Showing papers by "Russian Academy of Sciences published in 1974"

Brittle fracture of solids with arbitrary cracks

Abstract: One of the problems of fracture mechanics is the prediction of the propagation of cracks in solids. The present paper deals mainly with linear fracture mechanics which owes its origin to the works of A. A. Griffith [1, 2] and studies the development of cracks under sufficiently low loads when the behaviour of the material within a region sufficiently remote from the edges of cracks may be regarded as linearly elastic, At present, linear fracture mechanics [3] is restricted mainly to special kinds of loading geometry, with the crack extending rectilinearly (in a plane case) or in its plane (in a three-dimensional case). The main problem here is to establish a relationship between the dimensions of cracks and the loads applied. Within the framework of linear fracture mechanics the fracture itself and other non-linear phenomena that precede it are assumed to take place only within local regions which are small compared to the dimensions of cracks. The possibility that such a situation exists is associated with the fact that when the crack dimensions are sufficiently large the characteristic dimension of the end region is fully determined by a certain intrinsic dimension of the material structure. Therefore, if the material does not exhibit time dependency, the state of the end region at the moment of rupture becomes fully independent of the loads applied and the geometry of the solid, i.e. autonomous. The notion of autonomy [4] leads to the formulation of this theory as one of limit equilibrium. If the conditions of rectilinear extension of the crack (or those of the crack extension in its plane) are disturbed, there arises a problem of determining not only the dimensions of the crack, but also the path of the crack extension under such conditions of loading that a slow, quasi-static crack development is possible. This problem can be actually subdivided into two: (1) Criteria for the determination of the dimensions and paths of the crack extension, and (2) Expressions for the characteristics of the stress-strain state which are constituents of these criteria through the geometry of solid with cracks and the loads applied. As regards (1), there have been many assertions, and the connections between them are not quite clear at present. The first of the suggested criteria, namely that of local symmetry for the plane problem formulated by Barenblatt and Cherepanov [5, 6] and by Erdogan and Sih [7] can be within certain limits substantiated and generalized for the three-dimensional case. The guiding principle here is the treatment of the theory of cracks from the standpoint of the method of inner and outer expansions or that of singular perturbations [8]. The concept of the stress intensity factor which is basic in linear fracture mechanics is decisive in matching inner and outer expansions to find the main term of the asymptotic solution of the complete problem. Actually the construction of the theory of equilibrium cracks [4] implicitly employs this technique for a certain specific model. More explicit indications are given in Ref. 9. In the treatment of the problem of plastic zones in the vicinity of notches, the idea of the boundary layer is employed in Ref. 10. The problem of fracture of a solid is analysed from this standpoint in Ref. 11. As regards (2), progress has been hampered by the lack of efficient techniques for fording the stress-strain state of a solid having non-rectilinear cuts. A number of investigations have been carried out for cuts of a particular kind an arc of a circumference [12, 13], an arc of a parabola [l4], and a three-link broken line which is close to a straight line to such an extent that the boundary conditions are assumed referable to the direction of the middle portion [15, 16]. The problem of a semi-infinite curvilinear cut slightly deviating from a rectilinear one by expanding complex elastic potentials in the magnitude of deviation of the cut from the rectilinear axis tangent to the line of cut at its end is considered in Ref. 17. An exact solution of the problem of a semi-infinite cut having the form of a two-link broken line is given in Ref. 18. The present paper is devoted to the investigation of the development of cracks under arbitrary loading conditions. In Section 1 the criterion of local symmetry is substantiated and generalized for the three-dimensional case. In Section 2 an effective procedure of finding stress intensity factors for the plane case is given, in terms of which the criterion is formulated. Closed first approximation formulas for these magnitudes are presented in the case of a slightly curved crack, numerical calculations showing the applicability of the latter with an error not exceeding 10 to 15 with the angles of deviation of the crack from the straight line coming to 20°. In Section 3 equations of extension of curvilinear cracks are derived on the basis of the first approximation formulas and criterion of local symmetry. In Section 4 some examples are considered.

The Accretion of Matter by a Collapsing Star in the Presence of a Magnetic Field

Abstract: The exact nonstationary solution for the variation of the magnetic field in the Schwarzschild metric with a given spherically symmetric flow is obtained. Initially a homogeneous magnetic field increases with time, changing into a quasi-radial field. On the assumption of equipartition between the magnetic and kinetic energies of a falling gas, in the relativistic case, estimates of the stationary field and the intensity of synchrotron radiation are presented. A considerable part of the radiation is formed in the relativistic regionr≲(2.5 to 7.7)r g (r g is the gravitational radius of a black hole). Estimates are made for radiation from the relativistic region in the case of disc type accretion.

Direct measurement of electric current generation by cytochrome oxidase, H + -ATPase and bacteriorhodopsin.

Abstract: SUMMARY. A method for association of proteoliposomes with planar phospholipid membrane has been elaborated, by which operation of molecular electric generators, such as cytochrome oxidase, H+-ATPase and bacteriorhodopsin, can be followed using ordinary electrometer techniques.

The Tau Method for Inversion of Travel Times-I. Deep Seismic Sounding Data

Abstract: Summary A new method for solving the inverse problem of seismology is described in this paper. The problem is formulated as follows: the travel times of body waves are given at a discrete set of points, and we are required to find in the (V, Y) plane (V being the velocity and Y the depth) the closed area which contains all velocity-depth curves corresponding to the given data. The method is based on the use of the function τ(p) =T(p)–pX(p), p being the ray parameter, T the travel time, and X the epicentral distance. This method has the following advantages: it does not necessarily involve the estimation of p by numerical differentiation of the travel times; and it does not involve any interpolation of the travel-time curve between actual observations. Only two assumptions are made: spherical symmetry of the structure (the absence of horizontal inhomogeneities), and the postulation of a lower limit for the velocity in low velocity zones. The function τ(p) is estimated directly from the observed (Ti, Xi) as a singular solution of the Clairaut equation with free term (T(X)). Application of the method is illustrated using data from deep seismic sounding in Turkmenistan.

Atomic mechanism of fracture of solid polymers

Abstract: Macromolecular chain scission under mechanical stress has been studied by infrared spectroscopy. The dependence of accumulation of chemical bond scissions on temperature T and uniaxial tensile stress σ has been investigated. The rate constant K for bond dissociation under mechanical stress has been found to obey the modified Arrhenius equation: K = K0 exp{ − (EA − ασ)/RA}. The quantitative connection between the rate constant for bond dissociation and mechanical lifetime τ has been established. Analysis of the experimental data indicates that the strength and mechanical lifetime of polymers is determined by the kinetics of mechanochemical scission of the main chains of polymer molecules.

Heat and mass transfer between a rough wall and turbulent fluid flow at high Reynolds and Péclet numbers

Abstract: General dimensional and similarity arguments are applied to derive a heat and mass transfer law for fully turbulent flow along a rough wall. The derivation is quite analogous to Millikan's (1939) derivation of a skin-friction law for smooth-and rough-wall flows and to the derivation of the heat and mass transfer law for smooth-wall flows by Fortier (1968a, b) and Kader & Yaglom (1970, 1972).The equations derived for the heat or mass transfer coefficient (Stanton number) Ch and Nusselt number Nu include the constant term β of the logarithmic equation for the mean temperature or concentration of a diffusing substance. This term is a function of the Prandtl number, the dimensionless height of wall protrusions and of the parameters describing the shapes and spatial distribution of the protrusions. The general form of the function β is roughly estimated by a simplified analysis of the eddy-diffusivity behaviour in the proximity of the wall (in the gaps between the wall protrusions). Approximate values of the numerical coefficients of the equation for β are found from measurements of the mean velocity and temperature (or concentration) above rough walls. The equation agrees satisfactorily with all the available experimental data. It is noted that the results obtained indicate that roughness affects heat and mass transfer in two ways: it produces the additional disturbances augmenting the heat and mass transfer and simultaneously retards the fluid flow in the proximity of the wall. This second effect leads in some cases to deterioration of heat and mass transfer from a rough wall as compared with the case of a smooth wall at the same values of the Reynolds and Prandtl numbers.

Comparison of predicted and experimentally determined secondary structure of adenyl kinase

Abstract: IT is generally accepted that the action of a protein cannot be understood until its three-dimensional structure is known. At present, X-ray analysis of protein crystals is the only method of obtaining such structural information. It is to be feared, however, that many important proteins will never give suitable crystals so that one is obliged to consider other approaches to structure elucidation. Renaturation experiments indicated1–4 that the three-dimensional structure of many if not all proteins is a unique function of their amino acid sequence. Therefore, in principle one should be able to determine these structures by using only the information contained in the sequence. A first step in this direction is the prediction of secondary structures (α helices, β pleated sheets, β bends) in globular proteins from amino acid sequences. Several prediction schemes have been devised to this end5–23. It is the aim of this paper to demonstrate directly the current standing of such methods.

Rheological properties of anisotropic poly(para‐benzamide) solutions

Abstract: A study has been made of the viscous properties of poly(para-benzamide) (PBA) solutions in dimethyl acetamide, which undergo a transition from an isotopic to an anisotropic (liquid-crystal) state at a definite concentration C*. The polymer solutions behave in many respects (as regards the concentration and temperature dependence of viscosity, etc.) like solutions of low molecular weight compounds forming a liquid crystal phase, although the transitions are less pronounced in the polymer solutions owing to their polydispersity. It is shown that the viscometric method, being extremely sensitive to C*, is convenient for determining phase diagrams of anisotropic polymer solutions. The values of C* as related to the molecular weight of PBA have been determined, and a general criterion for transition from isotropic to anisotropic solutions established; the latter has the form (CM)* ≈ 1.3 × 105 at 20°C. This criterion is in line with the condition for the formation of the liquid-crystal structure in a dispersion of rodlike particles as proposed by Flory. Generalized concentration dependences of viscosity have been plotted by reducing concentration to C* and viscosity, to the maximum viscosity at the phase transition point. In investigating the flow properties of PBA solutions we revealed the existence of a yield point in the range of low shear stresses, and an intersection of the flow curves of solutions of different concentration at high shear stresses, which excludes a generalized representation of the flow curves in reduced ordinary-type coordinates.

S-c-S junctions as nonlinear elements of microwave receiving devices

Abstract: 2014 The analysis of possible phenomena in the superconductor-constriction-superconductor (S-c-S) junctions inserted into microwave circuits is carried out. The results of experiments in which properties of the junctions making them different in comparison with usual nonlinear microwave elements were studied are discussed. The characteristics of receiving devices such as amplifiers, detectors and converters operating on the basis of these phenomena are obtained. The limit characteristics of these devices in different regimes of operation are analysed and compared with experimentally achieved characteristics. It is shown that the noise properties of the receiving devices utilizing the S-c-S junctions close to ideal can be obtained for the frequencies lower than characteristic frequency of the junction. This frequency for known realizations of the S-c-S junctions (point contacts and thin film bridges of small dimensions) can reach of order of 500-1 000 GHz or in other words of the middle of the submillimeter waveband range. WIDE BAND DETECTION (II). 1. The introduction. 1.1 THE S-c-S JUNCTION AS AN « IDEAL » SUPERCONDUCTING ELEMENT OF THE RECEIVING DEVICES. The most of receiving devices utilizing Josephson effect realized for this moment are made on the basis of the S-c-S junctions. We define the S-c-S (superconductor-constriction-superconductor) junction [1] as a structure in which weak link of two superconducting electrodes is created in the form of short circuit section of the same superconductor as electrodes with effective dimension A less than coherence length 03BE. The point contacts (see the review [2]) and thin film bridges of small dimensions [3]-[8] are well-known realizations of the S-c-S junctions. It is not difficult to understand why the S-c-S junctions are wide-spread. The main requirements to nonlinear elements of superhighsensitive microwave receiver are the following. (i) The nonlinearity of high magnitude, for instance, maximum modulation coefficient for parametric elements (see, for instance [9]-[11]) or maximum curvature of i-v characteristic for detectors [12]. (ii) Low level of intrinsic noise. (iii) High cutoff frequency above which properties (i) and (ii) become get worse by some reason. The Josephson elements satisfy well the requirement (i). As it will be shown later the magnitude of nonlinearity of these elements is limited by fluctuations only. The intrinsic noise (requirement (ii)) is low for all known superconducting elements not taking into account flicker-effect at low frequencies in the point contacts [13] and granular superconductors [14]. Therefore the main parameter reasonable for comparison of different elements is the cutoff frequency. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/rphysap:019740090107900

Intensities and other spectral parameters of infrared amide bands of polypeptides in the α‐helical form

Abstract: Intensities and other spectral parameters of infrared amide I and II bands of α-helical polypeptides in solutions have been determined for poly(γ-benzylglutamate), poly(γ-ethylglutamate), and polymethionine in chloroform, polylysine, poly(glutamic acid), and fibrillar protein tropomyosin from rabbit muscles in heavy water. The majority of spectral parameters are characteristic. The half-width of the amide I band was found to vary in the range of 15–40 cm−1 for different polypeptides in the different solutions. The correlation between this parameter of the amide I band and the stability of the α-helix was estimated. A new weak band near 1537 cm−1 of unknown origin was observed for the hydrogen form of polypeptides in the α-helical state.

Two-band conduction of amorphous silicon nitride

Abstract: A method is proposed for determining the electron and hole components of stationary current flowing through an MIS structure and the hole and electron components of the stationary current in an MNOS structure have been determined. It is shown that the experimental results may be explained by a two-band Si3N4 conduction model. A two-band Si3N4 impurity conduction model with silicon microcrystals is examined, the latter serving as Poole-Frenkel centres in the nitride volume as well as trapping and recombination centres in the regions close to the electrodes. [Russian Text Ignored].

On the interaction of surface electrons in liquid helium with oscillations of the vapor-liquid interface

Abstract: This paper presents a detailed analysis of the interaction between surface electrons and thermal oscillations (ripplons) of the liquid helium surface. The results obtained enable us to check the validity of the many different approximate descriptions of the electron-ripplon interaction that have been given. The influence of the interaction upon the kinetics of surface electrons also has been studied, with a view to establishing the possibility of obtaining information on the capillary wave spectrum.

Kinetics of polymer crystallization from the melt (calorimetric approach)

Abstract: Crystallization kinetics for 12 polymers including polyolefins, polyesters, polyurethanes, polysiloxanes was measured by the evolution of heat in a modified Calvet-type calorimeter over wide temperature ranges. The results are analyzed in terms of the Avrami equation and a comparison between calorimetric and dilatometric results is carried out. It is concluded that, although in the majority of cases experimental results do not obey the Avrami equation, for some polymers the agreement is rather good. The Avrami parameter obtained, however, depends on the experimental technique. Possible reasons for this disagreement are discussed. Analysis of the calorimetric crystallization rate in the vicinity of the melting point by using the kinetic theory of crystallization shows that the growth is controlled by surface (two-dimentional) nucleation. Energy parameters for the crystallites were determined and it is shown that the surface energy of the crystallites depends on the molecular structure of the polymer. Temperature dependence of the calorimetric crystallization rate of the polymers for which crystallization rates could be determined above and below the maximum rate are analyzed using a kinetic equation with common approximations for the transport term. The influence of melting conditions on the crystallization rate was studied. The results indicate heterogeneous nucleation in the polymer melt. It is concluded that this may be due both to impurities and to high regularity of macromolecules in the polymer melt.

Algebraic curves over functional fields with a finite field of constants

Abstract: We prove a theorem of finiteness for curves of genus g>1, defined over a functional field of finite characteristic and having fixed invariants. As an application we obtain Tate's conjecture concerning homomorphisms of elliptic curves over a field of functions.

Pulsation regime of the thermonuclear explosion of a star's dense carbon core

Abstract: The hydrodynamical problem of nuclear explosion of a dense carbon core of a star with mass 1.40M ⊙ is solved numerically. In calculation the kinetics of carbon burning at the nuclear reaction C12+C12→M24+γ rate is included. Thus the inverse effect of hydrodynamical motion on the process of thermonuclear burning is taken into account, as compared with Bruenn's (1972) calculations. The calculations show that a pulsation regime of burning is realized (actually three pulses were obtained) which evolves to the detonation regime with full combustion and disruption of the star only at the third pulse. The effects of disintegration of iron group nuclei, neutronization of matter and neutrino losses in URCA processes have not yet been considered in calculations. The influence of initial conditions (mainly the temperature distributions) and the above mentioned effects, which have not been included in calculation, on the results of the hydrodynamical problem solution are discussed. The conclusion is made on new possibilities of formation of a gravitationally bound remnant of the explosion and a neutron star.