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This paper studies instability of a heavy inclusion in the Earth's upper layers by the linear theory method for small perturbations. The existence of such inclusions with increased density is associated with chemical inhomogeneity or phase transitions. The viscoelasticity of the geomaterial is described by the Maxwell rheological model. Two layouts of the inclusion with increased density are considered. The heavy inclusion in the cold upper elastic layer of the crust does not change its location under small perturbations, i.e., it is stable according to the linear theory. The heavy inclusion which is located in the hot viscous crustal layer underlying the upper cold layer, is unstable (slowly sinking into the underlying viscous mantle layers).

We investigate the stability of a dilute hydrogen plasma in mechanical, thermal and ionization equilibrium. We derive sufficient and necessary criteria for instability from a linear analysis.

Gravitational instability arising from thermal fluctuations in a static universe in considered in an extrapolation of a weakly non linear approximation, to calculate the mean square angular momentum of proto-galaxies at the critical time at which these protogalaxies detach themselves from the primeval homogeneous medium. The mean angular momentum of a given volume, containing in the mean a mass M, and the mean angular momentum of a given mass M, are shown to be quite different. It is suggested that it is the latter which should be compared with the observed angular momentum of galaxies. A numerical application shows that such a picture cannot account for the observed angular momentum of the Galaxy and at the same time for the existence of dwarf galaxies. A simple calculation suggests however that tidal interactions arising between neighbouring protogalaxies after the critical time of detachment would easily account for the observed angular momentum of spiral galaxies, if these interactions take place before the universe is set in a state of fully developed expansion

We investigate the stability of a dilute hydrogen plasma in mechanical, thermal and ionization equilibrium in the presence of an ionizing radiation field. New conclusions are reached concerning the effects of a strong field of energetic photons.

An evolution criterion is established for weakly-coupled gravitational systems without statistical inhomogeneities. Boltzmann's H decreases, without however approaching a limiting value. The evolution of the velocity distribution is towards a maxwellian, but the approach is deflected by an instability of the maxwellian distributions themselves. The velocity dispersion increases monotonically as new spatial correlations are created.

This paper is concerned with the gravitational instability of an incompressible fluid layer in a state of stationary and uniform rotation about an axis normal to the layer, in the gravitational field of a population II stellar distribution. It is found that the rotation inhibits the gravitational instability of the layer. When Ω2/πGρ exceeds 0.14, the layer is completely stable ; in the other cases there is a certain range of wave-lengths gravitationally unstable, and amongst them a wave-length of maximum instability.

Jeans's gravitational instability is studied by investigating the evolution of an initial (t = 0) disturbance of finite extent. We solve this problem by means of the Laplace transform technique, in the case of one-dimensional plane perturbations. We denote by a the linear dimension of the initial disturbance and we show, in considering the particular case in which this initial disturbance is characterized by a single wave-length, that the evolution of the density at the center of the perturbed region exhibits the pheno¬ menon of gravitational instability, when t → ∞, irrespective of the value of a as compared to Jeans's critical wave-length λc.

Abstract. Deep-seated gravitational creep in rock slopes, rock-flow or sackung is a special category of mass-movement, in which long-lasting small-scale movements prevail. The prime causes of these mass movements in the Alpine area seem to have been glacial retreat at ~15000 a B.P. Many sackung stabilize and some undergo the transition to rapid sliding. This paper concentrates on four mass-movements in crystalline complexes of the Austrian Alps which have been investigated for aspects of deep-seated gravitational creep and prediction of the transition to rapid sliding. The present-day extent of the creeping or sliding of the rock mass has been modelled by a process of progressive, stress induced damage. Subcritical crack growth has been assumed to control this process and also the velocity of the mass movement. A sliding surface and decreasing Coulomb stress at this surface as a function of slip is a precondition for instability. The development of the four examples has been modelled successfully by a rotational slider block model and the conception of subcritical crack growth and progressive smoothing of the sliding surface. The interrelations between velocity, pore water pressure, seismic activity and the state of the sliding surface have been derived. Finally we discuss how the hypothesis inherent in the models presented could be validated and used for prediction.

Gravitational waves from core-collapse supernovae are produced by the excitation of different oscillation modes in the protoneutron star (PNS) and its surroundings, including the shock. In this work we study the relationship between the post-bounce oscillation spectrum of the PNS–shock system and the characteristic frequencies observed in gravitational-wave signals from core-collapse simulations. This is a fundamental first step in order to develop a procedure to infer astrophysical parameters of the PNS formed in core-collapse supernovae. Our method combines information from the oscillation spectrum of the PNS, obtained through linear perturbation analysis in general relativity of a background physical system, with information from the gravitational-wave spectrum of the corresponding non-linear, core-collapse simulation. Using results from the simulation of the collapse of a 35 M⊙ pre-supernova progenitor we show that both types of spectra are indeed related and we are able to identify the modes of oscillation of the PNS, namely g-modes, p-modes, hybrid modes, and standing accretion shock instability (SASI) modes, obtaining a remarkably close correspondence with the time–frequency distribution of the gravitational-wave modes. The analysis presented in this paper provides a proof of concept that asteroseismology is indeed possible in the core-collapse scenario, and it may serve as a basis for future work on PNS parameter inference based on gravitational-wave observations. ; This work is supported by the Spanish MINECO (grant AYA2015-66899-C2-1-P) and the Generalitat Valenciana (PROMETEOII-2014-069). AP acknowledges support from the European Union under the Marie Sklodowska Curie Actions Individual Fellowship, grant agreement no. 656370.

This paper discusses some numerical results concerning the evolution of an initial disturbance of finite extent in Jeans's me¬ dium, when the linear dimension a of the initial perturbation is equal to or smaller than Jeans's critical length. The characteristic time of gravitational instability at the centre of the initial disturbance increa¬ ses when a decreases, but it is found that this increase is logarithmic and therefore extremely slow.

This paper presents a numerical study of gravitational instability in a compressible fluid cylinder of infinite length, with respect to linear, adiabatic and axisymetrical normal modes. It is found that these modes are unstable, and that a mode of maximum instability does exist at a wave-length comparable with the diameter of the cylinder. Moreover, the numerical analysis suggests that all wave-lengths are indeed unstable : i.e., there seems to be no marginal mode (no critical wave-length) ; a conclusion which can be corroborated by an analytical discussion.

The problem of the stability of a jet flow with a piecewise linear velocity profile in a stratified rotating atmosphere is considered. The linearized system of equations for perturbations is reduced to a single equation with respect to the amplitude of the longitudinal velocity component containing the turning points. In terms of Airy functions, an asymptotic solution of the equation is constructed that is valid for small values of the Rossby number. It is shown that the flow becomes unstable due to radiation of inertial-gravitational waves. An analytical expression is obtained for the growth rate of perturbations.

The problem of gravitational instability is treated front the point of view of the Boltzmann-Vlasov equation which is valid for a gaseous medium of extremely small density. A critical wave length λ1 is derived which is such that any perturbation whose wave-length is greater than λ1 is dynamically unstable whereas any other perturbation is stable. This critical wave-length is exactly the one which is given by Jeans hydrodyn amical theory for the case ɣ = 1, i.e., for isothermal perturbations. Moreover, there is no important difference between Jeans dispersion equation and the one obtained here.