65 research outputs found
Critical Unmixing of Polymer Solutions
We present Monte Carlo simulations of semidilute solutions of long
self-attracting chain polymers near their Ising type critical point. The
polymers are modeled as monodisperse self-avoiding walks on the simple cubic
lattice with attraction between non-bonded nearest neighbors. Chain lengths are
up to N=2048, system sizes are up to lattice sites and monomers. These simulations used the recently introduced pruned-enriched
Rosenbluth method which proved extremely efficient, together with a histogram
method for estimating finite size corrections. Our most clear result is that
chains at the critical point are Gaussian for large , having end-to-end
distances . Also the distance (where ) scales with the mean field exponent, . The critical density seems to scale with a non-trivial
exponent similar to that observed in experiments. But we argue that this is due
to large logarithmic corrections. These corrections are similar to the very
large corrections to scaling seen in recent analyses of -polymers, and
qualitatively predicted by the field theoretic renormalization group. The only
serious deviation from this simple global picture concerns the N-dependence of
the order parameter amplitudes which disagrees with a minimalistic ansatz of de
Gennes. But this might be due to problems with finite size scaling. We find
that the finite size dependence of the density of states (where is
the total energy and is the number of chains) is slightly but significantly
different from that proposed recently by several authors.Comment: minor changes; Latex, 22 pages, submitted to J. Chem. Phy
Studies of Phase Turbulence in the One Dimensional Complex Ginzburg-Landau Equation
The phase-turbulent (PT) regime for the one dimensional complex
Ginzburg-Landau equation (CGLE) is carefully studied, in the limit of large
systems and long integration times, using an efficient new integration scheme.
Particular attention is paid to solutions with a non-zero phase gradient. For
fixed control parameters, solutions with conserved average phase gradient
exist only for less than some upper limit. The transition from phase to
defect-turbulence happens when this limit becomes zero. A Lyapunov analysis
shows that the system becomes less and less chaotic for increasing values of
the phase gradient. For high values of the phase gradient a family of
non-chaotic solutions of the CGLE is found. These solutions consist of
spatially periodic or aperiodic waves travelling with constant velocity. They
typically have incommensurate velocities for phase and amplitude propagation,
showing thereby a novel type of quasiperiodic behavior. The main features of
these travelling wave solutions can be explained through a modified
Kuramoto-Sivashinsky equation that rules the phase dynamics of the CGLE in the
PT phase. The latter explains also the behavior of the maximal Lyapunov
exponents of chaotic solutions.Comment: 16 pages, LaTeX (Version 2.09), 10 Postscript-figures included,
submitted to Phys. Rev.
Scattering and Trapping of Nonlinear Schroedinger Solitons in External Potentials
Soliton motion in some external potentials is studied using the nonlinear
Schr\"odinger equation. Solitons are scattered by a potential wall. Solitons
propagate almost freely or are trapped in a periodic potential. The critical
kinetic energy for reflection and trapping is evaluated approximately with a
variational method.Comment: 9 pages, 7 figure
Bound states in a nonlinear Kronig-Penney model
We study the bound states of a Kronig Penney potential for a nonlinear
one-dimensional Schroedinger equation. This potential consists of a large, but
not necessarily infinite, number of equidistant delta-function wells. We show
that the ground state can be highly degenerate. Under certain conditions
furthermore, even the bound state that would normally be the highest can have
almost the same energy as the ground state. This holds for simple periodic
potentials as well.Comment: TeX file, figures available as postscript files upon reques
Interaction of Nonlinear Schr\"odinger Solitons with an External Potential
Employing a particularly suitable higher order symplectic integration
algorithm, we integrate the 1- nonlinear Schr\"odinger equation numerically
for solitons moving in external potentials. In particular, we study the
scattering off an interface separating two regions of constant potential. We
find that the soliton can break up into two solitons, eventually accompanied by
radiation of non-solitary waves. Reflection coefficients and inelasticities are
computed as functions of the height of the potential step and of its steepness.Comment: 14 pages, uuencoded PS-file including 10 figure
Simulations of grafted polymers in a good solvent
We present improved simulations of three-dimensional self avoiding walks with
one end attached to an impenetrable surface on the simple cubic lattice. This
surface can either be a-thermal, having thus only an entropic effect, or
attractive. In the latter case we concentrate on the adsorption transition, We
find clear evidence for the cross-over exponent to be smaller than 1/2, in
contrast to all previous simulations but in agreement with a re-summed field
theoretic -expansion. Since we use the pruned-enriched Rosenbluth
method (PERM) which allows very precise estimates of the partition sum itself,
we also obtain improved estimates for all entropic critical exponents.Comment: 5 pages with 9 figures included; minor change
Decay of Resonance Structure and Trapping Effect in Potential Scattering Problem of Self-Focusing Wave Packet
Potential scattering problems governed by the time-dependent Gross-Pitaevskii
equation are investigated numerically for various values of coupling constants.
The initial condition is assumed to have the Gaussian-type envelope, which
differs from the soliton solution. The potential is chosen to be a box or well
type. We estimate the dependences of reflectance and transmittance on the width
of the potential and compare these results with those given by the stationary
Schr\"odinger equation. We attribute the behaviors of these quantities to the
limitation on the width of the nonlinear wave packet. The coupling constant and
the width of the potential play an important role in the distribution of the
waves appearing in the final state of scattering.Comment: 18 pages, 12 figures; added 2 figure
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