There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The time-domain transmission-line equations for uniform multiconductor transmission lines in a conductive, homogeneous medium excited by a transient, nonuniform electromagnetic (EM) field, are derived from Maxwell's equations. Depending on how the line voltage is defined, two formulations are possible. One of these formulations is considerably more convenient to apply than the other. The assumptions made in the derivation of the transmission-line equations and the boundary conditions at the terminations are discussed. For numerical calculations, the transmission -line equations are represented by finite-difference techniques, and numerical examples are included.

Transient Response of Multiconductor Transmission Lines Excited by a Nonuniform Electromagnetic Field

Introduction to Electromagnetic Compatibility

1. The real variable 2. Scalars and vectors 3. Tensors 4. Matrices 5. Multiple integrals 6. Potential theory 7. Operational methods 8. Physical applications of the operational method 9. Numerical methods 10. Calculus of variations 11. Functions of a complex variable 12. Contour integration and Bromwich's integral 13. Contour integration 14. Fourier's theorem 15. The factorial and related functions 16. Solution of linear differential equations of the second order 17. Asymptotic expansions 18. The equations of potential, waves and heat conduction 19. Waves in one dimension and waves with spherical symmetry 20. Conduction of heat in one and three dimensions 21. Bessel functions 22. Applications of Bessel functions 23. The confluent hypergeometric function 24. Legendre functions and associated functions 25. Elliptic functions Notes Appendix on notation Index.

Methods of Mathematical Physics. By Harold Jeffreys and Bertha Swirles Jeffreys. Pp. viii, 679. 63s. 1946. (Cambridge University Press)

Natural disasters can cause large blackouts. Research into natural disaster impacts on electric power systems is emerging to understand the causes of the blackouts, explore ways to prepare and harden the grid, and increase the resilience of the power grid under such events. At the same time, new technologies such as smart grid, micro grid, and wide area monitoring applications could increase situational awareness as well as enable faster restoration of the system. This paper aims to consolidate and review the progress of the research field towards methods and tools of forecasting natural disaster related power system disturbances, hardening and pre-storm operations, and restoration models. Challenges and future research opportunities are also presented in the paper.

Research on Resilience of Power Systems Under Natural Disasters—A Review

High-voltage pulsed electric fields (PEFs) can be used to inactivate microorganisms in liquids. Applying PEF technology to food pasteurization is a promising nonthermal method, which may radically change food preservation processes and provide consumers with microbiologically safe, minimally processed, fresh-like products. A continuous-flow system in a laboratory-size prototype was constructed for the nonthermal pasteurization of liquid foods with PEF technology. Major components in the prototype include a high-voltage repetitive pulse generator, a coaxial liquid food treatment chamber, a fiber-optic temperature sensing instrument and a data acquisition system. Microbial inactivation tests were conducted in the continuous PEF treatment system. Repetitive high-voltage pulses with an exponential decaying waveshape were applied to the liquid food which was pumped through the treatment chamber. Test microorganisms selected for inactivation were Escherichia coli, Staphylococcus aureus and Saccharomyces cerevisiae. Over 6-order-of-magnitude reductions in the viability of selected microorganisms were achieved while the food temperature was maintained below 40/spl deg/C.

Inactivating microorganisms using a pulsed electric field continuous treatment system

The authors describe the quasi-static and radiation fields of simple three-dimensional sources and proceed to a two-dimensional source. It is shown that the quasi-static approximations result in an error of 0.000002% for fields at 100 m or less from the power line. This is followed by a discussion of how the quasi-static fields are coupled together by Maxwell's equations. It is shown that the electric field of a power line can formally be determined from the magnetic fields, but this cannot be done practically. The electric and magnetic fields are assumed to be independent and are related respectively to voltage and current. The conditions under which electric and magnetic fields are related by the free space impedance are discussed. In general, they are not for power line fields. Poynting's theorem is applied to the power line fields to describe the bulk power transferred along the power line as a result of the quasi-static fields and to calculate the insignificant amount of power radiated laterally away from the power line. >

Characteristics of low frequency electric and magnetic fields in the vicinity of electric power lines

Recently, it has been suggested that traditional quasi-static methods for evaluating power network grounding systems are not valid at high frequencies. However, the conditions under which exact full wave theory must be used have not been established. In this paper, exact full wave and quasi-static methods are used to evaluate touch and step potentials of a simple ground stake. It is shown that a sufficient condition for quasi-static theory to be valid is if the size of the buried electrode is less than one-tenth of a wavelength in the earth.

A comparison of exact and quasi-static methods for evaluating grounding systems at high frequencies

Treatment systems for treating flowable food products using electrical pulses to inactivate microbes. Systems described include one or more stages having flow-through processors. The flow-through processors have first and second electrodes which are spaced across a treatment chamber in which an intense electrical field is generated using bipolar electrical pulses. The treatment chamber is temperature stabilized to improve processing and minimize surface buildup on the electrodes. Oversized processor electrodes can be used such as in conjunction with an electrode spacer to provide a treatment zone having a relatively uniform and high electrical field strength.

Continuous flow electrical treatment of flowable food products

The relation between the exact theory and Carson's theory for the fields of straight wires above a homogeneous earth is derived. Sufficient conditions for the validity of Carson's equations are given. Cases for which Carson's theory is not valid are discussed. In addition, an image theory useful for magnetic induction problems is given and discussed.

Robert G. Olsen

Papers

Inactivating microorganisms using a pulsed electric field continuous treatment system

Characteristics of low frequency electric and magnetic fields in the vicinity of electric power lines

A comparison of exact and quasi-static methods for evaluating grounding systems at high frequencies

Continuous flow electrical treatment of flowable food products

On The Exact, Carson and Image Theories for Wires at or Above the Earth's Interface