F. J. Higuera

The lattice Boltzmann equation: a new tool for computational fluid-dynamics

Abstract We present a series of applications which demonstrate that the lattice Boltzmann equation is an adequate computational tool to address problems spanning a wide spectrum of fluid regimes, ranging from laminar to fully turbulent flows in two and three dimensions.

Gunn instability in finite samples of GaAs. II: Oscillatory states in long samples

Abstract An asymptotic description is given of the well known phenomenon of charge density waves propagating in long samples of n-type GaAs with Ohmic contacts and voltage bias. Depending on the resistivity of the contacts, two types of waves are identified; charge dipoles appear for high resistivity contacts and charge monopoles for low resistivity contacts. The critical value of the resistivity separating both regimes, as well as the threshold voltages above and below which the waves propagate for a given resistivity are determined for a standard model of the Gunn effect. The processes of birth and growth of a wave near the cathode and of death at the anode are analysed. The period of the waves and the time evolution of the current through the sample can be inferred from the asymptotic analysis.

Gunn instability in finite samples of GaAs: I. stationary states, stability and boundary conditions

Abstract The stationary states of a well-known phenomenological model of n-GaAs are characterized and constructed. Their dependence on realistic boundary conditions and their stability properties are analyzed. Two mathematical problems are studied corresponding to different biases. Under current bias, the total current is a known control parameter. Under voltage bias, the current is an unknown to be determined so as to keep the voltage constant. Under current bias, coexistence of multiple steady states is found for large enough samples. A theorem on stability under different bias conditions establishes, under appropriate conditions, a correspondence between critical values of the current and the voltage at which the basic stationary solution ceases to be stable. While under current bias, bifurcations from the stationary solution are branches of stationary solutions, under voltage bias bifurcating branches may be oscillatory. The consequences of this result for the bifurcation diagram of the Gunn instability are discussed.

The onset and end of the Gunn effect in extrinsic semiconductors

A Hopf bifurcation analysis of the spontaneous current oscillation in direct current (DC) voltage-biased extrinsic semiconductors is given for the classical model of the Gunn effect in n-GaAs. For semiconductor lengths L larger than a certain minimal value, the steady state is linearly unstable for voltages in an interval

The Gunn effect: instability of the steady state and stability of the solitary wave in long extrinsic semiconductors

( \phi _\alpha ,\phi _\omega )

Axisymmetric pulse recycling and motion in bulk semiconductors

. As L increases, the branch of time-periodic solutions bifurcating at simple eigenvalues when

Free-boundary problems describing two-dimensional pulse recycling and motion in semiconductors

\phi = \phi _\alpha

Two-Dimensional Gunn Effect

turns from subcritical to supercritical and then back to subcritical again. For very long semiconductors a quasi continuum of oscillatory modes bifurcates from the steady state at the onset of the instability. The bifurcating branch is then described by a scalar reaction-diffusion equation with cubic nonlinearity subject to antiperiodic boundary conditions on a subinterval of

Onset of the Gunn effect in semiconductors : Bifurcation analysis and numerical simulations

[ 0,L ]

Modified lattice gas method for high Reynolds number incompressible flows

. For the electron velocity curve we have considered, the bifurcation is subcritical, which may agree with experimental observations in n-GaAs. An extension o...