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1
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
Kaydet Alıntıla
Öz bulunamadı.
DOI : 10.81043/aperta.102157
Sayi :334
issue :1596
Sayfa :83-94
Sınıflandırma :
2
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 :
1985
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Kaydet Alıntıla
Cilt: 398
Sayı: 1815
Yayın Tarihi: 1985-04-09
ISSN: 0080-4630
3
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
4
On Overpotential and the Photovoltaic Process at Polarized Electrodes
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. J. Hillson , E. K. Rideal
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1949
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
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Kaydet Alıntıla
The acceleration of the electrodeposition of hydrogen and oxygen by light of wave-length from 4000 to 2000Å has been studied on different electrodes. The quantum efficiency of the photoreaction was determined as a function of the wave-length of the incident light and of the steady polarizing current. From these experiments it was concluded that the rate-determining step at these electrodes occurred after the discharge of the ions and that the overpotential corresponded to a stationary concentration of adsorbed atoms or radicals. It was further concluded that an electrode at which hydrogen is being evolved at a sensible rate is covered with a nearly complete layer of adsorbed hydrogen. The potential at which such evolution occurs is determined primarily by the negative potential necessary to displace adsorbed oxygen atoms or water molecules by hydrogen. Calculations of this potential, in the few cases where the necessary heats of adsorption are available, gave values in agreement with those observed experimentally. It was concluded that the rate-determining step on most cathodes, except platinum, was the electrochemical combination of an adsorbed atom with an ion in the double layer, and relations were obtained for the dependence of the overpotential on the current density and electrokinetic potential, which are in fairly good agreement with experiment. A similar mechanism is tentatively suggested for the electrode reaction at an anode at which oxygen is being evolved.
Cilt: 199
Sayı: 1058
Sayfa: pp. 295-310
Yayın Tarihi: 1949-11-07
ISSN: 0080-4630
5
The Application of Electronic Digital Computers to Molecular Orbital Problems. I. The Calculation of Bond Lengths in Aromatic Hydrocarbons
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) :
H. O. Pritchard , F. H. Sumner
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1954
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
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Kaydet Alıntıla
The Manchester computer has been programmed for the complete solution of molecular orbital problems not including overlap. The technique is applied to the calculation of bond lengths in eight aromatic hydrocarbons using a self-consistent molecular orbital approximation, and the results are compared with existing experimental values.
Cilt: 226
Sayı: 1164
Sayfa: pp. 128-140
Yayın Tarihi: 1954-10-21
ISSN: 0080-4630
6
Investigations on the Combustion of Hydrocarbons. I. The Influence of Molecular Structure on Hydrocarbon Combustion
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. R. Ubbelohde
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1935
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
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Kaydet Alıntıla
Cilt: 152
Sayı: 876
Sayfa: pp. 354-378
Yayın Tarihi: 1935-11-01
ISSN: 0080-4630
7
Atomic Transport via Point Defects in Crystals. II. Atomic Mobilities and Dielectric Relaxation
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. D. Franklin , A. B. Lidiard
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1984
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
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Kaydet Alıntıla
The general formulation of the kinetic theory of isothermal solid state diffusion applicable to systems showing small degrees of vacancy and interstitial disorder that was presented in a previous paper (Franklin & Lidiard, Proc. R. Soc. Lond. A 389, 405-431 (1983)) is here extended to describe atomic transport in such isothermal systems under the influence of external scalar potential fields (for example, electric, gravitational, centrifugal fields). For steady fields the results verify the correctness of the phenomenological equations suggested for solid state transport processes by the theory of non-equilibrium thermodynamics and provide expressions for the phenomenological transport coefficients (Lij) in terms of microscopic quantities characterizing the defect species and their movements. In particular, it is shown that the same expressions for these transport coefficients are obtained from the atomic fluxes coming from `drift' under applied fields, as from diffusion arising from imposed concentration gradients. The dielectric response function for use with time-dependent fields is also obtained. It is made up of two parts; one corresponding to the d.c. conductivity, the other to a set of Debye relaxation modes. It is demonstrated that the occurrence of association and dissociation reactions among the defects influences both the relaxation times and the strengths of these modes. A brief examination of the example of solute-vacancy pairs in a f.c.c. lattice shows that these influences can be substantial and qualitatively significant.
Cilt: 392
Sayı: 1803
Sayfa: pp. 457-473
Yayın Tarihi: 1984-04-09
ISSN: 0080-4630
8
The Sun's Magnetic Field and the Diurnal and Seasonal Variations in Cosmic Ray Intensity
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. Jánossy , P. Lockett
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1941
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
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Kaydet Alıntıla
The diurnal and seasonal variations in the vertical cosmic ray intensity, produced by a solar magnetic dipole field, are calculated at latitudes 0 and 45⚬, and compared with 'observed' data. It appears that the diurnal variation at latitude 45circ can be largely accounted for by assuming the existence of a solar dipole of moment 1· 1 × 1034 gauss cm.3, a value which is consistent with observational evidence. The diurnal variation at the equator, however, cannot be explained by the hypothesis of a solar magnetic dipole field. The seasonal variation in intensity inferred by the above value for the solar dipole moment is of the same order of magnitude as the observational variation, but shows a phase discrepancy of two months.
Cilt: 178
Sayı: 972
Sayfa: pp. 52-60
Yayın Tarihi: 1941-05-09
ISSN: 0080-4630
9
Thermally Driven Hydromagnetic Convection in a Rapidly Rotating Sphere
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. Fearn
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1979
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
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Kaydet Alıntıla
Buoyancy-induced convection is investigated in a rapidly rotating, self-gravitating fluid sphere internally heated by a uniform distribution of heat sources and under the influence of an azimuthal magnetic field whose strength is proportional to the distance $\overline{\omega}$* from the rotation axis. Attention is restricted to relatively small magnetic field strengths (as measured by the parameter Λ) such that the dominant force balance remains geostrophic. Convection is then confined to a thin cylindrical annulus, radius $\overline{\omega}$*0, about the rotation axis. A linear analysis is used to find the state of marginal stability together with the corresponding minimum critical value of the modified Rayleigh number, Rc (a measure of the buoyancy force required to maintain convective motions). Two distinct modes of instability are found to operate: `Rossby' and `magnetic'. When no magnetic field is applied (\Lambda = 0), and when the Prandtl number σ \simeq 1, the instability takes the form of a thermally driven Rossby wave propagating eastward but with group velocity westward. Modifications to this mode due to a non-zero magnetic field result in Rc being a complicated function Rc (Λ, q, σ), where q = κ/η and σ = ν/κ with ν, κ and η denoting the viscous, thermal and magnetic diffusivities. When it has a significant effect \[$\sigma\leqslantO$(1)\], the magnetic field inhibits the Rossby mode and convection moves towards the axis where the field is weaker ($\overline{\omega}$*0 \rightarrow 0). The presence of the magnetic field also permits new modes of instability which are facilitated by increasing field strength, with Rc \propto \Lambda-1. These magnetic modes propagate eastwards (westwards) when q < qm(q > qm) with qm \approx 2.8. Of particular interest to the Earth is the limit q \simeq 1 where the marginally stable magnetic mode takes the form of an undamped buoyancy wave in an unstably stratified fluid. No diffusive processes are operating at leading order and the only effect opposing convection is the geostrophic constraint.
Cilt: 369
Sayı: 1737
Sayfa: pp. 227-242
Yayın Tarihi: 1979-12-31
ISSN: 0080-4630
10
The Crystal Structure of Myoglobin. II. Finback Whale Myoglobin
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. C. Kendrew , P. J. Pauling
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1956
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
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Kaydet Alıntıla
Myoglobin of Balaenoptera physalus (finback whale) normally forms orthorhombic crystals with space group P21212 and cell dimensions a = 97· 4, b = 39· 8, c = 42· 5 Å; the unit cell contains four molecules. The intensities of the reflexions in the three principal zones have been used to compute Patterson projections, which exhibit rod-like features parallel to z. These rods are 10 Å apart in approximately hexagonal packing and have nodes at 5 Å intervals; they are taken to be the vector equivalents of a set of quasi-parallel polypeptide chains with the same orientation in real space, the mean chain direction being about the same in all four molecules in the cell. Further evidence for this conclusion is derived from the radial distribution of intensities, which is anisotropic in the sense that there is a marked preponderance of 10 Å reflexions in the [001] zone; and from the absolute magnitudes of the reflexions, which are compatible with the hypothesis that 25 to 50% of the molecule is made up of parallel polypeptide chains. If the chains were only approximately parallel they might account for a larger proportion of the molecule. The changes in the low-order reflexions produced by variation in the electron density of the suspension medium have been used to find the position of the molecules in the unit cell; confirmation of the results is found in the Patterson projections. The orientation of the haem group relative to the crystal axes is derived from measurements of paramagnetic resonance (Bennett & Ingram 1956 a) and of optical dichroism. It is concluded that the plane of the haem group is inclined at 41° to the mean chain direction. Unambiguous information about the structure of the molecule will only be obtained by the isomorphous replacement method; meanwhile the above results, taken in conjunction with others derived from different crystal forms of myoglobin, have been used to discuss some plausible models. The most favoured is 42 Å long (in the chain direction) and has a cross-section of 25 × 35 Å. A molecule having these dimensions might consist of two layers of polypeptide chains, each layer containing three chains. This arrangement is compatible with one of two favoured Fourier projections derived by applying the inequality relations of Cochran (1952) to the [001] zone.
Cilt: 237
Sayı: 1209
Sayfa: pp. 255-276
Yayın Tarihi: 1956-10-09
ISSN: 0080-4630
11
Energy Loss of Protons Passing through Hydrogen
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. Dalgarno , G. W. Griffing
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1955
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
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Kaydet Alıntıla
The cross-sections of processes involving protons and hydrogen atoms calculated by Bates, Dalgarno and Griffing using the Born approximation are employed to make a detailed analysis of the contributions of excitation, ionization and capture to the stopping power of a gas of atomic hydrogen for a beam consisting initially of protons. A range of beam energies from 10 keV to 3 MeV is covered. The computed total energy loss is compared with experimental data and the accuracy of the Born approximation for heavy particle collisions is discussed.
Cilt: 232
Sayı: 1190
Sayfa: pp. 423-434
Yayın Tarihi: 1955-11-08
ISSN: 0080-4630
12
Criticality in a Nearly Circular Cylinder
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. Adler
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1987
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
The problem of determining the critical conditions in a non-circular cylinder of infinite length is examined, in which the reaction is of zero order and where the Frank-Kamenetskii approximation to the reaction rate has been made. The generators are assumed parallel and the boundary of a cross section is given by $r = 1 + \epsilon \cos \theta (\epsilon \simeq 1)$, where (r, θ) are plane polar coordinates. The surface conditions assumed are (i) uniform temperature and (ii) newtonian cooling. By suitable expansions of the interior temperature and the Frank-Kamenetskii parameter δ, it is shown that the critical value of δ for (ii) is \begin{equation*}\begin{split} \delta_{\operatorname{crit}} (\epsilon, B) = \frac{8\sigma_c}{(1+\sigma_c)^2} \exp \Big\lbrack &- \frac{4\sigma_c}{B(1+\sigma_c)}\Big\rbrack \\ &x\Big\lbrack 1 - \epsilon^2\{\frac{\sigma^2_c}{1+\sigma_c} + \frac{1}{B} \sigma_c \frac{(1+3\sigma_c)}{(1+\sigma_c)^2}\Big\} + O(\epsilon^4)\Big\rbrack,\end{split}\end{equation*} where σc = -2/B + (1 + 4/B2)1/2, and where B is a Biot number proportional to the surface-heat transfer coefficient. For (i), the simple result $\delta_{\operatorname{crit}}(\epsilon, \infty) = 2 - \epsilon^2 + O(\epsilon^4)$, is obtained.
Cilt: 411
Sayı: 1841
Sayfa: pp. 413-419
Yayın Tarihi: 1987-06-08
ISSN: 0080-4630
13
Concluding Remarks
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. Bernal
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1958
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
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Kaydet Alıntıla
Cilt: 247
Sayı: 1251
Sayfa: pp. 536-538
Yayın Tarihi: 1958-10-21
ISSN: 0080-4630
14
The Thermal and Magnetic Properties of Chromium Methylamine Alum between 0· 01 and 1° K
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. E. Gardner , N. Kurti
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
Adiabatic demagnetizations and calorimetric measurements have been carried out with chromium methylamine alum. The results can be interpreted by a Stark splitting of the 4S ground state of the Cr3+ ion of (0· 27 ± 0· 01) °K. Absolute temperatures for this salt have been determined down to 0· 01° K. The Curie point was found at 0· 020° K.
Cilt: 223
Sayı: 1155
Sayfa: pp. 542-554
Yayın Tarihi: 1954-05-20
ISSN: 0080-4630
15
Esso Energy Award Lecture, 1982: Coordinating Traffic Signals to Reduce Fuel Consumption
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. I. Robertson
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1983
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
Congestion at traffic signals in Britain wastes between 500 and 1000 Ml of fuel every year; at least one half of this waste occurs in central urban areas. The waste can be reduced by coordinating the timings of adjacent signals but it is difficult to achieve good coordination because traffic flow patterns are complex and the effects of signal timing changes are widespread. To help solve this problem, the Transport and Road Research Laboratory has developed a computer program, called TRANSYT, that models traffic movements and optimises the signal timings to minimise delay and stops. This paper describes the principles of TRANSYT and how the method has been extended and used to predict and minimise vehicular fuel consumption in urban areas. Transyt calculates fixed time coordination plans that are optimised for average flow patterns, e.g. during a typical evening peak period. A new method, called SCOOT, continuously measures flows and congestion, predicts current queues and automatically adjusts the signal coordination as the traffic patterns vary. An outline is given of the principles of SCOOT and its potential uses as part of a driver information system.
Cilt: 387
Sayı: 1792
Sayfa: pp. 1-19
Yayın Tarihi: 1983-05-09
ISSN: 0080-4630
16
Front 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 :
1979
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Kaydet Alıntıla
Cilt: 365
Sayı: 1720
Yayın Tarihi: 1979-02-19
ISSN: 0080-4630
17
The Contrast, Breadths and Relative Intensities of Electron Diffraction Rings
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. S. Halliday
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1960
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
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Kaydet Alıntıla
A theoretical expression for the contrast of transmission electron diffraction patterns is developed, assuming kinematical conditions. The effects of the accelerating voltage, the specimen thickness, crystallite size and amorphous content are discussed. Experimental measurements of the contrast of diffraction patterns obtained with iron specimens are compared with the theoretical predictions. Theory and experiment show that the highest contrast is obtained in single scattering conditions and that the contrast is then independent of specimen thickness and accelerating voltage. In plural scattering conditions the contrast rapidly diminishes with increasing thickness and decreasing voltage. However, the reduced contrast remains constant if the ratio of the specimen thickness over the electron mean free path is kept constant. The experimental variation of the contrast with tins ratio agrees with that predicted, and has the same form for all rings, Results obtained with other materials by previous workers are shown to agree with the present theory and results. The effect of plural electron scattering on ring breadths and intensities has been measured. It is shown that broadening is caused by very small angle scattering of diffracted electrons, and that true estimates of crystallite size can be made only in single scattering conditions. The relative ring intensities are, however, unaffected even when the proportion of scattered electrons within the ring profiles is large. The effect of accelerating voltage on the extent of dynamical diffraction conditions is compared with that predicted by Blackman (1939). The experiments indicate that dynamical conditions arise with crystallites six times smaller than those predicted by Blackman.
Cilt: 254
Sayı: 1276
Sayfa: pp. 30-47
Yayın Tarihi: 1960-01-19
ISSN: 0080-4630
18
The Decomposition and Ignition of Peroxides. I. Diethylperoxide
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) :
E. J. Harris , A. C. Egerton
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: 168
Sayı: 932
Sayfa: pp. 1-18
Yayın Tarihi: 1938-10-10
ISSN: 0080-4630
19
The Wave Structure of Monochromatic Electromagnetic Radiation
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. F. Nye , J. V. Hajnal
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1987
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
The paper considers a general field of electromagnetic waves of a single frequency and identifies the salient structurally stable features of the three-dimensional pattern of polarization. The approach is geometrical rather than analytical, and it differs from previous treatments of this kind by being applicable even when the constituent plane waves are travelling in all directions. Lines and surfaces exist where the electric or magnetic vibration ellipse is singular. The field is divided into right-handed and left-handed regions by `T surfaces', the electric and magnetic T surfaces not being coincident. Lying in the T surfaces are `LT lines' where the vibration is linear, and cutting through the T surfaces are `CT lines' where the vibration is circular. Both kinds of lines are surrounded by characteristic patterns of vibration ellipses, which provide a singularity index, ± 1 for LT and ± 1/2 for CT. The analysis is applicable in a cavity, but a loss-free resonating cavity represents a highly degenerate case.
Cilt: 409
Sayı: 1836
Sayfa: pp. 21-36
Yayın Tarihi: 1987-01-08
ISSN: 0080-4630
20
Radiant-Interchange Configuration Factors Between Various Selected Plane Surfaces
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. Feingold
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1966
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
The radiant-interchange configuration factor F$_{1-2}$ (later referred to simply as 'factor') is defined as the fraction of the energy leaving an isothermal area A$_1$ that is incident upon another area A$_2$. The validity of Lambert's law of diffuse radiation is assumed. The calculation of such factors in the case of two rectangles having a common edge and forming an arbitrary angle is discussed, and a table of calculated values is presented. It is shown how the factors for two parallel, convex polygons, forming the bases of a right prism, can be derived from the results obtained for the rectangles. Values of such factors for a number of regular polygons are tabulated. A separate table gives factors for the honeycomb structure, much used in aviation and aerospace. The importance of much greater accuracy in the calculations than is generally thought necessary is shown by an example.
Cilt: 292
Sayı: 1428
Sayfa: pp. 51-60
Yayın Tarihi: 1966-05-03
ISSN: 0080-4630
21
Atmospheric Reactions of the HO2 Radical Studied by Laser Magnetic Resonance Spectroscopy
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. P. Burrows , D. I. Cliff , G. W. Harris , B. A. Thrush , J. P. T. Wilkinson
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1979
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
Measurement of the rotational spectra of HO2 and HO by laser magnetic resonance has been used to determine rate coefficients for reactions of HO2 in a fast flow system at low pressures and ambient temperatures. Processes of atmospheric importance were studied and the rate coefficients obtained were: O + HO2 = HO + O2, (4) k4 = (3.1 ± 1.0) × 10-11 cm3 molecule-1 s-1, HO + HO2 = H2O + O2, (8) k8 = (5.1 ± 1.7) × 10-11 cm3 molecule-1 s-1, NO + HO2 = NO2 + HO, (2) k2 = (8.2 ± 2.4) × 10-12 cm3 molecule-1 s-1, HO2 + Cl = HCl + O2, (17) k17 = (4.1 ± 1.4) × 10-11 cm3 molecule-1 s-1, HO2 + Cl = HO + ClO, (17a) k17a≤ 3 × 10-13 cm3 molecule-1 s-1, HO2 + SO2 = HO + SO3, (21) k21≤ 2 × 10-17 cm3 molecule-1 s-1, HO2 + SO2 + He = HO2SO2 + He, (21a) k21a≤ 4 × 10-34 cm6 molecule-1 s-1, HO2 + CO = HO + CO2, (22) k22≤ 2 × 10-17 cm3 molecule-1 s-1, HO2 + CO + He = HCO3 + He, (22a) k22a≤ 4 × 10-34 cm6 molecule-2 s-1. The disproportionation of two HO2 radicals was shown to proceed more slowly in argon carriers at total pressures around 2 Torr than had been reported at higher total pressures. Upper limits for k19 were HO2 + HO2 = H2O2 + O2 (19) found to lie in the range (7.5 ± 5.0) × 10-13 cm3 molecule-1 s -1.
Cilt: 368
Sayı: 1735
Sayfa: pp. 463-481
Yayın Tarihi: 1979-11-29
ISSN: 0080-4630
22
Further Development of the Three-Region Model of a Premixed Turbulent Flame. II. Instability Dominated Region 1
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. Ballal
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1979
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
An analysis of the balance equation for turbulent kinetic energy of an instability dominated region 1 is presented for a turbulent, premixed propane-air flame. The effects of intensity, scale and laminar burning velocity on the energy balance are also examined. Specifically, the nature of instability in a turbulent flame and its influence on the flame structure are highlighted. These results show that either increase in scale or reduction in intensity of approach turbulence increases the magnitude of all the terms in the balance equation. The core region of the flame is unaffected by a small scale instability, whereas, for a large scale instability, the ratio of turbulence production/viscous dissipation remains independent of scale. The dominant terms in the energy balance are found to be those of convection and advection when the structure of the flame turbulence consists mainly of a large scale fluctuating motion. Finally, increase in laminar burning velocity restores stability and causes transition to region 2, in which production and viscous dissipation predominate over convection and advection terms, respectively.
Cilt: 368
Sayı: 1733
Sayfa: pp. 283-293
Yayın Tarihi: 1979-10-29
ISSN: 0080-4630
23
Effect of a Repulsive Core in the Theory of Complex Nuclei
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) :
H. A. Bethe , J. Goldstone
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1957
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
Using Brueckner's method for the treatment of complex nuclei, the effect of an infinite repulsive core in the interaction between nucleons is studied. The Pauli principle is taken into account from the beginning. A spatial wave function for two nucleons is defined, and an integro-differential equation for this function is derived. Owing to the Pauli principle, the wave function contains no outgoing spherical waves. A solution is given for the case when only a repulsive core potential acts. The effective-mass approximation is investigated for virtual states of very large momentum.
Cilt: 238
Sayı: 1215
Sayfa: pp. 551-567
Yayın Tarihi: 1957-01-29
ISSN: 0080-4630
24
The Application of Singularity Theory to Isothermal Autocatalytic Reactions: The Influence of Uncatalysed Reactions
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) :
S. R. Kay , S. K. Scott , P. -G. Lignola
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1987
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
The influence of a direct, uncatalysed reaction A→ B rate = ku a on the stationary-state behaviour of the cubic `autocatalator' A + 2B→ 3B rate = k1 ab2, B→ C rate = k2 b in an isothermal, well-stirred, open reactor is studied by singularity methods. It is shown that the dependence on the mean residence time of the extent of conversion of A in the stationary state has five different patterns possible. Three of these are similar to those found in the absence of the uncatalysed step: unique, isola and mushroom. The two extra patterns, a breaking wave (a single, S-shaped hysteresis loop) and breaking wave plus isola, require non-zero ku. The uncatalysed reaction also effects the behaviour at long residence time where the system tends to complete conversion. This kinetic scheme represents the simplest, isothermal chemical model with a full unfolding of a winged-cusp singularity and requires only the minimum number of parameters. Sustained oscillatory behaviour, arising from Hopf bifurcations, is also exhibited and is again influenced by the uncatalysed step. The main results can be summarized as follows. ku = 0 multiple stationary states (isola, mushroom) and oscillations; $0 < k_u < \frac{1}{200} k_1 a^2_0$ multiple stationary states (isola, mushroom, breaking wave, breaking wave and isola) and oscillations; $\frac{1}{200} k_1 a^2_0 < k_u<\frac{1}{195} k_1 a^2_0$ multiple stationary states (isola, mushroom, breaking wave, breaking wave and isola), no oscillations; $\frac{1}{195} k_1 a^2_0 < k_u < \frac{1}{27} k_1 a^2_0$ multiple stationary states (breaking wave only), no oscillations; $\frac{1}{27} k_1 a^2_0 < k_u$ no multiple stationary states, no oscillations, (where a0 is the concentration of the reactant A in the feed to the reactor).
Cilt: 409
Sayı: 1837
Sayfa: pp. 433-448
Yayın Tarihi: 1987-02-09
ISSN: 0080-4630
25
A Model for Inhomogeneous Turbulent Flow
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. G. Saffman
Konu :
Science and Mathematics, General Science, Mathematics
Yıl :
1970
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Yayıncı Web Sitesi
Kaydet Alıntıla
A set of model equations is given to describe the gross features of a statistically steady or 'slowly varying' inhomogeneous field of turbulence and the mean velocity distribution. The equations are based on the idea that turbulence can be characterized by 'densities' which obey nonlinear diffusion equations. The diffusion equations contain terms to describe the convection by the mean flow, the amplification due to interaction with a mean velocity gradient, the dissipation due to the interaction of the turbulence with itself, and the diffusion also due to the self interaction. The equations are similar to a set proposed by Kolmogorov (1942). It is assumed that both an 'energy density' and a 'vorticity density' satisfy diffusion equations, and that the self diffusion is described by an eddy viscosity which is a function of the energy and vorticity densities; the eddy viscosity is also assumed to describe the diffusion of mean momentum by the turbulent fluctuations. It is shown that with simple and plausible assumptions about the nature of the interaction terms, the equations form a closed set. The appropriate boundary conditions at a solid wall and a turbulent interface, with and without entrainment, are discussed. It is shown that the dimensionless constants which appear in the equations can all be estimated by general arguments. The equations are then found to predict the von Kármán constant in the law of the wall with reasonable accuracy. An analytical solution is given for Couette flow, and the result of a numerical study of plane Poiseuille flow is described. The equations are also applied to free turbulent flows. It is shown that the model equations completely determine the structure of the similarity solutions, with the rate of spread, for instance, determined by the solution of a nonlinear eigenvalue problem. Numerical solutions have been obtained for the two-dimensional wake and jet. The agreement with experiment is good. The solutions have a sharp interface between turbulent and non-turbulent regions and the mean velocity in the turbulent part varies linearly with distance from the interface. The equations are applied qualitatively to the accelerating boundary layer in flow towards a line sink, and the decelerating boundary layer with zero skin friction. In the latter case, the equations predict that the mean velocity should vary near the wall like the 5/3 power of the distance. It is shown that viscosity can be incorporated formally into the model equations and that a structure can be given to the interface between turbulent and non-turbulent parts of the flow.
Cilt: 317
Sayı: 1530
Sayfa: pp. 417-433
Yayın Tarihi: 1970-06-23
ISSN: 0080-4630
26
The Production of V-Particles in Low-Energy Interactions
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. D. Millar
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
Cilt: 221
Sayı: 1146
Sayfa: pp. 412-413
Yayın Tarihi: 1954-01-27
ISSN: 0080-4630

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