Elastic Forming

In the second paper, Kirwan examined the quantity of pure acids taken up at the point of saturation by the various substances they unite with, such as mineral alkali, volatile alkali, various earths, and phlogiston. The main focus of the paper was, however, on the identity of phlogiston with the inflammable air, which supposedly explained its elusive nature.Much like fixed air, the inflammable air could exist in two states fixed and elastic. Since it assumed aerial and elastic form as soon as it was released from bodies, it could never be produced single and disengaged from other substances. The fixed form of the inflammable air had to be phlogiston ... 

An odd-rank tensor can be associated with even- or odd-parity contributions to a matrix element, and these are conventionally described as electric and magnetic multipole contributions, respectively (Stassis and Deckman 1976). The orbital matrix element contains magnetic multipole terms, whereas the spin matrix element contains both magnetic and electric multipole terms. In terms of the notation introduced in sect. 2, A K, /C 1) and B K, A 1) are magnetic multipole terms, and B K, K) is an electric multipole term. The latter term vanishes for 5 = 5, L = L and J = J that is it does not contribute to the elastic form factor of an isolated magnetic ion. 

Fabrics are usually made of viscoelastic, nonlinear, and time dependent materials, but resolving of this problem in a simple linear elastic form may lead us to a suf -ciently acceptable estimation nnder some dieumstances. Besides it can offer a basic framework to give an accoimt to some other complicate theories. 

Tissue Vibration. Noncontact methods are preferred for measuring the surface motion of tissues. Laser vibrometers are commercially available with sufficient bandwidth and resolution for most studies. A direct mass load on the skin, together with the skin s elasticity, forms a mechanical low-pass filter (see Simple Lumped Models in Sec. 10.3.1). If a device is to be mounted directly on the skin, it must be of low weight (e.g., <3 g) and possess a comparatively large attachment area (e.g., >S cm ), in order for vibration to be recorded without attenuation of the motion at 80 Hz. An upper frequency limit of 200 Hz is theoretically achievable (—3dB) with a transducer and skin mount weighing 3 g and an attachment area of 1.8 cm. ... 

Hie total elastic free energy, or the Helmholtz free energy, of a network consists of the sum of the free energies of the individual chains and the contributions coming from intermolecular correlations. Hie elementary theories of rubber elasticity ignore contributions from intermolecular effects. Improvements in the elementary models have been made by different researchers in different ways. In this section most of the models will be covered. Since the single-chain elasticity forms the basis of rubber elasticity, it will be discussed first in some detail. 

The Fj q ) are the electromagnetic elastic structure functions or elastic form factors of the proton, which can only depend on the momentum transfer q. In (15.2.2) k is the anomalous magnetic moment of the proton measured in Bohr magnetons, k = 1.79, and the term K/2mp is factored out for convenience. 

Note that we recover the e/x result by putting Fi = 1, F2 = 0 and rUp = nifi. We can thus say that the elastic form factor of a point-like particle such as the // is a constant, independent of This fact is of vital importance for the parton idea. 

We remarked earlier in Section 15.2 that the nucleon elastic form factors drop rapidly with Q, roughly as On the other hand the elastic form factors of the point-like muon were constants independent of Q. ... 

One of the most remarkable discoveries of the recent past is shown in Fig. 15.9. When values of the inelastic electromagnetic structure function W2 measured at SLAG are displayed in the form 1/W2 vs at fixed values of u or X [see (15.5.2)] it seems to be largely independent of for > l(GeV/c) in complete contrast to the behaviour of the elastic form factors. [This would not be true for —> 0 since because of (15.3.25)... 

Any dependence on is very weak. The scale in Fig. 16.2 should be carefully noted. Over such a range the elastic form factors drop by many orders of magnitude So the scaling behaviour holds remarkably well over a huge range of Q. ... 

Polyurethane is used for mbber (vulcollanes), elastic fibers (Lycra), hard or elastic forms (Moltoprene), stain, flooring, and wood and fabric coating. 

This will only be possible under the proportionality assumption discussed in Sect. 1.8. Applying this assumption, it is easy to show that f(t), g t) are connected by a simple formula. One can show furthermore that W/(r), Oij(r) are given by their static elasticity form while the time functions are easily determined from the boundary conditions. 

Therefore, the displacement is given by the elastic form, but with q r, t), a known quantity, substituted for the specified stress (up to a multiplying constant). If the specified stress is always zero, as happens in certain contact problems for example, g(r, t) will also be zero, and the normal boundary displacement will be given precisely by the elastic form. In contrast to the special case of expanding or stationary 5 (0, we can make no useful statement about the stress, in the general case. 

Thus a solution to the problem can be found on the basis of our initial assumption regarding the shape of the contact area. This in effect justifies that assumption. Since the solution was found by reducing the problem to elastic form,... 

Up to time when C t) passes through its maximum, D(t) is given by its elastic form. Putting... 

An EPDM (ethylene-propylene-ethylidene norbornene terpolymer) rubber was dissolved in o-dichlorobenzene with 1 phr of carbon-60. When cast onto a glass slide and dried, an insoluble film exhibiting reversible elasticity forms. 8 refs. 

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