Showing papers in "Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences in 1975"
TL;DR: In this paper, the authors describe a study of the adhesion between elastic solids and the effect of roughness on their adhesion, showing that roughness which is small compared with the overall deformation occurring at the region of the rubber-Perspex contact can produce an extremely large reduction in adhesion.
Abstract: This paper describes a study of the adhesion between elastic solids and the effect of roughness in reducing the adhesion. The experiments were carried out between optically smooth rubber spheres and a hard smooth flat surface of Perspex which could be roughened to various degrees. The radius of the rubber spheres was varied by a factor of 8, their elastic modulus by a factor of 10, while the centre line average (c.l.a.)of the roughened Perspex surface was varied from 0.12 to 1.5 μm. The results show that c.l.a. roughnesses which are small compared with the overall deformation occurring at the region of the rubber-Perspex contact can produce an extremely large reduction in adhesion. The effect is more marked for rubbers of higher modulus. On the other hand the curvature of the sphere (over the range examined) has little influence. For this reason and because the analytical problem of a sphere on a rough flat is extremely complicated a theoretical analysis has been developed for the simpler case of a smooth flat in contact with a rough flat surface. As in Greenwood & Williamson (1966) the rough surface is modelled by asperities all of the same radius of curvature and with heights following a Gaussian distribution of standard deviation σ. The overall contact force is obtained by applying the contact theory of Johnson, Kendall & Roberts (1971) to each individual asperity. The theory predicts that the adhesion expressed as a fraction of the maximum value depends upon a single parameter, 1/Δ e ,which is the ratio between a and the elastic displacement δ C that the tip of an asperity can sustain before it pulls off from the other surface. The analysis shows that the adhesion parameter may also be regarded as representing the statistical average of a competition between the compressive forces exerted by the higher asperities trying to prize the surfaces apart and the adhesive forces between the lower asperities trying to hold the surfaces together. Although the theory is derived for two nominally plane surfaces it is found to fit the experimental results for a sphere on a flat reasonably well.
838 citations
TL;DR: The quasi-normal modes of a black hole represent solutions of the relevant perturbation equations which satisfy the boundary conditions appropriate for purely outgoing (gravitational) waves at infinity and purely ingoing waves at the horizon as discussed by the authors.
Abstract: The quasi-normal modes of a black hole represent solutions of the relevant perturbation equations which satisfy the boundary conditions appropriate for purely outgoing (gravitational) waves at infinity and purely ingoing waves at the horizon. For the Schwarzschild black hole the problem reduces to one of finding such solutions for a one-dimensional wave equation (Zerilli's equation) for a potential which is positive everywhere and is of short-range. The notion of quasi-normal modes of such one-dimensional potential barriers is examined with two illustrative examples; and numerical solutions for Zerilli's potential are obtained by integrating the associated Riccati equation.
508 citations
TL;DR: In this paper, it was shown that if the wave function of a given electronic state changes sign when transported adiabatically round a loop in nuclear configuration space, then the state must become degenerate with another one at some point within the loop.
Abstract: It is proved that if the wave function of a given electronic state changes sign when transported adiabatically round a loop in nuclear configuration space, then the state must become degenerate with another one at some point within the loop. It is further shown that this condition is satisfied by certain unsymmetrical triatomic systems, thereby disposing of a recent claim that the non-crossing rule for diatomic molecules applies also to polyatomic molecules.
398 citations
TL;DR: In this paper, the theory for the stability of solitary waves developed by T. B. Benjamin was improved and applied equally to the Kortewegde Vries equation and to an alternative model equation for the propagation of long waves in nonlinear dispersive media.
Abstract: Improvements are made on the theory for the stability of solitary waves developed by T. B. Benjamin. The results apply equally to the Kortewegde Vries equation and to an alternative model equation for the propagation of long waves in nonlinear dispersive media.
363 citations
TL;DR: In this paper, the problem of obtaining a quantum description of the real Klein-Gordon system in a given curved space-time is discussed, and an algebraic approach is used to construct the *-algebra of quantum operators.
Abstract: The problem of obtaining a quantum description of the (real) Klein-Gordon system in a given curved space-time is discussed. An algebraic approach is used. The *-algebra of quantum operators is constructed explicitly and the problem of finding its *-representation is reduced to that of selecting a suitable complex structure on the real vector space of the solutions of the (classical) Klein-Gordon equation. Since, in a static space-time, there already exists, a satisfactory quantum field theory, in this case one already knows what the 'correct' complex structure is. A physical characterization of this 'correct' complex structure is obtained. This characterization is used to extend quantum field theory to non-static space-times. Stationary space-times are considered first. In this case, the issue of extension is completely straightforward and the resulting theory is the natural generalization of the one in static space-times. General, non-stationary space-times are then considered. In this case the issue of extension is quite complicated and we only present a plausible extension. Although the resulting framework is well-defined mathematically, the physical interpretation associated with it is rather unconventional. Merits and weaknesses of this framework are discussed.
345 citations
TL;DR: In this paper, an analysis of the factors that influence the performance of a Fourier transform n.m.r. spectrometer including field homogeneity, probe design, transient circuit behaviour, Johnson noise, non linear analysis, phase sensitive detection in quadrature, and signal processing is given.
Abstract: An analysis is given of the factors which influence the performance of a Fourier transform n.m.r. spectrometer including field homogeneity, probe design, transient circuit behaviour, Johnson noise, non linear analysis, phase sensitive detection in quadrature, and signal processing. The building of a spectrometer based upon the analysis of these factors is described, as is the use of a cyclically ordered phase sequence (CYCLOPS) which renders the use of quadrature Fourier transformation easy. Theoretical deductions are experimentally verified, and the performance of the instrument is demonstrated with spectra obtained from caesium and phosphorus resonances.
289 citations
TL;DR: In this article, a straight infinite vortex of finite cross section is deformed by the action of weak irrotational plane strain, and it is shown that the deformed vortex is unstable to disturbances whose axial wavelengths lie in a narrow band, whose width is proportional to the imposed strain.
Abstract: A straight infinite vortex of finite cross section is deformed by the action of weak irrotational plane strain. The deformed vortex is shown, in the absence of axial flow, to be unstable to disturbances whose axial wavelengths lie in a narrow band, whose width is proportional to the imposed strain. The band is centred on the wavelength of the helical wave which does not propagate on the unstrained circular vortex. Thus support is given to the instability mechanism proposed recently by Widnall, Bliss & Tsai (1974). The argument depends, however, on the mirror image of the helical wave also being a possible non-propagating disturbance on the unstrained vortex.
275 citations
TL;DR: In this article, the formation and development of a wave packet in the laminar boundary layer of a flat plate has been studied experimentally, where the packet was arti-ficially generated by a short duration acoustic pulse, which was injected into the boundary layer flow through a small hole in the plate.
Abstract: The formation and development of a wave packet in the laminar boundary layer of a flat plate has been studied experimentally. The packet was artificially generated by a short duration acoustic pulse, which was injected into the boundary layer flow through a small hole in the plate. The flow oscillations created by the passage of the packet were detected by a hotwire anemometer which was positioned just outside the boundary layer. Repeated excitation of the disturbance enabled the noise content of the data to be significantly reduced by signal averaging which was carried out online by a small computer. From records generated at a number of probe locations over the plate it has been possible to show how the packet developed as it propagated downstream. Contours of the signal amplitude from each of the downstream stations showed that the patch of waves was initially roughly elliptic, but this evolved into a distinctly bowed shape as the patch spread out as it progressed downstream. The smoothly contoured wave packet, with peak amplitudes close to the centre, gradually distorted and far downstream two amplitude maxima formed on either side of the centre line. The wave-like character of the fluctuations within the boundaries of the packet was revealed graphically through perspective projections of the signal records on the z, t plane ( z is across the span). These displays showed the gradual development from a small smooth packet close to the source to the final warped and distorted pattern. Spectral decomposition of the fluctuations at each streamwise measuring station provided information relating to the growth of narrow bands of waves. These showed that a particular band of oblique waves, which grew very rapidly at some stage, were linked to the observed distortions.
270 citations
TL;DR: In this article, an outline of the electrical properties expected in a disordered solid or fluid which shows a metal-insulator transition of Anderson type is given, where the Fermi energy of the electrons passes through a mobility edge separating extended states from states localized by disorder, as the composition or some other parameter is changed.
Abstract: An outline is given of the electrical properties expected in a disordered solid or fluid which shows a metal-insulator transition of Anderson type. This is one in which the Fermi energy of the electrons passes through a mobility edge separating extended states from states localized by disorder, as the composition or some other parameter is changed. Some of the experimental evidence for this kind of transition is described. In particular, a relatively detailed account is given of the two dimensional inversion layer system in which the relevant parameters may be varied in a single device by direct electrical means.
252 citations
TL;DR: In this paper, a number of exact relations for periodic water waves of finite amplitude in water of uniform depth were proved and the mean fluxes of mass, momentum and energy were shown to be equal to 2T(4T-3F) and (3T-2V) crespectively, where T and V denote the kinetic and potential energies and c is the phase velocity.
Abstract: A number of exact relations are proved for periodic water waves of finite amplitude in water of uniform depth. Thus in deep water the mean fluxes of mass, momentum and energy are shown to be equal to 2T(4T—3F) and (3T—2V) crespectively, where T and V denote the kinetic and potential energies and c is the phase velocity. Some parametric properties of the solitary wave are here generalized, and some particularly simple relations are proved for variations of the Lagrangian The integral properties of the wave are related to the constants Q, R and S which occur in cnoidal wave theory. The speed, momentum and energy of deep-water waves are calculated numerically by a method employing a new expansion parameter. With the aid of Pade approximants, convergence is obtained for waves having amplitudes up to and including the highest. For the highest wave, the computed speed and amplitude are in agreement with independent calculations by Yamada and Schwartz. At the same time the computations suggest that the speed and energy, for waves of a given length, are greatest when the height is less than the maximum. In this respect the present results tend to confirm previous computations on solitary waves.
220 citations
TL;DR: In this article, a generalized mathematical model for the autoignition of hydrocarbons under the conditions of high pressure and temperature achieved in a rapid-compression machine is presented; the model is able to simulate the essential phenomena of the two-stage autoignitions of alkanes under these conditions; these are a well defined cool flame that is often quenched rapidly and completely before the onset of a sharp ignition.
Abstract: We have developed a generalized mathematical model for the autoignition of hydrocarbons under the conditions of high pressure and temperature achieved in a rapid-compression machine. The model is able to simulate the essential phenomena of the two-stage autoignition of alkanes under these conditions; these are a well-defined cool flame that is often quenched rapidly and completely before the onset of a sharp ignition. It also predicts correctly the transition to single-stage autoignition at even higher temperatures and the variation with temperature of the characteristic induction periods. The model is based on a degenerate-branched-chain mechanism. We show that it must contain as necessary features two termination processes, one linear and the other quadratic in radial concentration, and two routes for the formation of branching agent, one of which involves intermediate products of oxidation. The model also predicts, without any adjustment of the kinetic parameters, the essential phenomena of cool-flame and ignition behaviour that are observed at low pressures.
TL;DR: In this article, a linear model of a wave packet in a laminar boundary layer is proposed to conform to a particular experimental situation where a packet was artificially excited by a localized pulsed perturbation at the wall boundary.
Abstract: A linear model of a wave packet in a laminar boundary layer is proposed. The model wave packet was chosen to conform to a particular experimental situation where a packet was artificially excited by a localized pulsed perturbation at the wall boundary. Appropriate quantities were computed from this model and these have been compared directly with experimental measurements. The model disturbance was built up from a linear combination of spatially growing modes summed numerically over all wavenumbers and frequencies. The input spectrum was assumed to be flat (all modes were equally excited), and the downstream development of the frequency—wavenumber spectrum was calculated on the basis of linear stability theory. The development of the model wave packet was compared with that of the experiment. It was found that the overall shapes of the disturbed region and the way it spread out as the packet travelled downstream were well predicted by the model behaviour. Detailed comparisons of the wave motion within the wave packet were also made and although encouraging correlation was achieved at stations close to the source this was not maintained far downstream where the experimental packet showed various irregularities. The wave packet generated by the summation of modes developed smoothly downstream without forming any of the types of distortions which had been observed in the experiment.
TL;DR: A coherent self-contained account of the equations governing the perturbations of the Schwarzschild black hole is given in this paper, in which the relations between the equations of Bardeen & Press, of Zerilli and of Regge & Wheeler are explicitly established.
Abstract: A coherent self-contained account of the equations governing the perturbations of the Schwarzschild black hole is given In particular, the relations between the equations of Bardeen & Press, of Zerilli and of Regge & Wheeler are explicitly established
TL;DR: In this paper, the formation and growth of soot aerosols in incident shock flows of benzene, toluene, ethylbenzene and indene, highly diluted with argon at temperatures in the range 1600-2300 K at a total carbon concentration in the shock-heated gases of 2.0 x 1017 atoms/cm3.
Abstract: We report a study of the formation and growth of soot aerosols in incident shock flows of benzene, toluene, ethylbenzene and indene, highly diluted with argon at temperatures in the range 1600-2300 K at a total carbon concentration in the shock-heated gases of 2.0 x 1017 atoms/cm3. The extent of conversion of hydrocarbon into soot, i.e. the soot yield, during the shock flow was determined from extinction measurements at two different visible wavelengths, while the rate of growth of the soot particles was obtained from the variation in the intensity of Rayleigh scattering of a 1W argon-ion laser beam by the soot particles. Of particular interest is our finding that the soot yield some 2.5 ms after the onset of shock heating falls rapidly with increasing temperature from near 100% at 1750-1800 K to less than 5 % at 2300 K
TL;DR: In this paper, the homogeneous rate theory of void growth is extended to include the possibility of forming vacancy loops when the irradiation produces cascade damage, and the analysis provides a basis for understanding and correlating the relative swelling generated during electron; heavy ion and fast neutron irradiation.
Abstract: The homogeneous rate theory of void growth is extended to include the possibility of forming vacancy loops when the irradiation produces cascade damage. The analysis provides a basis for understanding and correlating the relative swelling generated during electron; heavy ion and fast neutron irradiation. In order to illustrate the physical features of the model it is applied in some detail to calculating the volume swelling in solution treated M316 stainless steel for which there is a considerable amount of experimental data. The results from these calculations serve to expose the sensitivity of void swelling to the scale on which interstitial loops are nucleated. They also highlight the particular difficulty arising from the continuous generation of transmutation gas in predicting swelling under neutron irradiation at elevated temperatures.
TL;DR: The nature of slow crack and craze propagation in polymers and crack propagation in in inorganic glass has been considered in terms of time dependent processes by using a fracture mechanics analysis together with time dependent material parameters as discussed by the authors.
Abstract: The nature of slow crack and craze propagation in polymers and crack propagation in inorganic glass has been considered in terms of time dependent processes By using a fracture mechanics analysis together with time dependent material parameters, equations have been derived to describe crack and craze propagation in both inert and active environments Experimental data from a range of materials suggest that a crack opening displacement (cod) criterion governs the crack propagation behaviour Incorporation of a simple fluid flow model into the cod analysis has allowed the failure processes in liquid environments to be described The data on organic polymers and inorganic glass suggest that when there are no problems of maintaining the environmental supply, the crack growth behaviour is controlled by relaxation processes in the material At high crack speeds a transition from relaxation to fluid flow control occurs when the time scale is too short for the liquid flow to be maintained The flow of an environment in long crazes can be shown to influence their behaviour in a similar manner, while under other conditions relaxation controlled craze growth can occur
TL;DR: A theoretical condition for deflexion of Griffith crack meeting a plane perpendicular interface in a thick plate of uniform elastic properties was derived in this paper, which suggests that a short crack should be diverted along the interface when R ad co /4π(1 − V 2 )
Abstract: A theoretical condition has been derived for deflexion of a Griffith crack meeting a plane perpendicular interface in a thick plate of uniform elastic properties. The theory suggests that a short crack should be diverted along the interface when R ad co /4π(1 — V 2 ),
TL;DR: In this paper, the influence of turbulence intensity, scale and vorticity on burning velocity and flame structure is examined by using premixed propane-air mixtures supplied at atmospheric pressure to a combustion chamber 31cm long and lOcmx 10 cm cross-section.
Abstract: The influence of turbulence intensity, scale and vorticity on burning velocity and flame structure is examined by using premixed propane-air mixtures supplied at atmospheric pressure to a combustion chamber 31cm long and lOcmx 10 cm cross-section. The chamber is fitted with transparent side walls to permit flame observations and schlieren photography. Control over the turbulence level is achieved by means of grids located upstream of the combustion zone. By suitable modifications to grid geometry and flow velocity, it is possible to vary turbulence intensity and scale independently within the combustion zone in such a manner that their separate effects on burning velocity and flame structure are readily distinguished. From analysis of the results obtained three distinct regions may be identified, each having different characteristics in regard to the effect of scale on turbulent burning velocity. For each region a mechanism of turbulent flame propagation is proposed which describes the separate influences on burning velocity of turbulence intensity, turbulence scale, laminar flame speed and flame thickness. The arguments presented in support of this 3-region model are substantiated by the experimental data and by the pictorial evidence on flame structure provided by the schlieren photographs. This model also sheds light on some of the characteristics which turbulent flames have in common with laminar flames when the latter are subjected to pressure and velocity fluctuations. Finally the important role of vorticity is examined and it is found that turbulent flame speed is highest when the rate of production of vorticity is equal to about half the rate of viscous dissipation.
TL;DR: A number of steady (marginal) solutions of the induction equation governing the magnetic field created by a particular class of threedimensional flows in a sphere of conducting fluid surrounded by an insulator are derived numerically.
Abstract: A number of steady (marginal) solutions of the induction equation governing the magnetic field created by a particular class of threedimensional flows in a sphere of conducting fluid surrounded by an insulator are derived numerically. These motions possess a high degree of symmetry which can be varied to confirm numerically that the corresponding asymptotic limit of Braginsky is attained. The effect of altering the spatial scale of the motions without varying their vigour can also be examined, and it is found that dynamo action is at first eased by decreasing their characteristic size. There are, however, suggestions that the regenerative efficiency does not persistently increase to very small length scales, but ultimately decreases. It is further shown that time varying motions, in which the asymmetric components of flow travel as a wave round lines of latitude, can sustain fields having co-rotating asymmetric parts. It is demonstrated that, depending on their common angular velocity, these may exist at slightly smaller magnetic Reynolds numbers than the corresponding models having steady flows and fields. The possible bearing of the integrations on the production of the magnetic field of the Earth is considered, and the implied ohmic dissipation of heat in the core of the Earth is estimated for different values of the parameters defining the model.
TL;DR: In this article, a numerical solution method was described for the determination of oil film shape and film pressure in the lubricated contact between an elastic sphere rolling on an elastic plane with steady loading and an isothermal film.
Abstract: A numerical solution method is described for the determination of oil film shape and film pressure in the lubricated contact between an elastic sphere rolling on an elastic plane. Steady loading and an isothermal film are assumed. The Reynolds equation (governing film pressure) and the elasticity equation (governing deformation) are solved simultaneously for a lubricant with the pressure-viscosity characteristic $\eta $ = $\eta $$_{0}$e$^{\alpha p}$. A treatment of the elasticity equation is described such that the deformation matrix is sufficiently compact. To give generality to the solution a set of results was subjected to multiple regression, which indicated that the influence of load on film thickness was very small. The regression results compare well with published data. The effect of restricting the amount of lubricant to the contact was also studied. The computed film shapes under such 'starved' conditions were found to be very close to those found by optical interferometry.
TL;DR: In this article, it is suggested that the deformation energy is concentrated in narrow bands of material by adiabatic shear and the temperature rise in these regions could become high enough for initiation.
Abstract: Individual crystals of silver and lead azide have been impacted by spherical particles. Im pact was at normal incidence on flat faces of the explosives. A novel feature of the experiment was that the particles were very small compared with the millimetre dimension crystals. This meant that the impact damage was independent of the shape of the explosive. Initiation took place when critical conditions of particle size and velocity were exceeded. It was possible to examine the deformation produced when the impact conditions were just subcritical and show that it was primarily plastic. If the deformation energy were uniformly distributed around the indentation, only a small temperature rise would be produced. However, it is suggested that, because of thermal softening, the deformation is concentrated in narrow bands of material by adiabatic shear. The temperature rise in these regions could become high enough for initiation. The discussion is extended to compacted explosives and conditions are considered under which local plastic flow can take place. Finally, the advantages of microparticle impact for testing the sensitiveness of explosives, and situations where particle impact has practical interest are described.
TL;DR: In this article, a solution for the diffraction of a plane wave sound source by a semi-infinite half plane was obtained for the problem of diffraction in the shadow region, where the absorbing lining is on the side of the screen which makes the smallest angle to the source or the receiver from the edge.
Abstract: A solution is obtained for the problem of the diffraction of a plane wave sound source by a semi-infinite half plane. One surface of the half plane has a soft (pressure release) boundary condition, and the other surface a rigid boundary condition. Two unusual features arise in this boundary value problem. The first is the edge field singularity. It is found to be more singular than that associated with either a completely rigid or a completely soft semi-infinite half plane. The second is that the normal Wiener-Hopf method (which is the standard technique to solve half plane problems) has to be modified to give the solution to the present mixed boundary value problem. The mathematical problem which is solved is an approximate model for a rigid noise barrier, one face of which is treated with an absorbing fining. It is shown that the optimum attenuation in the shadow region is obtained when the absorbing lining is on the side of the screen which makes the smallest angle to the source or the receiver from the edge.
TL;DR: In this paper, it was shown that a positive value of excluded volume greatly increases the repulsive free energy compared with that for chains with zero excluded volume, particularly at large separation distances of the surfaces.
Abstract: Polymer-stabilized colloid particles are modelled theoretically by plane surfaces on to which polymer chains are adsorbed by one end only. Interactions between segments of the polymer are treated as an excluded volume effect. It is shown that for high surface densities the polymer distribution function exactly satisfies a one dimensional equation which is solved numerically for two values of excluded volume to give the polymer segment density distributions and the free energy of interaction for various separations of the plane surfaces. It is found that a positive value of excluded volume greatly increases the repulsive free energy compared with that for chains with zero excluded volume, particularly at large separation distances of the surfaces. Excluded volume effects must therefore play an important part in the stabilization of colloids by adsorbed polymer.
TL;DR: In this article, the rotational excitation of carbon monoxide in collision with hydrogen atoms is investigated and the applicability of two simplified close-coupling formulations, introduced by Rabitz and by McGuire & Kouri, is examined.
Abstract: A quantal study is carried out of the rotational excitation of carbon monoxide in collision with hydrogen atoms. The interaction potential at short range is constructed semi-empirically and joined to the Buckingham potential at long range. The close-coupling formulation is used to assess the reliability of the fixed-nuclei approximation, which is developed in terms of the adiabatic theory of electron-molecule scattering. The applicability of two simplified close-coupling formulations, introduced by Rabitz and by McGuire & Kouri, is examined. We found that the fixed nuclei method is unpromising at low energies and time-consuming at high energies. The two simplified close-coupling methods are capable of providing results of useful accuracy. The similarity in formulation of the fixed-nuclei and one of the close-coupling methods, both of which are body-frame treatments, and the differences in their results show that the rotational degree of freedom must be treated rigorously. The method of Rabitz is economical, and we adopted it to calculate the energy dependent rotation excitation cross sections for the scattering of H + CO. The results are presented in the form of Maxwellian-averaged rate coefficients in the temperature range of 5-150K. The efficiency with which the rotational levels of molecules are excited by impact with atomic and molecular hydrogen is a significant parameter in the quantitative interpretation of the physical conditions in which molecular absorption and emission occurs in interstellar clouds. The rotational excitation cross-sections are critical to the determination of the thermal balance of the clouds and possibly to their evolution towards the formation of protostars. Because of radiation trapping, collisions in which the rotational quantum number changes by more than unity are particularly important. For a rigid rotator model, there exists a rigorous close-coupling formulation (Arthurs & Dalgarno i960), the application of which is largely restricted to light molecules. In this paper, we use it to assess the reliability of the adiabatic approximation (Chase 1956) that has been successful in describing electron-molecule collisions
TL;DR: In this article, a crack may he accelerated or retarded when it meets an interface between two equally brittle materials of different elastic properties, and the relevance of these ideas to the design of tough composite structures is discussed.
Abstract: A novel theory is proposed to show how a crack may he accelerated or retarded when it meets an interface between two equally brittle materials of different elastic properties. Measurements of a model crack travelling through a brittle adhesive joint have substantially verified the theory. The results demonstrate that the toughness of a composite material, having a periodic stiffness change along the crack path, may be very much greater than the toughness of the individual components of the composite. The relevance of these ideas to the design of tough composite structures is discussed.
TL;DR: In this article, the NCO free radical absorption system was investigated with higher resolving power than in the earlier work of Dixon (1960), and a new value for the Renner parameter was determined.
Abstract: The $\tilde{A}$ $^{2}\Sigma ^{+}$-$\tilde{X}$ $^{2}\Pi \_{\text{i}}$(a) absorption system of the NCO free radical has been re-investigated with higher resolving power than in the earlier work of Dixon (1960). Particular emphasis has been directed to the rotational analyses of bands involving the three vibronic levels, $\mu ^{2}\Sigma ^{(+)}$, $^{2}\Delta \_{i}$(a) and k$^{2}\Sigma ^{(-)}$,, associated with the first level of the bending vibration in the ground state. A misassignment in the earlier work has been corrected and a new value for the Renner parameter determined, namely $\epsilon $ = -0.144 $\pm $ 0.001. This revised value removes the discrepancy noted in the earlier electron resonance results.
TL;DR: In this article, the melting of thin films of bismuth, consisting of individual crystallites, has been investigated in the electron microscope, and the dependence of the characteristic time for melting of an aggregate of particles on the temperature and morphology of the particles was studied in detail.
Abstract: The melting of thin films of bismuth, consisting of individual crystallites, has been investigated in the electron microscope. These films showed an unexpected behaviour in the neighbourhood of the melting point: when an aggregate of particles was held at a constant temperature, the number of particles remaining solid gradually decreased with time, although the actual melting process for each individual particle was extremely fast. This reduction in the number of solid particles with time is approximately exponential. The dependence of the characteristic time for the melting of an aggregate of particles on the temperature and morphology of the particles has been studied in detail. In particular, a platelet form had a sufficiently large time delay, even above the bulk melting point, to allow some of the crystallites to be superheated by up to 7 K.
TL;DR: In this paper, the mutual diffusion coefficient of the n -propanol-water and isopropanol-water systems was measured at a pressure of 10 5 Pa by means of a flow technique.
Abstract: Measurements of the mutual diffusion coefficient of the n -propanol-water and isopropanol-water systems have been performed at a pressure of 10 5 Pa by means of a flow technique. The results extend over the complete composition range for the mixtures and over the temperature range 25-65 °C. The reported diffusivities have an estimated uncertainty of + 2.5% Both the systems studied exhibit the minimum in the diffusivity as a function of composition at constant temperature which is characteristic of alcoho-lwater mixtures. In addition, a local maximum in the diffusivity occurs along an isotherm for alcohol-rich mixtures; this type of behaviour has not been observed hitherto. The data are compared with other transport and equilibrium properties for the mixtures, and with a simplified form of the statistical mechanical theory.
TL;DR: In this article, a unified mathematical treatment of thick and thin film elastohydrodynamic lubrication problems is presented, where the construction of approximate solutions is discussed by using Ritz-Galerkin methods with piecewise polynomial basis functions.
Abstract: A unified mathematical treatment of thick and thin film elastohydrodynamic lubrication problems is presented. The construction of approximate solutions is discussed by using Ritz-Galerkin methods with piecewise polynomial basis functions. In particular for the line contact problem, smooth Hermite and cubic spline spaces are used to obtain solutions over a wide load-speed range. Pressure ‘spikes’ are obtained.
TL;DR: The infrared spectrum of the 1:1 complex in the vapour phase between water and hydrogen fluoride has been observed for the first time, and measured over the range 4000-400 cm$^{-1}$ as discussed by the authors.
Abstract: The infrared spectrum of the 1:1 complex in the vapour phase between water and hydrogen fluoride has been observed for the first time, and measured over the range 4000-400 cm$^{-1}$. Three bands of the complex have been observed, one associated with the stretching vibration of HF, one with the bending of the water molecule, and the other with two bending vibrations of the hydrogen bond itself. The first band shows that HF forms the hydrogen bond. Interpretation of its fine structure gives the frequencies of two bending vibrations at 145 and 170 cm$^{-1}$. The structure of the band associated with the two bending vibrations at about 700 cm$^{-1}$ has been tentatively analysed to show that the complex is planar (C$_{2\text{v}}$) and to give a value of the Coriolis constant for the interaction of the two vibrations. The value of this constant shows that either the bending force field has an unusually large interaction force constant or one of the vibrations is anharmonic. With the help of an estimated value of the only remaining unknown vibration frequency of the complex, that of the intermolecular stretching vibration at 180 cm$^{-1}$, the bending vibration frequencies above, and an estimate of the extinction coefficient of the band associated with the HF stretch, the enthalpy of the association of water and hydrogen fluoride is calculated to be - 26 kJ mol$^{-1}$ at just above room temperature. From this a value of the potential energy well depth for the interaction has been found to be - 30 kJ mol$^{-1}$.