1,266 research outputs found

### Collapse transitions of a periodic hydrophilic hydrophobic chain

We study a single self avoiding hydrophilic hydrophobic polymer chain,
through Monte Carlo lattice simulations. The affinity of monomer $i$ for water
is characterized by a (scalar) charge $\lambda_{i}$, and the monomer-water
interaction is short-ranged. Assuming incompressibility yields an effective
short ranged interaction between monomer pairs $(i,j)$, proportional to
$(\lambda_i+\lambda_j)$. In this article, we take $\lambda_i=+1$ (resp.
($\lambda_i=- 1$)) for hydrophilic (resp. hydrophobic) monomers and consider a
chain with (i) an equal number of hydro-philic and -phobic monomers (ii) a
periodic distribution of the $\lambda_{i}$ along the chain, with periodicity
$2p$. The simulations are done for various chain lengths $N$, in $d=2$ (square
lattice) and $d=3$ (cubic lattice). There is a critical value $p_c(d,N)$ of the
periodicity, which distinguishes between different low temperature structures.
For $p >p_c$, the ground state corresponds to a macroscopic phase separation
between a dense hydrophobic core and hydrophilic loops. For $p <p_c$ (but not
too small), one gets a microscopic (finite scale) phase separation, and the
ground state corresponds to a chain or network of hydrophobic droplets, coated
by hydrophilic monomers. We restrict our study to two extreme cases, $p \sim
O(N)$ and $p\sim O(1)$ to illustrate the physics of the various phase
transitions. A tentative variational approach is also presented.Comment: 21 pages, 17 eps figures, accepted for publication in Eur. Phys. J.

### Interacting Elastic Lattice Polymers: a Study of the Free-Energy of Globular Rings

We introduce and implement a Monte Carlo scheme to study the equilibrium
statistics of polymers in the globular phase. It is based on a model of
"interacting elastic lattice polymers" and allows a sufficiently good sampling
of long and compact configurations, an essential prerequisite to study the
scaling behaviour of free energies. By simulating interacting self-avoiding
rings at several temperatures in the collapsed phase, we estimate both the bulk
and the surface free energy. Moreover from the corresponding estimate of the
entropic exponent $\alpha-2$ we provide evidence that, unlike for swollen and
$\Theta$-point rings, the hyperscaling relation is not satisfied for globular
rings.Comment: 8 pages; v2: typos removed, published versio

### Phase diagram of magnetic polymers

We consider polymers made of magnetic monomers (Ising or Heisenberg-like) in
a good solvent. These polymers are modeled as self-avoiding walks on a cubic
lattice, and the ferromagnetic interaction between the spins carried by the
monomers is short-ranged in space. At low temperature, these polymers undergo a
magnetic induced first order collapse transition, that we study at the mean
field level. Contrasting with an ordinary $\Theta$ point, there is a strong
jump in the polymer density, as well as in its magnetization. In the presence
of a magnetic field, the collapse temperature increases, while the
discontinuities decrease. Beyond a multicritical point, the transition becomes
second order and $\Theta$-like. Monte Carlo simulations for the Ising case are
in qualitative agreement with these results.Comment: 29 pages, 15 eps figures (one color figure). Submitted for
publication to Eur.Phys.J.

### Supercoil formation in DNA denaturation

We generalize the Poland-Scheraga (PS) model to the case of a circular DNA,
taking into account the twisting of the two strains around each other. Guided
by recent single-molecule experiments on DNA strands, we assume that the
torsional stress induced by denaturation enforces formation of supercoils whose
writhe absorbs the linking number expelled by the loops. Our model predicts
that, when the entropy parameter of a loop satisfies $c \le 2$, denaturation
transition does not take place. On the other hand for $c>2$ a first-order
denaturation transition is consistent with our model and may take place in the
actual system, as in the case with no supercoils. These results are in contrast
with other treatments of circular DNA melting where denaturation is assumed to
be accompanied by an increase in twist rather than writhe on the bound
segments.Comment: 4 pages, 3 figures, accepted for publication in PRE Rapid Com

### Facilitated diffusion on confined DNA

In living cells, proteins combine 3D bulk diffusion and 1D sliding along the
DNA to reach a target faster. This process is known as facilitated diffusion,
and we investigate its dynamics in the physiologically relevant case of
confined DNA. The confining geometry and DNA elasticity are key parameters: we
find that facilitated diffusion is most efficient inside an isotropic volume,
and on a flexible polymer. By considering the typical copy numbers of proteins
in vivo, we show that the speedup due to sliding becomes insensitive to fine
tuning of parameters, rendering facilitated diffusion a robust mechanism to
speed up intracellular diffusion-limited reactions. The parameter range we
focus on is relevant for in vitro systems and for facilitated diffusion on
yeast chromatin

### Topological and geometrical entanglement in a model of circular DNA undergoing denaturation

The linking number (topological entanglement) and the writhe (geometrical
entanglement) of a model of circular double stranded DNA undergoing a thermal
denaturation transition are investigated by Monte Carlo simulations. By
allowing the linking number to fluctuate freely in equilibrium we see that the
linking probability undergoes an abrupt variation (first-order) at the
denaturation transition, and stays close to 1 in the whole native phase. The
average linking number is almost zero in the denatured phase and grows as the
square root of the chain length, N, in the native phase. The writhe of the two
strands grows as the square root of N in both phases.Comment: 7 pages, 11 figures, revte

### Spinodal decomposition to a lamellar phase: effects of hydrodynamic flow

Results are presented for the kinetics of domain growth of a two-dimensional
fluid quenched from a disordered to a lamellar phase. At early times when a
Lifshitz-Slyozov mechanism is operative the growth process proceeds
logarithmically in time to a frozen state with locked-in defects. However when
hydrodynamic modes become important, or the fluid is subjected to shear, the
frustration of the system is alleviated and the size and orientation of the
lamellae attain their equilibrium values.Comment: 4 Revtex pages, 4 figures, to appear in Physical Review Letter

### Ranking knots of random, globular polymer rings

An analysis of extensive simulations of interacting self-avoiding polygons on
cubic lattice shows that the frequencies of different knots realized in a
random, collapsed polymer ring decrease as a negative power of the ranking
order, and suggests that the total number of different knots realized grows
exponentially with the chain length. Relative frequencies of specific knots
converge to definite values because the free energy per monomer, and its
leading finite size corrections, do not depend on the ring topology, while a
subleading correction only depends on the crossing number of the knots.Comment: 4 pages, 5 figure

### Nonequilibrium Kinetics of One-Dimensional Bose Gases

We study cold dilute gases made of bosonic atoms, showing that in the
mean-field one-dimensional regime they support stable out-of-equilibrium
states. Starting from the 3D Boltzmann-Vlasov equation with contact
interaction, we derive an effective 1D Landau-Vlasov equation under the
condition of a strong transverse harmonic confinement. We investigate the
existence of out-of-equilibrium states, obtaining stability criteria similar to
those of classical plasmas.Comment: 16 pages, 6 figures, accepted for publication in Journal of
Statistical Mechanics: Theory and Experimen

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