124 research outputs found
Surface Geometry of 5D Black Holes and Black Rings
We discuss geometrical properties of the horizon surface of five-dimensional
rotating black holes and black rings. Geometrical invariants characterizing
these 3D geometries are calculated. We obtain a global embedding of the 5D
rotating black horizon surface into a flat space. We also describe the
Kaluza-Klein reduction of the black ring solution (along the direction of its
rotation) which relates this solution to the 4D metric of a static black hole
distorted by the presence of external scalar (dilaton) and vector
(`electromagnetic') field. The properties of the reduced black hole horizon and
its embedding in \E^3 are briefly discussed.Comment: 10 pages, 9 figures, Revtex
Advanced Data Analytics towards Energy Efficient and Emission Reduction Retrofit Technology Integration in Shipping
An overview of integrating two energy efficient and emission reduction technologies to improve ship energy efficiency under advanced data analytics is presented in this study. The proposed technologies consist of developing engine and propulsion innovations that will be experimented under laboratory conditions and large-model-scale sea trials, respectively. These experiments will collect large amount of data sets that will be used to quantify the performance of both innovations under the advanced data analytics framework (ADAF). Hence, extensive details on the ADAF along with preliminary data sets collected from a case study vessel are presented in this study
Abelian BF theory and Turaev-Viro invariant
The U(1) BF Quantum Field Theory is revisited in the light of
Deligne-Beilinson Cohomology. We show how the U(1) Chern-Simons partition
function is related to the BF one and how the latter on its turn coincides with
an abelian Turaev-Viro invariant. Significant differences compared to the
non-abelian case are highlighted.Comment: 47 pages and 6 figure
Spherical structures on torus knots and links
The present paper considers two infinite families of cone-manifolds endowed
with spherical metric. The singular strata is either the torus knot or the torus link . Domains of existence for a
spherical metric are found in terms of cone angles and volume formul{\ae} are
presented.Comment: 17 pages, 5 figures; typo
Post Quantum Cryptography from Mutant Prime Knots
By resorting to basic features of topological knot theory we propose a
(classical) cryptographic protocol based on the `difficulty' of decomposing
complex knots generated as connected sums of prime knots and their mutants. The
scheme combines an asymmetric public key protocol with symmetric private ones
and is intrinsecally secure against quantum eavesdropper attacks.Comment: 14 pages, 5 figure
On the size of knots in ring polymers
We give two different, statistically consistent definitions of the length l
of a prime knot tied into a polymer ring. In the good solvent regime the
polymer is modelled by a self avoiding polygon of N steps on cubic lattice and
l is the number of steps over which the knot ``spreads'' in a given
configuration. An analysis of extensive Monte Carlo data in equilibrium shows
that the probability distribution of l as a function of N obeys a scaling of
the form p(l,N) ~ l^(-c) f(l/N^D), with c ~ 1.25 and D ~ 1. Both D and c could
be independent of knot type. As a consequence, the knot is weakly localized,
i.e. ~ N^t, with t=2-c ~ 0.75. For a ring with fixed knot type, weak
localization implies the existence of a peculiar characteristic length l^(nu) ~
N^(t nu). In the scaling ~ N^(nu) (nu ~0.58) of the radius of gyration of the
whole ring, this length determines a leading power law correction which is much
stronger than that found in the case of unrestricted topology. The existence of
such correction is confirmed by an analysis of extensive Monte Carlo data for
the radius of gyration. The collapsed regime is studied by introducing in the
model sufficiently strong attractive interactions for nearest neighbor sites
visited by the self-avoiding polygon. In this regime knot length determinations
can be based on the entropic competition between two knotted loops separated by
a slip link. These measurements enable us to conclude that each knot is
delocalized (t ~ 1).Comment: 29 pages, 14 figure
Quantum Knitting
We analyze the connections between the mathematical theory of knots and
quantum physics by addressing a number of algorithmic questions related to both
knots and braid groups.
Knots can be distinguished by means of `knot invariants', among which the
Jones polynomial plays a prominent role, since it can be associated with
observables in topological quantum field theory.
Although the problem of computing the Jones polynomial is intractable in the
framework of classical complexity theory, it has been recently recognized that
a quantum computer is capable of approximating it in an efficient way. The
quantum algorithms discussed here represent a breakthrough for quantum
computation, since approximating the Jones polynomial is actually a `universal
problem', namely the hardest problem that a quantum computer can efficiently
handle.Comment: 29 pages, 5 figures; to appear in Laser Journa
The Combinatorics of Alternating Tangles: from theory to computerized enumeration
We study the enumeration of alternating links and tangles, considered up to
topological (flype) equivalences. A weight is given to each connected
component, and in particular the limit yields information about
(alternating) knots. Using a finite renormalization scheme for an associated
matrix model, we first reduce the task to that of enumerating planar
tetravalent diagrams with two types of vertices (self-intersections and
tangencies), where now the subtle issue of topological equivalences has been
eliminated. The number of such diagrams with vertices scales as for
. We next show how to efficiently enumerate these diagrams (in time
) by using a transfer matrix method. We give results for various
generating functions up to 22 crossings. We then comment on their large-order
asymptotic behavior.Comment: proceedings European Summer School St-Petersburg 200
- …