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DISPERSION-RELATION AND WAVE SOLUTION FOR ANHARMONIC LATTICES AND KORTEWEG DELAUNAYS VRIES CONTINUA
Araştırma Makalesi

Araştırma Makalesi
Open Access
Kaynak :
Aperta - TÜBİTAK Açık Arşivi
Dergi:
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES
Yazar(lar) :
A ASKAR
Yıl :
1973
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES
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 Piri Tam Metin Bulucu
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Öz bulunamadı.
DOI : 10.81043/aperta.102157
Sayi :334
issue :1596
Sayfa :83-94
Sınıflandırma :
2
Front Matter
Dergi Makalesi

Dergi Makalesi
Kaynak 1:
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1968
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Kaydet Alıntıla
Cilt: 304
Sayı: 1479
Yayın Tarihi: 1968-05-07
ISSN: 0080-4630
Sınıflandırma :
3
Oriented Chemical Growth on Single Crystals of Zinc and Cadmium
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
L. N. D. Lucas
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1952
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
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Kaydet Alıntıla
The oriented chemical growth of the oxides are studied on different surfaces of single crystals of zinc and cadmium and also of the sulphide of cadmium. The contact planes between substrate and oriented overgrowth were found by determining the facets upon which a particular orientation occurs. The orientation is found to depend on the type of facet, and hence on the surface topography of the substrate which could be determined in favourable cases. The clean surfaces of the metallic crystals used were prepared by electrolytic methods. The inner potentials of zinc and zinc oxide have been measured.
Cilt: 215
Sayı: 1121
Sayfa: pp. 162-174
Yayın Tarihi: 1952-11-25
ISSN: 0080-4630
4
The Thermal and Magnetic Properties of Palladium-Silver Alloys
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
F. E. Hoare , J. C. Matthews , J. C. Walling
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1953
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
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Kaydet Alıntıla
The magnetic susceptibilities of a series of palladium-silver alloys from pure palladium to approximately 50 atomic% silver, have been measured over a range of temperature from 20 to 290° K. The specific heats of a similar series of alloys have been measured in the temperature range 11 to 20° K, and the results used to deduce the electronic specific heats. Owing to the variation of the Debye characteristic temperature with temperature these values are not considered to be of high precision beyond 15% silver content. Making a reasonable correction, however, it has been possible to deduce the band form for palladium. By extrapolation of the susceptibility results to 0° K the variation of Stoner's exchange interaction parameter with concentration has been investigated over a limited range.
Cilt: 216
Sayı: 1127
Sayfa: pp. 502-515
Yayın Tarihi: 1953-02-24
ISSN: 0080-4630
Sınıflandırma :
5
Ionic Recombination in an Ambient Gas. II. Computer Experiment with Specific Allowance for Binary Recombination
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
D. R. Bates , I. Mendaš
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1978
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
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Kaydet Alıntıla
A method of conducting computer experiments on ionic recombination in an ambient gas is described. Account may be taken of binary recombination, and its contribution to the total recombination coefficient may be separated. Recombination in molecular oxygen is treated as an example. It is found that the recombination coefficient for ambient gas (or termolecular) recombination by itself is as predicted by the quasi-equilibrium statistical method in the low density region and as predicted by the Langevin-Harper formula in the high density region. The slightly modified Natanson formula which was introduced to bridge the very wide gap between these two regions is not successful, the pattern of its failure being that it underestimates the influence which the mobilities of the ions have on the recombination coefficient. An unsuspected characteristic of binary recombination revealed by the investigation is that its rate coefficient depends on the density of the ambient gas. Before attempting to extrapolate laboratory data on the total ionic recombination coefficient to zero ambient gas density it is essential to take cognisance of the steep rise of the binary recombination coefficient in the very low density region.
Cilt: 359
Sayı: 1698
Sayfa: pp. 287-301
Yayın Tarihi: 1978-02-28
ISSN: 0080-4630
6
Lattice Statistics in a Magnetic Field. II. Order and Correlations of a Two-Dimensional Super-Exchange Antiferromagnet
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
M. E. Fisher
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1960
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
The long-range order and pair correlation functions of a two-dimensional super-exchange antiferromagnet in an arbitrary magnetic field are derived rigorously from properties of the standard square Ising lattice in zero field. (The model investigated was described in part I: it is a decorated square lattice with magnetic spins on the bonds coupled antiferromagnetically via non-magnetic spins on the vertices.) The behaviour near the transition temperature in a finite field is similar to that of the normal plane lattice, i.e. the long-range orders or spontaneous magnetizations of the sublattices vanish as (Tt - T)1/8 and the pair correlations behave as ωc + W(T - Tt) ln |T - Tt|. The configurational entropy is discussed and the anomalous entropy in the critical field at zero temperature is calculated exactly.
Cilt: 256
Sayı: 1287
Sayfa: pp. 502-513
Yayın Tarihi: 1960-07-19
ISSN: 0080-4630
7
The Interpretation and Use of Economic Predictions and Discussion
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
Terence Burns , A. Britton , Randolph Quirk , P. Mathias , John Mason
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1986
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
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Kaydet Alıntıla
Treasury forecasts, both published and unpublished, of GDP and retail prices are analysed with reference to average absolute forecast errors and a benchmark index of variation. Forecasts of both GDP and the RPI looking two years ahead have become more accurate since the early 1970s, but there has been no marked improvement in one year ahead forecasts. The accuracy of annualized forecasts of GDP improves, and that of the RPI forecasts deteriorates, as the forecast time horizon is progressively extended from one to eight quarters ahead. Some evidence of forecast bias is presented; in the period up to 1979, GDP tended to be over-predicted, and inflation under-predicted. Since 1980 this pattern has been reversed. Analysis of Treasury forecasts and an average of U.S. forecasts shows them to be about equally accurate. The role of forecasts in the implementation of economic policy is discussed. Systematic model-based forecasts provide a consistent framework of analysis, which can improve the operation of economic policy. But prediction errors, and the inertia of the economy, imply that there is only limited scope for discretionary, forecast-based, stabilization policy. Under the medium term financial strategy, MTFS, the policy emphasis has shifted to the medium term. The forecasts have been used to articulate assumptions for output, inflation and money GDP, and to provide the tax and expenditure framework behind the illustrative path of the PSBR. Without the forecasts, the conduct of monetary and fiscal policy would have been considerably more difficult. The paper concludes that, while reductions in the forecast errors of short-term forecasts may be difficult to achieve, there is hope that the accuracy of longer-term forecasts may continue to improve.
Cilt: 407
Sayı: 1832
Sayfa: pp. 103-125
Yayın Tarihi: 1986-09-08
ISSN: 0080-4630
8
A Critical Experimental Investigation of the Force Method of Determining the Dielectric Capacity of Conducting Liquids at Low Frequencies: Univalent Electrolytes in Aqueous Solution
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
W. J. Shutt , H. Rogan
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1936
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
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Kaydet Alıntıla
Cilt: 157
Sayı: 891
Sayfa: pp. 359-372
Yayın Tarihi: 1936-11-02
ISSN: 0080-4630
9
An X-Ray Study of the Dissociation of an Alloy of Copper, Iron and Nickel
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
Vera Daniel , H. Lipson
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1943
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
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Kaydet Alıntıla
A description is given of the unusual X-ray diffraction effects shown by the alloy Cu4FeNi3 while it is in the process of splitting up from one face-centred cubic structure into two. Before the formation of the tetragonal structures described by Bradley a state is formed in which each line of a powder photograph is accompanied by quite strong side-bands. An explanation of this is given and is shown to be in reasonable agreement with most of the quantitative data from the X-ray photographs. This explanation is that the original cubic lattice is regularly deformed by the segregation of the different atoms. From the positions of the side-bands the directions of the deformations and their average wave-length can be estimated. The intensities, however, do not fit in with the theory; they do not vary exactly in the way predicted. It is shown, however, that the variation is in closer agreement with this sort of modulation of the structure than with any other, but it has not, so far, been found possible to find any factor that will modify the intensities of the side-bands in the way required.
Cilt: 181
Sayı: 987
Sayfa: pp. 368-378
Yayın Tarihi: 1943-07-28
ISSN: 0080-4630
10
Address of the President, Sir Howard Florey, at the Anniversary Meeting, 30 November 1963
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1964
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
Cilt: 277
Sayı: 1368
Sayfa: pp. v-xvi
Yayın Tarihi: 1964-01-07
ISSN: 0080-4630
11
Preliminary Experiments on the Temperature-Wave Method of Measuring Specific Heats of Metals at Low Temperatures
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
D. H. Howling , E. Mendoza , J. E. Zimmerman
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1955
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
The apparatus used in the measurement of the low-temperature specific heat of a metal by the temperature-wave method consists basically of a rod of the metal, one end of which is in thermal contact with a bath while at intervals along the rod are a heater and two thermometers. Two quantities are measured: the first is the velocity of propagation down the rod of temperature waves of known frequency generated by an alternating current in the heater; the second is the temperature gradient down the rod produced by a steady current in the heater. These measurements allow respectively the thermal diffusivity D and the thermal conductivity k to be derived; the ratio k/D is the specific heat of the rod per unit volume. The accuracy with which this ratio can be measured is comparable with that of the conventional static method of specific-heat measurements. The most important differences between the two methods of specific-heat measurements are that (i) the static method requires the specimen to be carefully isolated from its surroundings, while in the temperature-wave method the specimen always remains in thermal contact with them, (ii) that the temperature-wave method uses much smaller specimens than the other, and (iii) that it is hoped that it will be applicable with little loss of accuracy down to the temperatures attainable by adiabatic demagnetization. The method was tried on copper and aluminium specimens in the liquid-helium temperature range, using frequencies between 16 and 1800 c/s. The design of suitable thermometers and electronic circuits is described. Among other corrections, those due to the finite length of the specimens were investigated and are discussed in detail, and a method of detecting and eliminating differences of thermal time-lags through the thermometers is described. The method appears to give results which are free from systematic errors.
Cilt: 229
Sayı: 1176
Sayfa: pp. 86-109
Yayın Tarihi: 1955-04-05
ISSN: 0080-4630
12
The Variation with Frequency of the Resistance of Superconducting Tin and Indium
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
M. D. Sturge
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1958
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
The ratio of the superconducting to the normal resistance of tin has been measured calorimetrically at frequencies between 220 and 8500 Mc/s, as a function of temperature, crystal orientation, and purity. Near the transition temperature the resistance varies with frequency in the way predicted by the two-fluid model. At lower temperatures the absolute resistance is roughly independent of purity and orientation. The predicted variation as the square of the frequency is observed up to 1500 Mc/s, but at higher frequencies the resistance varies more slowly. It is shown that this deviation from the square law can be explained by taking relaxation of the normal fluid into account only if the normal fluid is not a Fermi gas. The insensitivity of the superconducting resistance to impurity is shown to be evidence against the theory of Schafroth and Blatt (1956). Some approximate measurements on indium indicate that the superconducting resistance varies as the square of the frequency up to 5000 Mc/s.
Cilt: 246
Sayı: 1247
Sayfa: pp. 570-581
Yayın Tarihi: 1958-08-26
ISSN: 0080-4630
13
The Kinetics of Polysulphone Formation. IV. The Isomerization of cis- and trans-2-butene Accompanying Polysulphone Formation
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
G. M. Bristow , F. S. Dainton
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1955
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
It has been shown by infra-red spectroscopic measurements that, at temperatures near the 'ceiling temperature', the copolymerization of sulphur dioxide with either cis- or trans-2- butene is accompanied by the geometrical isomerization of the 2-butene. The results of some kinetic studies of this latter reaction, using a vapour-pressure technique, are reported. Over the range investigated (25 to 60°C inclusive) the rate of this isomerization reaction increases with temperature according to the normal Arrhenius law, the overall energies of activation using benzoyl peroxide as the initiator being 16· 5 ± 0· 6 kcal mole-1 for the cis to trans isomerization and 18· 3 ± 0· 4 kcal mole-1 for the trans to cis isomerization. Prolonged reaction leads to the attainment of cis-trans equilibrium, and the value of the relevant thermodynamic functions are cis-2-butene→ trans-2-butene; in liquid sulphur dioxide, xB = 0· 09; Δ H = - 1· 43 ± 0· 25 kcal mole-1, Δ S = -2· 8 ± 0· 8 cal deg-1 mole-1. These values differ from the values for an ideal liquid mixture of the cis- and trans-2-butenes. At 100°C and at high catalyst concentrations an additional isomerization reaction is detectable; namely, that of formation of 1-butene by double-bond migration. The geometrical isomerization data are entirely consistent with the conclusion that the polymers formed from cis- and trans-2-butene are stereoisomeric (see also part III) and that one form of addition in the propagation step has a slightly lower energy of activation than the other.
Cilt: 229
Sayı: 1179
Sayfa: pp. 525-536
Yayın Tarihi: 1955-05-24
ISSN: 0080-4630
14
Volume Information
Dergi Makalesi

Dergi Makalesi
Kaynak 1:
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1965
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Kaydet Alıntıla
Cilt: 286
Sayı: 1407
Sayfa: pp. 588-591
Yayın Tarihi: 1965-08-03
ISSN: 0080-4630
15
Bioluminescence
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
J. A. Nicol
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1962
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
Cilt: 265
Sayı: 1322
Sayfa: pp. 355-359
Yayın Tarihi: 1962-01-30
ISSN: 0080-4630
16
The Contraction of Satellite Orbits Under the Influence of Air Drag. VI. Near-Circular Orbits with Day-to-Night Variation in Air Density
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
G. E. Cook , D. G. King-Hele
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1968
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
The theory for the effect of air drag on satellite orbits was developed in Parts I to V of this series of papers on the assumption that the angular motion of perigee is controlled by gravitational forces and is not affected by air drag. If the orbital eccentricity is less than about 0·01, however, and the atmosphere exhibits a substantial day-to-night variation in density, the air drag itself significantly affects the angular motion of perigee. In these circumstances the mathematical theory takes a different and more complicated form, which is developed in the present paper. General equations are derived for the rates of change of parameters specifying the eccentricity and argument of perigee. Complete analytical solutions for the time variations of these parameters are obtained when e is of order 0·001, in two different forms, for (1) high drag, i.e. short lifetime, and (2) low drag. The results are illustrated by numerical examples.
Cilt: 303
Sayı: 1472
Sayfa: pp. 17-35
Yayın Tarihi: 1968-02-06
ISSN: 0080-4630
17
The Application of Integral Equation Methods to the Numerical Solution of Some Exterior Boundary-Value Problems
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
A. J. Burton , G. F. Miller
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1971
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
The application of integral equation methods to exterior boundary-value problems for Laplace's equation and for the Helmholtz (or reduced wave) equation is discussed. In the latter case the straightforward formulation in terms of a single integral equation may give rise to difficulties of non-uniqueness; it is shown that uniqueness can be restored by deriving a second integral equation and suitably combining it with the first. Finally, an outline is given of methods for transforming the integral operators with strongly singular kernels which occur in the second equation.
Cilt: 323
Sayı: 1553
Sayfa: pp. 201-210
Yayın Tarihi: 1971-06-08
ISSN: 0080-4630
18
Classical Theory of Radiating Electrons
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
P. A. M. Dirac
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1938
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
Cilt: 167
Sayı: 929
Sayfa: pp. 148-169
Yayın Tarihi: 1938-08-05
ISSN: 0080-4630
19
The Elastic Properties of Films in e.h.l. Contacts
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
R. F. Duckworth , G. R. Paul , A. Cameron
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1980
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
An optical elastohydrodynamic rig was constructed to measure the inwards radial force of a ball rolling on a plate. The axis of rotation of the ball could be set to give known amounts of side slip and spin. Hertz pressures up to 2 GPa could be achieved. Four fluids were used, a tractant, 5-phenyl 4 ether, a paraffinic cylinder stock and a highly refined synthetic hydrocarbon. It is shown that the film changes from a viscous to an elastic material the shear modulus and ultimate shear strength of which rise mostly linearly with pressure. Their ratio approaches 1/(2π) as predicted by Frenkel's theory (1926).
Cilt: 372
Sayı: 1749
Sayfa: pp. 155-168
Yayın Tarihi: 1980-08-26
ISSN: 0080-4630
20
Back Matter
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1967
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
Cilt: 299
Sayı: 1459
Yayın Tarihi: 1967-07-25
ISSN: 0080-4630
21
Non-Uniqueness in Thermoelectric Magnetohydrodynamic Heat Convection
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
J. A. Shercliff
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1982
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
The coupled equations of thermal convection and of thermoelectric magnetohydrodynamics in the high Hartmann number approximation are solved for motions inside a thin-walled conducting sphere, where the interfacial temperature and the surface heat transfer rates are both quadratic functions of the Cartesian coordinates. In this case the motion is pure rotation about an axis inclined at an arbitrary angle to the uniform magnetic field. To reduce the complexity of the problem some two- and four-parameter variants are considered. These reveal multiple nonuniqueness, bifurcation and catastrophe-type behaviour when the problem is specified in terms of known heat transfer rates. The stability of solutions is only briefly discussed. The implications for cells of liquid lithium in fusion reactor blankets and possible experiments are outlined.
Cilt: 382
Sayı: 1783
Sayfa: pp. 273-293
Yayın Tarihi: 1982-08-09
ISSN: 0080-4630
22
Determination of the Distribution of Some Parameters across the Combustion Zone of a Flat Flame
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
J. H. Burgoyne , F. J. Weinberg
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1954
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
A method has been developed for recording the variation of temperature through a plane flame as a means of analyzing the distribution of other variables. The method, which depends on refractive index gradient measurement, combined with an accurate observation of the initial temperature, is illustrated by results obtained with a very lean ethylene/air mixture. From the temperature distribution, together with a simultaneously measured value of the burning velocity and known physical properties of the gases, variations of other parameters through the flame are calculated.
Cilt: 224
Sayı: 1158
Sayfa: pp. 286-308
Yayın Tarihi: 1954-07-02
ISSN: 0080-4630
23
The Reactions of Atomic Oxygen with Phosphorus and with Phosphine
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
P. B. Davies , B. A. Thrush
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1968
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
A discharge flow system has been used to study the stoichiometry and chemiluminescence of the reaction of atomic oxygen with phosphorus and with phosphine. Visible chemiluminescence in both reactions extending down to 3600 Å and ultraviolet emission in the O + PH3 reaction are attributed respectively to the processes O + PO → PO2 and OH + PO → HOPO. Bond energies of these species and the mechanisms of formation of excited PO are discussed. It is deduced that P and PO only play minor roles in the O + P4 reaction and in the chain reaction between phosphorus and oxygen.
Cilt: 302
Sayı: 1469
Sayfa: pp. 243-252
Yayın Tarihi: 1968-01-02
ISSN: 0080-4630
24
On the Theory of the Catalysis of the Ortho-Para Transformation by Paramagnetic Gases
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
F. Kalckar , E. Teller
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1935
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
Cilt: 150
Sayı: 871
Sayfa: pp. 520-533
Yayın Tarihi: 1935-07-01
ISSN: 0080-4630
25
The Equivalence Between Two Perturbation Methods in Weakly Nonlinear Stability Theory for Parallel Shear Flows
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
K. Fujimura
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1989
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
Two perturbation methods used in weakly nonlinear stability theory, namely, the method of multiple scales and the amplitude expansion method, are examined for their equivalence through formal analyses and numerical calculation of the Landau constants. The method of multiple scales is shown to give results equivalent to those obtained from the amplitude expansion formulation for slightly supercritical states if a normalization condition is applied to the fundamental mode. The convergence of the expansion in the method of multiple scales is also discussed.
Cilt: 424
Sayı: 1867
Sayfa: pp. 373-392
Yayın Tarihi: 1989-08-08
ISSN: 0080-4630
26
The Friction and Transfer of Polytetrafluoroethylene
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
K. Rachel Makinson , D. Tabor
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1964
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
Earlier work has shown that the friction of polytetrafluoroethylene (PTFE) increases with increasing velocity and decreases with rise of temperature as though a relaxation process were involved. A study by microscopy, interference microscopy and electron microscopy of the friction tracks formed when PTFE slides on itself or on 'clean' glass shows that there are basically two friction regimes. At high speeds or low temperatures the friction is high (μ = 0.07 to 0.3) and there is fairly massive transfer and movement of polymer. The details depend on the sliding conditions but in general the transfer is in the form of lumps, ribbons or sheets, the thickness generally exceeding a few tenths of a micrometre. At low speeds and moderate temperatures a very different behaviour is observed: the friction is low (μ < 0.07) and a thin film of PTFE is laid down or drawn over the surfaces. This film may show strong adhesion to the surfaces if they are clean. It is very fibrous and has a thickness varying between about 100 and 400 Å; in addition it has a highly oriented crystal structure. The low friction under these conditions is not due to poor adhesion but to easy shear of relevant units of the PTFE crystal. As the speed of sliding is increased or the temperature diminished the viscous force to shear the film increases until a stage is reached where the shear force exceeds the strength of the boundaries between crystals or grains. The higher friction is then accompanied by the transfer of relatively large fragments of PTFE. These two regimes in the frictional behaviour may thus be interpreted in terms of a relaxation time for intra-crystalline flow. The small change in friction at higher speeds suggests that the shear of larger units within the polymer is not appreciably rate dependent.
Cilt: 281
Sayı: 1384
Sayfa: pp. 49-61
Yayın Tarihi: 1964-08-25
ISSN: 0080-4630
Sınıflandırma :
27
Chemical Shifts in Nuclear Resonances of Caesium Ions in Solutions
Dergi Makalesi

Dergi Makalesi
Kaynak :
JSTOR
Dergi:
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı:
The Royal Society
Yazar(lar) :
J. D. Halliday , R. E. Richards , R. R. Sharp
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1969
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
Chemical shifts of Cs+ nuclear resonances have been measured in aqueous salt solutions and in a wide variety of non-aqueous, mixed, and deuterated solvents. Shifts are found to be nonlinear with concentration down to 0.01 mol/dm3, the precise degree of nonlinearity depending upon the dielectric constant of the solvent. A priori calculations of shift magnitudes, based on Ramsay's shielding formula and a postulated short-range radial distribution function, have yielded calculated shifts in reasonable agreement with observed values. The physical interaction responsible for variations of shift with concentration appears to be repulsive overlap of ion wave functions. The nonlinear functional relation between shift and molar concentration results from the influence of the ionic atmosphere on the probability of interionic contact. The form of this nonlinearity is accurately predicted by the postulated radial distribution function.
Cilt: 313
Sayı: 1512
Sayfa: pp. 45-69
Yayın Tarihi: 1969-10-14
ISSN: 0080-4630

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