45 research outputs found
A new bond fluctuation method for a polymer undergoing gel electrophoresis
We present a new computational methodology for the investigation of gel
electrophoresis of polyelectrolytes. We have developed the method initially to
incorporate sliding motion of tight parts of a polymer pulled by an electric
field into the bond fluctuation method (BFM). Such motion due to tensile force
over distances much larger than the persistent length is realized by non-local
movement of a slack monomer at an either end of the tight part. The latter
movement is introduced stochastically. This new BFM overcomes the well-known
difficulty in the conventional BFM that polymers are trapped by gel fibers in
relatively large fields. At the same time it also reproduces properly
equilibrium properties of a polymer in a vanishing filed limit. The new BFM
thus turns out an efficient computational method to study gel electrophoresis
in a wide range of the electric field strength.Comment: 15 pages, 11 figure
Ballistic Annihilation
Ballistic annihilation with continuous initial velocity distributions is
investigated in the framework of Boltzmann equation. The particle density and
the rms velocity decay as and , with the
exponents depending on the initial velocity distribution and the spatial
dimension. For instance, in one dimension for the uniform initial velocity
distribution we find . We also solve the Boltzmann equation
for Maxwell particles and very hard particles in arbitrary spatial dimension.
These solvable cases provide bounds for the decay exponents of the hard sphere
gas.Comment: 4 RevTeX pages and 1 Eps figure; submitted to Phys. Rev. Let
Intrinsic profiles and capillary waves at homopolymer interfaces: a Monte Carlo study
A popular concept which describes the structure of polymer interfaces by
``intrinsic profiles'' centered around a two dimensional surface, the ``local
interface position'', is tested by extensive Monte Carlo simulations of
interfaces between demixed homopolymer phases in symmetric binary (AB)
homopolymer blends, using the bond fluctuation model. The simulations are done
in an LxLxD geometry. The interface is forced to run parallel to the LxL planes
by imposing periodic boundary conditions in these directions and fixed boundary
conditions in the D direction, with one side favoring A and the other side
favoring B. Intrinsic profiles are calculated as a function of the ``coarse
graining length'' B by splitting the system into columns of size BxBxD and
averaging in each column over profiles relative to the local interface
position. The results are compared to predictions of the self-consistent field
theory. It is shown that the coarse graining length can be chosen such that the
interfacial width matches that of the self-consistent field profiles, and that
for this choice of B the ``intrinsic'' profiles compare well with the
theoretical predictions.Comment: to appear in Phys. Rev.
A symmetric polymer blend confined into a film with antisymmetric surfaces: interplay between wetting behavior and phase diagram
We study the phase behavior of a symmetric binary polymer blend which is
confined into a thin film. The film surfaces interact with the monomers via
short range potentials. We calculate the phase behavior within the
self-consistent field theory of Gaussian chains. Over a wide range of
parameters we find strong first order wetting transitions for the semi-infinite
system, and the interplay between the wetting/prewetting behavior and the phase
diagram in confined geometry is investigated. Antisymmetric boundaries, where
one surface attracts the A component with the same strength than the opposite
surface attracts the B component, are applied. The phase transition does not
occur close to the bulk critical temperature but in the vicinity of the wetting
transition. For very thin films or weak surface fields one finds a single
critical point at . For thicker films or stronger surface fields
the phase diagram exhibits two critical points and two concomitant coexistence
regions. Only below a triple point there is a single two phase coexistence
region. When we increase the film thickness the two coexistence regions become
the prewetting lines of the semi-infinite system, while the triple temperature
converges towards the wetting transition temperature from above. The behavior
close to the tricritical point, which separates phase diagrams with one and two
critical points, is studied in the framework of a Ginzburg-Landau ansatz.
Two-dimensional profiles of the interface between the laterally coexisting
phases are calculated, and the interfacial and line tensions analyzed. The
effect of fluctuations and corrections to the self-consistent field theory are
discussed.Comment: Phys.Rev.E in prin
Interface localisation-delocalisation transition in a symmetric polymer blend: a finite-size scaling Monte Carlo study
Using extensive Monte Carlo simulations we study the phase diagram of a
symmetric binary (AB) polymer blend confined into a thin film as a function of
the film thickness D. The monomer-wall interactions are short ranged and
antisymmetric, i.e, the left wall attracts the A-component of the mixture with
the same strength as the right wall the B-component, and give rise to a first
order wetting transition in a semi-infinite geometry. The phase diagram and the
crossover between different critical behaviors is explored. For large film
thicknesses we find a first order interface localisation/delocalisation
transition and the phase diagram comprises two critical points, which are the
finite film width analogies of the prewetting critical point. Using finite size
scaling techniques we locate these critical points and present evidence of 2D
Ising critical behavior. When we reduce the film width the two critical points
approach the symmetry axis of the phase diagram and for we encounter a tricritical point. For even smaller film thickness the
interface localisation/delocalisation transition is second order and we find a
single critical point at .
Measuring the probability distribution of the interface position we determine
the effective interaction between the wall and the interface. This effective
interface potential depends on the lateral system size even away from the
critical points. Its system size dependence stems from the large but finite
correlation length of capillary waves. This finding gives direct evidence for a
renormalization of the interface potential by capillary waves in the framework
of a microscopic model.Comment: Phys.Rev.
Diblock copolymers at a homopolymer-homopolymer-interface: a Monte Carlo simulation
The properties of diluted symmetric A-B diblock copolymers at the interface
between A and B homopolymer phases are studied by means of Monte Carlo (MC)
simulations of the bond fluctuation model. We calculate segment density
profiles as well as orientational properties of segments, of A and B blocks,
and of the whole chain. Our data support the picture of oriented ``dumbbells'',
which consist of mildly perturbed A and B Gaussian coils. The results are
compared to a self consistent field theory (SCFT) for single copolymer chains
at a homopolymer interface. We also discuss the number of interaction contacts
between monomers, which provide a measure for the ``active surface'' of
copolymers or homopolymers close to the interface
Multilinear Back-Propagation Convergence Theorem
For neural networks, back-propagation is a traditional, efficient and popular learning algorithm that relies on a transparent gradient method. However, there is no general convergence theorem. This shortcoming is completely resolved by a generalization to multilinear neural networks. Physics Letters A 188 (1994) 27-31. Introduction. A neural network has usually two dynamical rules, a neuronal dynamics should provide the perfomance of tasks and the coupling dynamics should provide the adaption to tasks [1]. A traditional, efficent and popular coupling dynamics is back-propagation [2]. However, no general convergence theorem is known that guarantees the convergence of back-propagation to a coupling state so that the network performs a considered task [2,3]. In this paper, that shortcoming of back-propagation is completely overcome. For that purpose, a multilinear network [4,5] with a corresponding back-propagation learning algorithm is introduced. Then, for any task a multilinear netwo..