Publications of Henry Greenside    :chronological  combined listing:

%% Books   
@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 = {9780511627200},
   url = {http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521770507},
   Abstract = {© 2009 M. Cross and H. Greenside. 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}
}


%% Papers Published   
@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 = {Electroencephalography and Clinical Neurophysiology},
   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.},
   Key = {fds246523}
}

@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 = {INTRODUCTION: 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. METHODS AND RESULTS: 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. CONCLUSION: 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.},
   Key = {fds246519}
}

@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},
   Year = {1982},
   ISSN = {0167-2789},
   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.},
   Key = {Greenside82}
}

@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{fds325017,
   Author = {Jackson, DP},
   Title = {AJP Reviewers},
   Journal = {American journal of physics},
   Volume = {84},
   Number = {12},
   Pages = {901-902},
   Year = {2016},
   Month = {December},
   url = {http://dx.doi.org/10.1119/1.4966631},
   Doi = {10.1119/1.4966631},
   Key = {fds325017}
}

@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},
   Year = {1986},
   ISSN = {0010-4655},
   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.},
   Key = {fds246516}
}

@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},
   Pages = {016209 (12 pages)},
   Publisher = {American Physical Society},
   Year = {2006},
   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 λ1 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 λ1 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 λ1 is not intensive for aspect ratios Γ over the
             range 20<Γ<40 and that the scaling exponent of λ1
             near onset is consistent with the value predicted by the
             amplitude equation formalism. © 2006 The American Physical
             Society.},
   Doi = {10.1103/PhysRevE.74.016209},
   Key = {fds246533}
}

@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},
   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.},
   Key = {Egolf95}
}

@booklet{Greenside81b,
   Author = {Greenside, HS and Hamann, DR},
   Title = {Cl chemisorption on the Ag(001) surface: Geometry and
             electronic structure},
   Journal = {Physical Review B - Condensed Matter and Materials
             Physics},
   Volume = {23},
   Number = {10},
   Pages = {4879-4887},
   Year = {1981},
   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},
   Year = {1981},
   ISSN = {0038-1098},
   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.},
   Key = {Greenside81a}
}

@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},
   Year = {1976},
   Month = {March},
   url = {http://dx.doi.org/10.1021/ja00423a063},
   Doi = {10.1021/ja00423a063},
   Key = {fds325020}
}

@booklet{Holland84,
   Author = {Holland, B and Greenside, HS and Schluter, M},
   Title = {COHESIVE PROPERTIES OF Ge, Si, AND DIAMOND CALCULATED WITH
             MINIMUM BASIS SETS.},
   Journal = {Physica Status Solidi (B) Basic Research},
   Volume = {126},
   Number = {2},
   Pages = {511-515},
   Year = {1984},
   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 electron-ion 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.},
   Key = {Holland84}
}

@article{fds303666,
   Author = {Zoldi, SM and Greenside, HS},
   Title = {Comment on "Optimal Periodic Orbits of Chaotic
             Systems"},
   Volume = {80},
   Number = {8},
   Pages = {1790},
   Year = {1997},
   Month = {June},
   url = {http://arxiv.org/abs/chao-dyn/9707001v1},
   Abstract = {In a recent Letter, Hunt and Ott argued that SHORT-period
             unstable periodic orbits (UPOs) would be the invariant sets
             associated with a chaotic attractor that are most likely to
             optimize the time average of some smooth scalar performance
             function. In this Comment, we show that their conclusion
             does not hold generally and that optimal time averages may
             specifically require long-period UPOs. This situation can
             arise when long-period UPOs are able to spend substantial
             amounts of time in a region of phase space that is close to
             large values of the performance function.},
   Doi = {10.1103/PhysRevLett.80.1790},
   Key = {fds303666}
}

@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},
   Year = {1989},
   Month = {October},
   url = {http://dx.doi.org/10.1002/fld.1650091010},
   Doi = {10.1002/fld.1650091010},
   Key = {fds323241}
}

@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 - Condensed Matter and Materials
             Physics},
   Volume = {24},
   Number = {10},
   Pages = {6151-6155},
   Year = {1981},
   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{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},
   Year = {1990},
   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{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},
   Year = {1989},
   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}
}

@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},
   Year = {1984},
   Key = {Greenside84a}
}

@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},
   Year = {1987},
   ISSN = {0022-3115},
   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.},
   Key = {fds246517}
}

@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},
   Year = {1997},
   Month = {April},
   Key = {fds324070}
}

@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 = {Depression and 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}
}

@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}
}

@article{fds246532,
   Author = {Chiam, K-H and Lai, M-C and Greenside, HS},
   Title = {Efficient algorithm on a nonstaggered mesh for simulating
             Rayleigh-Bénard convection in a box},
   Journal = {Physical Review E - Statistical Physics, Plasmas, Fluids,
             and Related Interdisciplinary Topics},
   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{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},
   Volume = {13},
   Number = {3},
   Pages = {853-865},
   Year = {2003},
   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. © 2003 American
             Institute of Physics.},
   Doi = {10.1063/1.1594685},
   Key = {fds246564}
}

@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 converting fluid},
   Journal = {Physical Review E - Statistical, Nonlinear, and Soft Matter
             Physics},
   Volume = {71},
   Number = {3},
   Pages = {036205},
   Year = {2005},
   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. © 2005 The American
             Physical Society.},
   Doi = {10.1103/PhysRevE.71.036205},
   Key = {fds246535}
}

@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&lt;r&lt;45d in a Γ = 109
             aspect-ratio cell.},
   Doi = {10.1103/PhysRevE.58.R6903},
   Key = {fds246524}
}

@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- American Physical Society},
   Volume = {26},
   Number = {3},
   Pages = {390-390},
   Year = {1981},
   Key = {fds325018}
}

@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},
   Year = {1998},
   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.},
   Key = {fds246567}
}

@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{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},
   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}
}

@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 - Atomic, Molecular, and Optical
             Physics},
   Volume = {25},
   Number = {6},
   Pages = {3453-3456},
   Year = {1982},
   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}
}

@booklet{Zoldi97,
   Author = {Zoldi, SM and Greenside, HS},
   Title = {Karhunen-Lo`eve Decomposition of Extensive
             Chaos},
   Volume = {78},
   Number = {9},
   Pages = {1687 -- 1690},
   Year = {1996},
   Month = {October},
   url = {http://arxiv.org/abs/chao-dyn/9610007v1},
   Abstract = {We show that the number of KLD (Karhunen-Lo`eve
             decomposition) modes D_KLD(f) 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 xi_KLD(f) to be defined that is easily
             calculated from spatially localized data. We show that
             xi_KLD(f) 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.},
   Doi = {10.1103/PhysRevLett.78.1687},
   Key = {Zoldi97}
}

@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},
   ISSN = {0003-990X},
   url = {http://dx.doi.org/10.1001/archpsyc.55.3.275},
   Doi = {10.1001/archpsyc.55.3.275},
   Key = {fds246528}
}

@article{fds246568,
   Author = {Krystal, AD and Greenside, HS and Gottschalk, A and Bauer,
             MS},
   Title = {Low-dimensional chaos in bipolar disorder? [1] (multiple
             letters)},
   Journal = {Archives of General Psychiatry},
   Volume = {55},
   Number = {3},
   Pages = {275-},
   Year = {1998},
   ISSN = {0003-990X},
   url = {http://www.ncbi.nlm.nih.gov/pubmed/9510223},
   Doi = {10.1001/archpsyc.55.3.275},
   Key = {fds246568}
}

@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{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 Physics, Plasmas, Fluids,
             and Related Interdisciplinary Topics},
   Volume = {67},
   Number = {5 2},
   Pages = {056206/1-056206/13},
   Year = {2003},
   ISSN = {1063-651X},
   Abstract = {A procedure to construct a modified velocity field that does
             not have any mean flow in a convecting flow was developed.
             Application of the procedure showed that spiral defect chaos
             does not survive when the mean flow is quenched. Instead, a
             pattern characterized by textures of stripes with angular
             bends appeared. Furthermore, it was shown that the mean wave
             numbers of these quenched patterns approach those selected
             by focus-type singularities.},
   Key = {fds304573}
}

@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}
}

@booklet{Greenside88,
   Author = {Greenside, HS and Cross, MC and Jr, WMC},
   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},
   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}
}

@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},
   Pages = {017205/1-017205/4},
   Year = {2002},
   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≤L≤93, we show that the Lyapunov fractal
             dimension D scales microextensively, increasing linearly
             with L even for increments ΔL 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.
             © 2002 The American Physical Society.},
   Doi = {10.1103/PhysRevE.66.017205},
   Key = {Tajima02}
}

@booklet{Greenside84,
   Author = {Greenside, HS and Coughran, WM},
   Title = {Nonlinear pattern formation near the onset of
             Rayleigh-Bénard convection},
   Journal = {Physical Review A - Atomic, Molecular, and Optical
             Physics},
   Volume = {30},
   Number = {1},
   Pages = {398-428},
   Year = {1984},
   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{Greenside82a,
   Author = {Greenside, HS and Jr, WMC 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},
   Year = {1982},
   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{Greenside81,
   Author = {Greenside, HS and Helfand, E},
   Title = {NUMERICAL INTEGRATION OF STOCHASTIC DIFFERENTIAL EQUATIONS -
             2.},
   Journal = {The Bell System technical journal},
   Volume = {60},
   Number = {8},
   Pages = {1927-1940},
   Year = {1981},
   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.},
   Key = {Greenside81}
}

@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},
   Year = {1988},
   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{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}
}

@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- American Physical Society},
   Volume = {25},
   Number = {3},
   Pages = {240-240},
   Year = {1980},
   Key = {fds325019}
}

@article{fds325021,
   Author = {Blum, JJ and Greenside, H},
   Title = {Particle ejection from the cytoproct of Tetrahymena.},
   Journal = {Journal of Protozoology},
   Volume = {23},
   Number = {4},
   Pages = {500-502},
   Year = {1976},
   Month = {November},
   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.},
   Key = {fds325021}
}

@article{fds246566,
   Author = {Paul, MR and Chiam, K-H 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},
   Year = {2003},
   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{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}
}

@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},
   Year = {1981},
   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}
}

@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 = {154501/1-154501/4},
   Year = {2001},
   ISSN = {0031-9007},
   Abstract = {A joint computational and theoretical effort is made to
             further the quantitative understanding of complex dynamics
             in spatially extended nonequilibrium systems. It is shown
             that this approach can also be used to investigate
             spatiotemporal chaos in larger aspect ratio
             systems.},
   Key = {fds246573}
}

@booklet{Greenside83a,
   Author = {Greenside, HS and Schlüter, MA},
   Title = {Pseudopotential calculation of the ground-state properties
             of ferromagnetic bcc iron},
   Journal = {Physical Review B - Condensed Matter and Materials
             Physics},
   Volume = {27},
   Number = {5},
   Pages = {3111-3114},
   Year = {1983},
   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 - Condensed Matter and Materials
             Physics},
   Volume = {28},
   Number = {2},
   Pages = {535-543},
   Year = {1983},
   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}
}

@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},
   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}
}

@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},
   Year = {1994},
   Abstract = {SUSTAIVED nonequilibrium 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 simulations
             9-11 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 ξ 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.},
   Key = {fds246520}
}

@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{fds4449,
   Author = {Ming-Chih Lai and Keng-Hwee Chiam and M. C. Cross and H. S.
             Greenside},
   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},
   Key = {fds4449}
}

@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},
   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.},
   Doi = {10.1103/PhysRevLett.80.2306},
   Key = {fds246525}
}

@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},
   Year = {1994},
   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}
}

@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{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{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 SUPPL. A},
   Pages = {R2511-R2514},
   Year = {1998},
   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 (D = 8.8)
             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 l/√N as the number N of known UPOs
             increases.},
   Key = {fds246527}
}

@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}
}

@booklet{Greenside85,
   Author = {Greenside, HS and Cross, MC},
   Title = {Stability analysis of two-dimensional models of
             three-dimensional convection},
   Journal = {Physical Review A - Atomic, Molecular, and Optical
             Physics},
   Volume = {31},
   Number = {4},
   Pages = {2492-2501},
   Year = {1985},
   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{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}
}

@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 Topography},
   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.},
   Key = {fds246570}
}

@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},
   Year = {1996},
   Month = {December},
   Key = {fds324071}
}

@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},
   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}
}

@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 - Condensed Matter and Materials
             Physics},
   Volume = {24},
   Number = {8},
   Pages = {4745-4752},
   Year = {1981},
   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}
}

@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{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},
   Year = {2016},
   Month = {August},
   url = {http://dx.doi.org/10.1119/1.4948603},
   Doi = {10.1119/1.4948603},
   Key = {fds323240}
}

@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 = {Electroencephalography and Clinical Neurophysiology},
   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.},
   Key = {fds246522}
}

@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}
}

@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{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},
   Year = {1986},
   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}
}


%% Other   
@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}
}