Journal ArticleAmerican 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 ...
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Journal ArticleAmerican 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 ...
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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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysica 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 ...
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Journal ArticleChaos (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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysical 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 ...
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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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticleDepress 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 ...
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Journal ArticleBrain 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticleSIAM 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 exam ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticleElectroencephalogr 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 ...
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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 ...
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Journal ArticlePhysical 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< ...
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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 ...
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Journal ArticleElectroencephalogr 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysics 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 ...
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Journal ArticleNature · 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 ...
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Journal ArticleJournal 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 ...
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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 ...
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Journal ArticleInternational 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleInternational 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleJournal 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 ...
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Journal ArticleComputer 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 ...
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Journal ArticlePhysica 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 ...
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Journal ArticlePhysica 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysica 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 ...
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Journal ArticleSolid 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticlePhysical 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 ...
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Journal ArticleBell 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 ...
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Journal ArticleThe 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 ...
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