13,640 research outputs found
Strings of droplets propelled by coherent waves
Bouncing walking droplets possess fascinating properties due to their
peculiar wave/particule interaction. In order to study such walkers in a 1d
system, we considered the case of one or more droplets in an annular cavity. We
show that, in this geometry, walking droplets form a string of synchronized
bouncing droplets that share a common coherent wave propelling the group at a
speed faster than single walkers. The formation of this coherent wave and the
collective behavior of droplets is captured by a model.Comment: 5 Pages, 5 Figures, 2 supplementary movies (identical), supplementary
.pdf fil
The fragmentation criteria in local vertically stratified self-gravitating disk simulations
Massive circumstellar disks are prone to gravitational instabilities, which
trigger the formation of spiral arms that can fragment into bound clumps under
the right conditions. Two dimensional simulations of self-gravitating disks are
useful starting points for studying fragmentation, allowing for high-resolution
simulations of thin disks. However, convergence issues can arise in 2D from
various sources. One of these sources is the 2D approximation of self-gravity,
which exaggerates the effect of self-gravity on small scales when the potential
is not smoothed to account for the assumed vertical extent of the disk. This
effect is enhanced by increased resolution, resulting in fragmentation at
longer cooling timescales . If true, it suggests that the 3D simulations
of disk fragmentation may not have the same convergence problem and could be
used to examine the nature of fragmentation without smoothing self-gravity on
scales similar to the disk scale height. To that end, we have carried out local
3D self-gravitating disk simulations with simple cooling with fixed
background irradiation to determine if 3D is necessary to properly describe
disk fragmentation. Above a resolution of grid cells per scale
height, we find that our simulations converge with respect to the cooling
timescale. This result converges in agreement with analytic expectations which
place a fragmentation boundary at .Comment: 11 pages, 9 figures. Accepted for publication in Ap
Defined mutations in the 5' nontranslated sequence of Sindbis virus RNA
We have constructed 24 deletion mutants which contain deletions of from 1 to 15 nucleotides in the 5' nontranslated region of Sindbis virus RNA and tested the effect of these mutations on virus replication. The results showed that the first 44 nucleotides, which are capable of forming a hairpin structure, are important for virus replication, as all deletions tested in this region were either lethal or resulted in virus that grew poorly in comparison to the parental virus. Many of these deletions had different effects in mosquito cells than in chicken cells, suggesting that cellular factors, presumably proteins, bind to this region. This domain may function in at least two processes in viral replication. It seems likely that in the minus strand, this sequence element is bound by the viral replicase and promotes RNA replication. In the plus strand, this element may modulate initiation of translation of the nonstructural proteins. The results suggest that the hairpin structure itself is important. All deletions within it had deleterious effects on virus replication, and in particular, deletion of one of the G residues at nucleotide 7 or 8 or of one of the C residues at nucleotide 36 or 37 which are theoretically base-paired with these G's resulted in temperature-sensitive viruses that behaved very similarly. In contrast, large deletions between the 44-nucleotide hairpin and the translation start site at nucleotides 60 to 62 resulted in virus that grew as well as or better than the parental virus in both chicken and mosquito cells. The A residue at position 5 of the HRSP strain used was examined in more detail. Deletion of this A was lethal, whereas substitution by G resulted in a virus that grew poorly, despite the fact that G is present at position 5 in the AR339 parent of HRSP. U at position 5 resulted in a virus that grew less well than the A5 strain but better than the G5 mutant
Mutagenesis of the conserved 51-nucleotide region of Sindbis virus
We have constructed 25 site-specific mutations in a domain of 51 nucleotides in Sindbis virus that is highly conserved among all alphaviruses sequenced to date. These 51 nucleotides are capable of forming two hairpin structures and are found from nucleotides 155 to 205 in Sindbis virus within the region encoding nsP1. Of the mutations, 21 were silent and did not lead to a change in the amino acid sequence encoded. These silent mutations changed not only the linear sequence but also the stability of the hairpins in most cases. Two double mutants that were constructed led to the replacement of one base pair by another so that the linear sequence was altered but the nature of the hairpins was not. All of the mutants with silent mutations were viable, but 19 of the 21 mutants were severely impaired for growth in both chicken and mosquito cells. Compared with the parental virus, they grew slowly and produced virus at rates of 10(-1) to 10(-4) times the parental rate. Surprisingly, however, the plaques produced by these mutants were indistinguishable from those produced by the parental virus. Two of the silent mutations, found within the first hairpin structure, produced virus at a faster rate than the parental virus. It is clear that the exact sequence of this region is important for some aspect of virus replication. We suggest that one or more proteins, either virus encoded or cellular, bind to the hairpin structures in a sequence-specific fashion in a step that promotes replication of the viral RNA. Of the mutations that resulted in a change of coding, only one of four was viable, suggesting that the amino acid sequence encoded in this domain is essential for virus replication
Rational invariants of even ternary forms under the orthogonal group
In this article we determine a generating set of rational invariants of
minimal cardinality for the action of the orthogonal group on
the space of ternary forms of even degree . The
construction relies on two key ingredients: On one hand, the Slice Lemma allows
us to reduce the problem to dermining the invariants for the action on a
subspace of the finite subgroup of signed permutations. On the
other hand, our construction relies in a fundamental way on specific bases of
harmonic polynomials. These bases provide maps with prescribed
-equivariance properties. Our explicit construction of these
bases should be relevant well beyond the scope of this paper. The expression of
the -invariants can then be given in a compact form as the
composition of two equivariant maps. Instead of providing (cumbersome) explicit
expressions for the -invariants, we provide efficient algorithms
for their evaluation and rewriting. We also use the constructed
-invariants to determine the -orbit locus and
provide an algorithm for the inverse problem of finding an element in
with prescribed values for its invariants. These are
the computational issues relevant in brain imaging.Comment: v3 Changes: Reworked presentation of Neuroimaging application,
refinement of Definition 3.1. To appear in "Foundations of Computational
Mathematics
Roughening and preroughening in the six vertex model with an extended range of interaction
We study the phase diagram of the BCSOS model with an extended interaction
range using transfer matrix techniques, pertaining to the (100) surface of
single component fcc and bcc crystals. The model shows a 2x2 reconstructed
phase and a disordered flat phase. The deconstruction transition between these
phases merges with a Kosterlitz-Thouless line, showing an interplay of Ising
and Gaussian degrees of freedom. As in studies of the fully frustrated XY
model, exponents deviating from Ising are found. We conjecture that
tri-critical Ising behavior may be a possible explanation for the non-Ising
exponents found in those models.Comment: 25 pages in RevTeX 3.0, seven uuencoded postscript figures, REPLACED
because of submission error (figures were not included
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