747 research outputs found
Dynamics of Counterion Condensation
Using a generalization of the Poisson-Boltzmann equation, dynamics of
counterion condensation is studied. For a single charged plate in the presence
of counterions, it is shown that the approach to equilibrium is diffusive. In
the far from equilibrium case of a moving charged plate, a dynamical counterion
condensation transition occurs at a critical velocity. The complex dynamic
behavior of the counterion cloud is shown to lead to a novel nonlinear
force-velocity relation for the moving plate.Comment: 5 pages, 1 ps figure included using eps
Scaling and Universality in the Counterion-Condensation Transition at Charged Cylinders
We address the critical and universal aspects of counterion-condensation
transition at a single charged cylinder in both two and three spatial
dimensions using numerical and analytical methods. By introducing a novel
Monte-Carlo sampling method in logarithmic radial scale, we are able to
numerically simulate the critical limit of infinite system size (corresponding
to infinite-dilution limit) within tractable equilibration times. The critical
exponents are determined for the inverse moments of the counterionic density
profile (which play the role of the order parameters and represent the inverse
localization length of counterions) both within mean-field theory and within
Monte-Carlo simulations. In three dimensions (3D), correlation effects
(neglected within mean-field theory) lead to an excessive accumulation of
counterions near the charged cylinder below the critical temperature
(condensation phase), while surprisingly, the critical region exhibits
universal critical exponents in accord with the mean-field theory. In two
dimensions (2D), we demonstrate, using both numerical and analytical
approaches, that the mean-field theory becomes exact at all temperatures
(Manning parameters), when number of counterions tends to infinity. For finite
particle number, however, the 2D problem displays a series of peculiar singular
points (with diverging heat capacity), which reflect successive de-localization
events of individual counterions from the central cylinder. In both 2D and 3D,
the heat capacity shows a universal jump at the critical point, and the energy
develops a pronounced peak. The asymptotic behavior of the energy peak location
is used to locate the critical temperature, which is also found to be universal
and in accordance with the mean-field prediction.Comment: 31 pages, 16 figure
Denaturation of Heterogeneous DNA
The effect of heterogeneous sequence composition on the denaturation of
double stranded DNA is investigated. The resulting pair-binding energy
variation is found to have a negligible effect on the critical properties of
the smooth second order melting transition in the simplest (Peyrard-Bishop)
model. However, sequence heterogeneity is dramatically amplified upon adopting
a more realistic treatment of the backbone stiffness. The model yields features
of ``multi-step melting'' similar to those observed in experiments.Comment: 4 pages, LaTeX, text and figures also available at
http://matisse.ucsd.edu/~hw
The Origin And Loss Of Periodic Patterning In The Turtle Shell
The origin of the turtle shell over 200 million years ago greatly modified the amniote body plan, and the morphological plasticity of the shell has promoted the adaptive radiation of turtles. The shell, comprising a dorsal carapace and a ventral plastron, is a layered structure formed by basal endochondral axial skeletal elements (ribs, vertebrae) and plates of bone, which are overlain by keratinous ectodermal scutes. Studies of turtle development have mostly focused on the bones of the shell; however, the genetic regulation of the epidermal scutes has not been investigated. Here, we show that scutes develop from an array of patterned placodes and that these placodes are absent from a soft-shelled turtle in which scutes were lost secondarily. Experimentally inhibiting Shh, Bmp or Fgf signaling results in the disruption of the placodal pattern. Finally, a computational model is used to show how two coupled reaction-diffusion systems reproduce both natural and abnormal variation in turtle scutes. Taken together, these placodal signaling centers are likely to represent developmental modules that are responsible for the evolution of scutes in turtles, and the regulation of these centers has allowed for the diversification of the turtle shell
Phase diagram and magnetocaloric effect of CoMnGe_{1-x}Sn_{x} alloys
We propose the phase diagram of a new pseudo-ternary compound,
CoMnGe_{1-x}Sn_{x}, in the range x less than or equal to 0.1. Our phase diagram
is a result of magnetic and calometric measurements. We demonstrate the
appearance of a hysteretic magnetostructural phase transition in the range
x=0.04 to x=0.055, similar to that observed in CoMnGe under hydrostatic
pressure. From magnetisation measurements, we show that the isothermal entropy
change associated with the magnetostructural transition can be as high as 4.5
J/(K kg) in a field of 1 Tesla. However, the large thermal hysteresis in this
transition (~20 K) will limit its straightforward use in a magnetocaloric
device.Comment: 12 pages, 5 figure
A Simple Model for the DNA Denaturation Transition
We study pairs of interacting self-avoiding walks on the 3d simple cubic
lattice. They have a common origin and are allowed to overlap only at the same
monomer position along the chain. The latter overlaps are indeed favored by an
energetic gain.
This is inspired by a model introduced long ago by Poland and Sheraga [J.
Chem. Phys. {\bf 45}, 1464 (1966)] for the denaturation transition in DNA
where, however, self avoidance was not fully taken into account. For both
models, there exists a temperature T_m above which the entropic advantage to
open up overcomes the energy gained by forming tightly bound two-stranded
structures.
Numerical simulations of our model indicate that the transition is of first
order (the energy density is discontinuous), but the analog of the surface
tension vanishes and the scaling laws near the transition point are exactly
those of a second order transition with crossover exponent \phi=1. Numerical
and exact analytic results show that the transition is second order in modified
models where the self-avoidance is partially or completely neglected.Comment: 29 pages, LaTeX, 20 postscript figure
Gel-Electrophoresis and Diffusion of Ring-Shaped DNA
A model for the motion of ring-shaped DNA in a gel is introduced and studied
by numerical simulations and a mean-field approximation. The ring motion is
mediated by finger-shaped loops (hernias) that move in an amoeba-like fashion
around the gel obstructions. This constitutes an extension of previous
reptation tube treatments. It is shown that tension is essential for describing
the dynamics in the presence of hernias. It is included in the model as long
range interactions over stretched DNA regions. The mobility of ring-shaped DNA
is found to saturate much as in the well-studied case of linear DNA.
Experiments in polymer gels, however, show that the mobility drops
exponentially with the DNA ring size. This is commonly attributed to
dangling-ends in the gel that can impale the ring. The predictions of the
present model are expected to apply to artificial 2D obstacle arrays (W.D.
Volkmuth, R.H. Austin, Nature 358,600 (1992)) which have no dangling-ends. In
the zero-field case an exact solution of the model steady-state is obtained,
and quantities such as the average ring size are calculated. An approximate
treatment of the ring dynamics is given, and the diffusion coefficient is
derived. The model is also discussed in the context of spontaneous symmetry
breaking in one dimension.Comment: 8 figures, LaTeX, Phys. Rev. E - in pres
Bubbles, clusters and denaturation in genomic DNA: modeling, parametrization, efficient computation
The paper uses mesoscopic, non-linear lattice dynamics based
(Peyrard-Bishop-Dauxois, PBD) modeling to describe thermal properties of DNA
below and near the denaturation temperature. Computationally efficient notation
is introduced for the relevant statistical mechanics. Computed melting profiles
of long and short heterogeneous sequences are presented, using a recently
introduced reparametrization of the PBD model, and critically discussed. The
statistics of extended open bubbles and bound clusters is formulated and
results are presented for selected examples.Comment: to appear in a special issue of the Journal of Nonlinear Mathematical
Physics (ed. G. Gaeta
Formation of helical states in wormlike polymer chains
We propose a potential for wormlike polymer chains which can be used to model
the low-temperature conformational structures. We successfully reproduced helix
ground states up to 6.5 helical loops, using the multicanonical Monte Carlo
simulation method. We demonstrate that the coil-helix transition involves four
distinct phases: coil(gaslike), collapsed globular(liquidlike), and two helical
phases I and II (both solidlike). The helix I phase is characterized by a
helical structure with dangling loose ends, and the helix II phase corresponds
to a near perfect helix ordering in the entire crystallized chain.Comment: 5 pages, 2 figures, Submitted to PR
Creation of dense polymer brush layers by the controlled deposition of an amphiphilic responsive comb polymer
We introduce a copolymer with a comb topology that has been engineered to assemble in a brush configuration at an air-water interface. The molecule comprises a 6.1 kDa poly(methyl methacrylate) backbone with a statistical amount of poly[2-(dimethyl amino)ethyl methacrylate] polybase side chains averaging 2.43 per backbone.. Brush layers deposited with the hydrophobic PMMA backbone adsorbed to hydrophobized silicon are stable in water even when stored at pH values less than 2.0 for over 24 h. The use of a Langmuir trough allows a simple controlled deposition of the layers at a variety of grafting densities. Depth profiling of brush layers was performed using neutron reflectometry and reveals a significant shifting of the responsiveness of the layer upon changing the grafting density. The degree of swelling of the layers at a pH value of 4 (below the pK(b)) decreases as grafting density increases. Lowering the pH of the subphase during deposition causes the side chains to become charged and more hydrophilic extending to a brush-like configuration while at neutral pH the side chains lie in a "pancake" conformation at the interface. (C) 2009 Elsevier Ltd. All rights reserved
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