arXiv subjects

Henry Greenside

Publications and source records attributed to Henry Greenside.

5 recordsLinked to original sources

arXiv2016

The Electric Field of a Uniformly Charged Non-Conducting Cubic Surface

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 produced by a non-conducting cubic surface that is covered with a uniform surface charge density. We first discuss how to deduce qualitatively, using only elementary physics, the surprising fact that the electric field inside the cubic surface is nonzero and has a complex structure, pointing inwards towards the cube center from the midface of each cube 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. This example would be a good choice for group problem solving in a recitation or flipped classroom.

physics.ed-ph↗

arXiv2015

The External Magnetic Field Created by the Superposition of Identical Parallel Finite Solenoids

Using superposition and numerical approximations of a published analytical expression for the magnetic field generated by a finite solenoid, we show that the magnetic field external to parallel identical solenoids can be nearly uniform and substantial, even when the solenoids have lengths that are large compared to their radii. We study two arrangements of solenoids---a ring of parallel solenoids whose surfaces are tangent to a common cylindrical surface and to nearest neighbours, and a large finite hexagonal array of parallel solenoids---and summarize how the magnitude and uniformity of the resultant external field depend on the solenoid length and distances between solenoids. We also report some novel results about single solenoids, e.g., that the energy stored in the internal magnetic field exceeds the energy stored in the spatially infinite external magnetic field for even short solenoids. These results should be broadly interesting to undergraduates learning about electricity and magnetism as novel examples of superposition based on a familiar source of magnetic fields.

physics.class-ph↗

arXiv2006

Stable Propagation of a Burst Through a One-Dimensional Homogeneous Excitatory Chain Model of Songbird Nucleus HVC

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 non-bursting neurons with excitatory synaptic connections. Our results are obtained for two kinds of neuronal models, leaky integrate-and-fire (LIF) neurons and Hodgkin-Huxley (HH) 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.

q-bio.NC↗

arXiv2001

Microextensive Chaos of a Spatially Extended System

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 Delta{L} that are small compared to the average cell size of 9 and to various correlation lengths. This suggests that a spatially homogeneous chaotic system does not have to increase its size by some characteristic amount to increase its dynamical complexity, nor is the increase in dimension related to the increase in the number of linearly unstable modes.

nlin.PS↗

arXiv2001

Pattern Formation Near Onset of a Convecting Fluid In an Annulus

Numerical simulations of the time-dependent Swift-Hohenberg equation are used to test predictions of Cross [Phys. Rev. A 25:1065-1076 (1982)] that Rayleigh-Benard 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 the initial state. As r_1 is decreased for a fixed r_2 and for different choices of epsilon and initial states, 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.

nlin.PS↗