foa
The Partition Function and Level Density for Yang-Mills-Higgs Quantum Mechanics
We calculate the partition function and the asymptotic integrated
level density for Yang-Mills-Higgs Quantum Mechanics for two and three
dimensions (). Due to the infinite volume of the phase space
on energy shell for , it is not possible to disentangle completely the
coupled oscillators (-model) from the Higgs sector. The situation is
different for for which is finite. The transition from order
to chaos in these systems is expressed by the corresponding transitions in
and , analogous to the transitions in adjacent level spacing
distribution from Poisson distribution to Wigner-Dyson distribution. We also
discuss a related system with quartic coupled oscillators and two dimensional
quartic free oscillators for which, contrary to YMHQM, both coupling constants
are dimensionless.Comment: 10 pages, LaTeX; minor changes; version accepted for publication as a
Letter in J. Phys.
Algorithmic Integrability Tests for Nonlinear Differential and Lattice Equations
Three symbolic algorithms for testing the integrability of polynomial systems
of partial differential and differential-difference equations are presented.
The first algorithm is the well-known Painlev\'e test, which is applicable to
polynomial systems of ordinary and partial differential equations. The second
and third algorithms allow one to explicitly compute polynomial conserved
densities and higher-order symmetries of nonlinear evolution and lattice
equations.
The first algorithm is implemented in the symbolic syntax of both Macsyma and
Mathematica. The second and third algorithms are available in Mathematica. The
codes can be used for computer-aided integrability testing of nonlinear
differential and lattice equations as they occur in various branches of the
sciences and engineering. Applied to systems with parameters, the codes can
determine the conditions on the parameters so that the systems pass the
Painlev\'e test, or admit a sequence of conserved densities or higher-order
symmetries.Comment: Submitted to: Computer Physics Communications, Latex, uses the style
files elsart.sty and elsart12.st
- …