%% 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{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} } @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} } @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- American Physical Society}, Volume = {25}, Number = {3}, Pages = {240-240}, Year = {1980}, Key = {fds325019} } @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{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} } @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} } @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{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{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{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{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} } @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{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} } @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} } @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{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{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} } @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{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} } @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} } @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{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{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} } @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. Â© 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}, 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} } @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{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} } @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} } @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{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{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} } @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} } @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} } @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} } @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{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} } @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{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 = {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} } @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{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} } @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{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{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{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}, 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} } @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{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{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} } @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} } @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{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 = {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} } @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{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{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{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} } @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{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} } @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{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{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{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{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{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} } @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{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{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{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}, Year = {2018}, Month = {January}, url = {http://dx.doi.org/10.1119/1.5009446}, Abstract = {© 2018 American Association of Physics Teachers. 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} } %% 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} }