Henry Greenside

Journal Article American Journal of Physics · January 1, 2018 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 charge ... Full text Cite

AJP Reviewers

Journal Article American Journal of Physics · December 1, 2016 Full text Cite

The external magnetic field created by the superposition of identical parallel finite solenoids

Journal Article American Journal of Physics · August 1, 2016 We use superposition and numerical methods to show that the external magnetic field generated by parallel identical solenoids can be nearly uniform and substantial, even when the solenoids have lengths that are large compared to their radii. We examine bot ... Full text Cite

Pattern formation and dynamics in nonequilibrium systems

Book · January 1, 2009 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 networ ... Full text Cite

Stable propagation of a burst through a one-dimensional homogeneous excitatory chain model of songbird nucleus HVC.

Journal Article Physical review. E, Statistical, nonlinear, and soft matter physics · July 2006 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 ... Full text Cite

Characterization of the domain chaos convection state by the largest Lyapunov exponent.

Journal Article Physical review. E, Statistical, nonlinear, and soft matter physics · July 2006 Using numerical integrations of the Boussinesq equations in rotating cylindrical domains with realistic boundary conditions, we have computed the value of the largest Lyapunov exponent lambda1 for a variety of aspect ratios and driving strengths. We study ... Full text Cite

Enhanced tracer transport by the spiral defect chaos state of a convecting fluid.

Journal Article Physical review. E, Statistical, nonlinear, and soft matter physics · March 2005 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 c ... Full text Cite

Pattern formation and dynamics in Rayleigh-Bénard convection: Numerical simulations of experimentally realistic geometries

Journal Article Physica D: Nonlinear Phenomena · October 1, 2003 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 ... Full text Cite

Efficient simulation of three-dimensional anisotropic cardiac tissue using an adaptive mesh refinement method.

Journal Article Chaos (Woodbury, N.Y.) · September 2003 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 inve ... Full text Cite

Efficient algorithm on a nonstaggered mesh for simulating Rayleigh-Bénard convection in a box.

Journal Article Physical review. E, Statistical, nonlinear, and soft matter physics · August 2003 An efficient semi-implicit second-order-accurate finite-difference method is described for studying incompressible Rayleigh-Bénard convection in a box, with sidewalls that are periodic, thermally insulated, or thermally conducting. Operator-splitting and a ... Full text Cite

Mean flow and spiral defect chaos in Rayleigh-Bénard convection.

Journal Article Physical review. E, Statistical, nonlinear, and soft matter physics · May 2003 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 pat ... Full text Cite

Mean Flow Dynamics of Stripe Textures and Spiral Defect Chaos in Rayleigh-Benard Convection

Journal Article Physical Review E · 2003 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 pat ... Cite

Efficient algorithm on a nonstaggered mesh for simulating Rayleigh-Bénard convection in a box

Journal Article Physical Review E - Statistical, Nonlinear, and Soft Matter Physics · 2003 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 geometr ... Cite

Microextensive chaos of a spatially extended system.

Journal Article Physical review. E, Statistical, nonlinear, and soft matter physics · July 2002 By analyzing chaotic states of the one-dimensional Kuramoto-Sivashinsky equation for system sizes L in the range 79 < or = L < or = 93, we show that the Lyapunov fractal dimension D scales microextensively, increasing linearly with L even for increments De ... Full text Cite

Power-law behavior of power spectra in low Prandtl number Rayleigh-Bénard convection.

Journal Article Physical review letters · October 2001 The origin of the power-law decay measured in the power spectra of low Prandtl number Rayleigh-Bénard convection near the onset of chaos is addressed using long time numerical simulations of the three-dimensional Boussinesq equations in cylindrical domains ... Full text Cite

Pattern formation near onset of a convecting fluid in an annulus.

Journal Article Physical review. E, Statistical, nonlinear, and soft matter physics · October 2001 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 ... Full text Cite

Pattern formation near onset of a convecting fluid in an annulus

Journal Article Physical Review E - Statistical, Nonlinear, and Soft Matter Physics · 2001 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 o ... Cite

Simulating Complex Dynamics In Intermediate And Large-Aspect-Ratio Convection Systems

Journal Article · May 26, 2000 Buoyancy-induced (Rayleigh-Benard) convection of a fluid between two horizontal plates is a central paradigm for studying the transition to complex spatiotemporal dynamics in sustained nonequilibrium systems. To improve the analysis of experimental data an ... Link to item Cite

A space-time adaptive method for simulating complex cardiac dynamics.

Journal Article Physical review letters · February 2000 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 ... Full text Cite

EEG effects of ECT: implications for rTMS.

Journal Article Depress Anxiety · 2000 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 ne ... Full text Link to item Cite

Stationarity and redundancy of multichannel EEG data recorded during generalized tonic-clonic seizures.

Journal Article Brain Topogr · 2000 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 (E ... Full text Link to item Cite

Low-dimensional chaos in bipolar disorder [1] (multiple letters)

Journal Article Archives of Internal Medicine · March 9, 1998 Cite

Spatially Localized Unstable Periodic Orbits Of A High-Dimensional Chaotic System

Journal Article Phys. Rev. E · March 1998 Cite

Low-dimensional chaos in bipolar disorder?

Journal Article Arch Gen Psychiatry · March 1998 Full text Link to item Cite

Comment on “Optimal periodic orbits of chaotic systems”

Journal Article Physical Review Letters · February 23, 1998 A Comment on the Letter by Brian R. Hunt and Edward Ott, Phys. Rev. Lett. 76, 2254 (1996). The authors of the Letter offer a Reply. © 1998 The American Physical Society. ... Full text Cite

Size-dependent transition to high-dimensional chaotic dynamics in a two-dimensional excitable medium

Journal Article Physical Review Letters · January 1, 1998 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 wi ... Full text Cite

Extensive scaling and nonuniformity of the Karhunen-Loève decomposition for the spiral-defect chaos state

Journal Article Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics · January 1, 1998 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 [Formula Presented] (d is the fluid depth), which strongly suggests that SDC ... Full text Cite

Fractal basins of attraction associated with a damped Newton's method

Journal Article SIAM Review · January 1, 1998 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 i ... Full text Cite

Spatially localized unstable periodic orbits of a high-dimensional chaotic system

Journal Article Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics · January 1, 1998 Using an innovative damped-Newton method, we report the calculation and analysis of many distinct unstable periodic orbits (UPOs) for a high-fractal-dimension [formula presented] extensively chaotic solution of a partial differential equation. A majority o ... Full text Cite

Size-dependent transition to high-dimensional chaotic dynamics in a two-dimensional excitable medium

Journal Article Physical Review Letters · 1998 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 wi ... Cite

Extensive scaling and nonuniformity of the Karhunen-Loève decomposition for the spiral-defect chaos state

Journal Article Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics · 1998 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 c ... Cite

The largest Lyapunov exponent of the EEG during ECT seizures as a measure of ECT seizure adequacy.

Journal Article Electroencephalogr Clin Neurophysiol · December 1997 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 ... Full text Link to item Cite

Spatially Localized Unstable Periodic Orbits

Journal Article · April 3, 1997 Using an innovative damped-Newton method, we report the first calculation of many distinct unstable periodic orbits (UPOs) of a large high-dimensional extensively chaotic partial differential equation. A majority of the UPOs turn out to be spatially locali ... Link to item Cite

EEG correlates of the response to ECT

Journal Article BIOLOGICAL PSYCHIATRY · April 1, 1997 Link to item Cite

Karhunen-loève decomposition of extensive chaos

Journal Article Physical Review Letters · March 3, 1997 We show that the number of KLD (Karhunen-Loève decomposition) modes DKLD needed to capture a fraction f of the total variance of an extensively chaotic state scales extensively with subsystem volume V. This allows a correlation length ξKLD to be defined th ... Full text Cite

Spatiotemporal Chaos in Large Systems: The Scaling of Complexity with Size

Journal Article · December 3, 1996 The dynamics of a nonequilibrium system can become complex because the system has many components (e.g., a human brain), because the system is strongly driven from equilibrium (e.g., large Reynolds-number flows), or because the system becomes large compare ... Link to item Cite

Statistical analysis of redundancy and stationarity in multi-channel EEG.

Journal Article JOURNAL OF MATHEMATICAL PSYCHOLOGY · December 1, 1996 Link to item Cite

A comparison of EEG signal dynamics in waking, after anesthesia induction and during electroconvulsive therapy seizures.

Journal Article Electroencephalogr Clin Neurophysiol · August 1996 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 exp ... Full text Link to item Cite

Lyapunov spectral analysis of a nonequilibrium Ising-like transition.

Journal Article Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · April 1996 Full text Cite

Lyapunov spectral analysis of a nonequilibrium Ising-like transition

Journal Article Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics · 1996 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 fer ... Cite

Characterization of the transition from defect to phase turbulence.

Journal Article Physical review letters · March 1995 Full text Cite

Spatial variation of correlation times for 1D phase turbulence

Journal Article Physics Letters A · February 21, 1994 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. Th ... Full text Cite

Relation between fractal dimension and spatial correlation length for extensive chaos

Journal Article Nature · January 1, 1994 Sustained nonequiibrium systems can be characterized by a fractal dimension D≥0, which can be considered to be a measure of the number of independent degrees of freedom1. The dimension D is usually estimated from time series2 but the available algorithms a ... Full text Cite

A quantitative measurement of spatial order in ventricular fibrillation.

Journal Article Journal of cardiovascular electrophysiology · October 1993 IntroductionThe 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 ... Full text Cite

Dependence of extensive chaos on the spatial correlation length (substantial revision)

Journal Article · July 22, 1993 We consider spatiotemporal chaotic systems for which spatial correlation functions decay substantially over a length scale xi (the spatial correlation length) that is small compared to the system size L. Numerical simulations suggest that such systems gene ... Link to item Cite

Stochastic to deterministic crossover of fractal dimensions for a Langevin equation.

Journal Article Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · May 1993 Full text Cite

Recent advances in chaos theory

Journal Article International Conference on Fuzzy Theory and Technology Proceedings, Abstracts and Summaries · December 1, 1992 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 ... Cite

Implication of a power-law power-spectrum for self-affinity.

Journal Article Physical review. A, Atomic, molecular, and optical physics · August 1991 Full text Cite

Computation of zero β three-dimensional equilibria with magnetic islands

Journal Article Journal of Computational Physics · January 1, 1990 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 ... Full text Cite

Comments on a recent paper by W. Zijl

Journal Article International Journal for Numerical Methods in Fluids · January 1, 1989 A recent paper by W. Zijl, which reformulated the Navier–Stokes and Boussinesq equations in terms of Clebsch potentials, has an error that greatly reduces the generality of the results. Some other recent efforts to use such potentials in fluid and plasma d ... Full text Cite

Convergence properties of a nonvariational 3D MHD equilibrium code

Journal Article Journal of Computational Physics · January 1, 1989 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 h ... Full text Cite

Mean flows and the onset of chaos in large-cell convection.

Journal Article Physical review letters · May 1988 Full text Cite

Numerical solution of three-dimensional magnetic differential equations

Journal Article Journal of Computational Physics · January 1, 1988 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 algori ... Full text Cite

[title field missing]

Journal Article Phys. Rev. Lett. · 1988 Full text Cite

Edge turbulence measurements in TFTR

Journal Article Journal of Nuclear Materials · February 2, 1987 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 simila ... Full text Cite

Wave-number selection and persistent dynamics in models of convection

Journal Article Physica D · December 1986 Cite

Calculation of three-dimensional MHD equilibria with islands and stochastic regions

Journal Article Computer Physics Communications · January 1, 1986 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 ... Full text Cite

Wavebumber selection and persistent dynamics in models of convection

Journal Article Physica D: Nonlinear Phenomena · January 1, 1986 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 agains ... Full text Cite

Stability analysis of two-dimensional models of three-dimensional convection.

Journal Article Physical review. A, General physics · April 1985 Full text Cite

[title field missing]

Journal Article Phys. Rev. A · 1985 Full text Cite

Depolarization of d-t plasmas by recycling in material walls

Journal Article Journal Of Vacuum Science \& Technology A-vacuum Surfaces And Films · 1984 Cite

Cohesive Properties of Ge, Si, and Diamond Calculated with Minimum Basis Sets

Journal Article physica status solidi (b) · January 1, 1984 Ab initio calculations are presented of the cohesive properties of Ge, Si, and diamond. Electron‐electron interactions are treated within the local density functional approximation and electronion interactions are described by norm‐conserving pseudopotenti ... Full text Cite

Nonlinear pattern formation near the onset of Rayleigh-Bénard convection

Journal Article Physical Review A · January 1, 1984 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 ... Full text Cite

[title field missing]

Journal Article Phys. Rev. A · 1984 Full text Cite

Pseudopotentials for the 3d transition-metal elements

Journal Article Physical Review B · January 1, 1983 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 interac ... Full text Cite

Pseudopotential calculation of the ground-state properties of ferromagnetic bcc iron

Journal Article Physical Review B · January 1, 1983 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 wi ... Full text Cite

[title field missing]

Journal Article Phys. Rev. B · 1983 Full text Cite

Impracticality of a box-counting algorithm for calculating the dimensionality of strange attractors

Journal Article Physical Review A · January 1, 1982 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 c ... Full text Cite

Nonlinear pattern formation near the onset of Rayleigh-Bénard convection

Journal Article Physical Review Letters · January 1, 1982 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 foll ... Full text Cite

A simple stochastic model for the onset of turbulence in Rayleigh-Bénard convection

Journal Article Physica D: Nonlinear Phenomena · January 1, 1982 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 a ... Full text Cite

Numerical-integration of additive, stochastic differential-equations

Journal Article Bulletin Of The American Physical Society · 1981 Cite

Cl chemisorption on the Pd(001) surface: A self-consistent LCAO calculation of electronic structure

Journal Article Solid State Communications · January 1, 1981 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 su ... Full text Cite

Effect of magnetic-anisotropy on coexisting magnetic superconducting phases

Journal Article Bulletin Of The American Physical Society · 1981 Cite

Cl chemisorption on the Ag(001) surface: Geometry and electronic structure

Journal Article Physical Review B · January 1, 1981 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 ... Full text Cite

High-frequency intermittency of strange attractors

Journal Article Bulletin Of The American Physical Society · 1981 Cite

Comparative LCAO-LAPW study of C1 chemisorption on the Ag(001) surface

Journal Article Physical Review B · January 1, 1981 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 geometri ... Full text Cite

Structural-energy calculations based on norm-conserving pseudopotentials and localized Gaussian orbitals

Journal Article Physical Review B · January 1, 1981 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 def ... Full text Cite

Possible coexisting superconducting and magnetic states

Journal Article Physical Review Letters · January 1, 1981 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 ... Full text Cite

Numerical Integration of Stochastic Differential Equations—II

Journal Article Bell System Technical Journal · January 1, 1981 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 ... Full text Cite

FITTED NORM-CONSERVING PSEUDOPOTENTIALS AND TOTAL ENERGY STUDIES

Conference BULLETIN OF THE AMERICAN PHYSICAL SOCIETY · January 1, 1981 Link to item Cite

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 Article Bulletin Of The American Physical Society · 1980 Cite

NUMERICAL-SIMULATION OF A BROWNIAN PARTICLE IN AN EXTERNAL ANHARMONIC POTENTIAL

Conference BULLETIN OF THE AMERICAN PHYSICAL SOCIETY · January 1, 1980 Link to item Cite

Particle ejection from the cytoproct of Tetrahymena.

Journal Article The Journal of protozoology · November 1976 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 distin ... Full text Cite

Cocatalysis of Phenolate Phosphorylation in Biphasic Media

Journal Article Journal of the American Chemical Society · March 1, 1976 Full text Cite