Maxwell's equations are replaced by a set of finite difference equations. It is shown that if one chooses the field points appropriately, the set of finite difference equations is applicable for a boundary condition involving perfectly conducting surfaces. An example is given of the scattering of an electromagnetic pulse by a perfectly conducting cylinder.

/pdf/numerical-solution-of-initial-boundary-value-problems-1kka1ovapd.pdf

Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media

Wireless Communications

A Scaling Method for Priorities in Hierarchical Structures

/pdf/asymptotic-analysis-of-periodic-structures-14wjonu4ba.pdf

Asymptotic Analysis of Periodic Structures

Damage to the hippocampal system disrupts recent memory but leaves remote memory intact. The account presented here suggests that memories are first stored via synaptic changes in the hippocampal system, that these changes support reinstatement of recent memories in the neocortex, that neocortical synapses change a little on each reinstatement, and that remote memory is based on accumulated neocortical changes. Models that learn via changes to connections help explain this organization. These models discover the structure in ensembles of items if learning of each item is gradual and interleaved with learning about other items. This suggests that the neocortex learns slowly to discover the structure in ensembles of experiences. The hippocampal system permits rapid learning of new items without disrupting this structure, and reinstatement of new memories interleaves them with others to integrate them into structured neocortical memory systems.

Why there are complementary learning systems in the hippocampus and neocortex: insights from the successes and failures of connectionist models of learning and memory.

The geometrical theory of diffraction is an extension of geometrical optics which accounts for diffraction. It introduces diffracted rays in addition to the usual rays of geometrical optics. These rays are produced by incident rays which hit edges, corners, or vertices of boundary surfaces, or which graze such surfaces. Various laws of diffraction, analogous to the laws of reflection and refraction, are employed to characterize the diffracted rays. A modified form of Fermat’s principle, equivalent to these laws, can also be used. Diffracted wave fronts are defined, which can be found by a Huygens wavelet construction. There is an associated phase or eikonal function which satisfies the eikonal equation. In addition complex or imaginary rays are introduced. A field is associated with each ray and the total field at a point is the sum of the fields on all rays through the point. The phase of the field on a ray is proportional to the optical length of the ray from some reference point. The amplitude varies in accordance with the principle of conservation of energy in a narrow tube of rays. The initial value of the field on a diffracted ray is determined from the incident field with the aid of an appropriate diffraction coefficient. These diffraction coefficients are determined from certain canonical problems. They all vanish as the wavelength tends to zero. The theory is applied to diffraction by an aperture in a thin screen diffraction by a disk, etc., to illustrate it. Agreement is shown between the predictions of the theory and various other theoretical analyses of some of these problems. Experimental confirmation of the theory is also presented. The mathematical justification of the theory on the basis of electromagnetic theory is described. Finally, the applicability of this theory, or a modification of it, to other branches of physics is explained.

http://www.ferrocell.us/references/geometrical%20theory%20of%20diffraction.pdf

Geometrical Theory of Diffraction

A new equation is derived for large amplitude forced radial oscillations of a bubble in an incident sound field. It includes the effects of acoustic radiation, as in Keller and Kolodner’s equation, and the effects of viscosity and surface tension, as in the modified Rayleigh equation due to Plesset, Noltingk and Neppiras, and Poritsky. The free and forced periodic solutions are computed numerically. For large bubbles, such as underwater explosion bubbles, the free oscillations agree with those obtained by Keller and Kolodner. For small bubbles, such as cavitation bubbles, with small or intermediate forcing amplitudes, the results agree with those calculated by Lauterborn from the modified Rayleigh equation of Plesset et al. For large forcing amplitudes that equation yielded unsatisfactory results whereas the new equation yields quite satisfactory ones.

Bubble Oscillations of Large Amplitude

The flow about a spinning sphere moving in a viscous fluid is calculated for small values of the Reynolds number. With this solution the force and torque on the sphere are computed. It is found that in addition to the drag force determined by Stokes, the sphere experiences a force FL orthogonal to its direction of motion. This force is given by .Here a is the radius of the sphere, Ω is its angular velocity, V is its velocity, ρ is the fluid density and R is the Reynolds number, . For small values of R, the transverse force is independent of the viscosity μ. This force is in such a direction as to account for the curving of a pitched baseball, the long range of a spinning golf ball, etc. It is used as a basis for the discussion of the flow of a suspension of spheres through a tube.The calculation involves the Stokes and Oseen expansions. A representation of solutions of the Oseen equations in terms of two scalar functions is also presented.

The transverse force on a spinning sphere moving in a viscous fluid

On solutions of δu=f(u)

The visual cortex of many adult mammals has patches of cells that receive inputs driven by the right eye alternating with patches that receive inputs driven by the left eye. These ocular dominance patches (or "columns") form during early life as a consequence of competition between the activity patterns of the two eyes. A mathematical model of several biological mechanisms that can account for this development is presented. Analysis of this model reveals the conditions under which ocular dominance segregation will occur and determines the resulting patch width. Simulations of the model also exhibit other phenomena associated with early visual development, such as topographic refinement of cortical receptive fields, the confinement of input cell connections to patches, monocular deprivation plasticity including a critical period, and the effect of artificially induced strabismus. The model can be used to predict the results of proposed experiments and to discriminate among various mechanisms of plasticity.

https://science.sciencemag.org/content/sci/245/4918/605.full.pdf

Joseph B. Keller

Papers

Geometrical Theory of Diffraction

Bubble Oscillations of Large Amplitude

The transverse force on a spinning sphere moving in a viscous fluid

On solutions of δu=f(u)

Ocular dominance column development: analysis and simulation