520 research outputs found
Macroscopic loop formation in circular DNA denaturation
The statistical mechanics of DNA denaturation under fixed linking number is
qualitatively different from that of the unconstrained DNA. Quantitatively
different melting scenarios are reached from two alternative assumptions,
namely, that the denatured loops are formed in expense of 1) overtwist, 2)
supercoils. Recent work has shown that the supercoiling mechanism results in a
BEC-like picture where a macroscopic loop appears at Tc and grows steadily with
temperature, while the nature of the denatured phase for the overtwisting case
has not been studied. By extending an earlier result, we show here that a
macroscopic loop appears in the overtwisting scenario as well. We calculate its
size as a function of temperature and show that the fraction of the total sum
of microscopic loops decreases above Tc, with a cusp at the critical point.Comment: 5 pages, 3 figures, submitted for publicatio
Exact extreme value statistics at mixed order transitions
We study extreme value statistics (EVS) for spatially extended models
exhibiting mixed order phase transitions (MOT). These are phase transitions
which exhibit features common to both first order (discontinuity of the order
parameter) and second order (diverging correlation length) transitions. We
consider here the truncated inverse distance squared Ising (TIDSI) model which
is a prototypical model exhibiting MOT, and study analytically the extreme
value statistics of the domain lengths. The lengths of the domains are
identically distributed random variables except for the global constraint that
their sum equals the total system size . In addition, the number of such
domains is also a fluctuating variable, and not fixed. In the paramagnetic
phase, we show that the distribution of the largest domain length
converges, in the large limit, to a Gumbel distribution. However, at the
critical point (for a certain range of parameters) and in the ferromagnetic
phase, we show that the fluctuations of are governed by novel
distributions which we compute exactly. Our main analytical results are
verified by numerical simulations.Comment: 25 pages, 6 figures, 1 tabl
Fabrication of Nano-Scale Gaps in Integrated Circuits
Nano-size objects like metal clusters present an ideal system for the study
of quantum phenomena and for constructing practical quantum devices.
Integrating these small objects in a macroscopic circuit is, however, a
difficult task. So far the nanoparticles have been contacted and addressed by
highly sophisticated techniques which are not suitable for large scale
integration in macroscopic circuits. We present an optical lithography method
that allows for the fabrication of a network of electrodes which are separated
by gaps of controlled nanometer size. The main idea is to control the gap size
with subnanometer precision using a structure grown by molecular beam epitaxy.Comment: 4 pages, 3 figure
Denaturation of Circular DNA: Supercoil Mechanism
The denaturation transition which takes place in circular DNA is analyzed by
extending the Poland-Scheraga model to include the winding degrees of freedom.
We consider the case of a homopolymer whereby the winding number of the double
stranded helix, released by a loop denaturation, is absorbed by
\emph{supercoils}. We find that as in the case of linear DNA, the order of the
transition is determined by the loop exponent . However the first order
transition displayed by the PS model for in linear DNA is replaced by a
continuous transition with arbitrarily high order as approaches 2, while
the second-order transition found in the linear case in the regime
disappears. In addition, our analysis reveals that melting under fixed linking
number is a \emph{condensation transition}, where the condensate is a
macroscopic loop which appears above the critical temperature.Comment: 9 pages, 4 figure
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