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The gaseous oxidation of diethyl ether
A detailed study has been made of the gaseous oxidation of diethyl ether in the low-temperature region. The reaction has many characteristics of hydrocarbon oxidation, although there is one essential difference: excess oxygen tends to retard the rate of ether combustion. The principal products during the induction period are acetaldehyde, peracetic acid and ethanol. In the later stages of reaction, acetaldehyde and peracetic acid are consumed; ethanol and acetic acid being the principal end-products. It is assumed that an ‘ether radical’, CH
3
CHOCH
2
CH
3
, formed by the initiation process, decomposes to yield acetaldehyde and an ethyl radical. Subsequently, there are two concurrent reactions. First, the ethy radicals are oxidized throughout the course of the reaction, ethanol being the principal product of this process. Secondly, acetaldehyde is oxidized to peracetic acid, the peracetic acid decomposing in the later stages of reaction to form copious amounts of acetic acid. It is thought that the peracetic acid is the compound that is primarily responsible for chain-branching.
Tập 252 Số 1269 - Trang 260-272 - 1959
Theory of the nuclear hyperfine structure of paramagnetic resonance spectra in crystals
A theory is given of the nuclear hyperfine structure of the paramagnetic resonance in hydrated crystals. Starting from the states of a free ion, neglecting spin-dependent terms in the energy, successive steps of perturbation calculation introduce the effect of the crystalline electric field, the spin-orbit and spin-spin interactions, the coupling with an external magnetic field, and the coupling between the nucleus of the ion and the electrons. The self-consistent field approximation, in which the state of the free ion is described by a single electronic configuration, is found to be inadequate, and it is found necessary to consider admixtures, through configurational coupling, of configurations in which there are unpaired
s
-electrons, as these contribute significantly to the hyperfine splitting. A review of the application of the theory to the ions of the iron transition group is given.
Tập 205 Số 1080 - Trang 135-153 - 1951
The instabilities of gravity waves of finite amplitude in deep water I. Superharmonics In this paper we embark on a calculation of all the normal-mode perturbations of nonlinear, irrotational gravity waves as a function of the wave steepness. The method is to use as coordinates the stream-function and velocity potential in the steady, unperturbed wave (seen in a reference frame moving with the phase speed) together with the time t. The dependent quantities are the cartesian displacements and the perturbed stream function at the free surface. To begin we investigate the ‘superharmonics’, i.e. those perturbations having the same horizontal scale as the fundamental wave, or less. When the steepness of the fundamental is small, the normal modes take the form of travelling waves superposed on the basic nonlinear wave. As the steepness increases the frequency of each perturbation tends generally to be diminished. At a steepness ak ≈ 0.436 it appears that the two lowest modes coalesce and an instability arises. There is evidence that this critical steepness corresponds precisely with the steepness at which the phase velocity is a maximum, considered as a function of ak. The calculations are facilitated by the discovery of some new identities between the coefficients in Stokes’s expansion for waves of finite amplitude.
Tập 360 Số 1703 - Trang 471-488 - 1978
Stability of water waves We apply some general results for Hamiltonian systems, depending on the notion of signature of eigenvalues, to determine the circumstances under which collisions of imaginary eigenvalue for the linearized problem about a travelling water wave of permanent form are avoided or lead to loss of stability, up to non-degeneracy assumptions. A new superharmonic instability is predicted and verified.
Tập 406 Số 1830 - Trang 115-125 - 1986
The instabilities of gravity waves of finite amplitude in deep water II. Subharmonics
Calculation of the normal-mode perturbation of steep irrotational gravity waves, begun in part I, is here extended to a study of the subharmonic perturbations, namely those having horizontal scales greater than the basic wavelength (2π/k). At small wave amplitudes
a
, it is found that all perturbations tend to become neutrally stable; but as
ak
increases the perturbations coalesce in pairs to produce unstable modes. These may be identified with the instabilities analysed by Benjamin & Feir (1967) when ak is small. However, as ak increases beyond about 0.346, these modes become stable again. The maximum growth scale of this type of mode in the unstable range is only about 14 % per wave period, which value occurs at
ak
≈0.32. At values of
ak
near 0.41 a new type of instability appears which has initially zero frequency but a much higher growth rate. It is pointed out that this type might be expected to arise at wave amplitudes for which the first Fourier coefficient in the basic wave is at its maximum value, as a function of the wave height. The corresponding wave steepness was found by Schwartz (1974) to be
ak
= 0.412. A comparison of the calculated rates of growth are in rather good agreement with those observed by Benjamin (1967) in the range 0.07<
ak
<0.17
Tập 360 Số 1703 - Trang 489-505 - 1978
The Bakerian Lecture Towards synthesis of proteins
Proteins, as their name indicates, occupy the prime place in Nature’s architecture. It is worth remarking that Nature uses the structural type for diverse purposes, in addition to those familiar in enzymology, immunology, etc. A striking example is provided by the recent publication (Bradbury
et al
. 1976), showing that the C fragment of lipotropin (residues 61-91) is firmly bound by opiate receptors and is an analgesic 200 times as potent as morphine in molar terms. The pentapeptide comprising residues 61-65 of this sequence is already well known as enkephalin (Hughes
et al
. 1975). Reference should also be made to the host of hormones from the pituitary gland, hypothalamus, and intestinal tract. An example of the last is gastrin which has been studied at Liverpool, principally by R. A. Gregory in the Department of Physiology. Recently the structure of the big gastrins, isolated by Gregory & Tracy (1972), has been elucidated by Harris & Runswick (1974) following preliminary work in the Robert Robinson Laboratories (Barton, Choud- hury, Dancsi & Kenner 1973) (figure 1). This structure typifies the way in which small fragments are carved from a protein chain in order to provide an active hormone (Smyth 1975). Thus the gastrins originally described (Gregory & Tracy 1964; Kenner & Sheppard 1968) correspond to the sequence 18-34 of the big gastrins. The lysyl glutaminyl bond is enzymically cleaved, as can be achieved in the laboratory by trypsin, and then the N-terminal glutaminyl residue cyclizes to the pyroglutamyl structure (pyrrolidone carbonyl). The pyroglutamyl structure at the N-terminus of the big gastrins must have arisen in the same way. It should also be noted that the C-terminal amide, which is essential for biological activity (Tracy & Gregory 1964), very likely arises from enzymatic aminolysis of a protein chain extending further to the right; the extensive studies by Morley (1968) of structure- activity relations in the gastrin tetrapeptide indicate that the gastrin tetrapeptide embedded in a protein chain would not have hormonal activity until aminolysis had occurred, and therefore the gastrin sequence can be stored in a prohormone. The sequence of human big gastrin 1 (figure 1) has been synthesized by a collaborative effort between our laboratory at Liverpool and that of Professor E. Wünsch in the Max Planck Institute at Munich (Choudhury
et al
. 1976).
Tập 353 Số 1675 - Trang 441-457 - 1977
Some further measurements of upper atmospheric ionization In a previous communication an account was given of some measurements of upper atmospheric ionization in south-east England made by the critical frequency method. These measurements were confined principally to the Kennelly-Heaviside region (region E) and showed that the maximum ionization at that level in the ionosphere exhibits a diurnal and seasonal variation such as may be explained in terms of a solar ionizing agency travelling rectilinearly. It was found, for example, that the ionization reaches a maximum about noon, falls off rapidly as sunset approaches, and continues to decrease less rapidly during the night. A short time before ground sunrise a minimum of ionization is attained, after which the value increases rapidly until the noon maximum is again reached. In the same communication reasons were advanced, based on the radio measurements made by one of us during the solar eclipse of 1927, for believing the ionizing agency for this region to be ultra-violet light from the sun, as opposed to the view then prevailing that a neutral stream of corpuscles was the effective agent, and it was pointed out that the solar eclipse of August 31, 1932, visible in Canada, provided an excellent opportunity for deciding the matter. Using the same critical-frequency method, Dr. J. T. Henderson working at Vankleek Hill, Ontario, was able to set the question beyond doubt and it may now be regarded as established that ultra-violet light is the principal ionizing agency for the Kennelly-Heaviside region. The present communication deals with further measurements made in south-east England by the critical-frequency method in which it is applied to the study of diurnal and seasonal variations in ionization in the upper ionized region (region F) as well as in region E. Since 1932, many workers in different parts of the world have adopted the critical-frequency method for the measurement of maximum ionization content and it is hoped that, in due course, the results of a world-wide survey of the diurnal and seasonal variations in ionospheric conditions will be available. Meanwhile, we are able to compare our present results with those we have previously obtained and also with those obtained in America at places of lower latitude.
Tập 150 Số 871 - Trang 685-708 - 1935
Measurements on turbulent vortices in a cylinder wake
The wakes of circular cylinders were explored by means of hot wire anemometers in the range of Reynolds numbers based on diameter of from 10
3
to 4 x 10
4
. The vortex strength was determined and its variation with distance downstream and with Reynolds number was investigated. The vortex strengths agree with those obtained by application of Roshko’s (1954) method to our mean flow measurements. The vortex velocity distribution assumed was that of Hoffman & Joubert (1963) which was found to agree with our measurements when slight adjustments were made in the inner core region. Vortex paths, the formation region and three dimensional effects are also discussed.
Tập 294 Số 1438 - Trang 319-342 - 1966
On kinematic waves II. A theory of traffic flow on long crowded roads This paper uses the method of kinematic waves, developed in part I, but may be read independently. A functional relationship between flow and concentration for traffic on crowded arterial roads has been postulated for some time, and has experimental backing (§2). From this a theory of the propagation of changes in traffic distribution along these roads may be deduced (§§2, 3). The theory is applied (§4) to the problem of estimating how a ‘hump’, or region of increased concentration, will move along a crowded main road. It is suggested that it will move slightly slower than the mean vehicle speed, and that vehicles passing through it will have to reduce speed rather suddenly (at a ‘shock wave’) on entering it, but can increase speed again only very gradually as they leave it. The hump gradually spreads out along the road, and the time scale of this process is estimated. The behaviour of such a hump on entering a bottleneck, which is too narrow to admit the increased flow, is studied (§5), and methods are obtained for estimating the extent and duration of the resulting hold-up. The theory is applicable principally to traffic behaviour over a long stretch of road, but the paper concludes (§6) with a discussion of its relevance to problems of flow near junctions, including a discussion of the starting flow at a controlled junction. In the introductory sections 1 and 2, we have included some elementary material on the quantitative study of traffic flow for the benefit of scientific readers unfamiliar with the subject.
Tập 229 Số 1178 - Trang 317-345 - 1955
The theory of surface erosion by ion bombardment An eroding or growing solid surface is treated as an advancing nonlinear wavefront and characteristic methods are used to describe its progress, when the normal velocity of erosion is a well-defined function of spatial position, and time and surface orientation. Facets, points and edges can develop as the surface evolves and the formation of these are described in terms of the theory. Some interesting examples are computed that have important application in microfabrication, surface analysis and ion beam processing.
Tập 407 Số 1833 - Trang 405-433 - 1986