ON THE DURATION OF EXCURSIONS OF RANDOM FUNCTIONS**Zhur. tekh. fiz., 24, No. 1, 103 (1954). (With acknowledgements to Morris D. Friedman, Inc., Massachusetts.)

Кузнецов, П. И.; Stratonovich, R. L.; Tikhonov, V.I.

doi:10.1016/b978-1-4832-3230-0.50033-x

Cited by 14 publications

(25 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This means that an additional relaxation will occur at the wave front ~'= x,. If this additional relaxation is accompanied by rupture of the seam in the section x,, then following rupture a new relaxation wave will become formed, and if the gas pressure in the seam pores is high enough, a wave of fragmentation [4,5,7] will become formed. If condition (28) is not satisfied, the relaxation wave will pass through the whole of the region (0, x 0] according to law (25) and will be propagated farther into the depths of the seam.…”

Section: [Hat L 2h X + Hasmentioning

confidence: 99%

“…This process, regarded as the initial stage in the appearance and development of rock bursts, was discussed by the author [4] without allowance for convergence of the side rocks. In its main features it also reflects the dynamics of shock bumps [1,3].…”

mentioning

confidence: 99%

“…[1][2][3]. These have certain common features expressed in the mode of occurrence and in the character of the comparatively rapid stress redistributions, due in particular to propagation of a relaxation wave [4]. In these phenomena the interrelation at the contact surface between the worked seam and the side rocks is important [4-61.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Propagation of a relaxation wave near the free surface of a worked seam, with subsidence of the side rocks (in relation to the mechanism of shock bumps and gas bursts)

Kuznetsov¹

1971

Soviet Mining Science

View full text Add to dashboard Cite

It is well known that underground working of mineral seams is accompanied by dynamic phenomena known as shock bumps, rock bursts, sudden extrusions of the seam, etc. [1][2][3]. These have certain common features expressed in the mode of occurrence and in the character of the comparatively rapid stress redistributions, due in particular to propagation of a relaxation wave [4]. In these phenomena the interrelation at the contact surface between the worked seam and the side rocks is important [4-61. In those parts of the seam where it coheres (adheres) to the side (surrounding) rocks, the tangential stresses at the contact surfaces near the worked-out area reach their limiting values. In these sections, working of the seam may be accompanied by loss of cohesion and consequent propagation of a relaxation wave which is bound on one side by the free surface of the seam and on the other by the advancing front of the relaxation wave. Behind the relaxation wave front the seam will be extruded towards the working, owing to relief of the additional convergence of the side rocks due to the same relaxation.This process, regarded as the initial stage in the appearance and development of rock bursts, was discussed by the author [4] without allowance for convergence of the side rocks. In its main features it also reflects the dynamics of shock bumps [1,3]. In this article I will attempt to describe the propagation of a relaxation wave accompanied by very rapid extrusion of the seam into the worked-out area, with allowance for convergence of the side rocks, and thus to establish the complete interrelation between the worked seam and the side rocks during the occurrence of shock bumps and rock bursts.Let us consider the one-dimensional case of relaxation wave propagation. LetN(t) be the distance from the free surface of the worked seam to which the relaxation wave has been propagated in time t. We write the rate of ex~usion v of the seam behind the relaxation wave front ~t) (i.e,, in any cross section of the seam x <~(t)) in the form of a sum of translational and relative velocities:The translational velocity is governed by expansion of the seam due to load relaxation and to extrusion of its side rocks at the front ~(t). It will therefore ultimately depend only on time. The relative velocity is governed by additional extrusion of the seam due to convergence of the side rocks behind the relaxation wave front. To a reasonable approximation it can be written in the form Vrel = (t)(x -x I,where ~(t) is some function determined from the convergence of the side rocks due to relaxation of the load on the seam behind the wave front.

show abstract

Section: [Hat L 2h X + Hasmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Propagation of a relaxation wave near the free surface of a worked seam, with subsidence of the side rocks (in relation to the mechanism of shock bumps and gas bursts)

Kuznetsov¹

1971

Soviet Mining Science

View full text Add to dashboard Cite

show abstract

“…must be assessed on the basis of the results of tests on specimens representing the material of the medium. For this reason, the frequency of attributing to the material of the medium in the model cell any particular value of a sampied quantity [1] must not only reflect the frequency of realization of this value in tests on specimens (which might be a sufficient requirement to ensure statistical reliability of modeling), but must also take account of the fact that the statistics of the results of tests of the properties of specimens drawn from the medium may depend both on the size and shape of the specimens and on the fact that the specimen test conditions will usually not correspond to the conditions in which the element of the medium occurs in the real process. In the latter case we are faced with the problem of the scale factor, as well as with the problem of getting the specimen test conditions the same as those realized in the process under investigation.…”

mentioning

confidence: 99%

“…da---~ ~r 1/,T.-~ e (1) and that tests of o* are made on specimens with a characteristic dimension L in nearly static loading conditions. Of the value of L we shall say that further ~eduction in the specimen size does not lead to a change in A and 8 in distribution (1).…”

mentioning

confidence: 99%

Attaining statistical reliability in models of random properties of a continuous medium

Кузнецов¹

1973

Soviet Mining Science

View full text Add to dashboard Cite

By statistical reliability of models (SRM) of random properties of a medium based on the Monte Carlo method we mean the attainment of a state of affairs in which: a) real tests would furnish us with a statistic of the distribution of properties adequate to the statistic given by the process of simulated tests ("play') ; b) a calculation based on a Monte Carlo model of the final (or if necessary the intermediate) stages of a process in which randomness of certain properties of the medium is manifested will give, with the desired precision, the real characteristics of the stages of the process which are realized in experiment. This division of requirements has a definite foundation.The point is that some characteristics of a continuous medium (modulus of elasticity, strength, density, etc.) must be assessed on the basis of the results of tests on specimens representing the material of the medium. For this reason, the frequency of attributing to the material of the medium in the model cell any particular value of a sampied quantity [1] must not only reflect the frequency of realization of this value in tests on specimens (which might be a sufficient requirement to ensure statistical reliability of modeling), but must also take account of the fact that the statistics of the results of tests of the properties of specimens drawn from the medium may depend both on the size and shape of the specimens and on the fact that the specimen test conditions will usually not correspond to the conditions in which the element of the medium occurs in the real process. In the latter case we are faced with the problem of the scale factor, as well as with the problem of getting the specimen test conditions the same as those realized in the process under investigation.Both these problems leave their mark on the requirements imposed on the size of the model cell and on the process of sampling ('play') itself. This is taken into account in the formulation of the determinant condition for which we get reliability of our chosen Monte Carlo model of the random properties of a continuous medium. The question arises of whether we can satisfy these conditions. In fact, on the one hand, we acknowledge the insufficiency of the first condition; and on the other, uncertainty appears in the possibility of obtaining information, on the bases of the results of tests of the properties of a continuous medium (either on specimens or in situ), suitable for use in calculations on various processes occurring in it. Consequently, the question of the size of the model ceil, regarded by us as crucial for satisfaction of the conditions for SRM, must be decided separately for each class of problem. As an illustration of one possible approach to the determination of the size of the model ceil, let us consider the process of wave loading of a continuous medium with formation of cracks. For convenience we shall denote this problem by the letter S. As a random property of the medium in this process we shall take its tensile strength o ~ [2]. We shall regard the mate...

show abstract

Excitation of the Potential Relaxation Instability in a Weakly Magnetized Discharge Plasma by a Voltage Step

Gyergyek

Čerček

Stanojević

1996

Contrib. Plasma Phys.

View full text Add to dashboard Cite

An instability is triggered in a weakly magnetized discharge plasma by the application of a positive voltage step to a planar collector immersed into the plasma column with its surface perpendicular to the magnetic field lines. Time developement of the plasma densitytafter the application of the pulse is measured by a Langmuir probe. Radial and axial velocity of the plasma density perturbation are measFed. Radial velocity is consistent with the increase of the plasma potential in the current channel: Axial velocity is very high. It is interpreted as phase velocity of radial quasiperie dic motion of the plasma in and out of the current channel. Response time of the collector current to the applied voltage step is measured versus different parameters. Experimental results are in agreement with a qualitative model presented in previous work [l] where the observed instability is modeled as a two dimensional potential relaxation instability (PEU). Minor improvements of the previous model are proposed. A rarefaction pulse that moves towards the collector is found as the initial stage of the instability.

show abstract

ON THE DURATION OF EXCURSIONS OF RANDOM FUNCTIONS**Zhur. tekh. fiz., 24, No. 1, 103 (1954). (With acknowledgements to Morris D. Friedman, Inc., Massachusetts.)

Cited by 14 publications

References 3 publications

Propagation of a relaxation wave near the free surface of a worked seam, with subsidence of the side rocks (in relation to the mechanism of shock bumps and gas bursts)

Propagation of a relaxation wave near the free surface of a worked seam, with subsidence of the side rocks (in relation to the mechanism of shock bumps and gas bursts)

Attaining statistical reliability in models of random properties of a continuous medium

Excitation of the Potential Relaxation Instability in a Weakly Magnetized Discharge Plasma by a Voltage Step

Contact Info

Product

Resources

About