Multiple lumped resonator

Schrag,J.L., Johnson,R.M. Application of the Birnboim multiple lumped resonator principle to viscoelastic measurements of dilute macromolecular solutions. Rev. Sci. Inst. 42, 224-232 (1971). 

Figure 1.2 illustrates the multiple-lumped resonator apparatus and the associated electronics. A resonator consists of a stack of five cylindrical lumps joined by cylindrically shaped torsional spring elements of smaller diameters. The moment of inertia of each of the four lumps is... 

Fig. 1.2. Schematic diagram of multiple-lumped resonator apparatus and associated...

Recent applications of the former are treated in ref. 53, but mention must be made of measurements on dilute paramyosin " solutions by the Wisconsin group. The multiple lumped resonator remains the most accurate method for the measurement of dynamic moduli of dilute solutions (in this case 0.1 %) with a frequency range from 150 Hz to 8.1 kHz. 

FIG. 5-10. Simplified diagram (to scale) of multiple-lumped resonator apparatus and auxiliary electronics. (Schrag and Ferry. ) Reproduced, by permission from the American Institute of Physics, from The Review of Scientific Instruments, 42, 224 (1971). 

The first comparisons of data extrapolated to infinite dilution with molecular theory were made by Tanaka, Sakanishi, Kaneko, and Furuichi. " Rather good agreement with the Zimm theory was obtained, especially in 8-solvents, but with a relatively narrow frequency range. A wider range has been covered more recently with the Birnboim-Schrag multiple-lumped resonator. ... 

Therefore, the problems which faced the would-be designers of chain reactors early in 1941 were (1) the choice of the proper moderator to uranium ratio, and (2) the size and shape of the uranium lumps which would most likely lead to a self-sustaining chain reaction, i.e., give the highest multiplication factor. In order to solve these problems, one had to understand the behavior of the fast, of the resonance, and of the thermal neutrons. We were concerned with the second problem which itself consisted of two parts. The first was the measurement of the characteristics of the resonance lines of isolated uranium atoms, the second, the composite effect of this absorption on the neutron spectrum and total resulting absorption. One can liken the first task to the measurement of atomic constants, such as molecular diameter, the second one, to the task of kinetic gas theory which obtains the viscosity and other properties of the gas from the properties of the molecules. The first task was largely accomplished by Anderson and was fully available to us when we did our work. Anderson s and Fermi s work on the absorption of uranium, and on neutron absorption in general, also acquainted us with a number of technics which will be mentioned in the third and fourth of the reports of this series. Finally, Fermi, Anderson, and Zinn carried out, in collaboration with us in Princeton, one measurement of the resonance absorption. This will be discussed in the third article of this series. 

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