Magnetorotational instability in a nonuniform magnetic field

It is shown that the characteristics of the magnetorotational instability noticeably change in the presence of the inhomogeneity of a magnetic field in which rotation occurs. A decrease in the magnetic field with an increase in the distance from the rotation center, which is typical for astrophysical objects, can lead to a significant decrease in the threshold velocity of the object medium rotation, as well as to mitigation of the requirements on a rotation velocity profile that are necessary for the development of instability. Other examples that demonstrate the indicated effects are given.     

Magnetorotational instability in a nonuniform magnetic field

It is shown that the characteristics of the magnetorotational instability noticeably change in the presence of the inhomogeneity of a magnetic field in which rotation occurs. A decrease in the magnetic field with an increase in the distance from the rotation center, which is typical for astrophysical objects, can lead to a significant decrease in the threshold velocity of the object medium rotation, as well as to mitigation of the requirements on a rotation velocity profile that are necessary for the development of instability. Other examples that demonstrate the indicated effects are given. Original Russian Text ? V.I. Ilgisonis, I.V. Khalzov, 2007, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 86, No. 11, pp. 815–818.     

Ion diffusion in a Coulombic field

An analytic solution of counter-ion diffusion in a semi-infinite domain near a uniformly charged surface is obtained within the Smoluchowski-Poisson-Boltzmann treatment. The long-ranged Coulombic interaction results in a finite first-passage time to the charged surface, although higher moments of the first-passage time are infinite. This problem is directly related to an exactly solvable model of a lattice random walk with a position-dependent bias.     

Influence of a magnetic field on diffusion and thermal diffusion in gaseous mixtures

The influence of a magnetic field on the transport properties of binary mixtures of a polyatomic and a noble gas is studied theoretically. Using an inverse operator technique, first thermal conductivity and viscosity are treated. Then diffusion and thermal diffusion are discussed in detail, with special emphasis on the composition dependence. A relation connecting the magnitudes of the field effects on thermal conductivity, diffusion, and thermal diffusion is derived. This relation is used to estimate the field effect on diffusion.     

Convective instability and mass transport of diffusion layers in a Hele-Shaw geometry

We consider experimentally the instability and mass transport of flow in a Hele-Shaw geometry. In an initially stable configuration, a lighter fluid (water) is located over a heavier fluid (propylene glycol). The fluids mix via diffusion with some regions of the resulting mixture being heavier than either pure fluid. Density-driven convection occurs with downward penetrating dense fingers that transport mass much more effectively than diffusion alone. We investigate the initial instability and the quasisteady state. The convective time and velocity scales, finger width, wave number selection, and normalized mass transport are determined for 6000相似文献   

Growth instability in diffusion controlled polymerization

We report the observation of a sharp transition in the structure of polypyrrole prepared via diffusion controlled polymerization in a quasi-two dimensional electrochemical cell. As the oxidation potential is increased, the fractal dimension drops sharply from values near 2 (compact structures) to 1 as the growth becomes dendritic. At higher potentials, where the polymerization becomes diffusion limited, a continuum of structures is observed as the dendrites become irregular and the fractal dimension increases to 1.74+-0.01. The mean branch angle was also measured and found to decrease from 90° at the point of dendritic growth, to 45° at high potential.     

Effective diffusion in a stochastic velocity field

Analytical results are derived for the effective dispersion of a passive scalar in a stochastic velocity field evolving in a fast time scale. These results are favorably compared with direct computer simulation of stochastic differential equations containing multiplicative space-time correlated noise.     

Anomalous diffusion in a random velocity field

We construct diffusions in random velocity fields which present anomalous superdiffusive behavior. The mean square displacement can be made to have any power lawt for 1<2. Higher moments and characteristic functions are also investigated.     

Energy diffusion in a strong noise field

It is shown that, under the action of a perturbation with a continuous frequency spectrum, the rate of the energy diffusion of a quantum oscillator is described by an expression that formally follows from the Fermi golden rule, even when the conditions of the validity of this rule are violated, that is, in the parameter range where the transition rate is comparable to the frequency of transition between the system levels or exceeds it. This circumstance provides the quantum-classical correspondence for the energy diffusion rate in the quasi-classical domain.     

Thermal diffusion in a sinusoidal temperature field

Separation of liquid mixtures in a thermal gradient, known as the Ludwig-Soret effect or thermal diffusion, is governed by a nonlinear, partial differential equation. It is shown here that the nonlinear differential equation for a binary mixture can be reduced to a Hamiltonian system of equations and that a solution can be obtained for the linear problem. The calculation gives a closed form expression for the space and time dependence of the concentration profile of the mixture, valid at short times.     

Zero field steps in Josephson junctions

A study is made of the d.c. current steps of resonant Josephson tunnel junctions in zero applied magnetic field. The results are in good agreement with the experimental observations. The existence of even-order modes, the cut-off voltage and the temperature-dependent current steps are clearly demonstrated.     

Fluctuation effects in spin diffusion measurements in liquid He

We have measured spin diffusion coefficients of liquid ³He at a frequency of 920 kHz by pulsed NMR. By analyzing our data in the framework of the Leggett–Rice theory we got a spin diffusion coefficient and a Leggett–Rice parameter =λωτ simultaneously at each temperature. On approaching the superfluid transition the spin diffusion coefficients showed a deviation from predictions of the Fermi liquid theory. The deviation at low pressure was larger than that at high pressure. This anomaly may be due to the effects of fluctuations of superfluidity which were recently observed in the viscosity measurement of liquid ³He.     

Dynamics and instability of current-carrying microbeams in a longitudinal magnetic field

The dynamics and instability of current-carrying slender microbeams immersed in a longitudinal magnetic field is investigated by considering the material length scale effect of the microbeam. On the basis of modified couple stress theory, a theoretical model considering the effect of Lorentz forces is developed to analyze the free vibration and possible instability of the microbeam. Using the differential quadrature method, the governing equations of motion are solved and the lowest three natural frequencies are determined. The obtained results reveal that the electric current and the longitudinal magnetic field tend to reduce the microbeam's flexural stiffness. It is therefore shown that the lowest natural frequencies would decrease with increasing magnetic field parameter. The mode shapes of the microbeam are found to be generally three-dimensional spatial in the presence of the longitudinal magnetic field. It is interesting that buckling instability would concurrently occur in the first mode or in the higher-order modes when the magnetic field parameter becomes sufficiently large.     

Plasma diffusion across a magnetic field

Using a simple model of a slowly diffusing plasma across a strong magnetic field, it is demonstrated that plasma mass and energy evolves from an initially given density and temperature distribution into isothermal state with a self-similar diffusion profile that depends only on its initial mass and energy.     

Scalar field and gravitational instability

We study monopole perturbations of spherically symmetric scalar-vacuum and scalar-electrovacuum fields in general relativity and reduce the problem to a one-dimensional Schrödinger-like equation with a certain effective potential. Imposing certain boundary conditions, we select physically meaningful perturbations. Some of them grow exponentially and we conclude that the background system is unstable.