Dr. Henry
E. Kandrup is a Professor of Astronomy at the University
of Florida, with a joint appointment in the Department
of Physics. He is also a member of the Institute
for Fundamental Theory at the University of Florida, an interdisciplinary
program which includes Professors and Postdoctoral Fellows from the Departments
of Astronomy, Mathematics,
and
Physics. During the early 1990's, his
principal funding came from the
Gravitational
Physics Division of the National Science
Foundation. During the late 1990's, he was supported
by the Institute for Geophysics and Planetary Physics at Los Alamos National
Laboratory. Since 1 July 2000, he has been supported by
Extragalactic Astronomy and Cosmology in the
Division
of Astronomical Sciences
and/or Applied Mathematics in the
Division
of Mathematical Sciences
at the NSF.
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for a photograph.
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Research Associates, etc.
Dr. Balsa Terzic is a Postdoctoral Fellow in the Department of
Astronomy at the University of Florida. He received his Ph. D. in Mathematics
from Florida State University on Spring 2002 for a dissertation that involved
applications of nonlinear dynamics to problems related to galactic astronomy.
Kandrup and Terzic have already collaborated on three papers, `Semi-Analytic
Estimates of Lyapunov Exponents in Lower-Dimensional Systems', `Supermassive
Black Hole Binaries as Galactic Blenders,' and `Orbital Structure in
Oscillating Galactic Potentials,'
and are currently working on several new projects related to manifestations of
chaos in time-dependent Hamiltonian systems and the implications thereof for
violent relaxation.
Dr. Reva Kay Williams was a Postdoctoral Ford Foundation Minority
Fellow in the Department of Astronomy from 1993-1994, and a
Postdoctoral Research Associate from 1995-1997. Williams received her
Ph.D. in Astrophysics from Indiana University, Bloomington in December 1991.
She is internationally known as the first person to successfully work
out the Penrose mechanism to extract energy from a black hole
(1995, Phys. Rev. D, 51, 5387-5427), and she is the U.S.A.'s
first Black female Astrophysicist. Williams spent the last few
years as a Visiting Assistant Professor of Physics at North Carolina
A & T State University, and an Associate Professor of Astrophysics at
Bennett College.
Recent Graduates
Ioannis V. Sideris
received his Ph. D. in Astronomy in August 2002 for
a dissertation which focused on the meaning and manifestations of chaos
for the gravitational N-body problem. This and related work -- much impacting
on chaos in noneutral plasmas and charged particle beams -- has led already
to nine refereed publications, four conference proceedings, and another three
papers which have been submitted for publication. These includ inter alia
three refereed papers on the meaning of the continuum limit in the
gravitational N-body problem, one on noise-induced phase space transport, one
on a simple toy model that reproduces much of the physics observed in triaxial
Dehnen potentials, one on generating semi-analytic estimates of Lyapunov
exponents in lower-dimensional Hamiltonian systems, two papers involving
the physics of charged particle beams, and two exploring resonance-triggered
chaos in time-dependent galactic potentials.
Sideris is currently a postdoctoral fellow for Courtlandt Bohn
in the Department of Physics at Northern Illinois University, where he is
working with personnel from NIU and Fermilab on problems related to chaotic
phase mixing in both galaxies and charged particle beams.
Ilya V. Pogorelov received his Ph. D. in Physics in May 2001 for
a dissertation entitled ``Phase Space Transport and the Continuum Limit in
Nonlinear Hamiltonian Systems.'' The research contained therein had two
principal foci, namely (i) understanding how and why flows in complex
lower-dimensional Hamiltonian systems are impacted by low amplitude
irregularities, reflecting, e.g., internal discreteness effects or external
perturbations which are all too often ignored, and (ii) understanding the
nature of the continuum limit for the gravitational N-body problem, in
particular how to reconcile chaotic motions for arbitrarily large N-body
systems with the possibility of regular, and even integrable, behaviour in
the continuum limit. Subsequently, he was a postdoctoral fellow in Physics at
the University of Florida, where he worked with Jim Dufty on the nonlinear
dynamics of Quantum Plasmas. He is currently a research associate at Lawrence
Berkeley Laboratories, where he is working on a variety of problems related
to the modeling of complex systems. Ilya has collaborated with Kandrup and
others in the Gravitational Astrophysics Group on three
refereed papers -- one which involved the construction of spherically
symmetric phase space solutions to the collisionless Boltzmann equation of
general relativity (Vlasov-Einstein system) with specified spatial densities
and two which studied the role of both white and colored noise as sources of
accelerated phase space transport in two- and three-degree-of-freedom
Hamiltonian systems -- and two refereed conference proceedings. In addition,
he has collaborated with Dufty on several
other papers. His most recent paper, written in collaboration with Kandrup,
focused on generalisations of FPU-type models which go beyond the usual
nearest-neighbour couplings, demonstrating that such longer-range interactions
can actually facilitate localisation of energy in a single degree of freedom.
In addition to other activities, Ilya is currently preparing a paper
summarising his research on the continuum limit.
Eric O'Neill received his Ph. D. in Physics in May 2000. He has
collaborated with Kandrup on three publications involving the Hamiltonian
structure of the collisionless Boltzmann equation and the problem of stability,
both for relativistic star clusters and conformally static cosmological
models. The paper by Kandrup and O'Neill identifying a cosymplectic structure
for the Vlasov-Einstein system constitutes the first analytic work ever
on the problem of stability for collisionless equilibria in general relativity
not assumed to be spherically symmetric. O'Neill's dissertation topic involved
a systematic investigation of the Hamiltonian structure of collisionless
matter in the context of general relativity and two alternative theories
of gravity, namely the Brans-Dicke theory and Kibble's tetrad theory. A paper
on the Brans-Dicke theory was recently submitted to Physics Review D.
Christos V. Siopis received his Ph. D. in Astronomy
in December 1998 for a dissertation
entitled ``Nonuniqueness and structural stability
of self-consistent models of elliptical galaxies.'' The principal aim of this
thesis was to use Schwarzschild's method to construct models of self-consistent
galaxies for cuspy, triaxial galaxies that admit large numbers of chaotic
orbits. After receiving his Ph. D., he spent a year as a visitor with
Evanegelia Athanassoula at the Observatoire de Marseille where, inter alia,
he tested the stability of these models by performing N-body realisation on
the GRAPE (GRAvity PipE) computer system. He then returned to Greece for a
period of compulsory military service. He is currently a postdoc
in Astronomy at the University of Michigan in October 2001, where he is a
member of the Nuker Team. Siopis has collaborated with Kandrup
on two refereed publications related to chaos in near-equilibrium galactic
models, and is currently working with him on another.
Siopis has also collaborated on seven other papers, including:
a numerical investigation of the instability of the gravitational N-body
problem towards small changes in initial conditions; four papers on the
behaviour of energetically unbounded orbits in a nonspherical potential (a
simple variant of the problem of chaotic scattering); a paper which quantifies
the sense in which, over finite time intervals, two different notions of
chaos coincide, namely exponential instability towards small change in
initial conditions and broad band power; and a paper on interface instabilities
in the interstellar medium.
David E. Willmes
received his Ph. D. in Physics in December 1995. His dissertation considered
a number of different problems related to ``Noise, Shadowing, and the
Reliability of Numerical N-Body Simulations.'' Willmes collaborated with
Kandrup on two publications, one involving a numerical investigation of the
instability
of the N-body problem towards small changes in initial conditions, and
the other involving an analytic discussion of the effects of friction and
noise in nonintegrable potentials. In addition, he wrote three sole
author papers on the problem of shadowing in numerical simulations. A major
focus of his work was on the difficulty of identifying a meaningful notion
of ``average shadowing time'' for numerical integrations. He is now making
big bucks applying his scientific and computational skills to the service
of American capitalism in the private sector.
John Drury received his M. S. in Astronomy in May 1998. While in
Gainesville, he worked on several problems related to the possible
manifestations of chaos in Hamiltonian systems which manifest a systematic
secular time-dependence of the form encountered in cosmology. This led to one
publication coauthored with Kandrup.
Brendan O. Bradley received his M. S. in Astronomy in May 1995
and subsequently transfered to the Applied Mathematics Program at the
University
of New Mexico, where he received another M. S. He is currently supported
as a research fellow in the Ph. D. program at Boston University, where
he is engaged in dissertation research which involves applications of nonlinear
dynamics to biophysics. He has collaborated with Kandrup and others at
the University of Florida on five publications. Three of these involved
an analysis of the short time behaviour of ensembles of stochastic orbits,
evolving in a nonintegrable time-independent potential. The others involved
an analysis of how this behaviour is modified when the ensembles are subjected
to low amplitude periodic driving. He has also collaborated with the lovely
Michelle in the production of two little Bradleys (Bradlets?).
Students
Barbara L. Eckstein
is a senior graduate student in the Department of Astronomy, currently on
an extended leave of absence at the University of Michigan in scenic (and
civilised) Ann Arbor (Lucky Barbara!), where her husband Renato Dupke is a
postdoc in Astronomy. She has collaborated with Kandrup on four papers which
focus on short time characterisations
of chaotic orbit segments, including one establishing an interesting connection
between the degree of instability exhibited by the orbit, as probed by
short time Lyapunov exponents, and the complexity of the orbit, as measured
by the number of Fourier modes which contain significant power. She has
also collaborated with people at the Navel Research Laboratory in Washington
on two papers involving the use of wavelets and other more conventional
tools in effecting the compression of satellite data. Her dissertation
research involves an investigation of time-dependent resonant phenomena
in the context of inflationary models in cosmology, focusing in particular
on the possibility of exponential bursts of particle creation triggered
by parametric instability -- post-inflationary preheating.
Ileana Vass is a fourth year graduate student in the Department
of Astronomy who has begin working with Kandrup. In collaboration with
with Kandrup and Sideris, she has recently completed a numerical investigation
of how the introduction of an oscillatory time-dependence can induce (possibly
transient) chaos in an otherwise regular Hamiltonian system. The ultimate aim
of this and related work is to better understand the potential role of chaotic
phase mixing in explaining the remarkable efficiency of `violent relaxation,'
i.e., the collective relaxation of nearly collisionless systems of stars.
Her dissertation work will involve an analysis of the role of chaos in
fully self-consistent simulations of violent relaxation in galaxies and
galactic halos.
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Related Groups
Henry Kandrup is a member of the
an interdisciplinary group comprised of faculty from the Physics, Mathematics,
and Astronomy Departments at the University of Florida.
Members of the Gravitational Astrophysics Group interact intermittently
with two other groups:
The Theoretical
Astrophysics Group in the Department of Physics consists of five faculty
members, J. Robert Buchler (Professor), Steven L. Detweiler (Professor),
James N. Fry (Professor), James R. Ipser (Professor), and Bernard F. Whiting
(Professor), and has varied interests in cosmology, quantum gravity,
relativistic
astrophysics, nonlinear dynamics, and pulsating stars. In the past, the
Gravitational Astrophysics Group in Astronomy and the Astrophysics Group
in Physics have jointly coordinated a weekly inter-departmental
Astronomy-Physics
seminar series in Theoretical Astrophysics.
The Galaxy Group
in the Department of Astronomy consists of two faculty members, Stephen
T. Gottesman (Professor), and James H. Hunter (Professor), and has varied
interests in galactic and nonlinear dynamics.
In addition, various members of the Gravitational Astrophysics Group
have collaborated with Haywood Smith, Jr., an Associate Professor in Astronomy
with interests in galactic dynamics and computational astronomy.
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For the past several years, Henry Kandrup and Robert Buchler (from Physics)
have assumed joint responsibility for organising the:
Florida Workshops in Nonlinear Astronomy and Physics
These workshops, which typically run for three days each winter, are
intrinsically
interdisciplinary in nature, aiming to facilitate interactions amongst
workers (i) interested in diverse problems that involve similar methodologies
and/or (ii) applying very different methdologies to the same problem. The
proceedings have generally been published in the Annals of the New York
Academy of Sciences. Previous workshops include the following:
Workshop XV: ``The Onset of Nonlinearity,'' J. R. Buchler, J. N. Fry, and
H. E. Kandrup, Eds. Annals of the New York Academy of Sciences, in
preparation.
Workshop XIV: ``Astrophysical Turbulence and Convection,'' J. R. Buchler
and H. E. Kandrup, Eds. Annals of the New York Academy of Sciences, Vol. 898
(2000).
Workshop XIII: ``Nonlinear Dynamics and Chaos in Astrophysics,'' J.
R. Buchler, S. T. Gottesman and H. E. Kandrup, Eds. Annals of the New York
Academy of Sciences, Vol. 867 (1998).
Workshop XII: ``Long-Range Correlations in Astrophysical Systems'' J.
R. Buchler, J. W. Dufty and H. E. Kandrup, Annals of the New York Academy
of Sciences, Vol. 848 (1998).
Workshop XI: ``Nonlinear Signal and Image Processing,'' J. R. Buchler
and H. E. Kandrup, Eds. Annals of the New York Academy of Sciences, Vol.
808 (1996).
Workshop X: ``Waves in Astrophysics,'' J. H. Hunter and R. E. Wilson,
Eds. Annals of the New York Academy of Sciences, Vol. 773 (1995).
Workshop IX: ``Three-Dimensional Systems,'' H. E. Kandrup, S. T. Gottesman,
and J. R. Ipser, Eds. Annals of the New York Academy of Sciences, Vol.
751 (1995).
Workshop VIII: ``Stochastic Processes in Astrophysics,'' J. R. Buchler
and H. E. Kandrup, Eds. Annals of the New York Academy of Sciences, Vol.
706 (1993).
Workshop VII: ``Astrophysical Disks,'' S. F. Dermott, J. H. Hunter,
and R. E. Wilson, Eds. Annals of the New York Academy of Sciences, Vol.
675 (1992).
Workshop VI: ``Nonlinear Problems in Relativity and Cosmology,'' J.
R. Buchler, S. L. Detweiler, and J. R. Ipser, Eds. Annals of the New York
Academy of Sciences, Vol. 631 (1991).
Workshop V: ``Nonlinear Astrophysical Fluid Dynamics,'' J. R. Buchler,
and S. T. Gottesman, Eds. Annals of the New York Academy of Sciences, Vol.
617 (1990).
Workshop IV: ``Galactic Models,'' J. R. Buchler, S. Gottesman, and J.
Hunter, Eds. Annals of the New York Academy of Sciences, Vol. 596 (1989).
Workshop III: ``Integrability in Dynamical Systems,'' J. R. Buchler,
J. Ipser, and C. Williams, Eds. Annals of the New York Academy of Sciences,
Vol. 536 (1988).
Workshop II: ``Chaotic Phenomena in Astrophysics,'' J. R. Buchler and
H. Eichhorn, Eds. Annals of the New York Academy of Sciences, Vol. 497
(1987).
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Research Activities
The principal objective of the research undertaken by members of this group
has been the application of ideas and techniques from statistical mechanics
and nonlinear dynamics to problems in which self-gravity is important,
with the specific aim of addressing the special features which arise because
of gravity.
At present most of this work divides into seven general categories:
Transient chaos, chaotic phase mixing and violent relaxation.
Any successful theory of collisionless relaxation must explain both (i)
the rate and efficiency with which systems relax towards a nearly
time-independent state and (ii) the form of that time-independent state.
The aim of the research here is to address both these issues.
Subjecting a galactic potential to a period of time-dependence with a strong,
possibly damped, oscillatory component can give rise to large amounts of
transient chaos, and the chaotic phase mixing associated with this transient
chaos could play a major role in accounting for the speed and efficacy of
violent relaxation. This transient chaos appears to result from a resonant
coupling between the frequencies of the orbits or phase elements in the
system and the frequencies associated with the time-dependent pulsations,
a resonance which in many -- albeit not all -- cases is also very effective
in shuffling the energies of orbits or phase elements. Simulations are
underway to probe the extent to which simulations of violent relaxation
yield large measures of chaotic orbits, and the degree to which the speed
and `completeness' of violent relaxation correlate with the amount of chaos
and the strength of the time-dependent oscillations.
Manifestations of chaos in charged particle beams.
Theoretical and numerical investigations agree that, to a considerable
extent, the physics of `nearly collisionless' self-gravitating systems
should be similar to the physics of `nearly collisionless' nonneutral plasmas
and charged particle beams: It is the existence of long range order, rather
than the sign of the interactions, which drives much of what happens in
these systems. This suggests that predictions made regarding galaxy evolution
can also be translated into predictions regarding systems like accelerator
beams, a setting in which, unlike the case of galaxies, they can be tested
via real experiments in the laboratory. The Gravitational Astrophysics Group
is current collaborating with accelerator physicists -- both theorists and
experimentalists -- at Fermilab/Northern Illinois University and the
University of Maryland in the design of experiments involving charged particle
beams with the dual aims of (i) generating more sharply collimated beams
and, thereby, (ii) gaining new insights into galactic astronomy.
Successful simulations of surprising experiments have already provided
seemingly conclusive evidence that chaotic phase mixing can play a major role
in the degradation of a charged particle beam.
The short term goal here is
to perform experiments on the DOE-supported University of Maryland Electron
Ring
(UMER),
scheduled for commissioning by the end of 2003. The ring is 11 m in
circumference and transports an electron beam with 10 KeV kinetic energy, 100
mA
current, and 10 micron effective emittance. The nominal bunch contains of
order
10 billion electrons spanning a volume 1 cm in radius and 3 m in length.
However,
the bunch charge, and hence the collective space-charge force, is adjustable
over
a wide range. Two beam sources are available, a thermionic cathode and a
laser-driven photocathode system.
A localized modulation of the thermionic electron current can be applied using
a 5 ns laser pulse.
The level of modulation far exceeds what is achievable by grid pulsing alone,
and the technique enables the formation of initially localized particle clumps
of desired strength and position in the beam.
In addition, any desired multibeamlet distribution can easily be created by
masking the source beam.
The beam is then injected into the ring by means of a magnetic kicker system.
The ring confines and steers the beam by means of a magnet system comprising
alternating-gradient quadrupoles for transverse confinement, dipoles for
bending, and inductive modules for longitudinal confinement.
The system is designed so that the beam can be transported over 1 km, a
distance that spans some 500 - 1000 plasma periods (dynamical times).
Beam diagnostics presently installed on UMER include phosphor screens,
fast beam position monitors, fast energy analyzers, and both fast and
integrated transverse phase space monitors.
Collectively the diagnostics are capable of detailed, time-resolved
measurement of the full six-dimensional phase space distribution function of a
`charge bunch' as it cruises down the pipe with 5 ns resolution.
Because these diagnostics probe the same observables as generated in
simulations they provide the means for direct, detailed comparison with
theoretical and numerical predictions!
Accordingly, UMER can serve as a platform for a virtually unlimited range
of experiments to explore nonlinear, transient dynamics of systems interacting via
long range inverse square law forces. The plan is to exploit this capability to
access the physics of collisionless relaxation that large charged-particle and
self-gravitating systems share in common.
Specific short term goals include: tracking `violent relaxation'
in a bunch that is started far from equilibrium (i.e., subjected to a large
initial `mismatch'); determining as a function of bulk initial conditions the
fraction of the particles in such a bunch which are chaotic; determining the
extent to which the degree of (at least initial) chaos, as probed by the
relative measure of chaotic orbits and/or the size of a typical finite time
Lyapunov exponent, correlates with the time scale associated with collective
relaxation; and determining whether there is a systematic tendency for a
bunch to evolve towards an equilibrium or quasi-equilibrium state which
minimises the amount of chaos.
Manifestations of chaos in realistic galactic potentials.
Work here focuses on a variety of issues including:
(i) The role of chaos in determining the shapes of real galaxies.
Can one explain the fact that real ellipticals are slightly boxy or disky,
and that this boxiness or diskiness correlates with such properties as
rotation rate, steepness of cusp, or deviation from axisymmetry, in terms of
dynamical considerations? Is it, e.g., true that the observed deviations
from ellipticity conspire to reduce the relative number of chaotic orbits or to
increase the numbers of certain regular orbit types required as a skeleton
to support the observed structure?
(ii) Observational signatures of chaos. Are there certain specific
signatures which, if observed in real galaxies, could be interpreted as
prima facia evidence for chaos?
(iii) Secular variations in galaxy shapes. A variety of theoretical
arguments suggest that, rather than being viewed as objects `in equilibrium,'
galaxies should be viewed as objects which, as a result of the physics of
galaxy formation, quickly evolved towards a quasi-equilibrium but,
since then have evidenced a much slower systematic evolution, e.g., towards
more symmetrically shaped configurations.
In a similar fashion, and for much the same reason, one might expect systematic
evolutionary effects in galaxy clusters, e.g., as predicted by galaxy
harassment models. The objective here is to make precise such arguments and,
thereby, facilitate detailed predictions as to expected changes as a function
of redshift that could be tested using the Sloan Digital Sky Survey and
other low- to medium-redshift surveys.
Microchaos and macrochaos: the nature of the continuum limit in
the N-body problem.
Recent work has shown that at least two different `types' of chaos can be
present in the N-body problem: Close encounters between
nearby masses will trigger microchaos, a generic feature of the
N-body problem, resulting in orbits
characterised by very large Lyapunov exponents that do not
decrease with increasing N, even for an N-body system sampling a bulk density
distribution that corresponds to an integrable potential.
In addition, if the bulk potential admits global
stochasticity one will also observe macrochaos which is typically
characterised by much smaller, but still positive, Lyapunov exponents.
In the large N limit, the `range' of the microchaos becomes so short as to
be largely irrelevant in terms of macroscopic behaviour, but the interplay
between micro- and macrochaos can still prove important for systems like
galaxies and charged-particle beams. In particular, the fact that the
energy relaxation time is much longer than the time scales of interest does
not necessarily imply that discreteness effects can always be
ignored, especially if the system admits large measures of chaotic orbits.
`Clumps' of particles can disperse much faster than predicted in the
continuum limit and, in at least some cases, discreteness effects can induce
significant numbers of transitions between regular and chaotic behaviour.
This prediction has important potential implications for accelerators
where, in many cases, a naive application of the continuum limit does not
appear to be justified!
Structural stability of time-independent Hamiltonian systems
towards low-amplitude perturbations: the role of extrinsic diffusion.
The aim here is to determine
the conditions under which effects that are usually ignored, e.g., discreteness
effects, internal oscillations, and interactions with an external environment,
can be important on time scales short compared with the age of the Universe.
Most of this work is based on the assumption that the high frequency perturbing
influences can be modeled as friction and white noise and that lower frequency
contributions can be modeled as systematic (near-)periodic driving and/or
coloured noise. Specific areas of interest include: (1) the general theory of
modeling interactions between a system and its environment, allowing for long
range interactions of the sort arising for self-gravitating systems; (2)
Langevin simulations, which probe the response of ensembles of orbits to low
amplitude friction and noise, considering both the pointwise behaviour of
individual trajectories and the statistical properties of the ensembles; and
(3) the response of orbits to low amplitude periodic driving, again
considering both the pointwise behaviour of individual trajectories and the
statistical properties of orbit ensembles. Recent work on coloured noise with
a band-limited power spectrum has facilitated the first seemingly clear
understanding of why noise has the effect that it does.
Geometric interpretation of chaos in lower-dimensional Hamiltonian
systems.
Working in the context of a geometric reformulation, where the Hamiltonian
flow is viewed as a geodesic flow,
the objective has been to use thermodynamic arguments to provide estimates
of the size of the largest Lyapunov exponents in lower-dimensional Hamiltonian
systems. Until recently, most work in this setting assumed, at least
implicitly, that chaos reflects negative curvature: if, e.g., curvature is
everywhere negative, the Jacobi equation implies that initially nearby orbits
will always diverge exponentially. Recently, however, it has been recognised
that chaos can arise in positive-curvature settings, resulting instead from
a parametric instability. Following arguments first suggested by Marco Pettini
about a decade ago, the object of research hitherto has been to approximate
the `true' Jacobi equation by a stochastic oscillator equation and, by
identifying
an appropriate set of statistical properties, derive an approximate expression
for the largest Lyapunov exponent. Considerable progress has already been made
for the case of time-independent Hamiltonian systems, where the natural arena
is a Riemannian manifold equipped with an Eisenhart metric. In particular, a
clear understanding has begun to emerge as to when such an approach can work,
the breakdown of this approach under certain circumstances reflecting a
fundamental limitation to the application of thermodynamics to low-dimensional
systems. Attention is currently focusing on time-periodic
Hamiltonian systems, where one works with a higher-dimensional manifold
equipped with a Finsler metric. In this case, chaos can still arise via a
parametric resonance but, because it is triggered by a fixed, periodic
perturbation,
the physical picture appears best captured by a deterministic, rather than
stochastic,
oscillator equation which, for the trivial case of a driven harmonic
oscillator, reduces to a standard Matthieu equation.
Mathematical properties of the collisionless Boltzmann
equation, both Newtonianly and in general relativity.
At the present time, surprisingly little is known rigorously about an
evolution described by the collisionless Boltzmann equation. There are, e.g.,
no hard results regarding any coarse-grained approach towards `equilibrium.'
Even such a seemingly basic property as global existence was only proven about
ten years ago. Specific areas of
interest include: (1) an analysis of the Hamiltonian structure of the
collisionless Boltzmann equation, both Newtonianly and in general relativity;
(2) the
utilisation of this Hamiltonian structure to study the problem of stability
for time-independent equilibrium solutions to the collisionless Boltzmann
equation; (3) a generalisation of this approach to study the problem of
stability for time-dependent steady state solutions, e.g., in the context
of cosmology; and (4) the problems of existence and uniqueness for triaxial
equilibrium solutions to the collisionless Boltzmann equation in Newtonian
gravity.
Other areas of interest include:
-
Manifestations and implications of chaos in Hamiltonian systems which
incorporate a systematic time-dependence of the form encountered when
considering
various problems in classical and quantum physics in the context of an
expanding Universe. One problem of particular interest is the cosmological
N-body problem, as formulated in comoving coordinates.
-
Particle creation and entropy generation in the early Universe. At the
present time, the principal
focus here is on what Kofman, Linde, and Starobinskii term ``stochastic
resonance,'' a variant of the ordinary parametric amplification mechanism
proposed by Zel'dovich and Parker. Here the modes of the field acquire
time-dependence both because of redshifting associated with the
expanding Universe and because of a coupling to some oscillating
field such as the Inflaton.
-
Quantum corrections to the collisionless Boltzmann equation, appropriate
for a quantum field, which incorporate bose or fermi statistics, and the
implications of these corrections on the bulk properties of the flow.
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The problem of `noisy' chaotic scattering, i.e., the issue of how chaotic
scattering in Hamiltonian systems is impacted by small non-Hamiltonian
perturbations idealised as (in general colored) noise.
(the effects of randomness on randomness?)
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Lyapunov exponents and Fourier complexity as complimentary characterisations
of chaos over finite time intervals. There are two superfically very different
definitions of chaos in time-independent Hamiltonian systems. Chaotic orbits
manifest an exponentially sensitive dependence on initial conditions and, as
such, have positive Lyapunov exponents. They are also aperiodic, so that they
manifest broad band
`complex' Fourier spectra. To what extent is it true that, for
finite orbit segments, complex Fourier spectra correlate with large finite
time Lyapunov exponents? And can `orbital complexity' be used to identify
chaotic orbits in settings like self-consistent grid and tree codes where
computing estimates of the largest Lyapunov exponent may prove very difficult?
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Conferences and Invitations
Since 1991, Henry E. Kandrup has been an invited speaker at several
different international conferences:
-
Second International Conference on Gravitation and Cosmology, Ahmedabad,
India, December 1991: invited talk.
-
Workshop on Ergodic Concepts in Stellar Dynamics, Geneva, Switzerland,
March 1993: invited talk
-
International Conference on Mathematical Methods in Studying the Structure
and Dynamics of Gravitating Systems, Petrozavodsk, Russia, June 1993: one
invited and one contributed talk.
-
The Seventh International Marcel Grossmann Meeting on General Relativity,
Stanford, California, July 1994: invited plenary talk.
-
International Conference on Structure and Evolution of Stellar Systems,
Petrozavodsk, Russia, August 1995: invited talk.
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Los Alamos Workshop on Nonequilibrium Phase Transitions, Santa Fe, New
Mexico, July 1996: invited talk.
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Rutgers Conference on Galaxy Dynamics, Rutgers University, August 1998:
invited plenary talk
-
Workshop on Nonlinear Equations in Many-Particle Systems, Mathematische
Forschungsinstitut Oberwolfach, Germany, December 1999: invited talk
-
Stellar Dynamics: From Classic to Modern, Saint Petersburg State University,
Russia, August 2000: invited plenary talk
-
Observational Manifestations of Chaos in Astronomical Objects, Moscow State
University, Russia, August 2000: invited talk
-
Workshop on Beam Physics, University of Maryland, May 2001: invited talk
-
Nonlinear Dynamics in Many-Body Systems, University of Maryland
February 2002: invited
talk
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Division of Dynamical Astronomy, Americal Astronomical Society, Mt. Hood,
Oregon, April 2002: invited talk
-
Galaxies and Chaos, Theory and Observations, Academy of Athens, Greece,
September 2002: invited talk
-
Order and Chaos in Stellar and Planetary Systems, St. Petersburg State
University, Russia, August 2003: invited plenary review talk
In Spring 1997, Kandrup was a CNRS Visiting Professor at the Observatoire
de Marseille in France.
Henry Kandrup has been a regular participant in the summer programs
at the Aspen Center for Physics since 1988.
He has also presented eight invited talks at the annual Florida Workshops
on Nonlinear Astronomy, and edited seven of the conference proceedings.
During the past several years, Henry Kandrup has given invited colloquia
at the Institute for
Fusion Research at the University of Maryland, the Department of
Astronomy at the University of Michigan, the Theoretical
Division at Los Alamos National Laboratory, the Institute for Physical
Science and Technology at the University of Maryland, and the Inter-University
Centre for Astronomy and Astrophysics (IUCAA) in Pune, India.
He has also been a visitor at Princeton University, IUCAA, Los Alamos,
Northern Illinois University, the University of Maryland, and
Pulkhovo Observatory and Sternberg Astronomical Institute in Russia
Reva K. Williams was a participant at the Texas Meeting on
Relativistic
Astrophysics in December 1992, where she presented a poster paper. She
also presented a paper at the Marcel Grossman Meeting in Jerusalem in July
1997. In the past several years, she has given two Astronomy Colloquia
and two Astrophysics Seminars at the University of Florida.
David E. Willmes was a participant at the Texas Meeting on
Relativistic Astrophysics in December 1992. The following winter, he
participated in a Winter School on Nonlinear Dynamics in Jerusalem, where he
gave a talk on his original research.
He also presented two invited talks at the annual Florida Workshops
on Nonlinear Astronomy.
After receiving his Ph. D in Physics in December 1995, he started making
big bucks working for Northrop Grumman.
Christos Siopis was a participant at a Summer School on Galactic
Dynamics and N-body Simulations in Thessaloniki, Greece in July 1993, where
he presented a talk on his original research. In the summer of 1994, he
was a visitor at the University of Vienna and later a participant in a
Caltech Summer School on Planetary Sciences. In Spring 1996 he was an invited
participant at an Alexander von Humboldt Colloquium in Austria. In Summar
1998 he was an invited participant at a Summer School on Supercomputing
at Goodard Space Flight Center, before participating in the Rutgers Conference
on Galaxy Dynamics. He has also presented two invited talks at the annual
Florida Workshops on Nonlinear Astronomy.
He was an invited visitor at the Observatoire de Marseille for six weeks
in Spring 1997 where, in collaboration with E. Athanassoula's group, he
used the new GRAPE-3 and GRAPE-4 computer systems to effect N-body simulations
of models of cuspy, triaxial galaxies which he had constructed using
Schwarzschild's
method. He returned to Marseille after completing his Ph. D, where he
continued work on this project for a year before joining the Greek Air
Force. (Colonel Siopis?). In October 2001 he began a three year position as
Research Associate at the University of Michigan, where he is a member
of the `Nuker Team'.
Ilya V. Pogorelov was an invited participant to the Los Alamos
Workshop on Nonlinear Phase Transitions in Santa Fe, New Mexico in July
and August 1996.
He spent two months at Los Alamos each Summer in 1997, 1998, and
1999, where he participated (inter alia) in the development of numerical
codes to be used in solving the collisionless Boltzmann equation.
He received his Ph. D. in Physics in May 2001, and is currently working
as a Research Associate in the dynamics of Quantum Plasmas at the University
of Florida.
Ioannis V. Sideris was a visitor at Los Alamos in Summer 2000, where
he worked on code development for a variety of problems.
He received his Ph. D. in Astronomy in August 2002 and is currently
a Research Associate in Accelerator Dynamics at Northern Illinois
University. His work involves collaborations with physicists at NIU and
Fermilab on numerical simulations of physical processes in charged particle
beams, a major aim of which is to search for evidence for chaotic phase
mixing and transient chaos of the form also expected to arise in galactic
astronomy.
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External Collaborations
Members of this group are currently collaborating with:
-
1. Dr. Courtlandt
Bohn, Dr.
Ioannis V. Sideris, and other accelerator dynamicists at
Fermilab
and the Northern Illinois Center for Accelerator Design and Development
(NICADD).
- The principal focus of this collaboration is on understanding the
strong similarities that would be expected to exist between
manifestations of chaos in galactic astronomy and charged particle
beams. Kandrup has collaborated with Bohn and his postdoc Ioannis V.
Sideris, who received his Ph. D. in Astronomy at the University of
Florida, on a variety of projects, including inter alia
- (i) an analysis of the nature of the continuum limit in the N-body problem
for nonneutral plasmas;
- (ii) the use of `thermodynamic' arguments to estimate the values of
Lyapunov exponents in lower-dimensional time-independent Hamiltonian
systems;
- (iii) detailed comparisons of chaotic phase mixing in galaxies and charged
particle beams;
- (iv) manifestations of chaos in time-dependent potentials; and
- (v) the effects of non-Hamiltonian perturbations, e.g., friction and
(coloured) Gaussian noise, on orbits in time-dependent Hamiltonian systems.
-
2. Members of the University of Maryland
Institute for Research in Electronics
and Applied Physics, including inter alia:
-
Dr.
Martin Reiser,
Dr. Patrick O'Shea,
Dr. Rami Kishek, and
Dr.
Thomas Antonsen.
- The principal focus of this collaboration is on translating predictions
regarding manifestations of chaos in galaxies and nonneutral plasmas into
real experiments that can -- and will -- be performed using the University
of Maryland Electron
Ring
(UMER), which is currently under construction.
Kandrup has collaborated with members of this group on several papers which
explore manifestations of
chaotic phase mixing in the context of charged particle beams.
- The photograph below, taken in July 2003, shows the University of Maryland
Electron Ring (UMER) in a state of near-completion. UMER is currently scheduled
to be completed and commissioned by the end of 2003.
-
3. Dr.
Christos Siopis and others in the
Department
of Astronomy at the University of Michigan.
- Siopis, who received his Ph. D. in Astronomy at the University of
Florida, has collaborated with Kandrup on a lengthy investigation of the
manifestations of chaos in nonspherical generalisations of the so-called
Dehnen potentials, which have been proposed as a prototypical model for
a nonaxisymmetric cuspy elliptical galaxy. Kandrup and Siopis are also
contemplating the possibility of collaborating on a project which would
investigate the role of transient chaos in violent relaxation.
In the past, members of this group have also collaborated and/or otherwise
interacted with:
1. Dr. Salman Habib,
a member of Theoretical Division at Los
Alamos National Laboratory.
2. Dr. Katja
Lindenberg, a Professor in
the Department of Chemistry
and Biochemistry, University of California, San Diego
3. Dr. George Contopoulos, at the University
of Athens.
4. Dr. Evangelia
Athanassoula, at the Observatoire
de Marseille
5. Dr.
Pawel O. Mazur, a Professor of Physics at the
University
of South Carolina.
6. Dr. Arthur D. Chernin, at the
Sternberg
Institute, Moscow University.
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Publications since 1991
Henry E. Kandrup, ``A Stability Criterion for Any Collisionless Equilibrium
and Some Concrete Applications Thereof,'' Astrophysical Journal 370, 312
- 317 (1991).
Henry E. Kandrup and Haywood Smith, ``On the Sensitivity of the N-Body
Problem to Small Changes in Initial Conditions,'' Astrophysical Journal
374, 255 - 265 (1991).
Henry E. Kandrup, ``Hamiltonian Approach to Collisionless Stellar Dynamics
in General Relativity,'' Annals of the New York Academy of Sciences, 631,
88 - 96 (1991).
Henry E. Kandrup and Pawel O. Mazur, ``Generating a Hot Big Bang as a Quantum
Fluctuation,'' International Journal of Modern Physics A 6, 4041 - 4054
(1991).
Henry E. Kandrup, ``The Secular Instability of Rotating, Axisymmetric Star
Clusters,'' Astrophysical Journal 380, 511 - 514 (1991).
Henry E. Kandrup and M. Elaine Mahon, ``Gravitational Radiation from Colliding
Black Holes,'' Physical Review D 45, 1013 - 1016 (1992).
M. Elaine Mahon, ``Velocity Fields of Gas in Inclined Disks,'' Annals of
the New York Academy of Sciences 675, 115 - 125 (1992).
Henry E. Kandrup and Haywood Smith, ``On the Sensitivity of the N-Body
Problem to Small Changes in Initial Conditions. II,'' Astrophysical Journal
386, 635 - 645 (1992).
Henry E. Kandrup, Haywood Smith, and David E. Willmes, ``On the Sensitivity
of the N-Body Problem to Small Changes in Initial Conditions. III,'' Astrophysical
Journal 399, 627 - 633 (1992).
Salman Habib and Henry E. Kandrup, ``Nonlinear Noise in Cosmology,'' Physical
Review D 46, 5305 - 5314 (1992).
Henry E. Kandrup, ``Violations of the Strong Energy Condition for Interacting
Systems of Particles,'' Physical Review D 46, 5360 - 5366 (1992).
Henry E. Kandrup, ``Non-Violent Relaxation of Colliding Galaxies,'' in
Second International Conference on Gravitation and Cosmology, Ahmedabad,
India, 13 - 18 December 1991: Proceedings, Advances in Gravitation and
Cosmology, ed. B. R. Iyer, A. R. Prasanna, R. K. Varma, and C. V. Vishveshwara,
Vedam, New Delhi, 233 - 247 (1993).
Henry E. Kandrup, ``The Distribution of Forces in a Perturbed System of
Self-Gravitating Point Masses,'' Physics Letters A 173, 1 - 7 (1993).
George Contopoulos, Henry E. Kandrup, and David Kaufmann, ``Fractal Properties
of Escape from a Two-Dimensional Potential,'' Physica D 64, 310 - 323 (1993).
Henry E. Kandrup, M. Elaine Mahon, and Haywood Smith, ``Energy and Phase
Space Mixing for Self-Gravitating Systems of Stars,'' Astronomy and Astrophysics
271, 440 - 450 (1993).
Henry E. Kandrup and Eric O`Neill, ``Hamiltonian Structure of Collisionless
Newtonian Cosmologies and the Problem of Stability,'' Physical Review D
47, 3229 - 3234 (1993).
Henry E. Kandrup and Philip J. Morrison, ``Hamiltonian Structure of the
Vlasov-Einstein System and the Problem of Stability for Spherical Relativistic
Star Clusters,'' Annals of Physics 225 , 114 - 166 (1993).
Henry E. Kandrup and Eric O'Neill, ``Hamiltonian Structure of the Vlasov-Maxwell
System in a Curved Background Spacetime,'' Physical Review D 48, 4534 -
4544 (1994).
Henry E. Kandrup and M. Elaine Mahon, ``Stochastic Processes and the Gravitational
N-Body Problem,'' Annals of the New York Academy of Sciences 706, 81 -
99 (1994).
Henry E. Kandrup and David E. Willmes, ``Collisional Relaxation in a Nonintegrable
Potential,'' Astronomy and Astrophysics 283, 59 - 66 (1994).
Henry E. Kandrup, ``Stochastic Properties of the Gravitational -Body Problem,''
Astronomical and Astrophysical Transactions 7, 225 - 228 (1995).
Henry E. Kandrup, ``Collisional Relaxation in a Nonintegrable Mean Field
Potential,'' Astronomical and Astrophysical Transactions, 7, 229 - 231
(1995).
Haywood Smith, Henry E. Kandrup, M. Elaine Mahon, and Christos Siopis,
``The Approach to Integrability in N-Body Systems with a Central Point
Mass,'' in Ergodic Concepts in Stellar Dynamics: Springer Verlag Lecture
Notes in Physics, 430, ed. V. G. Gurzadyan and D. Pfenniger, Springer,
Berlin, 158 - 162 (1994).
Henry E. Kandrup and M. Elaine Mahon, ``Relaxation and Stochasticity in
a Truncated Toda Lattice,'' Physical Review E 49, 3735 - 3747 (1994).
Henry E. Kandrup, M. Elaine Mahon, and Haywood Smith, ``Global Stability
of Spherical Polytropes,'' Physical Review E 49, 3757 - 3760 (1994).
Henry E. Kandrup and Eric O`Neill, ``Hamiltonian Structure of the Vlasov-Einstein
System for Generic Collisionless Systems and the Problem of Stability,''
Physical Review D 49, 5115 - 5125 (1994).
Henry E. Kandrup, M. Elaine Mahon, and Haywood Smith, ``On the Sensitivity
of the N-Body Problem to Small Changes in Initial Conditions. IV,'' Astrophysical
Journal 428, 458 - 465 (1994).
Henry E. Kandrup, ``Reduced Hamiltonian Descriptions,'' Physical Review
D 50, 2425 - 2430 (1994).
Henry E. Kandrup and M. Elaine Mahon, ``Short Times Characterisations of
Stochasticity in Nonintegrable Galactic Potentials,'' Astronomy and Astrophysics
290, 762 - 770 (1994).
M. Elaine Mahon,``Orbits of Gas Clouds as Probes of the Shape of a Rotating
Triaxial Potential,'' Annals of the New York Academy of Sciences 751, 39
- 52 (1994).
Henry E. Kandrup and M. Elaine Mahon, ``Chaos and Noise in Galactic Dynamics,''
Annals of the New York Academy of Sciences 751, 93 - 111 (1994).
Christos Siopis, George Contopoulos, and Henry E. Kandrup, ``Escape Probabilities
from a Hamiltonian with Two Escape Channels,'' Annals of the New York Academy
of Sciences 751, 205 - 212 (1994).
David E. Willmes, ``Computer-Assisted Shadowing of Nonhyperbolic Maps,''
Annals of the New York Academy of Sciences 751, 213 - 221 (1994).
Henry E. Kandrup, Robert A. Abernathy, and Brendan O. Bradley, ``Resonant
Driving of Chaotic Orbits,'' Physical Review E 51, 5287 - 5297 (1995).
M. Elaine Mahon, Robert A. Abernathy, Brendan O. Bradley, and henry E.
Kandrup, ``Transient Ensemble Dynamics in Time-Independent Galactic Potentials,''
Monthly Notices of the Royal Astronomical Society 275, 443 - 453 (1995).
Henry E. Kandrup, Robert A. Abernathy, Brendan O. Bradley, and M. Elaine
Mahon, ``Chaos and Order in Time-Periodic Potentials and the Problem of
Structural Stability,'' Annals of the New York Academy of Sciences 773,
168 - 188 (1995).
Christos V. Siopis, Henry E. Kandrup, George Contopoulos, and Rudolf Dvorak,
``Universal Properties of Escape,'' Annals of the New York Academy of Sciences
773, 221 - 230 (1995).
J. H. Hunter, Jr., R. W. Whitaker, R. V. E. Lovelace and C. Siopis, ``Interface
Instabilities in the Interstellar Medium,'' Annals of the New York Academy
of Sciences 773, 32 - 43 (1995).
David E. Willmes, ``Shadowing and Noise in Nonhyperbolic Systems,'' Annals
of the New York Academy of Sciences 773, 242 - 255 (1995).
Henry E. Kandrup, ``Stochastic Processes of the Gravitational N-Body Problem,''
Astronomical and Astrophysical Transactions 7, 225 - 228 (1995).
Henry E. Kandrup, ``Collisional Relaxation in a Nonintegrable Mean Field
Potential,'' Astronomical and Astrophysical Transactions 7, 229 - 231 (1995).
Ilya V. Pogorelov and Henry E. Kandrup, ``Anisotropic Distribution Functions
for Relativistic Galactic Nuclei,'' Physical Review E 53, 1375 - 1381 (1996).
Salman Habib, Henry E. Kandrup, and M. Elaine Mahon, ``Chaos and Noise
in a Truncated Toda Potential,'' Physical Review E 53, 5473 - 5476 (1996)
Henry E. Kandrup, ``Chaos, Regularity, and Noise in Self-Gravitating Systems,''
in Proceedings of the Seventh Marcel Grossmann Meeting, ed. R. T. Jantzen
and G. Mac Kaiser, World Scientific, Singapore, 167 - 182 (1996).
Henry E. Kandrup and Barbara L. Eckstein, ``Transitional Dynamics of Chaotic
Galactic Orbits,'' Annals of the New York Academy of Sciences, 808, 139
- 159 (1996).
Henry E. Kandrup, ``Structural Stability of Orbits in Galactic Models towards
Low Amplitude Perturbations,'' Proceedings of the International Conference
on Structure and Evolution of Self-Gravitating Systems, ed. T. A. Agekian,
A. A. Mullari, and V. V. Orlov, St. Petersburg University, Russia, 245
- 247 (1997).
Henry E. Kandrup, Barbara L Eckstein, and Brendan O. Bradley, ``Chaos,
Complexity, and Short Time Lyapounov Exponents,'' Astronomy and Astrophysics
320, 65 - 73 (1997).
Salman Habib, Henry E. Kandrup, and M. Elaine Mahon, ``Chaos and Noise
in Galactic Potentials,'' Astrophysical Journal 480, 155 - 166 (1997).
Christos Siopis, Henry E. Kandrup, George Contopoulos, and Rudolf Dvorak,
``Universal Properties of Escape in Dynamical Systems,'' Proceedings of
the 4th Alexander von Humboldt Colloquium for Celestial Mechanics: The
Dynamical Behaviour of Our Planetary System, ed. R. Dvorak, and J. Henrard,
Kluwer, Dordrecht, 57 - 68 (1997).
Henry E. Kandrup, ``Geometric Approach to Chaos in Two-Dimensional Hamiltonian
Systems,'' Physical Review E 56, 2722 - 2732 (1997).
Henry E. Kandrup, ``Collisionless Relaxation in Galactic Dynamics and the
Evolution of Long Range Order,'' Annals of the New York Academy of Sciences
848 (1998) 28 - 47 (1998).
Henry E. Kandrup, ``Violent Relaxation, Phase Mixing, and Gravitational
Landau Damping,'' Astrophysical Journal 500, 120 - 128 (1998).
Henry E. Kandrup, ``Invariant Distributions and Collisionless Equilibria,''
Monthly Notices of the Royal Astronomical Society 299, 1139 - 1145 (1998)
Henry E. Kandrup, ``Phase Mixing in Time-Independent Hamiltonian Systems,''
Monthly Notices of the Royal Astronomical Society 301, 960 - 974 (1998).
Christos Siopis, Barbara L. Eckstein, and Henry E. Kandrup, ``Orbital
Complexity,
Short Time Lyapunov Exponents, and Phase Space Transport in Time-Dependent
Hamiltonian Systems,'' Annals of the New York Academy of Sciences 867,
41 - 60 (1998).
Henry E. Kandrup and John Drury, ``Chaos in Cosmological Hamiltonians,''
Annals of the New York Academy of Sciences 867, 306 - 320 (1998).
Henry E. Kandrup, ``Phase Space Transport in Noisy Hamiltonian Systems,''
Annals of the New York Academy of Sciences 867, 321 - 333 (1998).
Christos Siopis, ``Nonuniqueness and Structural Stability of Self-Consistent
Models of Elliptical Galaxies,'' Ph. D dissertation (1998).
Henry E. Kandrup, ``Collisionless Relaxation of Stellar Systems,'' ASP
Conference Series 182, 197 - 208 (1999)
Henry E. Kandrup, Christos Siopis, George Contopoulos, and Rudolf Dvorak,
``Diffusion and Scaling in Escapes from Two-Dimensional Hamiltonian Systems,''
Chaos 9, 381 - 392 (1999).
Ilya V. Pogorelov and Henry E. Kandrup, ``Noise-Induced Phase Space Transport
in Two-Dimensional Hamiltonian Systems.'' Physical Review E 60, 1567 - 1578
(1999).
Henry E. Kandrup, Ilya V. Pogorelov, and Ioannis V. Sideris, ``Chaotic Mixing
in Noisy Hamiltonian Systems,'' Monthly Notices of the Royal Astronomical
Society, Monthly Notices of the Royal Astronomical Society 311, 719 -
732 (2000).
Henry E. Kandrup, Ilya V. Pogorelov, and Ioannis V. Sideris, ``Phase Space
Transport in Noisy Hamiltonian Systems,'' Oberwolfacher Tagungsberichte,
(1999).
Christos Siopis and Henry E. Kandrup, ``Phase Space Transport in Cuspy
Triaxial Potentials: Can They Be Used to Construct Self-Consistent
Equilibria?'' Monthly Notices of the Royal Astronomical Society 319, 43 - 62
(2000).
Henry E. Kandrup, ``Chaotic Mixing in Galactic Dynamics,'' in Proceedings
of the International Conference on Stellar Dynamics: Classical to
Modern, 21 - 27 August 2000, St. Petersburg State University, edited
by L. P. Ossipkov and I. I. Nikiforov, St. Petersburg University
(2001), 213 - 223.
Christos Siopis, Ioannis V. Sideris, Ilya V. Pogorelov, and Henry E. Kandrup,
``Dynamics of Cuspy Triaxial Galaxies with a Supermassive Black
Hole,'' Proceedings of the International Conference on
Stellar Dynamics: Classical to Modern, 21 - 27 August 2000, St.
Petersburg State University, edited by L. P. Ossipkov and I. I.
Nikiforov, St. Petersburg University (2001), 420 - 426.
Henry E. Kandrup, ``Energy Relaxation in Galaxies Induced by an External
Environment and/or Incoherent Internal Pulsations,'' Monthly Notices of the
Royal Astronomical Society 323 (2001) 681 - 687
R. A. Kishek, C. L. Bohn, I. Haber, P. G. O'Shea, M. Reiser, and
H. Kandrup, ``Computational Investigation of Dissipation and Reversibility of
Space-Charge Driven Processes in Beams,'' Proceedings of the 2001 IEEE
Particle Accelerator Conference in Chicago, IL, edited by P. Lucas and S.
Weber, IEEE Cat. No. 01CH37268 (2001) 151 - 153
Henry E. Kandrup and Ioannis V. Sideris, ``Chaos and the Continuum Limit
in the Gravitational N-Body Problem. Integrable Potentials,''
Physical Review E 64 (2001) 056209-1 - 056209-11
Henry E. Kandrup ann Ioannis V. Sideris, ``Chaos in Cuspy Triaxial Galaxies
with a Supermassive Black Hole: A Simple Toy Model,'' Celestial Mechanics
and Dynamical Astronomy 82 (2002) 61 - 81
Courtlandt L. Bohn, Henry E. Kandrup, and Rami A. Kishek, ``Chaotic Mixing in
Charged-Particle Beams and Galaxies,'' Proceedings of Snowmass 2001, edited
by C. M. Sazama, eConf C01/06/30, M302 (2001)
Henry E. Kandrup, Ioannis V. Sideris, and Courtlandt L. Bohn, ``Chaos,
Ergodicity, and the Thermodynamics of Lower-Dimensional Hamiltonian
Systems,'' Physical Review E 65 (2002) 016214-1 - 016214-16
Ioannis V. Sideris and Henry E. Kandrup, ``Chaos and the Continuum Limit
in the Gravitational N-Body Problem. II. Non-Integrable Potentials,''
Physical Review E 65 (2002) 066203-1 - 066203-14
Henry E. Kandrup, ``Should Elliptical Galaxies Galaxies Be Idealised as
Collisionless Equilibria?'' Space Science Reviews 102 (2002) 101 - 114
Henry E. Kandrup and Ioannis V. Sideris, ``Smooth Potential Chaos and
N-Body Simulations,'' Astrophysical Journal 585 (2003) 244 - 250.
Henry E. Kandrup, Ileana M. Vass, and Ioannis V. Sideris, ``Transient Chaos
and Resonant Phase Mixing in Violent Relaxation,''
Monthly Notices of the Royal Astronomical Society 341 (2003) 927 - 936
Balsa Terzic and Henry E. Kandrup, ``Semi-Analytic Estimates of Lyapunov
Exponents in Lower-Dimensional Systems,''
Physics Letters A 311 (2003) 241 - 247
Henry E. Kandrup and Steven J. Novotny, ``Phase Mixing in Unperturbed and
Perturbed Hamiltonian Systems,'' Celestial Mechanics and Dynamical
Astronomy (2003), in press
Courtlandt L. Bohn, Ioannis V. Sideris, Henry E. Kandrup, and Rami A. Kishek,
``Phase Mixing of Chaotic orbits as an Irreversible `Relaxation' Mechanism,'
Proceedings of the 2002 DESY Workshop on Coherent Synchrotron Radiation
(Zeuthen Germany 14-18 January 2002) in press
Courtlandt L. Bohn, Ioannis V. Sideris, Henry E. Kandrup, and Rami A. Kishek,
``Mixing of Regular and Chaotic Orbits in Beams,'' Proceedings of XXI Linac
Conference (Gyeongiu, Korea 19-23 August 2002), Paper TU435, in press
Henry E. Kandrup and Christos Siopis, ``Chaos and Chaotic Phase Mixing in
Cuspy Triaxial Potentials,'' Monthly Notices of the Royal Astronomical
Society (2002), in press
Henry E. Kandrup, ``Chaos and Chaotic Phase Mixing in Galaxy Evolution and
Charged Particle Beams,''
Springer Lecture Notes in Physics (2003), in press
Henry E. Kandrup, Ioannis V. Sideris, Balsa Terzic, and Courtlandt L. Bohn,
``Supermassive Black Hole Binaries as Galactic Blenders,''
Astrophysical Journal (2003), in press
Henry E. Kandrup, Ioannis V. Sideris, and Courtlandt L. Bohn,
``Chaos and the Continuum Limit in Non-neutral Plasmas and Charged Particle
Beams,'' Physical Review Special Topics -- Accelerators and Beams (2003),
submitted
Balsa Terzic and Henry. E. Kandrup, ``Orbital Structure in Oscillating Galactic
Potentials,'' Monthly Notices of the Royal Astronomical Society (2003),
submitted
Courtlandt L. Bohn, Henry E. Kandrup, Rami A. Kishek, Patrick G. O'Shea,
Martin Reiser, and Ioannis V. Sideris, ``Chaos and Collective Relaxation in
Galaxies and Charged Particle Beams,'' Reviews of Modern Physics (2003),
submitted
Ioannis V. Sideris and Henry E. Kandrup, ``Noise-Enhanced Parametric Resonance
in Perturbed Galaxies,'' Astrophysical Journal (2003), submitted.
Ilya V. Pogorelov and Henry E. Kandrup,
``Energy trapping in loaded string models with long and short range couplings,''
to be submitted.
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Twenty-Plus Years of Gravitational Astrophysics
1980 -- generalised Holtsmark distributions and discreteness effects in
self-gravitating systems: Kandrup, Physics Reports 63, 1 - 59
1980 -- the gravothermal catastrophe as an instability of the collisional
Boltzmann equation:
Ipser and Kandrup, Astrophysical Journal 241, 1141 - 1147
1984 -- a relativistic analogue of the collisional Boltzmann equation for dense
star clusters: Israel and Kandrup, Annals of Physics 152, 30 - 84
1985 -- still the strongest theoretical result about the linear stability of
spherical
star clusters: Kandrup and Sygnet, Astrophysical Journal 298, 27 - 33
1986 -- Landau damping and phase mixing are the same thing, contrary to
conventional wisdom:
Habib, Kandrup, and Yip, Astrophysical Journal 309, 176 -
182
1988 -- entropy generation, particle creation, and the origins of the arrow of
time: Kandrup, Physical Review D 37, 3505 - 3521
1989 -- why stochastic inflation works: Kandrup, Physical Review D 39,
2245 - 2252
1989 -- a topological Hawking effect: Kandrup and Mazur, Modern Physics
Letters A 4, 1189 - 1196
1990 -- the instability of the N-body problem towards small changes in initial
conditions - theoretical predictions: Kandrup, Physica A 169, 73 - 94
1991 -- the instability of the N-body problem towards small changes in initial
conditions - numerical confirmation:
Kandrup and Smith, Astrophysical Journal
374, 255 - 265
1992 -- generalisations of the Fluctuation-Dissipation Theorem to a
cosmological setting: Habib and Kandrup, Physical Review D 46, 5305 - 5314
1993 -- partial remembrance of initial conditions in the N-body problem:
Kandrup, Mahon, and Smith, Astronomy and Astrophysics 271, 440 - 450
1994 -- Hamiltonian formulation of the Vlasov-Einstein system:
Kandrup and
O'Neill, Physical Review D 49, 5115 - 5125
1994 -- chaotic phase mixing:
Kandrup and Mahon, Physical Review E 49, 3735 - 3747
1994 -- short time Lyapunov exponents done right:
Kandrup and Mahon, Astronomy
and Astrophysics 290, 762 - 770
1995 -- transient ensemble dynamics in time-independent Hamiltonian systems:
Mahon, Abernathy, Bradley, and Kandrup, Monthly Notices 275, 443 - 453
1997 -- ``less chaotic'' orbits have ``less complex'' Fourier spectra:
Kandrup, Eckstein, and Bradley, Astronomy and Astrophysics 320, 65 - 73
1997 -- structural stability of Hamiltonian flows towards low amplitude
perturbations:
Habib, Kandrup, and Mahon, Astrophysical Journal 480, 155 - 165
1998 -- the conventional wisdom about isolating integrals is wrong!
Kandrup, Monthly Notices 299, 1139 - 1145
1999 -- diffusion, scaling, and possible universality in two-degree-of-freedom
Hamiltonian systems:
Kandrup, Siopis, Contopoulos, and Dvorak, Chaos 9, 381 - 392.
1999 -- extrinsic diffusion is a resonance phenomenon:
Pogorelov and Kandrup,
Physical Review E 60, 1567 - 1578
2001 -- energy relaxation induced by incoherent internal oscillations and
external irregularities:
Kandrup, Monthly Notices 323, 681 - 687
2001 -- why a chaotic N-body problem can have an integrable continuum
limit:
Kandrup and Sideris, Physical Review E 64, 056209-1 - 056209-14
2002 -- a thermodynamic theory of chaos in lower-dimensional systems:
Kandrup, Sideris, and Bohn, Physical Review E 65, 016214-1 - 016214-16
2002 -- the extent to which galaxies can be modeled by smooth potentials,
perturbed by friction and noise:
Sideris and Kandrup, Physical Review E 65, 066203-1 - 066203-14
2003 -- quantifying microchaos and macrochaos in the N-body problem
Kandrup and Sideris, Astrophysical Journal 585, 244
2003 -- resonance-induced transient chaos and violent relaxation
Kandrup, Vass, and Sideris, Monthly Notices 341, 927 - 936
2003 -- chaos and chaotic phase mixing in galaxy evolution and charged particle
beams
Kandrup, Springer Lecture Notes in Physics, in press
2003 -- supermassive black hole binaries as galactic blenders
Kandrup, Sideris, Terzic, and Bohn, Astrophysical Journal, in press
[77 kb, gzipped postscript]
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