Equations of motion for an anisotropic nonlinear elastic continuum in a gravitational field

Equations of motion for an anisotropic nonlinear elastic continuum in the gravitational field are written in a form convenient for numerical calculations. The energy-stress tensor is expressed through scalar and tensor products of three vectors imbedded in the continuum. Examples of expansion of the energy-stress tensor into scalar and tensor invariants corresponding to some crystal classes are given.     

Finite-size scaling and particle-size cutoff effects in phase-separating polydisperse fluids

We study the liquid-vapor phase behavior of a polydisperse fluid using grand canonical simulations and moment free energy calculations. The strongly nonlinear variation of the fractional volume of liquid across the coexistence region prevents naive extrapolation from detecting the cloud point. We describe a finite-size scaling method which, nevertheless, permits accurate determination of cloud points from simulations of a single system size. By varying a particle-size cutoff, we find that the cloud point density is highly sensitive to the presence of rare large particles; this could affect the reproducibility of experimentally measured phase behavior in colloids and polymers.     

Relativistic kinetics of an anisotropic plasmalike medium with damping in a field of gravitational radiation

An exact solution is obtained for the general relativistic kinetic equation with model collision integral that describes the motion of an initially homogeneous anisotropic plasma in a field of plane gravitational waves (GW) of arbitrary amplitude and polarization. The amplitude of the induced current is calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 70–74, December, 1984.     

Dynamical scaling of the structure factor of some non-Euclidean systems

Predictions of nonlinear theories on dynamics of new phase formation have been examined for the hydration of calcium silicates with light water and heavy water. In the case of hydration with light water, reasonable agreement has been observed with dynamical scaling hypothesis with a new measure of the characteristic length. The characteristic length does not follow a power law relation with time. Hydrating mass is found to be mass fractal throughout hydration, with mass fractal dimension increasing with time. But, in the case of hydration with heavy water, no agreement has been observed with the scaling hypothesis. Hydrating mass undergoes transition from mass fractal to surface fractal and finally again to mass fractal. The qualitative features of the kinetics of hydration, as measured in small-angle scattering experiments, are strikingly different for hydration with light water and heavy water.     

Convection in a gravitational field

We set up a classical stochastic model for the irreversible dynamics of a lattice gas under gravity. We show that for a class of initial states the system converges to equilibrium, which obeys the laws of thermostatics.Dedicated to Oliver Penrose.     

Dynamical systems study of chameleon scalar field

The present work is an extensive study of the viable stable solutions of chameleon scalar field models leading to possibilities of an accelerated expansion of the universe. It is found that for various combinations of the chameleon field potential V(?)$V\left(?\right)$ and the coupling f(?)$f\left(?\right)$ of the chameleon field with matter, a stable solution for an accelerated expansion is quite possible. The investigation provides a diagnostics for the stability criteria for all sorts of combinations of V(?)$V\left(?\right)$ and f(?)$f\left(?\right)$.     

Black hole in a gravitational field

An exact solution of the vacuum Einstein field equations representing a Schwarzschild black hole in an external gravitational field is derived using a formalism developed by Ernst.     

Electrostatic potential in a gravitational field

The electrostatic potential in a gravitational field is estimated up to the order ofe ² G ² in the framework of the conventional quantum field theory. It is shown that the electrostatic potential is different from the classical one. We find that this discrepancy is attributable to the process in which a particle emits three massless ones which are absorbed by three other particles.     

Dirac particles in a gravitational field

The semiclassical approximation for the Hamiltonian of Dirac particles interacting with an arbitrary gravitational field is investigated. The time dependence of the metric leads to new contributions to the in-band energy operator in comparison to previous works in the static case. In particular we find a new coupling term between the linear momentum and the spin, as well as couplings that contribute to the breaking of the particle–antiparticle symmetry.     

Relativistic gas in a gravitational field

Equations describing the kinetics and hydrodynamics of a relativistic gas in a gravitational field are obtained using the concept of a gravitational field as a physical field in a pseudo-Euclidean space-time.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 17–20, September, 1982.     

Einstein's theory of the gravitational field in a representation by orthogonal reference systems

Some difficulties in the theory of the gravitational field are discussed; these are associated with the nonlocalized field energy. Orthogonal reference systems are used to formulate the energy and momentum distribution in terms of generally covariant tensors.The authors are indebted to Professor D. D. Ivanenko for an interesting discussion of these problems.     

Dynamical chaos in a biharmonic field

We consider dynamical chaos in polarization oscillations in the case of biharmonic field using the Daffing equation. When the nonlinearity is small the Daffing equation can be solved by the perturbation method. The stochasticity criterion is calculated in the general case.Omsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizka, No. 7, pp. 99–103, July, 1992.     

Orbital equations in a weak gravitational field

With the obtainment of the Synge equations of motion in third approximation for a test particle, we determine the relativistic force in the field generated by a massive body obtained previously in terms of its potentials. Afterwards, in order to study the motion, we obtain the integral of energy and the integral of angular momentum. By means of them, the general form for the trajectory of an equatorial orbit and for the advance of its apsidal line are obtained. As we will see, the known diverse contributions for this advance appears in the general form after strong supplementary conditions on the potentials. As application, with such assumptions these contributions are derived in a unified way.     

Phase ordering dynamics in a gravitational field

We study the dynamics of phase ordering in the presence of an external gravitational field, namely a field that varies linearly with distance in one direction. Starting from microscopic considerations, we motivate reasonable phenomenological models for cases with nonconserved and conserved order parameter. We present detailed numerical results from our model for the case with conserved order parameter.     

Trapped Bose condensate in a gravitational field

The Bose condensation of atoms in finite 1D and 2D parabolic traps placed in a gravitational field is considered. The distortion of the trap potential in this field is modeled by a combination of two rectangular 1D and 2D traps. The change in the critical temperature T _c is found with regard to the cutoff and renormalization of the spectrum of these model potentials. The shift of the critical temperature T _c in the gravitational field is calculated. The shift sign and magnitude depend on the way of introducing the gravitational field. For a certain choice, three critical temperatures can be sequentially observed. These temperatures can be attributed to three Bose condensations that occur in the cyclic motion of the trap along the Earth (I)-space (II)-Earth (III) route.