7,465 research outputs found
Branching Interfaces with Infinitely Strong Couplings
A hierarchical froth model of the interface of a random -state Potts
ferromagnet in is studied by recursive methods. A fraction of the
nearest neighbour bonds is made inaccessible to domain walls by infinitely
strong ferromagnetic couplings. Energetic and geometric scaling properties of
the interface are controlled by zero temperature fixed distributions. For
, the directed percolation threshold, the interface behaves as for
, and scaling supports random Ising () critical behavior for all
's. At three regimes are obtained for different ratios of ferro vs.
antiferromagnetic couplings. With rates above a threshold value the interface
is linear ( fractal dimension ) and its energy fluctuations,
scale with length as , with .
When the threshold is reached the interface branches at all scales and is
fractal () with . Thus, at ,
dilution modifies both low temperature interfacial properties and critical
scaling. Below threshold the interface becomes a probe of the backbone geometry
(\df\simeq{\bar d}\simeq 1.305; = backbone fractal dimension ),
which even controls energy fluctuations ().
Numerical determinations of directed percolation exponents on diamond
hierarchical lattice are also presented.Comment: 16 pages, 3 Postscript figure
Pseudoknots in a Homopolymer
After a discussion of the definition and number of pseudoknots, we reconsider
the self-attracting homopolymer paying particular attention to the scaling of
the number of pseudoknots at different temperature regimes in two and three
dimensions. Although the total number of pseudoknots is extensive at all
temperatures, we find that the number of pseudoknots forming between the two
halves of the chain diverges logarithmically at (in both dimensions) and below
(in 2d only) the theta-temparature. We later introduce a simple model that is
sensitive to pseudoknot formation during collapse. The resulting phase diagram
involves swollen, branched and collapsed homopolymer phases with transitions
between each pair.Comment: submitted to PR
Strong gravitational field light deflection in binary systems containing a collapsed star
Large light deflection angles are produced in the strong gravitational field
regions around neutron stars and black holes. In the case of binary systems,
part of the photons emitted from the companion star towards the collapsed
object are expected to be deflected in the direction of the earth. Based on a
semi-classical approach we calculate the characteristic time delays and
frequency shifts of these photons as a function of the binary orbital phase.
The intensity of the strongly deflected light rays is reduced by many orders of
magnitude, therefore making the observations of this phenomenon extremely
difficult. Relativistic binary systems containing a radio pulsar and a
collapsed object are the best available candidates for the detection of the
strongly deflected photons. Based on the accurate knowledge of their orbital
parameters, these systems allow to predict accurately the delays of the pulses
along the highly deflected path, such that the sensitivity to very weak signals
can be substantially improved through coherent summation over long time
intervals. We discuss in detail the cases of PSR 1913+16 and PSR 1534+12 and
find that the system geometry is far more promising for the latter. The
observation of the highly deflected photons can provide a test of general
relativity in an unprecedented strong field regime as well as a tight
constraint on the radius of the collapsed object.Comment: 7 pages, uuencoded, gzip'ed, postscript file with figures included.
Accepted for pubblication in MNRA
Topological and geometrical entanglement in a model of circular DNA undergoing denaturation
The linking number (topological entanglement) and the writhe (geometrical
entanglement) of a model of circular double stranded DNA undergoing a thermal
denaturation transition are investigated by Monte Carlo simulations. By
allowing the linking number to fluctuate freely in equilibrium we see that the
linking probability undergoes an abrupt variation (first-order) at the
denaturation transition, and stays close to 1 in the whole native phase. The
average linking number is almost zero in the denatured phase and grows as the
square root of the chain length, N, in the native phase. The writhe of the two
strands grows as the square root of N in both phases.Comment: 7 pages, 11 figures, revte
The entropic cost to tie a knot
We estimate by Monte Carlo simulations the configurational entropy of
-steps polygons in the cubic lattice with fixed knot type. By collecting a
rich statistics of configurations with very large values of we are able to
analyse the asymptotic behaviour of the partition function of the problem for
different knot types. Our results confirm that, in the large limit, each
prime knot is localized in a small region of the polygon, regardless of the
possible presence of other knots. Each prime knot component may slide along the
unknotted region contributing to the overall configurational entropy with a
term proportional to . Furthermore, we discover that the mere existence
of a knot requires a well defined entropic cost that scales exponentially with
its minimal length. In the case of polygons with composite knots it turns out
that the partition function can be simply factorized in terms that depend only
on prime components with an additional combinatorial factor that takes into
account the statistical property that by interchanging two identical prime knot
components in the polygon the corresponding set of overall configuration
remains unaltered. Finally, the above results allow to conjecture a sequence of
inequalities for the connective constants of polygons whose topology varies
within a given family of composite knot types
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