%%
@article{fds325020,
Author = {Ridgway, RW and Greenside, HS and Freedman, HH},
Title = {Cocatalysis of Phenolate Phosphorylation in Biphasic
Media},
Journal = {Journal of the American Chemical Society},
Volume = {98},
Number = {7},
Pages = {1979-1980},
Publisher = {American Chemical Society (ACS)},
Year = {1976},
Month = {March},
url = {http://dx.doi.org/10.1021/ja00423a063},
Doi = {10.1021/ja00423a063},
Key = {fds325020}
}
@article{fds325021,
Author = {Blum, JJ and Greenside, H},
Title = {Particle ejection from the cytoproct of Tetrahymena.},
Journal = {The Journal of protozoology},
Volume = {23},
Number = {4},
Pages = {500-502},
Year = {1976},
Month = {November},
url = {http://dx.doi.org/10.1111/j.1550-7408.1976.tb03827.x},
Abstract = {Egestion of carmine particle-containing food vacuoles from
the cytoproct of Tetrahymena pyriformis has been analyzed by
high-speed cinemicrography. The vacuole may enter into
position in the cytoproct approximately 7 sec before
ejection, and forms a distinct bulge beyond the outline of
the cell surface for over 2 sec prior to ejection. The
ejection process itself requires 20-80 msec.},
Doi = {10.1111/j.1550-7408.1976.tb03827.x},
Key = {fds325021}
}
@booklet{Greenside80,
Author = {Greenside, HS and Hamann, DR},
Title = {Self-consistent lcao study of the square-root-2xsquare-root-2
cl adlayer on pd(001) and ag(001) surfaces - band-structure
and density of states},
Journal = {Bulletin Of The American Physical Society},
Volume = {25},
Number = {3},
Pages = {193-193},
Year = {1980},
Key = {Greenside80}
}
@article{fds325019,
Author = {WALDEN, RW and GREENSIDE, H and HOHENBERG, PC and AHLERS,
G},
Title = {NUMERICAL-SIMULATION OF A BROWNIAN PARTICLE IN AN EXTERNAL
ANHARMONIC POTENTIAL},
Journal = {BULLETIN OF THE AMERICAN PHYSICAL SOCIETY},
Volume = {25},
Number = {3},
Pages = {240-240},
Publisher = {AMER INST PHYSICS},
Year = {1980},
Month = {January},
Key = {fds325019}
}
@booklet{Greenside81e,
Author = {Greenside, HS},
Title = {High-frequency intermittency of strange attractors},
Journal = {Bulletin Of The American Physical Society},
Volume = {26},
Number = {3},
Pages = {444-444},
Year = {1981},
Key = {Greenside81e}
}
@booklet{Greenside81d,
Author = {Greenside, HS and Blount, EI and Varma, CM},
Title = {Effect of magnetic-anisotropy on coexisting magnetic
superconducting phases},
Journal = {Bulletin Of The American Physical Society},
Volume = {26},
Number = {3},
Pages = {276-276},
Year = {1981},
Key = {Greenside81d}
}
@booklet{Greenside81c,
Author = {Greenside, HS and Helfand, E and Walden, RW},
Title = {Numerical-integration of additive, stochastic
differential-equations},
Journal = {Bulletin Of The American Physical Society},
Volume = {26},
Number = {3},
Pages = {273-274},
Year = {1981},
Key = {Greenside81c}
}
@booklet{Greenside81,
Author = {Greenside, HS and Helfand, E},
Title = {Numerical Integration of Stochastic Differential
Equations—II},
Journal = {Bell System Technical Journal},
Volume = {60},
Number = {8},
Pages = {1927-1940},
Publisher = {Institute of Electrical and Electronics Engineers
(IEEE)},
Year = {1981},
Month = {January},
url = {http://dx.doi.org/10.1002/j.1538-7305.1981.tb00303.x},
Abstract = {In a previous paper, a method was presented to integrate
numerically nonlinear stochastic differential equations
(SDES) with additive, Gaussian, white noise. The method, a
generalization of the Runge‐Kutta algorithm, extrapolates
from one point to the next applying functional evaluations
at stochastically determined points. This paper extends (and
at one point corrects) algorithms for the simple class of
equations considered in the previous paper. In addition, the
method is expanded to treat vector SDES, equations with
time‐dependent functions, and SDES higher than first
order. The parameters for several explicit integration
schemes are displayed. © 1981 The Bell System Technical
Journal},
Doi = {10.1002/j.1538-7305.1981.tb00303.x},
Key = {Greenside81}
}
@booklet{Greenside81f,
Author = {Greenside, HS and Blount, EI and Varma, CM},
Title = {Possible coexisting superconducting and magnetic
states},
Journal = {Physical Review Letters},
Volume = {46},
Number = {1},
Pages = {49-53},
Publisher = {American Physical Society (APS)},
Year = {1981},
Month = {January},
ISSN = {0031-9007},
url = {http://dx.doi.org/10.1103/PhysRevLett.46.49},
Abstract = {The free energy is calculated for the various phases
possible in a superconductor containing a periodic array of
magnetic ions with ferromagnetic interactions. Suggestions
are made for experimental observation of coexisting
superconductivity and long-range magnetic order. © 1980 The
American Physical Society.},
Doi = {10.1103/PhysRevLett.46.49},
Key = {Greenside81f}
}
@booklet{Bachelet81,
Author = {Bachelet, GB and Greenside, HS and Baraff, GA and Schlter,
M},
Title = {Structural-energy calculations based on norm-conserving
pseudopotentials and localized Gaussian orbitals},
Journal = {Physical Review B},
Volume = {24},
Number = {8},
Pages = {4745-4752},
Publisher = {American Physical Society (APS)},
Year = {1981},
Month = {January},
ISSN = {0163-1829},
url = {http://dx.doi.org/10.1103/PhysRevB.24.4745},
Abstract = {The total energy, equilibrium lattice constant, and bulk
modulus are calculated for diamond, silicon, and GaP. These
ground-state calculations are carried out in a localized
Gaussian basis (20 orbitals per atom) using a real-space
formalism devised for defect crystal studies. High-precision
norm-conserving pseudopotentials simulate the interaction of
the valence electrons with the atomic cores. The results are
typically within 1-4% of experiment, which is not good
enough to determine absolute cohesive energies but should be
sufficient for studies of structural deformations and
elastic properties. An analysis and comparison with other
calculations show that the errors arise predominantly from
the use of a minimum local-orbital basis and not from
pseudopotentials. © 1981 The American Physical
Society.},
Doi = {10.1103/PhysRevB.24.4745},
Key = {Bachelet81}
}
@booklet{Hamann81,
Author = {Hamann, DR and Mattheiss, LF and Greenside, HS},
Title = {Comparative LCAO-LAPW study of C1 chemisorption on the
Ag(001) surface},
Journal = {Physical Review B},
Volume = {24},
Number = {10},
Pages = {6151-6155},
Publisher = {American Physical Society (APS)},
Year = {1981},
Month = {January},
ISSN = {0163-1829},
url = {http://dx.doi.org/10.1103/PhysRevB.24.6151},
Abstract = {A comparison is made between the results of self-consistent
linear-combination-of-atomic-orbitals and
linear-augmented-plane-wave calculations for a clean
three-layer Ag(001) slab and one with adsorbed C1 in c(2×2)
simple-overlayer and mixed-layer geometries. © 1981 The
American Physical Society.},
Doi = {10.1103/PhysRevB.24.6151},
Key = {Hamann81}
}
@booklet{Greenside81b,
Author = {Greenside, HS and Hamann, DR},
Title = {Cl chemisorption on the Ag(001) surface: Geometry and
electronic structure},
Journal = {Physical Review B},
Volume = {23},
Number = {10},
Pages = {4879-4887},
Publisher = {American Physical Society (APS)},
Year = {1981},
Month = {January},
ISSN = {0163-1829},
url = {http://dx.doi.org/10.1103/PhysRevB.23.4879},
Abstract = {Simple overlayer and mixed-layer geometries are studied for
the observed c(2×2) structure of atomic Cl adsorbed on the
Ag(001) surface. A self-consistent, Gaussian,
linear-combination-of-atomic-orbitals technique with a local
exchange-correlation potential is used. Reference
calculations are performed for bulk Ag, the clean Ag(001)
surface, and an isolated c(2×2)Cl layer. The calculated
total and partial density of states for the two geometries
are compared with angle-integrated and angle-resolved
photoemission experiments. The mixed-layer model gives close
agreement with experiment while the overlayer model predicts
a single Cl feature above the Ag d band, contrary to the
photoemission data. Discrepancies between these calculations
and a low-energy electron diffraction study of this system
are discussed. © 1981 The American Physical
Society.},
Doi = {10.1103/PhysRevB.23.4879},
Key = {Greenside81b}
}
@booklet{Greenside81a,
Author = {Greenside, HS and Hamann, DR},
Title = {Cl chemisorption on the Pd(001) surface: A self-consistent
LCAO calculation of electronic structure},
Journal = {Solid State Communications},
Volume = {39},
Number = {11},
Pages = {1129-1132},
Publisher = {Elsevier BV},
Year = {1981},
Month = {January},
ISSN = {0038-1098},
url = {http://dx.doi.org/10.1016/0038-1098(81)91098-X},
Abstract = {The total and partial densities of states and work functions
for the clean Pd(001) surface and for a c(2×2) Cl overlayer
on this surface are calculated using a self consistent
Gaussian LCAO technique. The adlayer increases the work
function of the clean surface by 0.8 eV and leads to a
distinct split off feature in the total density of states.
The band structure of the bands composing this feature are
compared to the bands of the isolated Cl layer. ©
1981.},
Doi = {10.1016/0038-1098(81)91098-X},
Key = {Greenside81a}
}
@article{fds325018,
Author = {SCHLUTER, M and BACHELET, GB and BARAFF, GA and HAMANN, DR and GREENSIDE, H},
Title = {FITTED NORM-CONSERVING PSEUDOPOTENTIALS AND TOTAL ENERGY
STUDIES},
Journal = {BULLETIN OF THE AMERICAN PHYSICAL SOCIETY},
Volume = {26},
Number = {3},
Pages = {390-390},
Publisher = {AMER INST PHYSICS},
Year = {1981},
Month = {January},
Key = {fds325018}
}
@booklet{Greenside82,
Author = {Greenside, HS and Ahlers, G and Hohenberg, PC and Walden,
RW},
Title = {A simple stochastic model for the onset of turbulence in
Rayleigh-Bénard convection},
Journal = {Physica D: Nonlinear Phenomena},
Volume = {5},
Number = {2-3},
Pages = {322-334},
Publisher = {Elsevier BV},
Year = {1982},
Month = {January},
ISSN = {0167-2789},
url = {http://dx.doi.org/10.1016/0167-2789(82)90026-4},
Abstract = {A simple stochastic model of a particle diffusing randomly
in an external two-well potential is proposed to stimulate
the onset of turbulence in a medium aspect ratio cylindrical
Rayleigh-Bénard cell. The model is studied numerically and
both time series and their power spectra are obtained. The
results are compared with experimental data as well as with
the results of deterministic models consisting of a finite
number of interacting modes. © 1982.},
Doi = {10.1016/0167-2789(82)90026-4},
Key = {Greenside82}
}
@booklet{Greenside82a,
Author = {Greenside, HS and Coughran, WM and Schryer, NL},
Title = {Nonlinear pattern formation near the onset of
Rayleigh-Bénard convection},
Journal = {Physical Review Letters},
Volume = {49},
Number = {10},
Pages = {726-729},
Publisher = {American Physical Society (APS)},
Year = {1982},
Month = {January},
ISSN = {0031-9007},
url = {http://dx.doi.org/10.1103/PhysRevLett.49.726},
Abstract = {It is shown that many of the experimentally observed
features of pattern formation in Rayleigh-Bénard convection
near onset can be understood in terms of a two-dimensional
relaxational equation. In particular, it is shown that
disordered roll patterns follow a complicated dynamics that
can require up to a hundred horizontal diffusion times to
reach equilibrium. © 1982 The American Physical
Society.},
Doi = {10.1103/PhysRevLett.49.726},
Key = {Greenside82a}
}
@booklet{Greenside82b,
Author = {Greenside, HS and Wolf, A and Swift, J and Pignataro,
T},
Title = {Impracticality of a box-counting algorithm for calculating
the dimensionality of strange attractors},
Journal = {Physical Review A},
Volume = {25},
Number = {6},
Pages = {3453-3456},
Publisher = {American Physical Society (APS)},
Year = {1982},
Month = {January},
ISSN = {1050-2947},
url = {http://dx.doi.org/10.1103/PhysRevA.25.3453},
Abstract = {An algorithm proposed by Takens, which can determine the
capacity (generalized dimensionality) of a dynamical system
from the time series of a single observable, is tested
numerically for several intrinsically stochastic models. The
algorithm is found to converge too slowly (if at all) to be
useful for the analysis of experimental data. © 1982 The
American Physical Society.},
Doi = {10.1103/PhysRevA.25.3453},
Key = {Greenside82b}
}
@article{fds366571,
Author = {GREENSIDE, HS},
Title = {[title field missing]},
Journal = {Phys. Rev. B},
Volume = {27},
Pages = {3111 pages},
Year = {1983},
url = {http://dx.doi.org/10.1103/PhysRevB.27.3111},
Doi = {10.1103/PhysRevB.27.3111},
Key = {fds366571}
}
@booklet{Greenside83a,
Author = {Greenside, HS and Schlüter, MA},
Title = {Pseudopotential calculation of the ground-state properties
of ferromagnetic bcc iron},
Journal = {Physical Review B},
Volume = {27},
Number = {5},
Pages = {3111-3114},
Publisher = {American Physical Society (APS)},
Year = {1983},
Month = {January},
ISSN = {0163-1829},
url = {http://dx.doi.org/10.1103/PhysRevB.27.3111},
Abstract = {We report the first use of parameter-free norm-conserving
pseudopotentials for a strongly spin-polarized material,
ferromagnetic bcc iron. Ground-state properties such as the
equilibrium lattice constant, magnetic moment, and bulk
modulus are calculated within the local-density-functional
approximation and agree within a few percent with
experiments. The deviations are, however, significantly
larger than what is typically found for materials with s,p
electrons. © 1983 The American Physical
Society.},
Doi = {10.1103/PhysRevB.27.3111},
Key = {Greenside83a}
}
@booklet{Greenside83,
Author = {Greenside, HS and Schlater, M},
Title = {Pseudopotentials for the 3d transition-metal
elements},
Journal = {Physical Review B},
Volume = {28},
Number = {2},
Pages = {535-543},
Publisher = {American Physical Society (APS)},
Year = {1983},
Month = {January},
ISSN = {0163-1829},
url = {http://dx.doi.org/10.1103/PhysRevB.28.535},
Abstract = {As an extension of recent work by Bachelet, Hamann, and
Schlater, high-quality transferable norm-conserving
pseudopotentials are derived for the 3d transition-metal
elements Sc21 through Cu29. As a new feature the nonlinear
exchange and correlation interaction between valence
electrons is treated explicitly which allows the potentials
to be used for spin-polarized calculations. The numerical
pseudopotentials are fit to a small set of analytic
functions which are convenient for a variety of
wave-function representations. The quality of the fits and
the transferability of the new pseudopotentials to strongly
spin-polarized excited states are excellent as test results
show. A complete table of the fitted pseudopotentials is
presented. © 1983 The American Physical
Society.},
Doi = {10.1103/PhysRevB.28.535},
Key = {Greenside83}
}
@booklet{Greenside84a,
Author = {Greenside, HS and Budny, RV and Post, DE},
Title = {Depolarization of d-t plasmas by recycling in material
walls},
Journal = {Journal Of Vacuum Science \& Technology A-vacuum Surfaces
And Films},
Volume = {2},
Number = {2},
Pages = {619-629},
Publisher = {American Vacuum Society},
Year = {1984},
url = {http://dx.doi.org/10.1116/1.572456},
Abstract = {The feasibility of using polarized deuterium (D) and tritium
(T) plasmas in fusion reactors may be seriously affected by
recycling in material walls. Theoretical and experimental
results are reviewed which show how the depolarization rates
of absorbed D and T depend on first wall parameters such as
the temperature, the bulk and surface diffusivities, the
density of electronic states at the Fermi surface, the
spectral density of microscopic fluctuating electric field
gradients, and the concentration of paramagnetic impurities.
Nuclear magnetic resonance (NMR) spectroscopy of
hydrogenated and deuterated amorphous semiconductors
suggests that low-Z nonmetallic materials may provide a
satisfactory first wall or limiter coating under reactor
conditions with characteristic depolarization times of
several seconds. Experiments are proposed to test the
consequences of our analysis. © 1984, American Vacuum
Society. All rights reserved.},
Doi = {10.1116/1.572456},
Key = {Greenside84a}
}
@article{fds366570,
Author = {GREENSIDE, HS},
Title = {[title field missing]},
Journal = {Phys. Rev. A},
Volume = {30},
Pages = {398 pages},
Year = {1984},
url = {http://dx.doi.org/10.1103/PhysRevA.30.398},
Doi = {10.1103/PhysRevA.30.398},
Key = {fds366570}
}
@booklet{Greenside84,
Author = {Greenside, HS and Coughran, WM},
Title = {Nonlinear pattern formation near the onset of
Rayleigh-Bénard convection},
Journal = {Physical Review A},
Volume = {30},
Number = {1},
Pages = {398-428},
Publisher = {American Physical Society (APS)},
Year = {1984},
Month = {January},
ISSN = {1050-2947},
url = {http://dx.doi.org/10.1103/PhysRevA.30.398},
Abstract = {A two-dimensional relaxational model equation is studied
numerically to investigate the role of lateral boundaries
and nonlinear terms in pattern formation. The model reduces
in perturbation theory to the same amplitude equation as the
one derived from the three-dimensional Boussinesq equations
for thermal convection. State-of-the-art numerical methods
are described that solve the initial-boundary-value problem
efficiently and accurately in large rectangular cells and
for long times, for both rigid and periodic boundary
conditions. The results of simulations for different aspect
ratios, Rayleigh numbers, and initial conditions are
discussed in detail. The interaction of defects, the effect
of lateral boundaries on the growth and saturation of linear
instabilities, and the origin of the long-time scales needed
to reach a stationary state are studied. Wave-number
selection is investigated using spatial Fourier analysis,
and evidence is presented that the band of stable wave
numbers is not uniformly occupied as a pattern evolves from
random initial conditions of all length scales. These
results are in good agreement with many of the observed
experimental features of pattern formation in small- and
large-aspect-ratio cells, and show some new features that
have not yet been seen. © 1984 The American Physical
Society.},
Doi = {10.1103/PhysRevA.30.398},
Key = {Greenside84}
}
@booklet{Holland84,
Author = {Holland, B and Greenside, HS and Schlüter, M},
Title = {Cohesive Properties of Ge, Si, and Diamond Calculated with
Minimum Basis Sets},
Journal = {physica status solidi (b)},
Volume = {126},
Number = {2},
Pages = {511-515},
Publisher = {WILEY},
Year = {1984},
Month = {January},
url = {http://dx.doi.org/10.1002/pssb.2221260210},
Abstract = {Ab initio calculations are presented of the cohesive
properties of Ge, Si, and diamond. Electron‐electron
interactions are treated within the local density functional
approximation and electronion interactions are described by
norm‐conserving pseudopotentials. The wave functions are
expanded in local Gaussian orbitals. Acceptable results for
equilibrium lattice constant, bulk modulus, and cohesive
energy are obtained with few (eight to twelve) Gaussian
functions per atom. The results, which are comparable to
converged plane wave or local orbital calculations suggest
the feasibility of studies of cohesive properties of systems
with large numbers of atoms. Copyright © 1984 WILEY‐VCH
Verlag GmbH & Co. KGaA},
Doi = {10.1002/pssb.2221260210},
Key = {Holland84}
}
@article{fds366569,
Author = {GREENSIDE, HS},
Title = {[title field missing]},
Journal = {Phys. Rev. A},
Volume = {31},
Pages = {2492 pages},
Year = {1985},
url = {http://dx.doi.org/10.1103/PhysRevA.31.2492},
Doi = {10.1103/PhysRevA.31.2492},
Key = {fds366569}
}
@booklet{Greenside85,
Author = {Greenside, HS and Cross, MC},
Title = {Stability analysis of two-dimensional models of
three-dimensional convection.},
Journal = {Physical review. A, General physics},
Volume = {31},
Number = {4},
Pages = {2492-2501},
Year = {1985},
Month = {April},
ISSN = {1050-2947},
url = {http://dx.doi.org/10.1103/physreva.31.2492},
Abstract = {Analytical and numerical methods are used to study the
linear stability of spatially periodic solutions for various
two-dimensional equations which model thermal convection in
fluids. This analysis suggests new model equations that will
be useful for investigating questions such as wave-number
selection, pattern formation, and the onset of turbulence in
large-aspect-ratio Rayleigh-Bénard systems. In particular,
we construct a nonrelaxational model that has stability
boundaries similar to those calculated for intermediate
Prandtl-number fluids. © 1985 The American Physical
Society.},
Doi = {10.1103/physreva.31.2492},
Key = {Greenside85}
}
@article{fds246516,
Author = {Reiman, A and Greenside, H},
Title = {Calculation of three-dimensional MHD equilibria with islands
and stochastic regions},
Journal = {Computer Physics Communications},
Volume = {43},
Number = {1},
Pages = {157-167},
Publisher = {Elsevier BV},
Year = {1986},
Month = {January},
ISSN = {0010-4655},
url = {http://dx.doi.org/10.1016/0010-4655(86)90059-7},
Abstract = {A three-dimensional MHD equilibrium code is described that
does not assume the existence of good flux surfaces. Given
an initial guess for the magnetic field, the code proceeds
by calculating the pressure driven current and then by
updating the field using Ampére's law. The numerical
algorithm to solve the magnetic differential equation for
the pressure driven current is described, and demonstrated
for model fields having islands and stochastic regions. The
numerical algorithm which solves Ampére's law in three
dimensions is also described. Finally, the convergence of
the code is illustrated for a particular stellarator
equilibrium with no large islands. © 1986.},
Doi = {10.1016/0010-4655(86)90059-7},
Key = {fds246516}
}
@article{fds304572,
Author = {Cross, MC and Tesauro, G and Greenside, HS},
Title = {Wavebumber selection and persistent dynamics in models of
convection},
Journal = {Physica D: Nonlinear Phenomena},
Volume = {23},
Number = {1-3},
Pages = {12-18},
Publisher = {Elsevier BV},
Year = {1986},
Month = {January},
ISSN = {0167-2789},
url = {http://dx.doi.org/10.1016/0167-2789(86)90105-3},
Abstract = {The wavenumber selected in nonlinear spatially periodic
states of driven systems is systematically investigated
using analytic and numerical techniques on equations
modeling convection. Different selection mechanisms yield
different results, arguing against the existence of a
general minimizing principle. Two incompatible selection
mechanisms operating together lead to a persistently dynamic
state. © 1986.},
Doi = {10.1016/0167-2789(86)90105-3},
Key = {fds304572}
}
@booklet{Cross86,
Author = {Cross, MC and Tesauro, G and Greenside, HS},
Title = {Wave-number selection and persistent dynamics in models of
convection},
Journal = {Physica D},
Volume = {23},
Number = {1-3},
Pages = {12-18},
Year = {1986},
Month = {December},
ISSN = {0167-2789},
url = {http://dx.doi.org/10.1016/0167-2789(86)90105-3},
Abstract = {The wavenumber selected in nonlinear spatially periodic
states of driven systems is systematically investigated
using analytic and numerical techniques on equations
modeling convection. Different selection mechanisms yield
different results, arguing against the existence of a
general minimizing principle. Two incompatible selection
mechanisms operating together lead to a persistently dynamic
state. © 1986.},
Doi = {10.1016/0167-2789(86)90105-3},
Key = {Cross86}
}
@article{fds246517,
Author = {Zweben, SJ and Manos, D and Budny, RV and Efthimion, P and Fredrickson,
E and Greenside, H and Hill, KW and Hiroe, S and Kilpatrick, S and McGuire,
K and Medley, SS and Park, HK and Ramsey, AT and Wilgen,
J},
Title = {Edge turbulence measurements in TFTR},
Journal = {Journal of Nuclear Materials},
Volume = {145-147},
Number = {C},
Pages = {250-254},
Publisher = {Elsevier BV},
Year = {1987},
Month = {February},
ISSN = {0022-3115},
url = {http://dx.doi.org/10.1016/0022-3115(87)90337-0},
Abstract = {The edge turbulence in TFTR is characterized by several
diagnostics. Langmuir probes and D-alpha imaging have
detected large amplitude, small-scale, broadband density
fluctuations in the scrape-off region near the wall.
Broadband fluctuations with a similar frequency spectrum are
detected by small-angle microwave scattering and magnetic
pickup loops. Increases in the turbulence level are seen
during neutral beam injection. Some preliminary analysis of
this data is presented. © 1987.},
Doi = {10.1016/0022-3115(87)90337-0},
Key = {fds246517}
}
@article{fds366568,
Author = {GREENSIDE, HS},
Title = {[title field missing]},
Journal = {Phys. Rev. Lett.},
Volume = {60},
Pages = {2269 pages},
Year = {1988},
url = {http://dx.doi.org/10.1103/PhysRevLett.60.2269},
Doi = {10.1103/PhysRevLett.60.2269},
Key = {fds366568}
}
@booklet{Reiman88,
Author = {Reiman, AH and Greenside, HS},
Title = {Numerical solution of three-dimensional magnetic
differential equations},
Journal = {Journal of Computational Physics},
Volume = {75},
Number = {2},
Pages = {423-443},
Publisher = {Elsevier BV},
Year = {1988},
Month = {January},
ISSN = {0021-9991},
url = {http://dx.doi.org/10.1016/0021-9991(88)90121-0},
Abstract = {A computer code is described that solves differential
equations of the form B · {down triangle, open}f = h for a
single-valued solution f, given a toroidal three-dimensional
divergence-free field B and a single-valued function h. The
code uses a new algorithm that Fourier decomposes a given
function in a set of flux coordinates in which the field
lines are straight. The algorithm automatically adjusts the
required integration lengths to compensate for proximity to
low order rational surfaces. Applying this algorithm to the
Cartesian coordinates defines a transformation to magnetic
coordinates, in which the magnetic differential equation can
be accurately solved. Our method is illustrated by
calculating the Pfirsch-Schlüter currents for a
stellarator. © 1988.},
Doi = {10.1016/0021-9991(88)90121-0},
Key = {Reiman88}
}
@booklet{Greenside88,
Author = {Greenside, HS and Cross, MC and Coughran, WM},
Title = {Mean flows and the onset of chaos in large-cell
convection.},
Journal = {Physical review letters},
Volume = {60},
Number = {22},
Pages = {2269-2272},
Year = {1988},
Month = {May},
ISSN = {0031-9007},
url = {http://dx.doi.org/10.1103/physrevlett.60.2269},
Abstract = {Numerical simulations of two-dimensional model equations
show that a coupling between amplitude and
vertical-vorticity fields allows chaotic flows near the
onset of Rayleigh-Bénard convection in large-aspect-ratio
domains. In cylindrical cells, mean flows arising from this
coupling lead to a chaotic nucleation of dislocations that
is remarkably similar to recent observations in convection
experiments. © 1988 The American Physical
Society.},
Doi = {10.1103/physrevlett.60.2269},
Key = {Greenside88}
}
@booklet{Greenside89,
Author = {Greenside, HS and Reiman, AH and Salas, A},
Title = {Convergence properties of a nonvariational 3D MHD
equilibrium code},
Journal = {Journal of Computational Physics},
Volume = {81},
Number = {1},
Pages = {102-136},
Publisher = {Elsevier BV},
Year = {1989},
Month = {January},
ISSN = {0021-9991},
url = {http://dx.doi.org/10.1016/0021-9991(89)90066-1},
Abstract = {Details are presented of the PIES code, which uses a
nonvariational algorithm for calculating fully
three-dimensional MHD equilibria. The convergence properties
of the code are studied for several axisymmetric and
nonaxisymmetric finite β equilibria that have magnetic
surfaces. © 1989.},
Doi = {10.1016/0021-9991(89)90066-1},
Key = {Greenside89}
}
@article{fds323241,
Author = {Greenside, HS},
Title = {Comments on a recent paper by W. Zijl},
Journal = {International Journal for Numerical Methods in
Fluids},
Volume = {9},
Number = {10},
Pages = {1302-1304},
Publisher = {WILEY},
Year = {1989},
Month = {January},
url = {http://dx.doi.org/10.1002/fld.1650091010},
Abstract = {A recent paper by W. Zijl, which reformulated the
Navier–Stokes and Boussinesq equations in terms of Clebsch
potentials, has an error that greatly reduces the generality
of the results. Some other recent efforts to use such
potentials in fluid and plasma dynamics are briefly
discussed. Copyright © 1989 John Wiley & Sons,
Ltd},
Doi = {10.1002/fld.1650091010},
Key = {fds323241}
}
@booklet{Reiman90,
Author = {Reiman, AH and Greenside, HS},
Title = {Computation of zero β three-dimensional equilibria with
magnetic islands},
Journal = {Journal of Computational Physics},
Volume = {87},
Number = {2},
Pages = {349-365},
Publisher = {Elsevier BV},
Year = {1990},
Month = {January},
ISSN = {0021-9991},
url = {http://dx.doi.org/10.1016/0021-9991(90)90257-2},
Abstract = {A Picard iteration scheme has been implemented for the
computation of toroidal, fully three-dimensional, zero β
equilibria with islands and stochastic regions.
Representation of the variables in appropriate coordinate
systems has been found to be a key to making the scheme work
well. In particular, different coordinate systems are used
for solving magnetic differential equations and Ampere's
law. The current profile is adjusted when islands and
stochastic regions appear. An underrelaxation of the current
profile modifications is generally needed for stable
iteration of the algorithm. Some examples of equilibrium
calculations are presented. © 1990.},
Doi = {10.1016/0021-9991(90)90257-2},
Key = {Reiman90}
}
@booklet{Greis91,
Author = {Greis, NP and Greenside, HS},
Title = {Implication of a power-law power-spectrum for
self-affinity.},
Journal = {Physical review. A, Atomic, molecular, and optical
physics},
Volume = {44},
Number = {4},
Pages = {2324-2334},
Year = {1991},
Month = {August},
ISSN = {1050-2947},
url = {http://dx.doi.org/10.1103/physreva.44.2324},
Abstract = {We examine numerically the self-affine scaling of time
series with an imposed power-law power spectrum P()=C-, for
different exponents 13, and for different sequences of
phases. We use two different criteria for testing
self-affinity, a fractal dimension of the graph of the time
series, and a more sensitive test based on the scaling of
moments of probability distributions. For 2, our results
suggest that time series with a power-law spectrum are only
approximately self-affine, even in the best case of
long-time series with high-dimensional, -function-correlated,
uniformly distributed phases. Scaling curves are most
sensitive to phases with long correlation times, are weakly
dependent on the shape of the phase probability
distribution, and are independent of the fractal dimension
of the phases. © 1991 The American Physical
Society.},
Doi = {10.1103/physreva.44.2324},
Key = {Greis91}
}
@article{fds246518,
Author = {Greenside, HS},
Title = {Recent advances in chaos theory},
Journal = {International Conference on Fuzzy Theory and Technology
Proceedings, Abstracts and Summaries},
Pages = {14},
Year = {1992},
Month = {December},
Abstract = {After reviewing the definition and some implications of
chaos, I will discuss three recent advances in chaos theory
which have implications for fuzzy logic and its
applications. One advance is how to control nonlinear
chaotic systems by small calculatable perturbations. Another
advance is improved methods for forecasting nonlinear time
series by local approximations to the underlying strange
attractor. A third advance is recent numerical simulations
of model partial differential equations, which indicate how
high-dimensional temporal chaos and spatial modes are
interrelated.},
Key = {fds246518}
}
@booklet{Egolf93,
Author = {Egolf, DA and Greenside, HS},
Title = {Stochastic to deterministic crossover of fractal dimensions
for a Langevin equation.},
Journal = {Physical review. E, Statistical physics, plasmas, fluids,
and related interdisciplinary topics},
Volume = {47},
Number = {5},
Pages = {3753-3756},
Year = {1993},
Month = {May},
ISSN = {1063-651X},
url = {http://dx.doi.org/10.1103/physreve.47.3753},
Abstract = {Using algorithms of Higuchi and of Grassberger and
Procaccia, we study numerically how fractal dimensions cross
over from finite-dimensional Brownian noise at short-time
scales to finite values of deterministic chaos at
longer-time scales for data generated from a Langevin
equation that has a strange attractor in the limit of zero
noise. Our results suggest that the crossover occurs at such
short time scales that there is little chance of
finite-dimensional Brownian noise being incorrectly
identified as deterministic chaos. © 1993 The American
Physical Society.},
Doi = {10.1103/physreve.47.3753},
Key = {Egolf93}
}
@article{fds362548,
Author = {Egolf, DA and Greenside, HS},
Title = {Dependence of extensive chaos on the spatial correlation
length (substantial revision)},
Year = {1993},
Month = {July},
Abstract = {We consider spatiotemporal chaotic systems for which spatial
correlation functions decay substantially over a length
scale xi (the spatial correlation length) that is small
compared to the system size L. Numerical simulations suggest
that such systems generally will be extensive, with the
fractal dimension D growing in proportion to the system
volume for sufficiently large systems (L >> xi).
Intuitively, extensive chaos arises because of spatial
disorder. Subsystems that are sufficiently separated in
space should be uncorrelated and so contribute to the
fractal dimension in proportion to their number. We report
here the first numerical calculation that examines
quantitatively how one important characterization of
extensive chaos---the Lyapunov dimension density---depends
on spatial disorder, as measured by the spatial correlation
length xi. Surprisingly, we find that a representative
extensively chaotic system does not act dynamically as many
weakly interacting regions of size xi.},
Key = {fds362548}
}
@article{fds246519,
Author = {Bayly, PV and Johnson, EE and Wolf, PD and Greenside, HS and Smith, WM and Ideker, RE},
Title = {A quantitative measurement of spatial order in ventricular
fibrillation.},
Journal = {Journal of cardiovascular electrophysiology},
Volume = {4},
Number = {5},
Pages = {533-546},
Year = {1993},
Month = {October},
ISSN = {1045-3873},
url = {http://www.ncbi.nlm.nih.gov/pubmed/8269320},
Abstract = {<h4>Introduction</h4>The degree of organization in
ventricular fibrillation (VF) is not known. As an objective
measurement of spatial order, spatial correlation functions
and their characteristic lengths were estimated from
epicardial electrograms of pigs in VF.<h4>Methods and
results</h4>VF was induced by premature stimulation in five
pigs. Electrograms were simultaneously recorded with a 22 x
23 array of unipolar electrodes spaced 1.12 mm apart. Data
were obtained by sampling the signals at 2000 Hz for 20
minutes immediately after the initiation of FV. Correlations
between all pairs of signals were computed at various times.
Correlation lengths were estimated from the decay of average
correlation as a function of electrode separation. The
correlation length of the VF in pigs was found to be
approximately 4 to 10 mm, varying as fibrillation
progressed. The degree of correlation decreased in the first
4 seconds after fibrillation then increased over the next
minute.<h4>Conclusion</h4>The correlation length is much
smaller than the scale of the heart, suggesting that many
independent regions of activity exist on the epicardium at
any one time. On the other hand, the correlation length is 4
to 10 times the interelectrode spacing, indicating that some
coherence is present. These results imply that the heart
behaves during VF as a high dimensional, but not random,
system involving many spatial degrees of freedom, which may
explain the lack of convergence of fractal dimension
estimates reported in the literature. Changes in the
correlation length also suggest that VF reorganizes slightly
in the first minute after an initial breakdown in
structure.},
Doi = {10.1111/j.1540-8167.1993.tb01242.x},
Key = {fds246519}
}
@article{fds246520,
Author = {Egolf, DA and Greenside, HS},
Title = {Relation between fractal dimension and spatial correlation
length for extensive chaos},
Journal = {Nature},
Volume = {369},
Number = {6476},
Pages = {129-131},
Publisher = {Springer Nature},
Year = {1994},
Month = {January},
url = {http://dx.doi.org/10.1038/369129a0},
Abstract = {Sustained nonequiibrium systems can be characterized by a
fractal dimension D≥0, which can be considered to be a
measure of the number of independent degrees of freedom1.
The dimension D is usually estimated from time series2 but
the available algorithms are unreliable and difficult to
apply when D is larger than about 5 (refs 3,4). Recent
advances in experimental technique5-8 and in parallel
computing have now made possible the study of big systems
with large fractal dimensions, raising new questions about
what physical properties determine D and whether these
physical properties can be used in place of time-series to
estimate large fractal dimensions. Numerical simulations9-11
suggest that sufficiently large homogeneous systems will
generally be extensively chaotic12, which means that D
increases linearly with the system volume V. Here we test an
hypothesis that follows from this observation: that the
fractal dimension of extensive chaos is determined by the
average spatial disorder as measured by the spatial
correlation length ε associated with the equal-time
two-point correlation function - a measure of the
correlations between different regions of the system. We
find that the hypothesis fails for a representative
spatiotemporal chaotic system. Thus, if there is a length
scale that characterizes homogeneous extensive chaos, it is
not the characteristic length scale of spatial disorder. ©
1994 Nature Publishing Group.},
Doi = {10.1038/369129a0},
Key = {fds246520}
}
@booklet{Egolf94,
Author = {Egolf, DA and Greenside, HS},
Title = {Spatial variation of correlation times for 1D phase
turbulence},
Journal = {Physics Letters A},
Volume = {185},
Number = {4},
Pages = {395-400},
Publisher = {Elsevier BV},
Year = {1994},
Month = {February},
ISSN = {0375-9601},
url = {http://dx.doi.org/10.1016/0375-9601(94)90173-2},
Abstract = {For one-dimensional phase-turbulent solutions of the
Kuramoto-Sivashinsky equation with rigid boundary
conditions, we show that there is a substantial variation of
the correlation time τc(x) with spatial position x in
moderately large systems of size L. These results suggest
that some time-averaged properties of spatiotemporal chaos
do not become homogeneous away from boundaries for large
systems and for long times. © 1994.},
Doi = {10.1016/0375-9601(94)90173-2},
Key = {Egolf94}
}
@booklet{Egolf95,
Author = {Egolf, DA and Greenside, HS},
Title = {Characterization of the transition from defect to phase
turbulence.},
Journal = {Physical review letters},
Volume = {74},
Number = {10},
Pages = {1751-1754},
Year = {1995},
Month = {March},
url = {http://dx.doi.org/10.1103/physrevlett.74.1751},
Abstract = {For the complex Ginzburg-Landau equation on a large periodic
interval, we show that the transition from defect to phase
turbulence is more accurately described as a smooth
crossover rather than as a sharp continuous transition. We
obtain this conclusion by using a parallel computer to
calculate various order parameters, especially the density
of space-time defects, the Lyapunov dimension density, and
correlation lengths. Remarkably, the correlation length of
the field amplitude fluctuations is, within a constant
factor, equal to the length scale defined by the dimension
density.},
Doi = {10.1103/physrevlett.74.1751},
Key = {Egolf95}
}
@booklet{Ohern96,
Author = {O'Hern, CS and Egolf, DA and Greenside, HS},
Title = {Lyapunov spectral analysis of a nonequilibrium Ising-like
transition},
Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids,
and Related Interdisciplinary Topics},
Volume = {53},
Number = {4 SUPPL. A},
Pages = {3374-3386},
Year = {1996},
url = {http://arxiv.org/abs/chao-dyn/9506009v1},
Abstract = {By simulating a nonequilibrium coupled map lattice that
undergoes an Ising-like phase transition we show that the
Lyapunov spectrum and related dynamical quantities such as
the dimension correlation length ξδ, are insensitive to
the onset of long-range ferromagnetic order In particular
the dimension correlation length ξδ remains finite and of
order 1 lattice spacing while the two-point correlation
length diverges to infinity. As a function of lattice
coupling constant g and for certain lattice maps, the
Lyapunov dimension density and other dynamical order
parameters go through a minimum. The occurrence of this
minimum as a function of , depends on the number of nearest
neighbors of a lattice point but not on the lattice
symmetry, on the lattice dimensionality, or on the position
of the Ising-like transition. In one-space dimension, the
spatial correlation length associated with magnitude
fluctuations and the length ξδ are approximately equal,
with both varying linearly with the radius of the lattice
coupling.},
Doi = {10.1103/physreve.53.3374},
Key = {Ohern96}
}
@article{fds246523,
Author = {Krystal, AD and Greenside, HS and Weiner, RD and Gassert,
D},
Title = {A comparison of EEG signal dynamics in waking, after
anesthesia induction and during electroconvulsive therapy
seizures.},
Journal = {Electroencephalogr Clin Neurophysiol},
Volume = {99},
Number = {2},
Pages = {129-140},
Year = {1996},
Month = {August},
ISSN = {0013-4694},
url = {http://www.ncbi.nlm.nih.gov/pubmed/8761049},
Abstract = {Evidence suggests that quantitative dynamical measures of
electroencephalogram (EEG) signals are more appropriate for
characterizing the differences between states in an
individual rather than as absolute indices. One such
measure, the largest Lyapunov exponent (lambda 1), appears
to have potential for identifying seizure activity and for
being of clinical utility for characterizing
electroconvulsive therapy (ECT) seizures. As a result, we
compared lambda 1 for the EEG recorded in 8 depressed
subjects in 3 states: (1) during right unilateral ECT
seizures, (2) during the pre-ECT waking state, and (3)
following anesthesia administration but prior to ECT.
Spectral amplitude and autocorrelation were also calculated
in these states, allowing a comparison of these measures
with lambda 1. We hypothesized that lambda 1 would be lowest
during the ECT seizures, suggestive of greater EEG signal
predictability over time during the seizures. We found that
during the seizures lambda 1 was smaller, while spectral
amplitude was larger. Significant inter-state differences
were not found for the left temporal and occipital regions
suggesting that these measures might serve as markers of the
degree of seizure involvement of specific brain regions.
Spectral amplitude and lambda 1 were uncorrelated and varied
independently in some cases. The autocorrelation time was
shortest in the waking EEG, and longest for the
post-anesthesia EEG, and did not account for the differences
seen in lambda 1. In contrast, the persistence of
oscillations in the autocorrelation functions was greater
for the ictal EEG than the other two states and may relate
to lambda 1.},
Doi = {10.1016/0013-4694(96)95090-7},
Key = {fds246523}
}
@article{fds324071,
Author = {Zoldi, SM and Krystal, AD and Greenside, HS},
Title = {Statistical analysis of redundancy and stationarity in
multi-channel EEG.},
Journal = {JOURNAL OF MATHEMATICAL PSYCHOLOGY},
Volume = {40},
Number = {4},
Pages = {354-355},
Publisher = {ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS},
Year = {1996},
Month = {December},
Key = {fds324071}
}
@article{fds362547,
Author = {Greenside, HS},
Title = {Spatiotemporal Chaos in Large Systems: The Scaling of
Complexity with Size},
Year = {1996},
Month = {December},
Abstract = {The dynamics of a nonequilibrium system can become complex
because the system has many components (e.g., a human
brain), because the system is strongly driven from
equilibrium (e.g., large Reynolds-number flows), or because
the system becomes large compared to certain intrinsic
length scales. Recent experimental and theoretical work is
reviewed that addresses this last route to complexity. In
the idealized case of a sufficiently large, nontransient,
homogeneous, and chaotic system, the fractal dimension D
becomes proportional to the system's volume V which defines
the regime of extensive chaos. The extensivity of the
fractal dimension suggests a new way to characterize
correlations in high-dimensional systems in terms of an
intensive dimension correlation length $\xi_\delta$. Recent
calculations at Duke University show that $\xi_\delta$ is a
length scale smaller than and independent of some commonly
used measures of disorder such as the two-point and
mutual-information correlation lengths. Identifying the
basic length and time scales of extensive chaos remains a
central problem whose solution will aid the theoretical and
experimental understanding of large nonequilibrium
systems.},
Key = {fds362547}
}
@booklet{Zoldi97,
Author = {Zoldi, SM and Greenside, HS},
Title = {Karhunen-loève decomposition of extensive
chaos},
Journal = {Physical Review Letters},
Volume = {78},
Number = {9},
Pages = {1687-1690},
Publisher = {American Physical Society (APS)},
Year = {1997},
Month = {March},
url = {http://arxiv.org/abs/chao-dyn/9610007v1},
Abstract = {We show that the number of KLD (Karhunen-Loève
decomposition) modes DKLD needed to capture a fraction f of
the total variance of an extensively chaotic state scales
extensively with subsystem volume V. This allows a
correlation length ξKLD to be defined that is easily
calculated from spatially localized data. We show that ξKLD
has a parametric dependence similar to that of the dimension
correlation length and demonstrate that this length can be
used to characterize high-dimensional inhomogeneous
spatiotemporal chaos. © 1997 The American Physical
Society.},
Doi = {10.1103/PhysRevLett.78.1687},
Key = {Zoldi97}
}
@article{fds324070,
Author = {Krystal, AD and Coffey, CE and Weiner, RD and Rapp, PE and Albano, A and Greenside, HS and DeMasi, M and Cellucci, C},
Title = {EEG correlates of the response to ECT},
Journal = {BIOLOGICAL PSYCHIATRY},
Volume = {41},
Pages = {189-189},
Publisher = {ELSEVIER SCIENCE INC},
Year = {1997},
Month = {April},
Key = {fds324070}
}
@article{fds362546,
Author = {Zoldi, SM and Greenside, HS},
Title = {Spatially Localized Unstable Periodic Orbits},
Year = {1997},
Month = {April},
Abstract = {Using an innovative damped-Newton method, we report the
first calculation of many distinct unstable periodic orbits
(UPOs) of a large high-dimensional extensively chaotic
partial differential equation. A majority of the UPOs turn
out to be spatially localized in that time dependence occurs
only on portions of the spatial domain. With a particular
weighting of 127 UPOs, the Lyapunov fractal dimension D=8.8
can be estimated with a relative error of 2%. We discuss the
implications of these spatially localized UPOs for
understanding and controlling spatiotemporal
chaos.},
Key = {fds362546}
}
@article{fds246522,
Author = {Krystal, AD and Zaidman, C and Greenside, HS and Weiner, RD and Coffey,
CE},
Title = {The largest Lyapunov exponent of the EEG during ECT seizures
as a measure of ECT seizure adequacy.},
Journal = {Electroencephalogr Clin Neurophysiol},
Volume = {103},
Number = {6},
Pages = {599-606},
Year = {1997},
Month = {December},
ISSN = {0013-4694},
url = {http://www.ncbi.nlm.nih.gov/pubmed/9546486},
Abstract = {Attributes of the electroencephalogram (EEG) recorded during
electroconvulsive therapy (ECT) seizures appear promising
for decreasing the uncertainty that exists about how to
define a therapeutically adequate seizure. In the present
report we study whether one promising and not yet tested
ictal EEG measure, the largest Lyapunov exponent (lambda1),
is useful in this regard. We calculated lambda1 from 2
channel ictal EEG data recorded in 25 depressed subjects who
received right unilateral ECT. We studied the relationship
of lambda1 to treatment therapeutic outcome and to an
indirect measure of treatment therapeutic potency, the
extent to which the stimulus intensity exceeds the seizure
threshold. We found lambda1 could be reliably calculated
from ictal EEG data and that the global mean, maximum, and
standard deviation of lambda1 were smaller in the more
therapeutically potent moderately suprathreshold ECT and in
therapeutic responders. These results imply a more
predictable or consistent pattern of EEG seizure activity
over time in more therapeutically effective ECT seizures.
These findings also suggest the promise of lambda1 as a
marker of ECT seizure therapeutic adequacy and build on our
previous work suggesting that lambda1 may be useful for
classifying seizures and for reflecting the relative
physiologic impact of seizure activity.},
Doi = {10.1016/s0013-4694(97)00062-x},
Key = {fds246522}
}
@article{fds246524,
Author = {Zoldi, SM and Liu, J and Bajaj, KMS and Greenside, HS and Ahlers,
G},
Title = {Extensive scaling and nonuniformity of the Karhunen-Loève
decomposition for the spiral-defect chaos
state},
Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids,
and Related Interdisciplinary Topics},
Volume = {58},
Number = {6 SUPPL. A},
Pages = {R6903-R6906},
Year = {1998},
url = {http://arxiv.org/abs/chao-dyn/9808006v1},
Abstract = {By analyzing large-aspect-ratio spiral-defect chaos (SDC)
convection images, we show that the Karhunen-Loève
decomposition (KLD) scales extensively for subsystem sizes
larger than 4d (d is the fluid depth), which strongly
suggests that SDC is extensively chaotic. From this
extensive scaling, the intensive length ξKLD is computed
and found to have a different dependence on the Rayleigh
number than the two-point correlation length ξ2. Local
computations of ξKLD reveal a spatial nonuniformity of SDC
images that extends over radii 18d<r<45d in a Γ = 109
aspect-ratio cell.},
Doi = {10.1103/PhysRevE.58.R6903},
Key = {fds246524}
}
@article{fds246525,
Author = {Strain, MC and Greenside, HS},
Title = {Size-dependent transition to high-dimensional chaotic
dynamics in a two-dimensional excitable medium},
Journal = {Physical Review Letters},
Volume = {80},
Number = {11},
Pages = {2306-2309},
Year = {1998},
Month = {January},
url = {http://arxiv.org/abs/chao-dyn/9710006v2},
Abstract = {The spatiotemporal dynamics of an excitable medium with
multiple spiral defects is shown to vary smoothly with
system size from short-lived transients for small systems to
extensive chaos for large systems. A comparison of the
Lyapunov dimension density with the average spiral defect
density suggests an average dimension per spiral defect
varying between 3 and 7. We discuss some implications of
these results for experimental studies of excitable media.
© 1998 The American Physical Society.},
Doi = {10.1103/PhysRevLett.80.2306},
Key = {fds246525}
}
@article{fds246527,
Author = {Zoldi, SM and Greenside, HS},
Title = {Spatially localized unstable periodic orbits of a
high-dimensional chaotic system},
Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids,
and Related Interdisciplinary Topics},
Volume = {57},
Number = {3},
Pages = {R2511-R2514},
Publisher = {American Physical Society (APS)},
Year = {1998},
Month = {January},
url = {http://dx.doi.org/10.1103/PhysRevE.57.R2511},
Abstract = {Using an innovative damped-Newton method, we report the
calculation and analysis of many distinct unstable periodic
orbits (UPOs) for a high-fractal-dimension [formula
presented] extensively chaotic solution of a partial
differential equation. A majority of the UPOs turn out to be
spatially localized in that time dependence occurs only on
portions of the spatial domain. With a escape-time weighting
of 127 UPOs, the attractor’s fractal dimension can be
estimated with a relative error of 2%. Statistical errors
are found to decrease as [formula presented] as the number
[formula presented] of known UPOs increases. © 1998 The
American Physical Society.},
Doi = {10.1103/PhysRevE.57.R2511},
Key = {fds246527}
}
@article{fds246567,
Author = {Epureanu, BI and Greenside, HS},
Title = {Fractal basins of attraction associated with a damped
Newton's method},
Journal = {SIAM Review},
Volume = {40},
Number = {1},
Pages = {102-109},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {1998},
Month = {January},
url = {http://dx.doi.org/10.1137/S0036144596310033},
Abstract = {An intriguing and unexpected result for students learning
numerical analysis is that Newton's method, applied to the
simple polynomial z3 - 1 = 0 in the complex plane, leads to
intricately interwoven basins of attraction of the roots. As
an example of an interesting open question that may help to
stimulate student interest in numerical analysis, we
investigate the question of whether a damping method, which
is designed to increase the likelihood of convergence for
Newton's method, modifies the fractal structure of the basin
boundaries. The overlap of the frontiers of numerical
analysis and nonlinear dynamics provides many other problems
that can help to make numerical analysis courses
interesting.},
Doi = {10.1137/S0036144596310033},
Key = {fds246567}
}
@article{fds303666,
Author = {Zoldi, SM and Greenside, HS},
Title = {Comment on “Optimal periodic orbits of chaotic
systems”},
Journal = {Physical Review Letters},
Volume = {80},
Number = {8},
Pages = {1790},
Publisher = {American Physical Society (APS)},
Year = {1998},
Month = {February},
url = {http://arxiv.org/abs/chao-dyn/9707001v1},
Abstract = {A Comment on the Letter by Brian R. Hunt and Edward Ott,
Phys. Rev. Lett. 76, 2254 (1996). The authors of the Letter
offer a Reply. © 1998 The American Physical
Society.},
Doi = {10.1103/PhysRevLett.80.1790},
Key = {fds303666}
}
@article{fds246568,
Author = {Krystal, AD and Greenside, HS},
Title = {Low-dimensional chaos in bipolar disorder?},
Journal = {Arch Gen Psychiatry},
Volume = {55},
Number = {3},
Pages = {275-276},
Year = {1998},
Month = {March},
ISSN = {0003-990X},
url = {http://www.ncbi.nlm.nih.gov/pubmed/9510223},
Doi = {10.1001/archpsyc.55.3.275},
Key = {fds246568}
}
@article{fds246569,
Author = {Zoldi, SM and Greenside, HS},
Title = {Spatially Localized Unstable Periodic Orbits Of A
High-Dimensional Chaotic System},
Journal = {Phys. Rev. E},
Volume = {57},
Number = {3},
Pages = {R2511-R2514},
Year = {1998},
Month = {March},
Key = {fds246569}
}
@article{fds4565,
Author = {Scott M. Zoldi and Henry S. Greenside},
Title = {Spatially Localized Unstable Periodic Orbits Of A
High-Dimensional Chaotic System},
Journal = {Phys. Rev. E},
Volume = {57},
Number = {3},
Pages = {R2511-R2514},
Year = {1998},
Month = {March},
Key = {fds4565}
}
@article{fds246528,
Author = {Krystal, AD and Greenside, HS and Gottschalk, A and Bauer, MS and Whybrow, PC},
Title = {Low-dimensional chaos in bipolar disorder [1] (multiple
letters)},
Journal = {Archives of Internal Medicine},
Volume = {158},
Number = {5},
Pages = {275},
Year = {1998},
Month = {March},
ISSN = {0003-990X},
url = {http://dx.doi.org/10.1001/archpsyc.55.3.275},
Doi = {10.1001/archpsyc.55.3.275},
Key = {fds246528}
}
@article{fds4451,
Author = {Henry S. Greenside},
Title = {Spatiotemporal Chaos in Large Systems: The Scaling of
Complexity With Size},
Series = {CRM Proceedings and Lecture Notes},
Pages = {9-40},
Booktitle = {Semi-Analytic Methods for the Navier Stokes
Equations},
Publisher = {American Mathematical Society, Providence,
RI},
Editor = {K. Coughlin},
Year = {1999},
Key = {fds4451}
}
@article{fds4566,
Author = {Andrew D. Krystal and Scott Zoldi and Raquel Prado and Henry S.
Greenside and Mike West},
Title = {The Spatiotemporal Dynamics of Generalized Tonic-Clonic
Seizure EEG Data: Relevance To the Clinical Practice of
Electroconvulsive Therapy},
Booktitle = {Nonlinear Dynamics in Brain Function},
Publisher = {In Press},
Year = {1999},
Key = {fds4566}
}
@article{fds4567,
Author = {A. D. Krystal and M. West and R. Prado and H. S. Greenside and R. D.
Weiner and S. M. Zoldi},
Title = {The EEG Effects of ECT: Implications for
rTMS},
Booktitle = {Progress in Neuropsychopharmacology and Biological
Psychiatry},
Publisher = {In Press},
Year = {1999},
Key = {fds4567}
}
@article{fds246529,
Author = {Krystal, AD and West, M and Prado, R and Greenside, H and Zoldi, S and Weiner, RD},
Title = {EEG effects of ECT: implications for rTMS.},
Journal = {Depress Anxiety},
Volume = {12},
Number = {3},
Pages = {157-165},
Year = {2000},
ISSN = {1091-4269},
url = {http://www.ncbi.nlm.nih.gov/pubmed/11126190},
Abstract = {Electroconvulsive therapy (ECT) involves the use of
electrical stimulation to elicit a series of generalized
tonic-clonic seizures for therapeutic purposes and is the
most effective treatment known for major depression. These
treatments have significant neurophysiologic effects, many
of which are manifest in the electroencephalogram (EEG). The
relationship between EEG data and the response to ECT has
been studied since the 1940s, but for many years no
consistent correlates were found. Recent studies indicate
that a number of specific EEG features recorded during the
induced seizures (ictal EEG) as well as before and after a
course of treatment (interictal EEG) are related to both the
therapeutic efficacy and cognitive side effects. Similar to
ECT, repetitive transcranial magnetic stimulation (rTMS),
which involves focal electromagnetic stimulation of cortical
neurons, has also been studied as an antidepressant therapy
and also appears to have neurophysiologic effects, although
these have not been as fully investigated as is the case
with ECT. Given the similarity of these treatments, it is
natural to consider whether advances in understanding the
electrophysiologic correlates of the ECT response might have
implications for rTMS. The present article reviews the
literature on the EEG effects of ECT and discusses the
implications in terms of the likely efficacy and side
effects associated with rTMS in specific anatomic locations,
the potential for producing an antidepressant response with
rTMS without eliciting seizure activity, eliciting focal
seizures with rTMS, and the possibility of using rTMS to
focally modulate seizure induction and spread with ECT to
optimize treatment.},
Doi = {10.1002/1520-6394(2000)12:3<157::AID-DA7>3.0.CO;2-R},
Key = {fds246529}
}
@article{fds246570,
Author = {Zoldi, SM and Krystal, A and Greenside, HS},
Title = {Stationarity and redundancy of multichannel EEG data
recorded during generalized tonic-clonic
seizures.},
Journal = {Brain Topogr},
Volume = {12},
Number = {3},
Pages = {187-200},
Year = {2000},
ISSN = {0896-0267},
url = {http://www.ncbi.nlm.nih.gov/pubmed/10791682},
Abstract = {To improve our understanding of the physiology of
generalized tonic-clonic (GTC) seizures, we have
investigated the stationarity and redundancy of 21-electrode
EEG data recorded from ten patients during GTC seizures
elicited by electroconvulsive therapy (ECT). Stationarity
was examined by calculating probability density functions
(pdfs) and power spectra over small equal-length
non-overlapping time windows and then by studying, visually
and quantitatively, the evolution of these quantities over
the duration of the seizures. Our analysis shows that some
seizures had no demonstrable stationarity, that most
seizures had time intervals of at least a few seconds that
were statistically stationary by several criteria, and that,
in some seizures, there were leads which were delayed in
manifesting the statistical changes associated with seizure
onset evident in other leads. The redundancy analysis
demonstrated for the first time posterior-to-anterior time
delays in the mid-ictal region of GTC seizures. The
implications of these findings are discussed for the
analysis of GTC seizure EEG data, for the physiology of GTC
seizures, and for ECT research.},
Doi = {10.1023/a:1023489807177},
Key = {fds246570}
}
@article{fds246571,
Author = {Cherry, EM and Greenside, HS and Henriquez, CS},
Title = {A space-time adaptive method for simulating complex cardiac
dynamics.},
Journal = {Physical review letters},
Volume = {84},
Number = {6},
Pages = {1343-1346},
Year = {2000},
Month = {February},
ISSN = {0031-9007},
url = {http://www.ncbi.nlm.nih.gov/pubmed/11017514},
Abstract = {For plane-wave and many-spiral states of the experimentally
based Luo-Rudy 1 model of heart tissue in large (8 cm
square) domains, we show that a space-time-adaptive
time-integration algorithm can achieve a factor of 5
reduction in computational effort and memory-but without a
reduction in accuracy-when compared to an algorithm using a
uniform space-time mesh at the finest resolution. Our
results indicate that such an algorithm can be extended
straightforwardly to simulate quantitatively
three-dimensional electrical dynamics over the whole human
heart.},
Doi = {10.1103/physrevlett.84.1343},
Key = {fds246571}
}
@article{fds362545,
Author = {Lai, MC and Chiam, KH and Cross, MC and Greenside,
HS},
Title = {Simulating Complex Dynamics In Intermediate And
Large-Aspect-Ratio Convection Systems},
Booktitle = {18th Symposium on Energy Engineering Sciences},
Publisher = {Argonne National Laboratory},
Year = {2000},
Month = {May},
Abstract = {Buoyancy-induced (Rayleigh-Benard) convection of a fluid
between two horizontal plates is a central paradigm for
studying the transition to complex spatiotemporal dynamics
in sustained nonequilibrium systems. To improve the analysis
of experimental data and the quantitative comparison of
theory with experiment, we have developed a
three-dimensional finite-difference code that can integrate
the three-dimensional Boussinesq equations (which govern the
evolution of the temperature, velocity, and pressure fields
associated with a convecting flow) efficiently in large
box-shaped domains with experimentally appropriate lateral
boundary conditions. We discuss some details of this code
and present two applications, one to the occurrence of
quasiperiodic dynamics with as many as 5 incommensurate
frequencies in a moderate-aspect-ratio 10x5 convection cell,
and one to the onset of spiral defect chaos in square cells
with aspect ratios varying from Gamma=16 to
56.},
Key = {fds362545}
}
@article{fds318449,
Author = {Sensoy, B and Greenside, H},
Title = {Pattern formation near onset of a convecting fluid in an
annulus},
Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {64},
Number = {4 II},
Pages = {462041-4620410},
Year = {2001},
Abstract = {A computer code was developed and applied to study pattern
formation near onset of the Swift-Hohenberg model in annular
domains of varying aspect ratios. Several kinds of initial
conditions including small-amplitude random fields and
high-symmetry states of straight, radial or concentric rolls
were used to explore the possible basis of attraction. As
the aspect ratio becomes larger, new patterns were observed
that were characterized by radially oriented grain
boundaries.},
Key = {fds318449}
}
@article{fds246572,
Author = {Sensoy, B and Greenside, H},
Title = {Pattern formation near onset of a convecting fluid in an
annulus.},
Journal = {Physical review. E, Statistical, nonlinear, and soft matter
physics},
Volume = {64},
Number = {4 Pt 2},
Pages = {046204},
Year = {2001},
Month = {October},
ISSN = {1539-3755},
url = {http://www.ncbi.nlm.nih.gov/pubmed/11690122},
Abstract = {Numerical simulations of the time-dependent Swift-Hohenberg
equation are used to test the predictions of Cross [Phys.
Rev. A 25, 1065 (1982)] that Rayleigh-Bénard convection in
the form of straight rolls or of an array of dislocations
may be observed in an annular domain, depending on the
values of inner radius r(1), outer radius r(2), reduced
Rayleigh number epsilon, and initial states. As r(1) is
decreased for a fixed r(2) and for different choices of
epsilon and of symmetric and random initial state, we find
that there are indeed ranges of these parameters for which
the predictions of Cross are qualitatively correct. However,
when the radius difference r(2)-r(1) becomes larger than a
few roll diameters, a new pattern is observed consisting of
stripe domains separated by radially oriented grain
boundaries. The relative stabilities of the various patterns
are compared by evaluating their Lypunov functional
densities.},
Doi = {10.1103/physreve.64.046204},
Key = {fds246572}
}
@article{fds246573,
Author = {Paul, MR and Cross, MC and Fischer, PF and Greenside,
HS},
Title = {Power-law behavior of power spectra in low Prandtl number
Rayleigh-Bénard convection.},
Journal = {Physical review letters},
Volume = {87},
Number = {15},
Pages = {154501},
Year = {2001},
Month = {October},
ISSN = {0031-9007},
url = {http://dx.doi.org/10.1103/physrevlett.87.154501},
Abstract = {The origin of the power-law decay measured in the power
spectra of low Prandtl number Rayleigh-Bénard convection
near the onset of chaos is addressed using long time
numerical simulations of the three-dimensional Boussinesq
equations in cylindrical domains. The power law is found to
arise from quasidiscontinuous changes in the slope of the
time series of the heat transport associated with the
nucleation of dislocation pairs and roll pinch-off events.
For larger frequencies, the power spectra decay
exponentially as expected for time continuous deterministic
dynamics.},
Doi = {10.1103/physrevlett.87.154501},
Key = {fds246573}
}
@article{Tajima02,
Author = {Tajima, S and Greenside, HS},
Title = {Microextensive chaos of a spatially extended
system.},
Journal = {Physical review. E, Statistical, nonlinear, and soft matter
physics},
Volume = {66},
Number = {1 Pt 2},
Pages = {017205},
Year = {2002},
Month = {July},
ISSN = {1539-3755},
url = {http://ojps.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PLEEE8000066000001017205000001&idtype=cvips},
Abstract = {By analyzing chaotic states of the one-dimensional
Kuramoto-Sivashinsky equation for system sizes L in the
range 79 < or = L < or = 93, we show that the Lyapunov
fractal dimension D scales microextensively, increasing
linearly with L even for increments Delta L that are small
compared to the average cell size of 9 and to various
correlation lengths. This suggests that a spatially
homogeneous chaotic system does not have to increase its
size by some characteristic amount to increase its dynamical
complexity.},
Doi = {10.1103/physreve.66.017205},
Key = {Tajima02}
}
@article{fds246532,
Author = {Chiam, KH and Lai, MC and Greenside, HS},
Title = {Efficient algorithm on a nonstaggered mesh for simulating
Rayleigh-Bénard convection in a box},
Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
Physics},
Volume = {68},
Number = {2 2},
Pages = {026705/1-026705/10},
Year = {2003},
ISSN = {1063-651X},
url = {http://arxiv.org/abs/nlin/0302057v1},
Abstract = {A semi-implicit finite-difference algorithm for integrating
the Boussinesq equations in two- and three-dimensional
boxes, with sidewalls that are periodic, thermally
insulated, or thermally conducting is presented. The
approach is useful for simple geometries such as a box,
cylinder, torus, and annulus, with boundary conditions such
that various linear operators are separable so that fast
direct methods can be applied. The resulting algorithm is
sufficiently efficient that aspect ratios up to Γ≈20 can
be studied on a single-processor workstation over several
days.},
Doi = {10.1103/physreve.68.026705},
Key = {fds246532}
}
@article{fds246565,
Author = {Chiam, K-H and Paul, MR and Cross, MC and Greenside,
H},
Title = {Mean Flow Dynamics of Stripe Textures and Spiral Defect
Chaos in Rayleigh-Benard Convection},
Journal = {Physical Review E},
Volume = {67},
Number = {5 2},
Pages = {056206},
Year = {2003},
ISSN = {1063-651X},
Abstract = {We describe a numerical procedure to construct a modified
velocity field that does not have any mean flow. Using this
procedure, we present two results. First, we show that, in
the absence of the mean flow, spiral defect chaos collapses
to a stationary pattern comprising textures of stripes with
angular bends. The quenched patterns are characterized by
mean wave numbers that approach those uniquely selected by
focus-type singularities, which, in the absence of the mean
flow, lie at the zigzag instability boundary. The quenched
patterns also have larger correlation lengths and are
comprised of rolls with less curvature. Secondly, we
describe how the mean flow can contribute to the commonly
observed phenomenon of rolls terminating perpendicularly
into lateral walls. We show that, in the absence of the mean
flow, rolls begin to terminate into lateral walls at an
oblique angle. This obliqueness increases with the Rayleigh
number},
Key = {fds246565}
}
@article{fds304573,
Author = {Chiam, K-H and Paul, MR and Cross, MC and Greenside,
HS},
Title = {Mean flow and spiral defect chaos in Rayleigh-Bénard
convection.},
Journal = {Physical review. E, Statistical, nonlinear, and soft matter
physics},
Volume = {67},
Number = {5 Pt 2},
Pages = {056206},
Year = {2003},
Month = {May},
ISSN = {1063-651X},
url = {http://dx.doi.org/10.1103/physreve.67.056206},
Abstract = {We describe a numerical procedure to construct a modified
velocity field that does not have any mean flow. Using this
procedure, we present two results. First, we show that, in
the absence of the mean flow, spiral defect chaos collapses
to a stationary pattern comprising textures of stripes with
angular bends. The quenched patterns are characterized by
mean wave numbers that approach those uniquely selected by
focus-type singularities, which, in the absence of the mean
flow, lie at the zigzag instability boundary. The quenched
patterns also have larger correlation lengths and are
comprised of rolls with less curvature. Secondly, we
describe how the mean flow can contribute to the commonly
observed phenomenon of rolls terminating perpendicularly
into lateral walls. We show that, in the absence of the mean
flow, rolls begin to terminate into lateral walls at an
oblique angle. This obliqueness increases with the Rayleigh
number.},
Doi = {10.1103/physreve.67.056206},
Key = {fds304573}
}
@article{fds246564,
Author = {Cherry, EM and Greenside, HS and Henriquez, CS},
Title = {Efficient simulation of three-dimensional anisotropic
cardiac tissue using an adaptive mesh refinement
method.},
Journal = {Chaos (Woodbury, N.Y.)},
Volume = {13},
Number = {3},
Pages = {853-865},
Year = {2003},
Month = {September},
url = {http://dx.doi.org/10.1063/1.1594685},
Abstract = {A recently developed space-time adaptive mesh refinement
algorithm (AMRA) for simulating isotropic one- and
two-dimensional excitable media is generalized to simulate
three-dimensional anisotropic media. The accuracy and
efficiency of the algorithm is investigated for anisotropic
and inhomogeneous 2D and 3D domains using the Luo-Rudy 1
(LR1) and FitzHugh-Nagumo models. For a propagating wave in
a 3D slab of tissue with LR1 membrane kinetics and
rotational anisotropy comparable to that found in the human
heart, factors of 50 and 30 are found, respectively, for the
speedup and for the savings in memory compared to an
algorithm using a uniform space-time mesh at the finest
resolution of the AMRA method. For anisotropic 2D and 3D
media, we find no reduction in accuracy compared to a
uniform space-time mesh. These results suggest that the AMRA
will be able to simulate the 3D electrical dynamics of
canine ventricles quantitatively for 1 s using 32 1-GHz
Alpha processors in approximately 9 h.},
Doi = {10.1063/1.1594685},
Key = {fds246564}
}
@article{fds246566,
Author = {Paul, MR and Chiam, KH and Cross, MC and Fischer, PF and Greenside,
HS},
Title = {Pattern formation and dynamics in Rayleigh-Bénard
convection: Numerical simulations of experimentally
realistic geometries},
Journal = {Physica D: Nonlinear Phenomena},
Volume = {184},
Number = {1-4},
Pages = {114-126},
Publisher = {Elsevier BV},
Year = {2003},
Month = {October},
url = {http://dx.doi.org/10.1016/S0167-2789(03)00216-1},
Abstract = {Rayleigh-Bénard convection is studied and quantitative
comparisons are made, where possible, between theory and
experiment by performing numerical simulations of the
Boussinesq equations for a variety of experimentally
realistic situations. Rectangular and cylindrical geometries
of varying aspect ratios for experimental boundary
conditions, including fins and spatial ramps in plate
separation, are examined with particular attention paid to
the role of the mean flow. A small cylindrical convection
layer bounded laterally either by a rigid wall, fin, or a
ramp is investigated and our results suggest that the mean
flow plays an important role in the observed wavenumber.
Analytical results are developed quantifying the mean flow
sources, generated by amplitude gradients, and its effect on
the pattern wavenumber for a large-aspect-ratio cylinder
with a ramped boundary. Numerical results are found to agree
well with these analytical predictions. We gain further
insight into the role of mean flow in pattern dynamics by
employing a novel method of quenching the mean flow
numerically. Simulations of a spiral defect chaos state
where the mean flow is suddenly quenched is found to remove
the time dependence, increase the wavenumber and make the
pattern more angular in nature. Published by Elsevier
B.V.},
Doi = {10.1016/S0167-2789(03)00216-1},
Key = {fds246566}
}
@article{fds246535,
Author = {Chiam, K-H and Cross, MC and Greenside, HS and Fischer,
PF},
Title = {Enhanced tracer transport by the spiral defect chaos state
of a convecting fluid.},
Journal = {Physical review. E, Statistical, nonlinear, and soft matter
physics},
Volume = {71},
Number = {3 Pt 2A},
Pages = {036205},
Year = {2005},
Month = {March},
ISSN = {1539-3755},
url = {http://dx.doi.org/10.1103/physreve.71.036205},
Abstract = {To understand how spatiotemporal chaos may modify material
transport, we use direct numerical simulations of the
three-dimensional Boussinesq equations and of an
advection-diffusion equation to study the transport of a
passive tracer by the spiral defect chaos state of a
convecting fluid. The simulations show that the transport is
diffusive and is enhanced by the spatiotemporal chaos. The
enhancement in tracer diffusivity follows two regimes. For
large Péclet numbers (that is, small molecular
diffusivities of the tracer), we find that the enhancement
is proportional to the Péclet number. For small Péclet
numbers, the enhancement is proportional to the square root
of the Péclet number. We explain the presence of these two
regimes in terms of how the local transport depends on the
local wave numbers of the convection rolls. For large
Péclet numbers, we further find that defects cause the
tracer diffusivity to be enhanced locally in the direction
orthogonal to the local wave vector but suppressed in the
direction of the local wave vector.},
Doi = {10.1103/physreve.71.036205},
Key = {fds246535}
}
@article{fds246533,
Author = {Jayaraman, A and Scheel, JD and Greenside, HS and Fischer,
PF},
Title = {Characterization of the domain chaos convection state by the
largest Lyapunov exponent.},
Journal = {Physical review. E, Statistical, nonlinear, and soft matter
physics},
Volume = {74},
Number = {1 Pt 2},
Pages = {016209},
Publisher = {American Physical Society},
Year = {2006},
Month = {July},
ISSN = {1539-3755},
url = {http://dx.doi.org/10.1103/physreve.74.016209},
Abstract = {Using numerical integrations of the Boussinesq equations in
rotating cylindrical domains with realistic boundary
conditions, we have computed the value of the largest
Lyapunov exponent lambda1 for a variety of aspect ratios and
driving strengths. We study in particular the domain chaos
state, which bifurcates supercritically from the conducting
fluid state and involves extended propagating fronts as well
as point defects. We compare our results with those from
Egolf, [Nature 404, 733 (2000)], who suggested that the
value of lambda1 for the spiral defect chaos state of a
convecting fluid was determined primarily by bursts of
instability arising from short-lived, spatially localized
dislocation nucleation events. We also show that the
quantity lambda1 is not intensive for aspect ratios Gamma
over the range 20<Gamma<40 and that the scaling exponent of
lambda1 near onset is consistent with the value predicted by
the amplitude equation formalism.},
Doi = {10.1103/physreve.74.016209},
Key = {fds246533}
}
@article{fds246534,
Author = {Li, M and Greenside, H},
Title = {Stable propagation of a burst through a one-dimensional
homogeneous excitatory chain model of songbird nucleus
HVC.},
Journal = {Physical review. E, Statistical, nonlinear, and soft matter
physics},
Volume = {74},
Number = {1 Pt 1},
Pages = {011918},
Year = {2006},
Month = {July},
ISSN = {1539-3755},
url = {http://www.ncbi.nlm.nih.gov/pubmed/16907138},
Abstract = {We demonstrate numerically that a brief burst consisting of
two to six spikes can propagate in a stable manner through a
one-dimensional homogeneous feedforward chain of nonbursting
neurons with excitatory synaptic connections. Our results
are obtained for two kinds of neuronal models: leaky
integrate-and-fire neurons and Hodgkin-Huxley neurons with
five conductances. Over a range of parameters such as the
maximum synaptic conductance, both kinds of chains are found
to have multiple attractors of propagating bursts, with each
attractor being distinguished by the number of spikes and
total duration of the propagating burst. These results make
plausible the hypothesis that sparse, precisely timed
sequential bursts observed in projection neurons of nucleus
HVC of a singing zebra finch are intrinsic and causally
related.},
Doi = {10.1103/physreve.74.011918},
Key = {fds246534}
}
@book{fds246514,
Author = {H. Greenside and Cross, M and Greenside, H},
Title = {Pattern formation and dynamics in nonequilibrium
systems},
Pages = {1-535},
Publisher = {Cambridge University Press},
Address = {New York},
Year = {2009},
Month = {January},
ISBN = {9780521770507},
url = {http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521770507},
Abstract = {Many exciting frontiers of science and engineering require
understanding the spatiotemporal properties of sustained
nonequilibrium systems such as fluids, plasmas, reacting and
diffusing chemicals, crystals solidifying from a melt, heart
muscle, and networks of excitable neurons in brains. This
introductory textbook for graduate students in biology,
chemistry, engineering, mathematics, and physics provides a
systematic account of the basic science common to these
diverse areas. This book provides a careful pedagogical
motivation of key concepts, discusses why diverse
nonequilibrium systems often show similar patterns and
dynamics, and gives a balanced discussion of the role of
experiments, simulation, and analytics. It contains numerous
worked examples and over 150 exercises. This book will also
interest scientists who want to learn about the experiments,
simulations, and theory that explain how complex patterns
form in sustained nonequilibrium systems.},
Doi = {10.1017/CBO9780511627200},
Key = {fds246514}
}
@misc{fds225755,
Author = {H. Greenside},
Title = {Using an Android Tablet with Active Stylus To Create
Screencasts Easily and Inexpensively},
Year = {2014},
url = {http://cit.duke.edu/blog/2014/06/using-android-tablet-active-stylus-create-screencasts-easily-inexpensively/},
Key = {fds225755}
}
@article{fds323240,
Author = {Lim, MX and Greenside, H},
Title = {The external magnetic field created by the superposition of
identical parallel finite solenoids},
Journal = {American Journal of Physics},
Volume = {84},
Number = {8},
Pages = {606-615},
Publisher = {American Association of Physics Teachers
(AAPT)},
Year = {2016},
Month = {August},
url = {http://dx.doi.org/10.1119/1.4948603},
Abstract = {We use superposition and numerical methods to show that the
external magnetic field generated by parallel identical
solenoids can be nearly uniform and substantial, even when
the solenoids have lengths that are large compared to their
radii. We examine both a ring of solenoids and a large
hexagonal array of solenoids. In both cases, we discuss how
the magnitude and uniformity of the external field depend on
the length of and the spacing between the solenoids. We also
discuss some novel properties of a single solenoid, e.g.,
that even for short solenoids the energy stored in the
internal magnetic field exceeds the energy stored in the
spatially infinite external magnetic field. These results
should be broadly interesting to undergraduates learning
about electricity and magnetism.},
Doi = {10.1119/1.4948603},
Key = {fds323240}
}
@article{fds325017,
Author = {Jackson, DP},
Title = {AJP Reviewers},
Journal = {American Journal of Physics},
Volume = {84},
Number = {12},
Pages = {901-902},
Publisher = {American Association of Physics Teachers
(AAPT)},
Year = {2016},
Month = {December},
url = {http://dx.doi.org/10.1119/1.4966631},
Doi = {10.1119/1.4966631},
Key = {fds325017}
}
@article{fds332010,
Author = {McCreery, K and Greenside, H},
Title = {The electric field of a uniformly charged cubic
shell},
Journal = {American Journal of Physics},
Volume = {86},
Number = {1},
Pages = {36-44},
Publisher = {American Association of Physics Teachers
(AAPT)},
Year = {2018},
Month = {January},
url = {http://dx.doi.org/10.1119/1.5009446},
Abstract = {As an integrative and insightful example for undergraduates
learning about electrostatics, we discuss how to use
symmetry, Coulomb's law, superposition, Gauss's law, and
visualization to understand the electric field E(x,y,z)
produced by a uniformly charged cubic shell. We first
discuss how to deduce qualitatively, using freshman-level
physics, the perhaps surprising fact that the interior
electric field is nonzero and has a complex structure,
pointing inwards from the middle of each face of the shell
and pointing outwards towards each edge and corner. We then
discuss how to understand the quantitative features of the
electric field by plotting an analytical expression for E
along symmetry lines and on symmetry surfaces of the
shell.},
Doi = {10.1119/1.5009446},
Key = {fds332010}
}