Self-similar evolution of the surface morphology of a stressed amorphous alloy foil

A time-ordered sequence of topographic images of a stressed amorphous Fe₇₀Cr₁₅B₁₅ ribbon is presented. It is shown that the surface of this material (unlike polycrystalline metal foil) has a fractal structure due to the nonequilibrium conditions of its formation. As a tensile stress of about 500 MPa is applied to the surface, the fractal dimension of the surface increases from 1.21±0.02 to 1.34±0.03, then drops to 1.12±0.03, and finally increases to 1.22±0.02. In about 1.5 hours, a complex surface morphology characterized by a roughness amplitude of several tens of nanometers evolves into a regular pattern of shear bands with amplitude of about 300 nm. Self-affine changes in surface morphology are explained by competition between several processes, including crack propagation, surface smoothing, and self-diffusion.     

Energy criterion for relief formation on a strained surface

The strain-induced roughening revealed by scanning tunneling microscopy on the surface of elastically strained Ge(111) crystals and Fe₇₀Cr₁₅B₁₅ amorphous alloy foils is discussed. It is demonstrated that the strained-induced roughening can be considered a channel for a decrease in the elastic energy of the strained surface. The diffusion mechanism of relief formation on a strained Ge(111) surface is proposed and justified.     

Problem of the choice of time in cosmology

A class of gauge conditions is obtained from an isotropic cosmological model with a conformally invariant scalar field, leading to a Hamiltonian dynamics with a time independent Hamiltonian which coincides with that of a harmonic oscillator. The quantum dynamics of the model is considered, and the inevitability of a singularity in its quantum version is shown.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 29–32, January, 1990.In conclusion, the authors thank L. D. Faddeev and V. V. Nesterenko for useful discussions.     

Quantum dynamics of an isotropic cosmological model with relativistic gas

A canonical time parameter corresponding to the synchronous reference frame is found for an isotropic cosmological model with relativistic gas. Canonical quantization of the model is performed. In the quantum theory, the radius of the Universe is an operator-valued function of time, whose values at different moments of time commute among themselves, and the state of the Universe itself does not change with time. In particular, this means that in experiments in which the radius of the Universe is measured, the presence of singularity is unavoidable within a finite interval of time in the past, and, for closed models, in the future.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 9–14, July, 1990.The authors thank L. D. Faddeev for his interest to their work, and V. A. Franke for stimulating discussions.     

Thermomechanics of Deformations in an Anharmonic Solid Body

Physics of the Solid State - The macroscopic laws determining the temperature and deformations of an anharmonic solid body in a given external temperature force field have been stated in the form...     

On the statistical distribution in a deformed solid

A modification of the Gibbs distribution in a thermally insulated mechanically deformed solid, where its linear dimensions (shape parameters) are excluded from statistical averaging and included among the macroscopic parameters of state alongside with the temperature, is proposed. Formally, this modification is reduced to corresponding additional conditions when calculating the statistical sum. The shape parameters and the temperature themselves are found from the conditions of mechanical and thermal equilibria of a body, and their change is determined using the first law of thermodynamics. Known thermodynamic phenomena are analyzed for the simple model of a solid, i.e., an ensemble of anharmonic oscillators, within the proposed formalism with an accuracy of up to the first order by the anharmonicity constant. The distribution modification is considered for the classic and quantum temperature regions apart.     

The energy of a closed universe in a reference frame formed by a set of freely moving clocks

The Hamiltonian of a closed universe is found in a reference frame formed by a set of freely moving clocks. In this physically defined gauge the energy of the universe is positively defined.Leningrad State Technical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 104–106, October, 1992.     

Standard clocks in quantum cosmology

A method is proposed for determining the classical time parameter in quantum cosmology that does not destroy the covariance of the theory.St. Petersburg Technical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 20–24, November, 1993.     

A geometrical property of action in gravitation theory

It is shown that in regard to the special spacial foliation associated with the gas of a standard clock, the action of gravitation theory is proportional to the time parameter, while the coefficient of proportionality is equal to the energy of the gravitational field and other fields in the reference system formed by the gas of the standard clock.St. Petersburg State Technical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 81–84, November, 1993.     

Equation of State and Statistical Distribution in a Macroscopic System

Physics of the Solid State - A representation is proposed for the statistical sum for a macroscopic body in the form of a Euclidean functional integral in which the body deformation is a classical...