1,364 research outputs found
A new model for mixing by double-diffusive convection (semi-convection): I. The conditions for layer formation
The process referred to as "semi-convection" in astrophysics and
"double-diffusive convection in the diffusive regime" in Earth and planetary
sciences, occurs in stellar and planetary interiors in regions which are stable
according to the Ledoux criterion but unstable according to the Schwarzschild
criterion. In this series of papers, we analyze the results of an extensive
suite of 3D numerical simulations of the process, and ultimately propose a new
1D prescription for heat and compositional transport in this regime which can
be used in stellar or planetary structure and evolution models.
In a preliminary study of the phenomenon, Rosenblum et al. (2011) showed
that, after saturation of the primary instability, a system can evolve in one
of two possible ways: the induced turbulence either remains homogeneous, with
very weak transport properties, or transitions into a thermo-compositional
staircase where the transport rate is much larger (albeit still smaller than in
standard convection).
In this paper, we show that this dichotomous behavior is a robust property of
semi-convection across a wide region of parameter space. We propose a simple
semi-analytical criterion to determine whether layer formation is expected or
not, and at what rate it proceeds, as a function of the background
stratification and of the diffusion parameters (viscosity, thermal diffusivity
and compositional diffusivity) only. The theoretical criterion matches the
outcome of our numerical simulations very adequately in the numerically
accessible "planetary" parameter regime, and can easily be extrapolated to the
stellar parameter regime.
Subsequent papers will address more specifically the question of quantifying
transport in the layered case and in the non-layered case.Comment: Submitted to Ap
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
Dynamics of fingering convection II: The formation of thermohaline staircases
Regions of the ocean's thermocline unstable to salt fingering are often
observed to host thermohaline staircases, stacks of deep well-mixed convective
layers separated by thin stably-stratified interfaces. Decades after their
discovery, however, their origin remains controversial. In this paper we use 3D
direct numerical simulations to shed light on the problem. We study the
evolution of an analogous double-diffusive system, starting from an initial
statistically homogeneous fingering state and find that it spontaneously
transforms into a layered state. By analysing our results in the light of the
mean-field theory developed in Paper I, a clear picture of the sequence of
events resulting in the staircase formation emerges. A collective instability
of homogeneous fingering convection first excites a field of gravity waves,
with a well-defined vertical wavelength. However, the waves saturate early
through regular but localized breaking events, and are not directly responsible
for the formation of the staircase. Meanwhile, slower-growing, horizontally
invariant but vertically quasi-periodic gamma-modes are also excited and grow
according to the gamma-instability mechanism. Our results suggest that the
nonlinear interaction between these various mean-field modes of instability
leads to the selection of one particular gamma-mode as the staircase
progenitor. Upon reaching a critical amplitude, this progenitor overturns into
a fully-formed staircase. We conclude by extending the results of our
simulations to real oceanic parameter values, and find that the progenitor
gamma-mode is expected to grow on a timescale of a few hours, and leads to the
formation of a thermohaline staircase in about one day with an initial spacing
of the order of one to two metres.Comment: 18 pages, 9 figures, associated mpeg file at
http://earth.uni-muenster.de/~stellma/movie_small.mp4, submitted to JF
Guiding of Rydberg atoms in a high-gradient magnetic guide
We study the guiding of Rb 59D Rydberg atoms in a linear,
high-gradient, two-wire magnetic guide. Time delayed microwave ionization and
ion detection are used to probe the Rydberg atom motion. We observe guiding of
Rydberg atoms over a period of 5 ms following excitation. The decay time of the
guided atom signal is about five times that of the initial state. We attribute
the lifetime increase to an initial phase of -changing collisions and
thermally induced Rydberg-Rydberg transitions. Detailed simulations of Rydberg
atom guiding reproduce most experimental observations and offer insight into
the internal-state evolution
Tracking and data systems support for the Helios project. Volume 2: DSN support of Project Helios April 1975 - May 1976
Deep Space Network activities in the development of the Helios B mission from planning through entry of Helios 2 into first superior conjunction (end of Mission Phase II) are summarized. Network operational support activities for Helios 1 from first superior conjunction through entry into third superior conjunction are included
TOFtracker: combination of time-of-flight and high-accuracy bidimensional tracking in a single gaseous detector
A 5-gap timing RPC equipped with patterned electrodes coupled to both charge-sensitive and
timing circuits yields a time accuracy of 77 ps along with a position accuracy of 38 μm. These
results were obtained by calculating the straight-line fit residuals to the positions provided by a
3-layer telescope made out of identical detectors, detecting almost perpendicular cosmic-ray
muons. The device may be useful for particle identification by time-of-flight, where
simultaneous measurements of trajectory and time are necessary
Assigning channels via the meet-in-the-middle approach
We study the complexity of the Channel Assignment problem. By applying the
meet-in-the-middle approach we get an algorithm for the -bounded Channel
Assignment (when the edge weights are bounded by ) running in time
. This is the first algorithm which breaks the
barrier. We extend this algorithm to the counting variant, at the
cost of slightly higher polynomial factor.
A major open problem asks whether Channel Assignment admits a -time
algorithm, for a constant independent of . We consider a similar
question for Generalized T-Coloring, a CSP problem that generalizes \CA. We
show that Generalized T-Coloring does not admit a
-time algorithm, where is the
size of the instance.Comment: SWAT 2014: 282-29
Lower Bounds for the Graph Homomorphism Problem
The graph homomorphism problem (HOM) asks whether the vertices of a given
-vertex graph can be mapped to the vertices of a given -vertex graph
such that each edge of is mapped to an edge of . The problem
generalizes the graph coloring problem and at the same time can be viewed as a
special case of the -CSP problem. In this paper, we prove several lower
bound for HOM under the Exponential Time Hypothesis (ETH) assumption. The main
result is a lower bound .
This rules out the existence of a single-exponential algorithm and shows that
the trivial upper bound is almost asymptotically
tight.
We also investigate what properties of graphs and make it difficult
to solve HOM. An easy observation is that an upper
bound can be improved to where
is the minimum size of a vertex cover of . The second
lower bound shows that the upper bound is
asymptotically tight. As to the properties of the "right-hand side" graph ,
it is known that HOM can be solved in time and
where is the maximum degree of
and is the treewidth of . This gives
single-exponential algorithms for graphs of bounded maximum degree or bounded
treewidth. Since the chromatic number does not exceed
and , it is natural to ask whether similar
upper bounds with respect to can be obtained. We provide a negative
answer to this question by establishing a lower bound for any
function . We also observe that similar lower bounds can be obtained for
locally injective homomorphisms.Comment: 19 page
- …