Search results for "Linear stability"
showing 10 items of 32 documents
Local thermal non-equilibrium effects in the Darcy–Bénard instability of a porous layer heated from below by a uniform flux
2013
Abstract The influence of the lack of thermal equilibrium between the solid phase and the fluid phase on the convective instability in a porous medium is studied. A horizontal layer with parallel and impermeable bounding walls is considered. The lower wall is assumed to be isoflux, and the upper wall isothermal. The basic motionless state is perturbed with small-amplitude disturbances, so that a linear analysis of the instability is carried out with a streamfunction-temperature formulation of the local balance equations. Then, the governing equations are solved for the normal modes, leading to an eigenvalue problem for the neutral stability. This eigenvalue problem is solved analytically, t…
Thermodynamics of computation and linear stability limits of superfluid refrigeration of a model computing array
2019
We analyze the stability of the temperature profile of an array of computing nanodevices refrigerated by flowing superfluid helium, under variations in temperature, computing rate, and barycentric velocity of helium. It turns out that if the variation in dissipated energy per bit with respect to temperature variations is higher than some critical values, proportional to the effective thermal conductivity of the array, then the steady-state temperature profiles become unstable and refrigeration efficiency is lost. Furthermore, a restriction on the maximum rate of variation in the local computation rate is found.
Linear theory of the Rayleigh–Taylor instability at a discontinuous surface of a relativistic flow
2017
We address the linear stability of a discontinuous surface of a relativistic flow in the context of a jet that oscillates radially as it propagates. The restoring force of the oscillation is expected to drive a Rayleigh-Taylor instability (RTI) at the interface between the jet and its cocoon. We perform a linear analysis and numerical simulations of the growth of the RTI in the transverse plane to the jet flow with a uniform acceleration. In this system, an inertia force due to the uniform acceleration acts as the restoring force for the oscillation. We find that not only the difference in the inertia between the two fluids separated by the interface but also the pressure at the interface h…
On the thermal instability in a horizontal rectangular porous channel heated from below by a constant flux
2014
Published version of an article in the journal: Journal of Physics: Conference Series. Also available from the publisher at: http://dx.doi.org/10.1088/1742-6596/501/1/012003 Open Access The onset of thermoconvective instability in a rectangular horizontal channel filled with a fluid-saturated porous medium is studied. The channel is heated from below with a constant flux. The top wall is maintained at a uniform constant temperature, while the lateral boundaries are permeable and perfectly conducting. The stability of the basic motionless state is analysed with respect to small-amplitude disturbances. The eigenvalue problem for the neutral stability condition is solved analytically for the n…
Labyrinthine instability of miscible magnetic fluids
2002
Abstract We consider an inhomogeneous magnetic fluid (MF), modeling a miscible MF pair, in a Hele–Shaw cell under a normal field. A linear stability analysis for the sharp straight interface (analytically) and for the diffused one (numerically) is performed. For the former case, the neutral curves and the stability diagram are found along with the critical wavelength and parameter values. Oscillatory or monotonous instabilities are shown to occur. For the diffused interface, we recognize the importance of 2D flow viscous effects along with the conventional wall friction and observe that in strong fields the dominant wavelength scales as the cell gap.
Existence and stability of periodic solutions in a neural field equation
2017
We study the existence and linear stability of stationary periodic solutions to a neural field model, an intergo-differential equation of the Hammerstein type. Under the assumption that the activation function is a discontinuous step function and the kernel is decaying sufficiently fast, we formulate necessary and sufficient conditions for the existence of a special class of solutions that we call 1-bump periodic solutions. We then analyze the stability of these solutions by studying the spectrum of the Frechet derivative of the corresponding Hammerstein operator. We prove that the spectrum of this operator agrees up to zero with the spectrum of a block Laurent operator. We show that the no…
Formation of Coherent Structures in Kolmogorov Flow with Stratification and Drag
2014
We study a weakly stratified Kolmogorov flow under the effect of a small linear drag. We perform a linear stability analysis of the basic state. We construct the finite dimensional dynamical system deriving from the truncated Fourier mode approximation. Using the Reynolds number as bifurcation parameter we build the corresponding diagram up to Re=100. We observe the coexistence of three coherent structures.
Edge pinch instability of liquid metal sheet in a transverse high-frequency AC magnetic field
2006
We analyze the linear stability of the edge of a thin liquid metal layer subject to a transverse high-frequency AC magnetic field. The layer is treated as a perfectly conducting liquid sheet that allows us to solve the problem analytically for both a semi-infinite geometry with a straight edge and a thin disk of finite radius. It is shown that the long-wave perturbations of a straight edge are monotonically unstable when the wave number exceeds some critical value $k_c,$ which is determined by the surface tension and the linear density of the electromagnetic force acting on the edge. The higher the density of electromagnetic force, the shorter the critical wavelength. The perturbations with…
Shapes of a gas bubble rising in the vertical Hele–Shaw cell with magnetic liquid
2005
Abstract Dynamics of the bubble rising in the vertical Hele–Shaw cell with magnetic liquid in the normal magnetic field is studied. Linear stability analysis of the circular shape is carried out. Development of the instability with respect to the lowest symmetric mode is simulated by the boundary integral equation technique.
Generalization of the Lorenz-Haken model to atomic systems with different relaxation rates for the two laser levels
1995
Abstract The fundamental Lorenz-Haken laser model is generalized to the case of a two-level amplifying medium with different external relaxation rates for the two levels and with internal relaxation. This represents one further degree of freedom, and important quantitative differences in the laser dynamics. i.e., in the stationary solutions, linear stability analysis, and timedependent solutions, are found. No significant qualitative differences, however, are observed.