13 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
Twist/Writhe Partitioning in a Coarse-Grained DNA Minicircle Model
Here we present a systematic study of supercoil formation in DNA minicircles
under varying linking number by using molecular dynamics simulations of a
two-bead coarse-grained model. Our model is designed with the purpose of
simulating long chains without sacrificing the characteristic structural
properties of the DNA molecule, such as its helicity, backbone directionality
and the presence of major and minor grooves. The model parameters are extracted
directly from full-atomistic simulations of DNA oligomers via Boltzmann
inversion, therefore our results can be interpreted as an extrapolation of
those simulations to presently inaccessible chain lengths and simulation times.
Using this model, we measure the twist/writhe partitioning in DNA minicircles,
in particular its dependence on the chain length and excess linking number. We
observe an asymmetric supercoiling transition consistent with experiments. Our
results suggest that the fraction of the linking number absorbed as twist and
writhe is nontrivially dependent on chain length and excess linking number.
Beyond the supercoiling transition, chains of the order of one persistence
length carry equal amounts of twist and writhe. For longer chains, an
increasing fraction of the linking number is absorbed by the writhe.Comment: 21 pages, 7 figures, 1 tabl
Phase transitions in tetrahedral Ising lattices
Ankara : Department of Physics and Institute of Engineering and Sciences, Bilkent Univ., 1993.Thesis (Master's) -- Bilkent University, 1993.Includes bibliographical references leaves 38-40After a review of the Renormalization CJroup theory, the phase diagram
of unisotro])ic tetrahedral Ising lattice is explored l)y the motivation gained
through the recent experimental findings about SiGe alloys. Renormalization
Group approcich and the mean-field R(J approximation previously pro])osed
by Kinzel ¿ire used. Four different ordered pluises are olxserved. The critical
expoiKMit // is Ciih’uhited using the liiUNirized t.ra.nsform<ition ¿iround the fixed
points and ('om|)fii’ed with previous works. It is ('oiu'luded tluit the newly
observed orderings in Si(!e superlattices are induced by surface effects.Kabakçıoğlu, AlkanM.S
A Quantum Otto Engine with Shortcuts to Thermalization and Adiabaticity
We investigate the energetic advantage of accelerating a quantum harmonic
oscillator Otto engine by use of shortcuts to adiabaticity (for the power and
compression strokes) and to equilibrium (for the hot isochore), by means of
counter-diabatic (CD) driving. By comparing various protocols with and without
CD driving, we find that, applying both type of shortcuts leads to enhanced
power and efficiency even after the driving costs are taken into account. The
hybrid protocol not only retains its advantage in the limit cycle, but also
recovers engine functionality (i.e., a positive power output) in parameter
regimes where an uncontrolled, finite-time Otto cycle fails. We show that
controlling three strokes of the cycle leads to an overall improvement of the
performance metrics compared with controlling only the two adiabatic strokes.
Moreover, we numerically calculate the limit cycle behavior of the engine and
show that the engines with accelerated isochoric and adiabatic strokes display
a superior power output in this mode of operation.Comment: 12 pages, 7 figure
Machine learning in and out of equilibrium
The algorithms used to train neural networks, like stochastic gradient
descent (SGD), have close parallels to natural processes that navigate a
high-dimensional parameter space -- for example protein folding or evolution.
Our study uses a Fokker-Planck approach, adapted from statistical physics, to
explore these parallels in a single, unified framework. We focus in particular
on the stationary state of the system in the long-time limit, which in
conventional SGD is out of equilibrium, exhibiting persistent currents in the
space of network parameters. As in its physical analogues, the current is
associated with an entropy production rate for any given training trajectory.
The stationary distribution of these rates obeys the integral and detailed
fluctuation theorems -- nonequilibrium generalizations of the second law of
thermodynamics. We validate these relations in two numerical examples, a
nonlinear regression network and MNIST digit classification. While the
fluctuation theorems are universal, there are other aspects of the stationary
state that are highly sensitive to the training details. Surprisingly, the
effective loss landscape and diffusion matrix that determine the shape of the
stationary distribution vary depending on the simple choice of minibatching
done with or without replacement. We can take advantage of this nonequilibrium
sensitivity to engineer an equilibrium stationary state for a particular
application: sampling from a posterior distribution of network weights in
Bayesian machine learning. We propose a new variation of stochastic gradient
Langevin dynamics (SGLD) that harnesses without replacement minibatching. In an
example system where the posterior is exactly known, this SGWORLD algorithm
outperforms SGLD, converging to the posterior orders of magnitude faster as a
function of the learning rate.Comment: 24 pages, 6 figure
Deep Spin-Glass Hysteresis Area Collapse and Scaling in the Ising Model
We investigate the dissipative loss in the Ising spin glass in three
dimensions through the scaling of the hysteresis area, for a maximum magnetic
field that is equal to the saturation field. We perform a systematic analysis
for the whole range of the bond randomness as a function of the sweep rate, by
means of frustration-preserving hard-spin mean field theory. Data collapse
within the entirety of the spin-glass phase driven adiabatically (i.e.,
infinitely-slow field variation) is found, revealing a power-law scaling of the
hysteresis area as a function of the antiferromagnetic bond fraction and the
temperature. Two dynamic regimes separated by a threshold frequency
characterize the dependence on the sweep rate of the oscillating field. For
, the hysteresis area is equal to its value in the adiabatic
limit , while for it increases with the
frequency through another randomness-dependent power law.Comment: 6 pages, 6 figure
Denaturation of Circular DNA: Supercoils and Overtwist
The denaturation transition of circular DNA is studied within a
Poland-Scheraga type approach, generalized to account for the fact that the
total linking number (LK), which measures the number of windings of one strand
around the other, is conserved. In the model the LK conservation is maintained
by invoking both overtwisting and writhing (supercoiling) mechanisms. This
generalizes previous studies which considered each mechanism separately. The
phase diagram of the model is analyzed as a function of the temperature and the
elastic constant associated with the overtwisting energy for any given
loop entropy exponent, . As is the case where the two mechanisms apply
separately, the model exhibits no denaturation transition for . For
and we find that the model exhibits a first order transition.
The transition becomes of higher order for any . We also calculate
the contribution of the two mechanisms separately in maintaining the
conservation of the linking number and find that it is weakly dependent on the
loop exponent .Comment: 10 pages, 6 figure
Strongly Asymmetric Tricriticality of Quenched Random-Field Systems
In view of the recently seen dramatic effect of quenched random bonds on
tricritical systems, we have conducted a renormalization-group study on the
effect of quenched random fields on the tricritical phase diagram of the spin-1
Ising model in . We find that random fields convert first-order phase
transitions into second-order, in fact more effectively than random bonds. The
coexistence region is extremely flat, attesting to an unusually small
tricritical exponent ; moreover, an extreme asymmetry of the phase
diagram is very striking. To accomodate this asymmetry, the second-order
boundary exhibits reentrance.Comment: revtex, 4 pages, 2 figs, submitted to PR
Delocalization Transition of a Rough Adsorption-Reaction Interface
We introduce a new kinetic interface model suitable for simulating
adsorption-reaction processes which take place preferentially at surface
defects such as steps and vacancies. As the average interface velocity is taken
to zero, the self- affine interface with Kardar-Parisi-Zhang like scaling
behaviour undergoes a delocalization transition with critical exponents that
fall into a novel universality class. As the critical point is approached, the
interface becomes a multi-valued, multiply connected self-similar fractal set.
The scaling behaviour and critical exponents of the relevant correlation
functions are determined from Monte Carlo simulations and scaling arguments.Comment: 4 pages with 6 figures, new comment