单摆系统的振动研究

通过求解变张力弦振动微分方程的边值问题,给出摆线与摆球的质量比为任意值时单摆系统运动的一般解和本征频率满足的方程.利用该方程求得高精度的单摆系统周期数值解,特别是拟合出单摆系统作基频振动时一个范围大、精度高的周期近似公式.同时将理论与实验进行比较,结果二者相符.     

Studies of a primitive model of mixtures of nonpolar molecules with water

The paper presents calculations of the properties of binary mixtures of hard spheres and directionally associating hard spheres, a simple model for mixtures of nonpolar molecules with water that was developed by Nezbeda and his coworkers. Extensive results from Monte Carlo simulations in the isobaric, isothermal ensemble are presented for the density, configurational energy and chemical potentials in the mixtures for fluid states over a range of temperatures, pressures and compositions. A species exchange technique is used to compute the chemical potential difference between components in the mixtures. The results obtained are compared with the predictions of first-order thermodynamic perturbation theory (TPT). It is found that this theory provides an accurate picture of the system over most of the conditions considered. Calculations are also made of vapour–liquid coexistence for the model using TPT and calculations of solid–fluid coexistence for the model using TPT and existing results for the free energy of the pure component solids. It is found that the vapour–liquid coexistence for the model is pre-empted by the solid–fluid coexistence, as had previously been found for the pure component directionally associating hard sphere system.     

On the magnetostatics of chains of magnetic nanoparticles

A novel approach is presented for the computation of the magnetostatic energy of straight and bent chains of identical, uniformly magnetized particles of arbitrary shape. The formalism relies on the concept of the magnetometric tensor field, and allows for closed form expressions for the magnetostatic energy, demagnetization factor, Young's modulus, and bending modulus of chains in terms of the shape amplitude of the particles. Analytical solutions are presented for straight chains of spheres, cubes, and cylinders, and for bent chains of spheres. Numerical results include chains of octahedra, tetrahedra, cuboctahedra, and bi-cones. The axial demagnetization factor for the bi-cone shape is derived in analytical form. An approximate energy expression, using the full shape-dependent interaction formalism for short separation distances, and the standard dipolar interaction expression for larger distances, is introduced.     

The concept of the use of recycled uranium for increasing the degree of security of export deliveries of fuel for light-water reactors

The present paper deals with investigation of the possibilities for reducing the risk of proliferation of fissionable materials by means of increasing the degree of protection of fresh fuel intended for light-water reactors against unsanctioned use in the case of withdrawal of a recipient country of deliveries from IAEA safeguards. It is shown that the use of recycled uranium for manufacturing export nuclear fuel makes transfer of nuclear material removed from the fuel assemblies for weapons purposes difficult because of the presence of isotope ²³²U, whose content increases when one attempts to enrich uranium extracted from fresh fuel. In combination with restricted access to technologies for isotope separation by means of establishing international centers for uranium enrichment, this technical measure can significantly reduce the risk of proliferation associated with export deliveries of fuel made of low-enriched uranium. The assessment of a maximum level of contamination of nuclear material being transferred by isotope ²³²U for the given isotope composition of the initial fuel is obtained. The concept of further investigations of the degree of security of export deliveries of fuel assemblies with recycled uranium intended for light-water reactors is suggested.     

Calculation of displacement function of crystal atoms in the presence of temperature gradient

The thermal conductivity equation is solved with allowance for experimental conditions. An expression for the displacement function is derived. A method for calculating the displacement functions for different axes of symmetry of a crystal is proposed.     

Stages of transformation of block elements

The property to have various representations is investigated for the block elements describing the solutions of boundary-value problems for sets of partial differential equations in the regions with a boundary. These representations have various destinations. One of the representations, which is called packed, is convenient for constructing solutions in block structures on the basis of solutions in separate blocks. Another representation, which is called unpacked, is convenient for a detailed investigation of the properties of solutions in an individual block of the block structure.     

Kinematic theory of diffraction by matter of any kind and the theory of liquids

An expression for the intensity function scattered coherently by an arbitrarily distorted lattice has been derived which degenerates under well-defined conditions to the well-known formulae valid for crystals, liquids and gases or amorphous substances. A new method for the analysis of the radial distribution function (RDF) of simple liquids has been suggested. RDF curves for liquid argon near the triple point have been analysed to obtain the distance statistics of neighbours and their coordination numbers. Using the first-neighbour statistics an expression for the partition function for matter of any kind and, in particular, for simple liquids has been deduced.     

Thickness dependence of temperature coefficient of resistance of MnBi films

In-situ measurements of the temperature coefficient of resistance of electron-beam evaporated MnBi films are reported for the thickness range 30–180 nm. The thickness dependence of the temperature coefficient of resistance curves are plotted for different weight ratios, annealing times and substrate temperatures. The temperature coefficient of resistance shows marked size effect, and is negative for lower thicknesses (<100nm) and positive for higher thicknesses. The experimental data is in good agreement with the Mayadas-Shatzkes theory. The thickness dependence of the Curie temperature also indicates marked size effect.     

Resonance conditions of acceleration of clusters of plasma between parallel conductors

Data for the maximum attainable velocity of a cluster were found from magnetohydrodynamic equations and from relations for the electric circuit of conductors and sources for the acceleration of clusters of plasma between parallel conductors with an external magnetic field. These equations give the relationship between the parameters of the external circuit, the mass of the accelerated cluster and the magnetic induction of the external magnetic field, and simultaneously the length of the conductors which is necessary for attaining maximum velocity. The conditions obtained were called resonance conditions.     

Behaviour of the equation of state of some liquid n-alkanes at high pressures

The equation of state of several liquid n-alkanes is analyzed along a series of isotherms in the liquid region. It is found that, for a substantial range of pressures for each isotherm, the experimental data are well reproduced by an equation of state, which was initially proposed for the high density hard-spheres system and later proved to be valid for several simple and molecular liquids, if we determined an effective excluded volume for each isotherm and provided that, in molecular liquids, we treat rotational degrees of freedom as equivalent translational ones.     

Permittivity of plasma and nonstationary theory of nonlocal transport

A regular procedure is proposed for finding the solution to a linearized kinetic equation for charged particles with the Landau collision integral in a plasma with large Z. The expression for longitudinal permittivity of a collisional plasma, which is obtained using this procedure for the entire range of frequencies and wavenumbers, as well as the collision parameter, is transformed to the known expressions in the corresponding asymptotic limits. The nonlocal transport equations for small perturbations are also formulated for arbitrary relations between the characteristic space and time scales of the plasma; these relations considerably extend the limits of applicability for previously developed theories.     

The equation of state of solids

An equation of state for solids, in reduced variables, is obtained within the context of a system-independent formulation of the thermodynamics of high pressures. This formulation is valid for materials obeying a linear relationship between shock and particle velocities. An adequate set of scaling factors for pressure, compression, specific energy, and temperature, is first introduced. A modified Mie-Grüneisen equation, as well as many other thermodynamic relationships and coefficients, are then expressed in terms of reduced variables. Explicit expressions for the temperature along the Hugoniot, and for the equation of state, are obtained. It is also shown that when given in their reduced form, each of the two thermodynamic coefficients appearing in the equation of state can be considered as having the same constant value for many different materials. The possibility and convenience of using a “standard material” is discussed. Numerical results obtained using this reduced variables formalism are in good agreement with those computed or measured, by different authors, for various materials over a wide range of pressures. This is a good indication of the “universality” of the reduced equations obtained, and of the usefulness of the formalism.     

The effect of carbon monoxide on the work function of evaporated films of titanium and erbium

Small doses of CO reduced φ by ~50 mV for Er films but did not reduce it for Ti films. The sign and magnitude of this reduction of φ can be accounted for by a simple geometrical model. Larger doses increased φ for both metals. Each increase of φ for Er before saturation was followed by a slow decrease, but this effect was seen only occasionally with Ti. The difference between φ for the clean film and φ for the saturated film was 0.49 ± 0.05 eV for CO/Ti and 0.71 ± 0.11 eV for CO/Er. The bulk structure of both films was found to be randomly oriented hcp. The surface cleanliness of the Ti films was checked by their Auger spectrum; this spectrum changed slowly owing to beam effects and to the reaction of Ti with residual gases. The results are compatible with the dissociative adsorption of CO, provided that there is some reconstruction of the surface.     

Modeling and Calculation of the Dynamics of Spectra with Allowance for Isomerization of Complex Molecules

A semiempirical parametric method for modeling of dynamic (time-resolved) electron-vibrational spectra of complex molecules with allowance for isomer-isomer transformations is proposed. It is based on the method developed earlier for construction of three-dimensional spectra of complex molecules without regard for isomer-isomer transformations. All the matrix elements necessary for calculation of spectra can be determined by the methods developed earlier. The time dependence of the population of a large number of vibronic levels has been determined using the iteration numerical method of integrating kinetic equations. Handy computational algorithms and a specialized software for a personal computer have been developed. The computer experiments conducted have shown that the method proposed can be used for modeling of dynamic spectra of complex molecules with allowance for their isomer-isomer transformations in the real-time scale.     

Estimation of the optical properties of seawater from measurements of exit radiance

An inverse analysis for simultaneous estimation of the radiation phase function, single scattering albedo and optical thickness in natural waters, from the knowledge of the exit radiance measurements, is presented. A forward and an inverse model are utilized in our analysis. The forward model uses an analytical discrete-ordinates method for solving the radiative transfer equation and the inverse model contains an algorithm for least-squares estimation that is iteratively solved for retrieving the desired optical properties. The experimental data are simulated with synthetic data corrupted with noise. The results show that the optical properties, with the exception of the optical thickness, can be recovered with high accuracy, even for data with up to 10% noise.     

Theory of infra-red and optical spectra of antiferromagnets

The contributions of magnons to the optical properties of antiferromagnets having the rutile structure are discussed. The properties considered are electric-dipole active two-magnon absorption in the infra-red, and magnon sidebands on sharp-line exciton transitions in the visible. The discussion is based on a thorough treatment of the properties of excitons and magnons in the antiferromagnetically ordered state. The site-group and space-group symmetries of the magnetic excitations are derived and the selection rules for electric and magnetic dipole transitions are determined. The occurrence of magnetic Davydov splittings of the excitons is investigated, and their symmetry properties throughout the Brillouin zone are derived. The functional dependences of exciton energy on wave vector are calculated. Applications of the theory are made to experimental results on excitons and magnons in MnF₂, FeF₂ and CoF₂.

The possible mechanisms for two-magnon and magnon-sideband absorption are discussed, and the influence of crystal symmetry on these mechanisms is described. The two-magnon state responsible for electric-dipole absorption is identified and selection rules for electric-dipole activity are presented. A spin Hamiltonian for the two-magnon process is set up and used to derive expressions for absorption coefficients for electric vector parallel and perpendicular to the crystal c-axis. Comparison with experiment for MnF₂ yields numerical values for the parameters of the basic coupling mechanism. The exciton-magnon states which give rise to magnon-sideband absorption are explicitly constructed and electric-dipole selection rules are derived for all possible types of sideband. Spin Hamiltonians for the various magnonsideband absorption processes are presented and used to derive expressions for sideband shapes. The results are applied to the experimental spectra for MnF₂ and FeF₂ and the sideband shapes in MnF₂ are calculated numerically. The sideband shapes observable in emission spectra are also briefly discussed.     

Determination of the sign of the order parameter from MAS spectra of oriented molecules

The use of the intensities of the spinning sidebands in the magic-angle spinning spectra of oriented molecules is proposed for the determination of the signs of the order parameters. The method is demonstrated for benzene and chloroform oriented in nematic phases of liquid crystals. On the basis of the theoretical expressions derived for the various order sidebands, the applicability of the method for different experimental conditions is discussed.     

Influence of rate of change of frequency on the overall pitch of frequency-modulated tones

The mechanism(s) determining pitch may assign less weight to portions of a sound where the frequency is changing rapidly. The present experiments explored the possible effect of this on the overall pitch of frequency-modulated sounds. Pitch matches were obtained between an adjustable unmodulated sinusoid and a sinusoidal carrier that was frequency modulated using a highly asymmetric function with the form of a repeating U or inverted U shaped function. The amplitude was constant during the 400-ms presentation time of each stimulus, except for 10-ms raised-cosine onset and offset ramps. In experiment 1, the carrier level was 50 dB SPL and the geometric mean of the instantaneous frequency of the modulated carrier, fc, was either 0.5, 1, 2, or 8 kHz. The modulation rate (fm) was 5, 10, or 20 Hz. The overall depth (maximum to minimum) of the FM was 8% of fc. For all carrier frequencies, the matched frequency was shifted away from the mean carrier frequency, downwards for the U shaped function stimuli and upwards for the repeated inverted U shaped function stimuli. The shift was typically slightly greater than 1% of fc, and did not vary markedly with fc. The effect of fm was small, but there was a trend for the shifts to decrease with increasing fm for fc = 0.5 kHz and to increase with increasing fm for fc = 2 kHz. In experiment 2, the carrier level was reduced to 20 dB SL and matches were obtained only for fc = 2 kHz. Shifts in matched frequency of about 1% were still observed, but the trend for the shifts to increase with increasing fm no longer occurred. In experiment 3, matches were obtained for a 4-kHz carrier at 50 dB SPL. Shifts of about 1% again occurred, which did not vary markedly with fm. The shifts in matched frequency observed in all three experiments are not predicted by models based on the amplitude- or intensity-weighted average of instantaneous frequency (EWAIF or IWAIF). The shifts (and the pitch shifts observed earlier for two-tone complexes and for stimuli with simultaneous AM and FM) are consistent with a model based on the assumption that the overall pitch of a frequency-modulated sound is determined from a weighted average of period estimates, with the weight attached to a given estimate being inversely related to the short-term rate of change of period and directly related to a compressive function of the amplitude.