14,604 research outputs found
Localized Activation of Bending in Proximal, Medial and Distal Regions of Sea-Urchin Sperm Flagella
Spermatozoa from the sea urchin, Colobocentrotus atratus, were partially demembranated by extraction with solutions containing Triton X-100 at a concentration which was insufficient to solubilize the membranes completely. The resulting suspension was a mixture containing some spermatozoa in which a proximal, medial, or distal portion of the flagellum was membrane-covered, while the remaining portion was naked axoneme. In reactivating solutions containing 12 µM ATP, only the naked portions of the flagellum became motile. In reactivating solutions containing 0.8 mM ADP, the membrane-covered regions became motile and beat at 6-10 beats/s, while the naked regions remained immobile, or beat very slowly at about 0.3 beat/s. Activation of membrane-covered regions in ADP solutions probably results from the membrane restricting the diffusion of ATP which is formed from ADP by the axonemal adenylate kinase. The results indicate that any region of the flagellum has the capacity for autonomous beating, and that special properties of the basal end of the flagellum are not required for bend initiation. However, the beating of different regions of the flagellum is not completely independent, for in a fair number of spermatozoa the beating of the distal, membrane-covered region in 0.8 mM ADP was intermittent, and was turned on and off in phase with the much slower bending cycle in the proximal region of naked axoneme
Moduli, Scalar Charges, and the First Law of Black Hole Thermodynamics
We show that under variation of moduli fields the first law of black
hole thermodynamics becomes , where are the scalar charges. We also show
that the ADM mass is extremized at fixed , , when the moduli
fields take the fixed value which depend only on electric
and magnetic charges. It follows that the least mass of any black hole with
fixed conserved electric and magnetic charges is given by the mass of the
double-extreme black hole with these charges. Our work allows us to interpret
the previously established result that for all extreme black holes the moduli
fields at the horizon take a value depending only
on the electric and magnetic conserved charges: is such
that the scalar charges .Comment: 3 pages, no figures, more detailed versio
Critical Pebbling Numbers of Graphs
We define three new pebbling parameters of a connected graph , the -,
-, and -critical pebbling numbers. Together with the pebbling number, the
optimal pebbling number, the number of vertices and the diameter of the
graph, this yields 7 graph parameters. We determine the relationships between
these parameters. We investigate properties of the -critical pebbling
number, and distinguish between greedy graphs, thrifty graphs, and graphs for
which the -critical pebbling number is .Comment: 26 page
Black Hole Solutions of Kaluza-Klein Supergravity Theories and String Theory
We find U(1)_{E} \times U(1)_{M} non-extremal black hole solutions of
6-dimensional Kaluza-Klein supergravity theories. Extremal solutions were found
by Cveti\v{c} and Youm\cite{C-Y}. Multi black hole solutions are also
presented. After electro-magnetic duality transformation is performed, these
multi black hole solutions are mapped into the the exact solutions found by
Horowitz and Tseytlin\cite{H-T} in 5-dimensional string theory compactified
into 4-dimensions. The massless fields of this theory can be embedded into the
heterotic string theory compactified on a 6-torus. Rotating black hole
solutions can be read off those of the heterotic string theory found by
Sen\cite{Sen3}.Comment: 23 pages text(latex), a figure upon reques
Topology, Entropy and Witten Index of Dilaton Black Holes
We have found that for extreme dilaton black holes an inner boundary must be
introduced in addition to the outer boundary to give an integer value to the
Euler number. The resulting manifolds have (if one identifies imaginary time)
topology and Euler number in contrast to
the non-extreme case with . The entropy of extreme dilaton black
holes is already known to be zero. We include a review of some recent ideas due
to Hawking on the Reissner-Nordstr\"om case. By regarding all extreme black
holes as having an inner boundary, we conclude that the entropy of {\sl all}
extreme black holes, including black holes, vanishes. We discuss the
relevance of this to the vanishing of quantum corrections and the idea that the
functional integral for extreme holes gives a Witten Index. We have studied
also the topology of ``moduli space'' of multi black holes. The quantum
mechanics on black hole moduli spaces is expected to be supersymmetric despite
the fact that they are not HyperK\"ahler since the corresponding geometry has
torsion unlike the BPS monopole case. Finally, we describe the possibility of
extreme black hole fission for states with an energy gap. The energy released,
as a proportion of the initial rest mass, during the decay of an
electro-magnetic black hole is 300 times greater than that released by the
fission of an nucleus.Comment: 51 pages, 4 figures, LaTeX. Considerably extended version. New
sections include discussion of the Witten index, topology of the moduli
space, black hole sigma model, and black hole fission with huge energy
releas
Some Comments on Gravitational Entropy and the Inverse Mean Curvature Flow
The Geroch-Wald-Jang-Huisken-Ilmanen approach to the positive energy problem
to may be extended to give a negative lower bound for the mass of
asymptotically Anti-de-Sitter spacetimes containing horizons with exotic
topologies having ends or infinities of the form , in
terms of the cosmological constant. We also show how the method gives a lower
bound for for the mass of time-symmetric initial data sets for black holes with
vectors and scalars in terms of the mass, of the double extreme
black hole with the same charges. I also give a lower bound for the area of an
apparent horizon, and hence a lower bound for the entropy in terms of the same
function . This shows that the so-called attractor behaviour extends
beyond the static spherically symmetric case. and underscores the general
importance of the function . There are hints that higher dimensional
generalizations may involve the Yamabe conjectures.Comment: 13pp. late
Nucleating Black Holes via Non-Orientable Instantons
We extend the analysis of black hole pair creation to include non- orientable
instantons. We classify these instantons in terms of their fundamental
symmetries and orientations. Many of these instantons admit the pin structure
which corresponds to the fermions actually observed in nature, and so the
natural objection that these manifolds do not admit spin structure may not be
relevant. Furthermore, we analyse the thermodynamical properties of
non-orientable black holes and find that in the non-extreme case, there are
interesting modifications of the usual formulae for temperature and entropy.Comment: 27 pages LaTeX, minor typos are correcte
Rational combinations of Betti diagrams of complete intersections
We investigate decompositions of Betti diagrams over a polynomial ring within
the framework of Boij-S\"oderberg theory. That is, given a Betti diagram, we
determine if it is possible to decompose it into the Betti diagrams of complete
intersections. To do so, we determine the extremal rays of the cone generated
by the diagrams of complete intersections and provide a rudimentary algorithm
for decomposition.Comment: This research was conducted at the Willamette Mathematics Consortium
RE
Entropy for dilatonic black hole
The area formula for entropy is extended to the case of a dilatonic black
hole. The entropy of a scalar field in the background of such a black hole is
calculated semiclassically. The area and cutoff dependences are normal {\it
except in the extremal case}, where the area is zero but the entropy nonzero.Comment: 13 pages (Applicability of area formula justified and a reference
added
The Action of Instantons with Nut Charge
We examine the effect of a non-trivial nut charge on the action of
non-compact four-dimensional instantons with a U(1) isometry. If the instanton
action is calculated by dimensionally reducing along the isometry, then the nut
charge is found to make an explicit non-zero contribution. For metrics
satisfying AF, ALF or ALE boundary conditions, the action can be expressed
entirely in terms of quantities (including the nut charge) defined on the fixed
point set of the isometry. A source (or sink) of nut charge also implies the
presence of a Misner string coordinate singularity, which will have an
important effect on the Hamiltonian of the instanton.Comment: 25 page
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