Small Moment Of Inertia Research Articles

The solid molecular hydrogens in the condensed phase: Fundamentals and static properties

The molecular hydrogens (${\mathrm{H}}_{2}$, ${\mathrm{D}}_{2}$, HD, etc.) form the simplest of all molecular solids. The combination of the light mass, small moment of inertia, weak interactions, and the quasi-metastable ortho-para species result in a fascinating low-temperature behavior that can be understood to a large extent from considerations of first principles. After discussing single molecule properties and intermolecular interactions we discuss in detail the ortho-para properties, conversion and diffusion. This is followed by a description of the crystal structures and the orientational ordering phenomena. The thermodynamic properties are reviewed. The article is concluded with a discussion of the translational ground state of the solid and the effect of the large zero-point motion on the solid state properties. A large number of data are collected in tables and graphs to provide a reference source.

Application of rare earth magnets to coaxial synchronous couplings

The use of rare earth magnets in coaxial couplings allows for some typical advantages. Some of these are: reduction of the total construction volume, higher operating temperature, larger air gap if necessary, no danger of demagnetization and smaller moment of inertia. A calculation approach and optimixation principles are discussed.

ANALYSIS AND CHARACTERISTICS OF THE DISK-ROTOR INDUCTION MOTOR

ABSTRACT The induction motor with an axial air gap and a flat homogeneous disk-rotor shows some performance characteristics that are superior to conventional induction machines. Large rotational speeds and small moments of inertia promise high power densities and small mechanical time constants. This paper presents an analytical model which includes the two-dimensional current distribution in the secondary, thus extending a previous simplified treatment. The model also accounts for fringing phenomena and can handle a secondary with a radius-dependent thickness and conductivity. Numerical results for the local distributions of field, current density, and forces; a typical torque-speed characteristic; a current locus; and an equivalent circuit are presented and serve as a basis for discussion and comparison.

Note on the ill-conditioned eigenvalue problem in elastic vibrations

Two cases which could cause ill-conditioning of the lower modes and frequencies of an undamped elastic structure are discussed. The first case is when rigid body motions are connected to a relatively small moment of inertia. The second case is when the stiffness matrix is ill-conditioned with respect to the solution of linear equations. It is shown that the first kind of ill-conditioning is not serious provided that an appropriate method of computation is used. The second kind, which is more common and more serious, is dealt with in more detail. It is shown how the results may be improved in various ways by applying the Natural Factor approach of Argyris and Brönlund and computing singular values and vectors.

Analytic interpolation of the eigenvalues of an asymmetric rotator

The behavior of the eigenvalues of the asymmetric rotator as functions of a continuous variable z = l( l+1) is considered. The eigenvalue problem for the Hamiltonian matrix in a basis of eigenstates of I 2 and I 3, where I 3 is parallel to one of the principal moments of inertia, is studied by transforming it to a Sturm-Liouville problem. It is found that a proper eigenvalue problem is obtained only if I 3 is parallel to the largest or smallest moment of inertia. It is shown in this case that an eigenvalue λ is an analytic function for z in the neighborhood of the real axis, but may have branch points off the real axis, and that λ is real for z real. The behavior of the eigenvalues as the intermediate moment of inertia approaches one of the others is considered in some detail.

Vibrational relaxation of carbon monosulphide

The relaxation of vibrationally excited CS, formed in the flash-initiated reaction: O(3P)+CS2→ SO + CS, has been studied by monitoring the absorption of the A1Π—X1Σ+(2,1) band photoelectrically. Rates of decay were measured in the presence of various added gases, and hence rate constants determined for the de-excitation of CS(ν= 1) by ortho-H2, para-H2, HD, 3He, D2, 4He, N2O, CO2, H2O, D2O, H2S and D2S. The much greater efficiency of N2O compared to CO2 shows clearly how the probability of vibration-vibration energy exchange is enhanced if both species are infra-red active. Vibration-rotation energy transfer may occur with the collision partners which have small moments of inertia. Where appropriate, experimental transition probabilities are compared to those predicted by Sharma's recently published theory.

Electron Capture by Rotational Excitation of Polar Molecules

The problem of electron capture by a polar molecule with simultaneous rotational excitation of the molecule is analyzed. Capture cross sections and lifetimes of temporary negative-ion states so formed are calculated on the assumption that the electron interacts primarily at large distances from the molecule by means of the dipole field and forms only loosely bound ionic states. The capture probability is proportional to the ratio ${(\frac{D}{I})}^{2}$, where $D$ is the dipole moment and $I$ the moment of inertia of the molecule about a perpendicular axis passing through the center of the dipole. Electron capture by rotational excitation is most probable for polar molecules that have both a relatively large dipole moment and a small moment of inertia. In order for this process to make effective contributions to momentum-transfer cross sections measured, e. g., in electron-swarm experiments, the spacing of the rotational levels of the molecule must be of the order of thermal energies, so that a relatively large number of electrons can be captured and released. These circumstances, viz., the relatively large value of $\frac{D}{I}$ and the right spacing of rotational levels, appear to offer an explanation of the particular behavior of ${\mathrm{H}}_{2}$O, ${\mathrm{D}}_{2}$O, and ${\mathrm{H}}_{2}$S among a number of polar molecules with which recent swarm experiments have been made. According to the theory, some other molecules (e. g., N${\mathrm{H}}_{3}$, HF, HCl, and ${\mathrm{H}}_{2}$${\mathrm{O}}_{2}$) should exhibit a similar behavior. Lifetimes of negative ions formed by this process are estimated to be of the order of ${10}^{\ensuremath{-}13}$ sec.

Computed band envelopes for electronic and vibrational spectra of large symmetric top molecules

Band envelopes have been computed for six types of large symmetric top molecule (three prolate and three oblate) similar in size to the benzene molecule. The changes in the rotational constants from the lower state to the upper state have been chosen to include those typical of both vibrational and electronic spectra. Although the correspondence between computed and observed envelopes is exact only for symmetric top molecules, it is anticipated that the computed envelopes can be usefully applied to the spectra of near-symmetric tops. This is due largely to the fact that near-symmetric top molecules with large moments of inertia show symmetric top characteristics to a greater extent than molecules with small moments of inertia and the same degree of asymmetry.

慣性能率を極度に小さくした風向計とその応用

慣性能率を極度に小さくした風向計とその応用

Vibration—Rotation Energy Transfer

A simple two-parameter model for vibration→rotation energy transfer fits the vibrational relaxation data for 25 different molecules with small moments of inertia. Thirty-five data are fit within a factor of 3. The model is limited to molecules in which the rotational velocities of the atoms are greater than the translational velocity of the molecule and in which the rotational level spacings are small compared to kT. The successful correlation of nearly all of the data available on these molecules leads to the conclusion that vibration→rotation energy transfer is a real and important effect. The theory provides an explanation of vibrational relaxation in a number of mixtures.

Studies on the Stiffness of Culms in Barley Plants (Hordeum sativum, JESSEN) : 10. Bending rigidity of culms.

A brittle culm variety, Sekitorisai-No. 1, and a stiff culm variety, Haganemugi (Hordeum sativum, JESSEN) were used to study the relation between YOUNG's modulus (E) and bending rigidity (EI) in internodes and nodes. YOUNG's modulus measured by OLSEN's type stiffness tester, and bending rigidity calculated from YOUNG's modulus and moment of inertia. There was not so great differences of YOUNG's modulus between both varieties, but YOUNG's modulus in Sekitorisai-No. 1 was slightly larger than of Haganemugi. Regarding the position of internodes and nodes, it was recognized that the uppermost position of internode and node had the largest YOUNG's modulus, medium in the base position, and the smallest in the intermediate position. The bending rigidity of Haganemugi is larger than that of Sekitorisai- No. 1, and it is larger in the base position, and on the other hand small in the upper position. The stiffness of culm has relation to the diameter of buckling load, and buckling load is related to the bending rigidity as long as the culm length is constant. In theoretically, YOUNG's modulus and moment of inertia have the same relation to the bending rigidity. In the case of same bending rigidity with the different mome nt of inertia, YOUNG's modulus are larger in culms with smaller moment of inertia, and vice versa. So the increase of YOUNG's modulus is valuable for concering the stiffness of culms with the small moment of inertia. Moment of inertia was determined by the outer diameter and the inner one. A large moment of inertia was regarded in culms with large outer diameter or the with small inner diameter. In the case of the same moment of inertia with different outer and inner diameter, the cross section area of culm tissue was small in culms with large outer and inner diameter than with small outer and inner diameter.

Isotope effects in phase equilibria; a new tool for the study of intermolecular forces

The renascence of interest in isotope effects in phase equilibria during the past decade has provided a new body of experimental data pertaining to intermolecular forces. Concurrent advances in the quantum theory of the liquid and solid states have led to the formulation of the mass dependence of the quantum partition function and its temperature dependence. The theory shows that in the first approximation the isotope effects in phase equilibria are determined by the mean value of the second derivative of the intermolecular potential. For monatomic systems a new set of molecular parameters have been derived for neon, krypton, and xenon based on the WHALLEY-SCHNEIDER parameters for argon. For the condensed rare gases, it has been shown that independent particle models, e.g. anharmonic Einstein model of the crystal and quantum cell models in the liquid, cannot account for the observed isotope effects. The isotope effect on melting is discussed in terms of the structure of the solid and the nearest neighbor numbers of the liquid.For polyatomic molecules, a wealth of new information and a number of new phenomena associated with intermolecular forces have been discovered. It is found that in the first approximation the intermolecular potential appears as the sum of atomic interactions. A development of this method leads to a direct and quantitative explanation of a number of hitherto incomprehensible phenomena. Isotopic substitution provides a direct demonstration of hindered rotation in the liquid. Two new types of quantum effects associated with molecular rotation have been found. The first type is a coupling of the molecular rotation with the molecular translation in the field of the intermolecular force. The effect persists even for free rotation and is most pronounced for molecules with small moments of inertia. The effect has been quantitatively investigated through the phase equilibrium behaviour of the isotopic and rotational forms of hydrogen. The second effect is a coupling of the molecular rotation with the molecular vibration in the field associated with the hindered rotation. A quantitative investigation of this rotation-vibration interaction has been made by the study of the vapor pressures of the deuteroethylenes. Studies of isotopic phase equilibria together with molecular spectroscopy of the condensed state provide information concerning the perturbation of the intramolecular vibrations by the intermolecular forces.

Molecular Geometry and the Vapor Pressure of Isotopic Molecules. The Equivalent Isomers cis-, gem-, and trans-Dideuteroethylenes

The vapor pressures of trans-, cis-, and gem-dideuteroethylenes have been intercompared directly by mercury manometry over the temperature range 120°—180°K. The trans isomer has been compared with ordinary ethylene over the same temperature range. The vapor pressures of cis- and gem-dideuteroethylene are equal to within a few hundredths of a percent. The trans compound has a greater vapor pressure than either the cis or gem compounds (about 0.1% at 130°K and 0.05% at 180°K). At these same temperatures the trans-dideuteroethylene has a vapor pressure 1.2% and 1.6%, respectively, greater than ordinary ethylene. The difference between the dideuteroethylenes is correlated with differences in molecular geometry. It is shown that the trans is the most volatile of the dideutero isomers, because it has the smallest moment of inertia about the C=C axis. The vapor pressure data are then direct evidence for hindered rotation in the liquid.

The near ultraviolet spectra of HCOF and DCOF

The absorption spectra of HCOF and DCOF were studied between 2000 A and 2700 A. The maximum of intensity (2100 A, ϵ ∼50 1/cm-mole) is so far removed from the origin of the absorption (2680 A, ϵ ∼0.01 1/cm-mole) that a large difference of configuration of the molecule is indicated for the two electronic states involved. The vibrational and rotational analyses of the spectra show the nature of the difference. Three vibrational frequencies of the excited state are established: for HCOF, ν 2 = 1111, ν 5 = 451, ν 6 = 190; for DCOF, ν 2 = 1098, ν 5 = 450, ν 6 = 120 cm −1. The prominence of these frequencies in the spectra indicates an excited state geometrical structure whose major differences from that of the lower state are: a longer CO bond distance, a smaller FCO bond angle, and appreciable deviation from planarity. No evidence of inversion of the pyramidal structure was found. Analysis of partially resolved rotational fine structure showed that the smallest moment of inertia was increased about 30% by the transition while the average of the large moments was virtually unchanged. These changes show that the CO distance is increased about 0.18 A while the FCO angle is decreased roughly 13°, and they are compatible with a nonplanar structure for the molecule in its excited state. The electronic transition may be designated A-A′. No diffuseness (predissociation) of fine structure has been established.

Thermodynamic Properties of Internal Rotators with Small Moments of Inertia

Thermodynamic Properties of Internal Rotators with Small Moments of Inertia

Energy Levels and Thermodynamic Functions for Molecules with Internal Rotation. IV. Extended Tables for Molecules with Small Moments of Inertia

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTEnergy Levels and Thermodynamic Functions for Molecules with Internal Rotation. IV. Extended Tables for Molecules with Small Moments of InertiaJames C. M. Li and Kenneth S. PitzerCite this: J. Phys. Chem. 1956, 60, 4, 466–474Publication Date (Print):April 1, 1956Publication History Published online1 May 2002Published inissue 1 April 1956https://doi.org/10.1021/j150538a020RIGHTS & PERMISSIONSArticle Views205Altmetric-Citations39LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (829 KB) Get e-Alerts

ON THE DAMPING OF THE FREE NUTATION OF THE EARTH

The free (420d) nutation is known to be heavily damped, the characteristic damping time being less than ten periods. The origin of this damping is unknown, but must be due to dissipative, non-rigid-body movements of the Earth. The view, which has been widely held, that this may arise from the relative motion between the liquid core of the Earth and the mantle is shown to be based on an error. When account is taken of its small moment of inertia, the core cannot be held responsible for this damping, nor can a limit be derived for its viscosity. This confines the origin of the damping to a non-elastic behaviour of the mantle.

On the Damping of Free Nutation of the Earth

The free (420d) nutation is known to be heavily damped, the characteristic damping time being less than ten periods. The origin of this damping is unknown, but must be due to dissipative, non-rigid-body movements of the Earth. The view, which has been widely held, that this may arise from the relative motion between the liquid core of the Earth and the mantle is shown to be based on an error. When account is taken of its small moment of inertia, the core cannot be held responsible for this damping, nor can a limit be derived for its viscosity. This confines the origin of the damping to a non-elastic behaviour of the mantle.

OPTICS OF RECORDING OSCILLOGRAPHS

This note reviews the results of A. C. Hardy and applies them to the design of lens and mirror systems of recording oscillographs, such as those used in seismic prospecting. Requirements are given for maximum intensity of illumination in the recording paper consistent with small moment of inertia of the moving mirror.

A Method for Determining the Ultimate Strength of a Column Swaged at Ends

Let ABC, Fig. 2, be a pin ended strut of length La deflected under its Euler load . Let DBE be a pin ended strut with a smaller moment of inertia, a shorter length Lb, but with the same ultimate column strength, deflected under its Euler load . It is assumed that the ends of the two struts lie on the straight line which is the line of action of the force P and that they are so deflected by this force that their elastic axes are tangent at B. On page 564, Vol. II , of Strength of Materials by Timoshenko, it is shown that at any point the deflection of a strut fixed at one end and with a sufficiently large axial load applied at the other end is given by the equation y=5(l —cos Kx). The origin for and x is at the fixed end and 6 is the maximum deflection which occurs a t the free end. For convenience the deflection at any point may be measured from the line of action of the force which passes through the free end and is parallel to the x axis: d — y = 5cosKx. It is evident that the fixed ended strut may be considered to be half of a symmetrical pin ended strut and that the value, d cos Kx, yields the ordinates to the elastic curve of a pin ended strut when the origin is at the intersection of a line drawn through the ends and the plane of symmetry. If the origin is a t the end of the strut, the value of the ordinate to the elastic curve at any point measured from the line of action of the force P through the ends becomes 5 sin Kx. AtB, Fig. 2, we have the deflection equal to