Guillermo Terrones

The onset of convective instability in a triply diffusive fluid layer

The onset of instability is investigated in a triply diffusive fluid layer in which the density depends on three stratifying agencies having different diffusivities. It is found that, in some cases, three critical values of the Rayleigh number are required to specify the linear stability criteria. As in the case of another problem requiring three Rayleigh numbers for the specification of linear stability criteria (the rotating doubly diffusive case studied by Pearlstein 1981), the cause is traceable to the existence of disconnected oscillatory neutral curves. The multivalued nature of the stability boundaries is considerably more interesting and complicated than in the previous case, however, owing to the existence of heart-shaped oscillatory neutral curves. An interesting consequence of the heart shape is the possibility of ‘quasi-periodic bifurcation’ to convection from the motionless state when the twin maxima of the heart-shaped oscillatory neutral curve lie below the minimum of the stationary neutral curve. In this case, there are two distinct disturbances, with (generally) incommensurable values of the frequency and wavenumber, that simultaneously become unstable at the same Rayleigh number. This work complements the earlier efforts of Griffiths (1979 a ), who found none of the interesting results obtained herein.

Ejecta source model based on the nonlinear Richtmyer-Meshkov instability

We describe a simple algebraic model for the particulate spray that is ejected from a shocked metal surface based on the nonlinear evolution of the Richtmyer-Meshkov instability (RMI). The RMI is a shock-driven hydrodynamic instability at a material interface in which the dense and tenuous fluids penetrate each other as spikes and bubbles, respectively. In our model, the ejecta areal density is determined by the product of the post-shock metal density and the saturated bubble amplitude, which depends on both the amplitude and wavelength of the initial surface imperfections of the metal. The maximum ejecta velocity is determined by the ever-growing spikes, which are accelerated relative to the RMI growth rate by the spatial harmonics that sharpen them. The model is formulated to fit new hydrodynamics and molecular dynamics simulations of the RMI and validated by existing ejecta experiments over a wide range of material properties, shock strengths, and surface perturbations. The results are also contrasted ...

Stability and bifurcation of spatially coherent solutions of the damped-driven NLS equation

An analytical study is conducted of the structure, stability, and bifurcation of the spatially dependent time-periodic solutions of the damped-driven sine-Gordon equation in the nonlinear Schrodinger approximation. Locked states are found for which the spatial structure consists of coherent excitations localized about

Structure, Chirality, and Formation of Giant Icosahedral Fullerenes and Spherical Graphitic Onions

x = 0

The onset of convection in a multicomponent fluid layer

or

Second shock ejecta measurements with an explosively driven two-shockwave drive

L/2

The study of high-speed surface dynamics using a pulsed proton beam

. A bifurcation analysis reveals the relationship of these spatially localized solutions to the spatially independent ones and provides a cutoff wavenumber above which there are no spatially dependent solutions; this establishes an upper bound on the number of local excitations comprising the spatial pattern. A linear stability analysis shows that the spatially localized solutions undergo a Hopf bifurcation to temporal quasi-periodicity as the driver amplitude

Explosively driven two-shockwave tools with applications

\Gamma

Quantification of ejecta from shock loaded metal surfaces

is increased. For sufficiently high driver frequencies, the temporally periodic solution regains its stability (via another Hopf bifurcation) in a

Rayleigh-Taylor instability at spherical interfaces between viscous fluids: Fluid/vacuum interface

\Gamma