70,574 research outputs found
Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study
We study the singular effects of vanishingly small surface tension on the
dynamics of finger competition in the Saffman-Taylor problem, using the
asymptotic techniques described in [S. Tanveer, Phil. Trans. R. Soc. Lond. A
343, 155 (1993)]and [M. Siegel, and S. Tanveer, Phys. Rev. Lett. 76, 419
(1996)] as well as direct numerical computation, following the numerical scheme
of [T. Hou, J. Lowengrub, and M. Shelley,J. Comp. Phys. 114, 312 (1994)]. We
demonstrate the dramatic effects of small surface tension on the late time
evolution of two-finger configurations with respect to exact (non-singular)
zero surface tension solutions. The effect is present even when the relevant
zero surface tension solution has asymptotic behavior consistent with selection
theory.Such singular effects therefore cannot be traced back to steady state
selection theory, and imply a drastic global change in the structure of
phase-space flow. They can be interpreted in the framework of a recently
introduced dynamical solvability scenario according to which surface tension
unfolds the structually unstable flow, restoring the hyperbolicity of
multifinger fixed points.Comment: 16 pages, 15 figures, submitted to Phys. Rev
The development of transient fingering patterns during the spreading of surfactant coated films
The spontaneous spreading of an insoluble surfactant monolayer on a thin liquid film produces a complex waveform whose time variant shape is strongly influenced by the surface shear stress. This Marangoni stress produces a shocklike front at the leading edge of the spreading monolayer and significant film thinning near the source. For sufficiently thin films or large initial shear stress, digitated structures appear in the wake of the advancing monolayer. These structures funnel the oncoming flow into small arteries that continuously tip-split to produce spectacular dendritic shapes. A previous quasisteady modal analysis has predicted stable flow at asymptotically long times [Phys. Fluids A 9, 3645 (1997)]. A more recent transient analysis has revealed large amplification in the disturbance film thickness at early times [O. K. Matar and S. M. Troian, "Growth of nonmodal transient structures during the spreading of surfactant coated films," Phys. Fluids A 10, 1234 (1998)]. In this paper, we report results of an extended sensitivity analysis which probes two aspects of the flow: the time variant character of the base state and the non-normal character of the disturbance operators. The analysis clearly identifies Marangoni forces as the main source of digitation for both small and large wave number disturbances. Furthermore, initial conditions which increase the initial shear stress or which steepen the shape of the advancing front produce a larger transient response and deeper corrugations in the film. Disturbances applied just ahead of the deposited monolayer rapidly fall behind the advancing front eventually settling in the upstream region where their mobility is hampered. Recent findings confirm that additional forces which promote film thinning can further intensify disturbances [O. K. Matar and S. M. Troian, "Spreading of surfactant monolayer on a thin liquid film: Onset and evolution of digitated structures," Chaos 9, 141 (1999). The transient analysis presented here corroborates our previous results for asymptotic stability but reveals a source for digitation at early times. The energy decomposition lends useful insight into the actual mechanisms preventing efficacious distribution of surfactant
The Dynamic Behavior of Soft Gamma Repeaters
Soft Gamma Repeaters (SGRs) undergo changes in their pulse properties and
persistent emission during episodes of intense burst activity. Both SGR 1900+14
and SGR 1806-20 have shown significant changes in their spin-down rates during
the last several years, yet the bulk of this variability is not correlated with
burst activity. SGR 1900+14 has undergone large changes in flux and a dramatic
pulse profile change following burst activity in 1998. The flux level of SGR
162741 has been decreasing since its only recorded burst activity. Here, we
review the global properties of SGRs as well as the observed dynamics of the
pulsed and persistent emission properties of SGR 1900+14, SGR 1806-20 and SGR
1627-41 during and following burst active episodes and discuss what
implications these results have for the burst emission mechanism, the magnetic
field dynamics of magnetars, the nature of the torque variability, and SGRs in
general.Comment: Invited review to appear in "High Energy Studies of Supernova
Remnants and Neutron Stars" (COSPAR 2002). 12 pages, 7 figure
Growth saturation of unstable thin films on transverse-striped hydrophilic-hydrophobic micropatterns
Using three-dimensional numerical simulations, we demonstrate the growth
saturation of an unstable thin liquid film on micropatterned
hydrophilic-hydrophobic substrates. We consider different transverse-striped
micropatterns, characterized by the total fraction of hydrophilic coverage and
the width of the hydrophilic stripes. We compare the growth of the film on the
micropatterns to the steady states observed on homogeneous substrates, which
correspond to a saturated sawtooth and growing finger configurations for
hydrophilic and hydrophobic substrates, respectively. The proposed
micropatterns trigger an alternating fingering-spreading dynamics of the film,
which leads to a complete suppression of the contact line growth above a
critical fraction of hydrophilic stripes. Furthermore, we find that increasing
the width of the hydrophilic stripes slows down the advancing front, giving
smaller critical fractions the wider the hydrophilic stripes are. Using
analytical approximations, we quantitatively predict the growth rate of the
contact line as a function of the covering fraction, and predict the threshold
fraction for saturation as a function of the stripe width.Comment: 11 pages, 5 figure
Dynamics of fingering convection I: Small-scale fluxes and large-scale instabilities
Double-diffusive instabilities are often invoked to explain enhanced
transport in stably-stratified fluids. The most-studied natural manifestation
of this process, fingering convection, commonly occurs in the ocean's
thermocline and typically increases diapycnal mixing by two orders of magnitude
over molecular diffusion. Fingering convection is also often associated with
structures on much larger scales, such as thermohaline intrusions, gravity
waves and thermohaline staircases. In this paper, we present an exhaustive
study of the phenomenon from small to large scales. We perform the first
three-dimensional simulations of the process at realistic values of the heat
and salt diffusivities and provide accurate estimates of the induced turbulent
transport. Our results are consistent with oceanic field measurements of
diapycnal mixing in fingering regions. We then develop a generalized mean-field
theory to study the stability of fingering systems to large-scale
perturbations, using our calculated turbulent fluxes to parameterize
small-scale transport. The theory recovers the intrusive instability, the
collective instability, and the gamma-instability as limiting cases. We find
that the fastest-growing large-scale mode depends sensitively on the ratio of
the background gradients of temperature and salinity (the density ratio). While
only intrusive modes exist at high density ratios, the collective and
gamma-instabilities dominate the system at the low density ratios where
staircases are typically observed. We conclude by discussing our findings in
the context of staircase formation theory.Comment: 23 pages, 9 figures, submitted to JF
Model for Human, Artificial & Collective Consciousness (Part I)
Borrowing the functional modeling approach common in systems and software engineering, an implementable model of the functions of human consciousness proposed to have the capacity for general problem solving ability transferable to any domain, or true self-aware intelligence, is presented. Being a functional model that is independent of implementation, this model is proposed to also be applicable to artificial consciousness, and to platforms that organize individuals into what is defined here as a first order collective consciousness, or at higher orders into what is defined here as Nth order collective consciousness. Part I of this two-part article includes: Summary; Introduction; Set of Postulates One; Set of Postulates Two; Overview of the Model; Model of Homeostasis; Model of the Functional Units; Model of the Body System; Model of the Other Basic Life Processes; Model of the Other Functional Systems; Model of Perceptions in the Perceptual Fields; Model of Body Processes as Paths in the Perceptual Field; & Model of Conscious Awarenes
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