389 research outputs found
Order-by-Disorder in the XY Pyrochlore Antiferromagnet Revisited
We investigate the properties of the XY pyrochlore antiferromagnet with local
planar anisotropy. We find the ground states and show that the
configurational ground state entropy is subextensive. By computing the free
energy due to harmonic fluctuations and by carrying out Monte Carlo
simulations, we confirm earlier work indicating that the model exhibits thermal
order-by-disorder leading to low temperature long-range order consisting of
discrete magnetic domains. We compute the spin wave spectrum and show that
thermal and quantum fluctuations select the same magnetic structure. Using
Monte Carlo simulations, we find that the state selected by thermal
fluctuations in this XY pyrochlore antiferromagnet can survive the addition of
sufficiently weak nearest-neighbor pseudo-dipolar interactions to the spin
Hamiltonian. We discuss our results in relation to the Er2Ti2O7 pyrochlore
antiferromagnet.Comment: 13 pages, 6 figure
Experimental validation of nonextensive scaling law in confined granular media
In this letter, we address the relationship between the statistical
fluctuations of grain displacements for a full quasistatic plane shear
experiment, and the corresponding anomalous diffusion exponent, . We
experimentally validate a particular case of the so-called Tsallis-Bukman
scaling law, , where is obtained by fitting the
probability density function (PDF) of the measured fluctuations with a
-Gaussian distribution, and the diffusion exponent is measured independently
during the experiment. Applying an original technique, we are able to evince a
transition from an anomalous diffusion regime to a Brownian behavior as a
function of the length of the strain-window used to calculate the displacements
of grains in experiments. The outstanding conformity of fitting curves to a
massive amount of experimental data shows a clear broadening of the fluctuation
PDFs as the length of the strain-window decreases, and an increment in the
value of the diffusion exponent - anomalous diffusion. Regardless of the size
of the strain-window considered in the measurements, we show that the
Tsallis-Bukman scaling law remains valid, which is the first experimental
verification of this relationship for a classical system at different diffusion
regimes. We also note that the spatial correlations show marked similarities to
the turbulence in fluids, a promising indication that this type of analysis can
be used to explore the origins of the macroscopic friction in confined granular
materials.Comment: 8 pages 4 figure
Torsional Directed Walks, Entropic Elasticity, and DNA Twist Stiffness
DNA and other biopolymers differ from classical polymers due to their
torsional stiffness. This property changes the statistical character of their
conformations under tension from a classical random walk to a problem we call
the `torsional directed walk'. Motivated by a recent experiment on single
lambda-DNA molecules [Strick et al., Science 271 (1996) 1835], we formulate the
torsional directed walk problem and solve it analytically in the appropriate
force regime. Our technique affords a direct physical determination of the
microscopic twist stiffness C and twist-stretch coupling D relevant for DNA
functionality. The theory quantitatively fits existing experimental data for
relative extension as a function of overtwist over a wide range of applied
force; fitting to the experimental data yields the numerical values C=120nm and
D=50nm. Future experiments will refine these values. We also predict that the
phenomenon of reduction of effective twist stiffness by bend fluctuations
should be testable in future single-molecule experiments, and we give its
analytic form.Comment: Plain TeX, harvmac, epsf; postscript available at
http://dept.physics.upenn.edu/~nelson/index.shtm
Metastable tight knots in a worm-like polymer
Based on an estimate of the knot entropy of a worm-like chain we predict that
the interplay of bending energy and confinement entropy will result in a
compact metastable configuration of the knot that will diffuse, without
spreading, along the contour of the semi-flexible polymer until it reaches one
of the chain ends. Our estimate of the size of the knot as a function of its
topological invariant (ideal aspect ratio) agrees with recent experimental
results of knotted dsDNA. Further experimental tests of our ideas are proposed.Comment: 4 pages, 3 figure
Gel Electrophoresis of DNA Knots in Weak and Strong Electric Fields
Gel electrophoresis allows to separate knotted DNA (nicked circular) of equal
length according to the knot type. At low electric fields, complex knots being
more compact, drift faster than simpler knots. Recent experiments have shown
that the drift velocity dependence on the knot type is inverted when changing
from low to high electric fields. We present a computer simulation on a lattice
of a closed, knotted, charged DNA chain drifting in an external electric field
in a topologically restricted medium. Using a simple Monte Carlo algorithm, the
dependence of the electrophoretic migration of the DNA molecules on the type of
knot and on the electric field intensity was investigated. The results are in
qualitative agreement with electrophoretic experiments done under conditions of
low and high electric fields: especially the inversion of the behavior from low
to high electric field could be reproduced. The knot topology imposes on the
problem the constrain of self-avoidance, which is the final cause of the
observed behavior in strong electric field.Comment: 17 pages, 5 figure
Tight open knots
The most tight conformations of prime knots are found with the use of the
SONO algorithm. Their curvature and torsion profiles are calculated. Symmetry
of the knots is analysed. Connections with the physics of polymers are
discussed.Comment: 11 pages, 8 figure
- …