Louis Gold

Statistics of Polymer Molecular Size Distribution for an Invariant Number of Propagating Chains

A detailed study of the polymer statistics for a reaction system resembling the ethylene oxide initiator case is made allowing for different rates of initiation ki and propagation kp. The modified Poisson distribution that results necessitates evaluation of rather complicated summations in order to characterize the number xn and weight average xw molecular weights. It is found that r = kp/ki as large as 106 still does not shift (xw/xn)max beyond the range 1.3 to 1.4. But under any circumstance, depletion of monomer assures homogeneous polymers, regardless of r.

Generalized poisson distributions

Poisson distributions evidently can be treated in a unified manner by dealing with the G.P. which contains a characteristic parameterq. The properties of the PEBL, long recognized as significant in a variety of statistical applications like telephone trunking, queueing, etc., may be deduced by passage to the limitq = 1.

Kinetic Theory of Space-Charge I: Cut-off Character of the Static Magnetron†

ABSTRACT Collisional damping in the equations of motion for electrons in the magnetron space-charge is shown to lead to rather complex behaviour. The strong scattering limit manifests a current-voltage dependence which not only can account for departures from Childs Law, but also for failure of extant theories of the magnetron to predict the long puzzling observation of a smeared cut-off. While a Boltzmann transport refinement may provide a more rigorous approach to the problem, it is believed that the mystery of the cut-off phenomenon is essentially dissipated by the phenomenological development.

Solutions for the Static Junction

ABSTRACT The characteristic non-linear differential equation which arises from Poissons relation for the static distribution of charge is analysed for its solutions when either rather loose or restrictive boundary conditions provail. While the former admits a number of closed form solutions, an inverse series solution, appropriate particularly for diverse impurity distributions in the p-n junction, is developed for the spatial variation of the electrostatic potential.

Non-Linear Phenomenological Theory of Plasma Oscillations†

ABSTRACT A transformation involving replacement of a spatial coordinate by a time coordinate loads to ready analysis of cooperative plasma interaction with the effect of collisions introduced by a phenomenological artifice. It dovelops that damped oscillations of a frequency ω/4πcan arise when the condition ω2 = 4ωp2-v2>0 prevails, ωp being the Langmuir-Tonks angular plasma frequency while v is an effective collisional frequency. The important deduction of the present theory, not contained in conventional linearized treatments, is the intensity of these standing waves which is found to be augmented by collisions but at the sacrifice of efficiency. In general, increasing the current and plasma temperature tend to promote oscillation whereas the role of plasma density is somewhat more involved with evidence of an optimal effect. The influence of a magnetic field is investigated in the no-damping limit and found to augment the resonance of the plasma while concomitantly altering the intensity in a, manner in...

Note on the relativistic harmonic oscillator

Abstract The relativistic harmonic oscillator is solved by an inverse fractional power series as has been done for the simple pendulum.The striking similarity of these two kinds of non-linear motion is thus demonstrated.The entire analysis is amply dealt with, without resort to elliptic integrals.

Molecular Size Distribution in the Copolymerization of N‐Carboxyamino Acid Anhydrides

The theory of molecular size distributions which are intrinsically Poisson in character is extended to cover two complementary aspects of copolymerization which are specifically adapted to polypeptide synthesis via the N‐carboxyamino acid anhydride (Leuchs monomer). The statistical aspects for (1) discrete monomer reacting with a Poisson ensemble of initiators and (2) the circumstance of an array of monomers copolymerized by a discrete initiator are delineated. Explicit relations for the number and weight average molecular weights are derived.

Space-Charge in the Relativistic Magnetron†

ABSTRACT Three relativistic solutions for the space-charge behaviour in a magnetron at high energies are calculated. At energies bordering on the classical region, a perturbation form of result is obtained by noting the series solution for the classical case, the Hull cut-off relation entering as a parameter. Then with the relativistic cut-off as a parameter, separate series are developed for the intermediate and extreme relativistic domains.

Wave mechanics for hydrogen atom in cylindrical coordinates: Non-separable eigensolutions

Abstract The solution of the hydrogen atom in cylindrical coordinates serves to demonstrate the manner in which non-separable differential equations can be treated. The eigenvalues for the H atom are so deduced in a simpler fashion and the correspondence to the conventional spherical coordinate results is pointed out. In this manner the important matter of degeneracy is entered into; the quest for non-separable solutions must be characterized by appropriate attention to this detail.

Transit Time and Space-Charge in the Spherical Diode†

ABSTRACT The formalism of time-dependent. Poisson equation leads to findings for the transit time and current—voltage behaviour of the spherical diode very much reminiscent of the cylindrical structure results previously derived for both zero and finite initial electron velocities. The effect of cathode-anode inversion is also examined.