738 research outputs found
Elastic Correlations in Nucleosomal DNA Structure
The structure of DNA in the nucleosome core particle is studied using an
elastic model that incorporates anisotropy in the bending energetics and
twist-bend coupling. Using the experimentally determined structure of
nucleosomal DNA [T.J. Richmond and C.A. Davey, Nature {\bf 423}, 145 (2003)],
it is shown that elastic correlations exist between twist, roll, tilt, and
stretching of DNA, as well as the distance between phosphate groups. The
twist-bend coupling term is shown to be able to capture these correlations to a
large extent, and a fit to the experimental data yields a new estimate of G=25
nm for the value of the twist-bend coupling constant
Tsunami observations by coastal ocean radar
When tsunami waves propagate across the open ocean, they are steered by the Coriolis effect and refraction due to gentle gradients in the bathymetry on scales longer than the wavelength. When the wave encounters steep gradients at the edges of continental shelves and at the coast, the wave becomes nonlinear and conservation of momentum produces squirts of surface current at the head of submerged canyons and in coastal bays. High frequency (HF) coastal ocean
radar is well conditioned to observe the surface current bursts at the edge of the continental shelf and give a warning of 40 minutes to 2 hours when the shelf is 50
to 200km wide. The period of tsunami waves is invariant over changes in bathymetry and is in the range 2 to 30 minutes. Wavelengths for tsunamis (in 500 to 3000m depth) are in the range 8.5 to over 200 km, and on a shelf where the depth is about 50m (as in the Great Barrier Reef (GBR)) the wavelengths are in the range 2.5 to 30 km. In the use of HF radar technology, there is a trade-off between the precision of surface current speed measurements and time
resolution. It is shown that the phased array HF ocean surface radar being deployed in the GBR and operating in a routine way for mapping surface currents, can resolve surface current squirts from tsunamis in the wave period
range 20 to 30 minutes and in the wavelength range greater than about 6 km. An advantage in signal-to-noise ratio can be obtained from the prior knowledge of the spatial pattern of the squirts at the edge of the continental shelf, and it is estimated that, with this analysis, the time resolution of the GBR radar may be reduced to about 2.5 minutes, which corresponds to a capability to detect tsunamis at the shelf edge in the period range 5 to 30 minutes. It is estimated that the lower limit of squirt velocity detection at the shelf edge would correspond to a tsunami with water elevation of about 2.5 cm in the open ocean. This means
that the GBR HF radar is well conditioned for use as a monitor of small, as well as larger, tsunamis and has the potential to contribute to the understanding of tsunami genesis research
Heat conductivity of DNA double helix
Thermal conductivity of isolated single molecule DNA fragments is of
importance for nanotechnology, but has not yet been measured experimentally.
Theoretical estimates based on simplified (1D) models predict anomalously high
thermal conductivity. To investigate thermal properties of single molecule DNA
we have developed a 3D coarse-grained (CG) model that retains the realism of
the full all-atom description, but is significantly more efficient. Within the
proposed model each nucleotide is represented by 6 particles or grains; the
grains interact via effective potentials inferred from classical molecular
dynamics (MD) trajectories based on a well-established all-atom potential
function. Comparisons of 10 ns long MD trajectories between the CG and the
corresponding all-atom model show similar root-mean-square deviations from the
canonical B-form DNA, and similar structural fluctuations. At the same time,
the CG model is 10 to 100 times faster depending on the length of the DNA
fragment in the simulation. Analysis of dispersion curves derived from the CG
model yields longitudinal sound velocity and torsional stiffness in close
agreement with existing experiments. The computational efficiency of the CG
model makes it possible to calculate thermal conductivity of a single DNA
molecule not yet available experimentally. For a uniform (polyG-polyC) DNA, the
estimated conductivity coefficient is 0.3 W/mK which is half the value of
thermal conductivity for water. This result is in stark contrast with estimates
of thermal conductivity for simplified, effectively 1D chains ("beads on a
spring") that predict anomalous (infinite) thermal conductivity. Thus, full 3D
character of DNA double-helix retained in the proposed model appears to be
essential for describing its thermal properties at a single molecule level.Comment: 16 pages, 12 figure
Local Simulation Algorithms for Coulombic Interactions
We consider dynamically constrained Monte-Carlo dynamics and show that this
leads to the generation of long ranged effective interactions. This allows us
to construct a local algorithm for the simulation of charged systems without
ever having to evaluate pair potentials or solve the Poisson equation. We
discuss a simple implementation of a charged lattice gas as well as more
elaborate off-lattice versions of the algorithm. There are analogies between
our formulation of electrostatics and the bosonic Hubbard model in the phase
approximation. Cluster methods developed for this model further improve the
efficiency of the electrostatics algorithm.Comment: Proceedings Statphys22 10 page
Local Simulation Algorithms for Coulomb Interaction
Long ranged electrostatic interactions are time consuming to calculate in
molecular dynamics and Monte-Carlo simulations. We introduce an algorithmic
framework for simulating charged particles which modifies the dynamics so as to
allow equilibration using a local Hamiltonian. The method introduces an
auxiliary field with constrained dynamics so that the equilibrium distribution
is determined by the Coulomb interaction. We demonstrate the efficiency of the
method by simulating a simple, charged lattice gas.Comment: Last figure changed to improve demonstration of numerical efficienc
Poincaré on the Foundation of Geometry in the Understanding
This paper is about Poincaré’s view of the foundations of geometry. According to the established view, which has been inherited from the logical positivists, Poincaré, like Hilbert, held that axioms in geometry are schemata that provide implicit definitions of geometric terms, a view he expresses by stating that the axioms of geometry are “definitions in disguise.” I argue that this view does not accord well with Poincaré’s core commitment in the philosophy of geometry: the view that geometry is the study of groups of operations. In place of the established view I offer a revised view, according to which Poincaré held that axioms in geometry are in fact assertions about invariants of groups. Groups, as forms of the understanding, are prior in conception to the objects of geometry and afford the proper definition of those objects, according to Poincaré. Poincaré’s view therefore contrasts sharply with Kant’s foundation of geometry in a unique form of sensibility. According to my interpretation, axioms are not definitions in disguise because they themselves implicitly define their terms, but rather because they disguise the definitions which imply them
Conformations of closed DNA
We examine the conformations of a model for a short segment of closed DNA.
The molecule is represented as a cylindrically symmetric elastic rod with a
constraint corresponding to a specification of the linking number. We obtain
analytic expressions leading to the spatial configuration of a family of
solutions representing distortions that interpolate between the circular form
of DNA and a figure-eight form that represents the onset of interwinding. We
are also able to generate knotted loops. We suggest ways to use our approach to
produce other configurations relevant to studies of DNA structure. The
stability of the distorted configurations is assessed, along with the effects
of fluctuations on the free energy of the various configurations.Comment: 39 pages in REVTEX with 14 eps figures. Submitted to Phys. Rev. E.
This manuscript updates, expands and revises, to a considerable extent, a
previously posted manuscript, entitled "Conformations of Circular DNA," which
appeared as cond-mat/970104
Conformations of Linear DNA
We examine the conformations of a model for under- and overwound DNA. The
molecule is represented as a cylindrically symmetric elastic string subjected
to a stretching force and to constraints corresponding to a specification of
the link number. We derive a fundamental relation between the Euler angles that
describe the curve and the topological linking number. Analytical expressions
for the spatial configurations of the molecule in the infinite- length limit
were obtained. A unique configuraion minimizes the energy for a given set of
physical conditions. An elastic model incorporating thermal fluctuations
provides excellent agreement with experimental results on the plectonemic
transition.Comment: 5 pages, RevTeX; 6 postscript figure
Influence of a knot on the strength of a polymer strand
Many experiments have been done to determine the relative strength of
different knots, and these show that the break in a knotted rope almost
invariably occurs at a point just outside the `entrance' to the knot. The
influence of knots on the properties of polymers has become of great interest,
in part because of their effect on mechanical properties. Knot theory applied
to the topology of macromolecules indicates that the simple trefoil or
`overhand' knot is likely to be present with high probability in any long
polymer strand. Fragments of DNA have been observed to contain such knots in
experiments and computer simulations. Here we use {\it ab initio} computational
methods to investigate the effect of a trefoil knot on the breaking strength of
a polymer strand. We find that the knot weakens the strand significantly, and
that, like a knotted rope, it breaks under tension at the entrance to the knot.Comment: 3 pages, 4 figure
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