Showing papers by "Moscow State University 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.

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.

Hydrogen bonding in adsorption on silica

Abstract: A spectral and calorimetric investigation was carried out into hydrogen bonding between the surface hydroxyl groups of silica and molecules of n -hexane, cyclohexane, carbon tetrachloride, benzene, nitromethane, acetonitrile, acetone, diethyl ether, dioxane, tetrahydrofuran, pyridine, and triethylamine. The integral intensity of the absorption band due to the stretching vibration of free hydroxyl groups on the surface of aerosil and the integral intensities of the absorption bands of these hydroxyl groups perturbed by adsorbed molecules were determined. From the difference in the heats of adsorption on hydroxylated and strongly dehydroxylated surfaces of a pure macroporous silica the heats of formation of the hydrogen bond between adsorbed molecules and free surface hydroxyl groups were evaluated. They were compared with the change in the integral intensity of the stretching vibration band of the hydroxyl groups resulting from adsorption and with their frequency shifts. The relation between the spectral and energetic characteristics of the hydrogen bond resulting from adsorption is approximately the same as that which occurs when the hydrogen bond is formed in solution.

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

Gravitational-wave bursts from the nuclei of distant galaxies and quasars: Proposal for detection using Doppler tracking of interplanetary spacecraft

Abstract: Supermassive black holes which exist in the nuclei of many quasars and galaxies are examined along with the collapse which forms these holes and subsequent collisions between them which produce strong, broad-band bursts of gravitational waves. Such bursts might arrive at earth as often as 50 times per year--or as rarely as once each 300 years. The detection of such bursts with dual-frequency Doppler tracking of interplanetary spacecraft is considered.

A boundary uniqueness theorem for holomorphic functions of several complex variables

Abstract: If D ⊂ Cn is a region with a smooth boundary and M ⊂ ∂D is a smooth manifold such that for some point p ∈ M the complex linear hull of the tangent plane Tp(M) coincides with Cn, then for each functionf e A(D) the conditionf¦M=0 implies thatf=0 in D.

Local Structure of Mature Dust Storms

Abstract: An attempt is made to describe the local structure of a dust storm during its mature stage, when the storm can be considered as steady. Vertical profiles of wind, dust concentration and temperature are obtained by using boundary layer equations for a fluid carrying heavy particles and taking into account the thermal stratification. The nondimensional parameters which determine the structure of the flow are the Richardson and the Kolmogorov flux numbers, the latter describing the part of turbulent energy spent on suspension of the dust particles. The work done by the flow for suspension is always positive, which results in a decrease of the turbulent energy and an increase in the stability of the flow. As a result, other conditions being equal, the flow is accelerated. Observational data are presented which confirm this effect. A self-similar singular solution describes the saturated flow which carries the largest possible amount of dust. Other solutions approach this limiting one with increasing ...

Enzymic generators of membrane potential in mitochondria.

Abstract: If one assumes the energy transduction between and ATP to be reversible, one can conclude that the coupling membrane has two types of membrane potential generators: oxidative and dephosphorylative. If this is the case, an attempt may be made to separate these two enzymatic systems and reconstitute membraneous vesicles inlaid with purified oxidative, or alternatively dephosphorylative enzymes competent in the formation of membrane potential. Such an attempt was made in this group. To study the problem in question, we used the method of Racker and colleagues 2-( for the resolution and reconstitution of mitochondrial oxidative phosphorylation, and the method of Liberman and colleagues L O to measure the membrane potential. The latter consists of using artificial phospholipid membrane as a selective electrode for phenyldicarbaundecaborane anion (PCB-) and other synthetic anionic penetrants. As was found earlier, the formation of membrane potential (with the positive charge inside the vesicles) results in an uptake of PCBby the vesicles.‘), Two enzymatic systems isolated from beef heart mitochondria were studied: cytochrome oxidase, purified by the method of Yonetani,8 and oligomycinsensitive ATPase, obtained by the method of Kagawa and Racker.2 Cholate solutions of mitochondrial phospholipids and corresponding enzyme proteins were mixed and then dialyzed to remove the cholate. The particles reconstituted during dialysis were separated by centrifugation. An electron microscope study showed that the particles were closed vesicles with membranes -70 A thick. Phospholipids were found to compose the greater part (60-90%) of the reconstituted particles, which were defined as “proteoliposomes.” In the first series of experiments,9 cytochrome oxidase proteoliposomes were studied. They were prepared from cholate solutions of mitochondrial phospholipids and of cytochrome oxidase supplemented with cytochrome c. After dialysis, cytochrome c that had attached to the outer surface of the reconstituted proteoliposomes was removed by washing with isotonic NaCI. The PCBresponses of the cytochrome oxidase proteoliposomes are shown in FIGURE 1. It is seen that the addition of phenazine methosulfate (PMS) to proteoliposomes that have been preequilibrated with PCBin the presence of ascorbate results in a PCBuptake (curves a, c, and e) that is sensitive to cyanide (curves a and e ) , to trifluoromethoxycarbonyl cyanide phenylhydra-

Regression problems with controllable variables subject to error

Abstract: SUMMARY The problem is studied of estimating parameters when controllable variables are subject to errors. Strongly consistent estimators with an asymptotically normal distribution are proposed and an iterative procedure for their calculation is suggested. A numerical example is given in illustration.

On the synthesis of self-correcting schemes from functional elements with a small number of reliable elements

Abstract: We describe an asymptotic optimal method for the synthesis of self-correcting schemes from functional elements which requires a limited number of reliable elements for the correction of a fixed number of errors.

Recessive super-suppression in yeast.

Abstract: The mechanism of recessive nonsense-suppression was studied in haploid strains of yeast Saccharomyces cerevisiae which were temperature-sensitive due to recessive suppressors. It was demonstrated that these strains carry a defect in protein synthesis leading to the temperature sensitivity of translation. Examination of separate translation events in parent sup - and suppressor-carrying strains has shown that recessive suppression is most likely caused by a mutant protein participating in or affecting the termination of peptide chains on ribosomes.

Green's Functions Approach to the Theory of Hopping Conductivity in Disordered Semiconductors

Abstract: It is shown that care should be taken when the phonon-assisted hopping conductivity is evaluated using the formal expansion in powers of the electron–phonon coupling constant g. This expansion appears to be divergent in the low-frequency range, and the divergent terms should be partially summed up to give a correct lowest-order contribution to the conductivity. The resulting expressions can be obtained as well by using a standard decoupling procedure in the equations for the higher-order Green's functions. Es wird gezeigt, das man bei der Berechnung der phononen-assistierten Hopping-Leitfahigkeit mit der formalen Entwicklung nach der Elektronen–Phononen-Kopplungskonstante g achtgeben sollte. Diese Entwicklung scheint im Niederfrequenzbereich divergent zu sein und die divergenten Terme mussen partiell aufsummiert werden, um einen korrekten Beitrag niedrigster Ordnung zur Leitfahigkeit zu erhalten. Der resultierende Ausdruck last sich genauso durch ein Standard-Entkopplungsverfahren in den Gleichungen fur die Greenschen Funktionen hoherer Ordnung erhalten.

Discrete groups generated by reflections in the faces of symplicial prisms in Lobachevskian spaces

Abstract: The paper provides the Coxeter schemes of all the discrete groups generated by reflections in the faces of simplicial prisms the combinatory type of which is the product of a simplex and a segment in Lobachevskian spaces.

The analysis of restricted circular twice-averaged three body problem in the case of close orbits

Abstract: It is known that the restricted circular Three Body Problem with the perturbing function being twice averaged (by the longitudes of the point with zero-mass and the one with the least finite mass) could be integrated. Due to the complexity of one of the known integrals the full investigation of this problem so far does not exist. Only investigations of limiting cases are known. This paper shows a new limiting class of solution of this problem and gives its qualitative investigation. The space orbits of the ‘asteroids’ everywhere close to the circular orbit of the body with the least finite mass are considered. Certain qualitative singularities of the behavior of solutions, connected with the critical inclination (Krasinsky, 1972) are noted. The paper also shows an analogous class of solutions of the twice-averaged problem, dealing with the perturbing of the satellite's orbit by the ‘mascon’.