123 research outputs found
Localization and freezing of a Gaussian chain in a quenched random potential
The Gaussian chain in a quenched random potential (which is characterized by
the disorder strength ) is investigated in the - dimensional space
by the replicated variational method. The general expression for the free
energy within so called one - step - replica symmetry breaking (1 - RSB)
scenario has been systematically derived. We have shown that the replica
symmetrical (RS) limit of this expression can describe the chain center of mass
localization and collapse. The critical disorder when the chain becomes
localized scales as (where is the length
of the Kuhn segment length and is the chain length) whereas the chain
gyration radius . The freezing of
the internal degrees of freedom follows to the 1-RSB - scenario and is
characterized by the beads localization length . It was
demonstrated that the solution for appears as a metastable
state at and behaves similarly to the corresponding frozen
states in heteropolymers or in - spin random spherical model.Comment: 18 pages, 6 figures, submitted to J. Chem. Phy
Polymer chain in a quenched random medium: slow dynamics and ergodicity breaking
The Langevin dynamics of a self - interacting chain embedded in a quenched
random medium is investigated by making use of the generating functional method
and one - loop (Hartree) approximation. We have shown how this intrinsic
disorder causes different dynamical regimes. Namely, within the Rouse
characteristic time interval the anomalous diffusion shows up. The
corresponding subdiffusional dynamical exponents have been explicitly
calculated and thoroughly discussed. For the larger time interval the disorder
drives the center of mass of the chain to a trap or frozen state provided that
the Harris parameter, , where is a
disorder strength, is a Kuhnian segment length, is a chain length and
is the Flory exponent. We have derived the general equation for the non -
ergodicity function which characterizes the amplitude of frozen Rouse
modes with an index . The numerical solution of this equation has
been implemented and shown that the different Rouse modes freeze up at the same
critical disorder strength where the exponent
and does not depend from the solvent quality.Comment: 17 pages, 6 figures, submitted to EPJB (condensed matter
Dynamics of polymeric manifolds in melts: Hartree approximation
The Martin-Siggia-Rose functional technique and the self-consistent Hartree
approximation is applied to the dynamics of a D-dimensional manifold in a melt
of similar manifolds.The generalized Rouse equation is derived and its static
and dynamic properties are studied. The static upper critical dimension
discriminate between Gaussian and non-Gaussian regimes, whereas its dynamic
counterpart discriminates between Rouse- and renormalized-Rouse behavior. The
dynamic exponents are calculated explicitly. The special case of linear chains
shows agreement with MD- and MC-simulations.Comment: 4 pages,1 figures, accepted by EPJB as a Rapid Not
Dynamics of a polymer test chain in a glass forming matrix: The Hartree Approximation
In this paper the Martin-Siggia-Rose formalism is used to derive a
generalized Rouse equation for a test chain in a matrix which can undergo the
glass transition. It is shown that the surrounding matrix renormalizes the
static properties of the test chain. Furthermore the freezing of the different
Rouse modes is investigated. This yields freezing temperatures which depend
from the Rouse mode index.Comment: to be published in Journal de Physique I
Weak violation of universality for Polyelectrolyte Chains: Variational Theory and Simulations
A variational approach is considered to calculate the free energy and the
conformational properties of a polyelectrolyte chain in dimensions. We
consider in detail the case of pure Coulombic interactions between the
monomers, when screening is not present, in order to compute the end-to-end
distance and the asymptotic properties of the chain as a function of the
polymer chain length . We find where
and is the exponent which characterize
the long-range interaction . The exponent is
shown to be non-universal, depending on the strength of the Coulomb
interaction. We check our findings, by a direct numerical minimization of the
variational energy for chains of increasing size . The
electrostatic blob picture, expected for small enough values of the interaction
strength, is quantitatively described by the variational approach. We perform a
Monte Carlo simulation for chains of length . The non universal
behavior of the exponent previously derived within the variational
method, is also confirmed by the simulation results. Non-universal behavior is
found for a polyelectrolyte chain in dimension. Particular attention is
devoted to the homopolymer chain problem, when short range contact interactions
are present.Comment: to appear in European Phys. Journal E (soft matter
The USA: Challenges of the Superpower
Since the collapse of the Soviet Union function and mission of the United States in the contemporary world system is one of the most debatable problems of academic litera-ture. This article is an attempt to analyze most recent socioeconomic and political tendencies of the USA for better understanding the scale of ongoing transformation of the society. As the level of integration of contemporary world is very high, transfor-mation of the USA provokes tectonic changes and transformation of the world system, its structure and nature. This study argues that, although the US primacy in the world is significantly challenged and shaken by external and internal factors, the USA still preserves its traditional function of economic, financial, military and political superpow-er, but in a quite different environment. The article predominantly uses materials drawn from the Central Intelligence Agency (CIA, The World Fact book 2012); U.S. Census Bureau, Statistical Abstract of the USA - 2012, the US Federal Budgets 2010-2012, and other valuable literature and sources
Detachment of semiflexible polymer chains from a substrate - a Molecular Dynamics investigation
Using Molecular Dynamics simulations, we study the force-induced detachment
of a coarse-grained model polymer chain from an adhesive substrate. One of the
chain ends is thereby pulled at constant speed off the attractive substrate and
the resulting saw-tooth profile of the measured mean force vs height
$D$ of the end-segment over the plane is analyzed for a broad variety of
parameters. It is shown that the observed characteristic oscillations in the $<
f >$-$D$ profile depend on the bending and not on the torsional stiffness of
the detached chains. Allowing for the presence of hydrodynamic interactions
(HI) in a setup with explicit solvent and DPD-thermostat, rather than the case
of Langevin thermostat, one finds that HI have little effect on the -
profile. Also the change of substrate affinity with respect to the solvent from
solvophilic to solvophobic is found to play negligible role in the desorption
process. In contrast, a changing ratio of the
binding energies of - and -segments in the detachment of an
-copolymer from adhesive surface strongly changes the - profile
whereby the -spikes vanish when .
Eventually, performing an atomistic simulation of a (bio)-polymer {\it
polyglycine}, we demonstrate that the simulation results, derived from our
coarse-grained model, comply favorably with those from the all-atom simulation.Comment: Latex, 12 pages, 8 figures, to appear in JC
Polyelectrolyte chains in poor solvent. A variational description of necklace formation
We study the properties of polyelectrolyte chains under different solvent
conditions, using a variational technique. The free energy and the
conformational properties of a polyelectrolyte chain are studied minimizing the
free energy , depending on trial probabilities that
characterize the conformation of the chain. The Gaussian approximation is
considered for a ring of length and for an open chain of length
in poor and theta solvent conditions, including a Coulomb repulsion
between the monomers. In theta solvent conditions the blob size is measured and
found in agreement with scaling theory, including charge depletion effects,
expected for the case of an open chain. In poor solvent conditions, a globule
instability, driven by electrostatic repulsion, is observed. We notice also
inhomogeneous behavior of the monomer--monomer correlation function,
reminiscence of necklace formation in poor solvent polyelectrolyte solutions. A
global phase diagram in terms of solvent quality and inverse Bjerrum length is
presented.Comment: submitted to EPJE (soft matter
The Hartree approximation in dynamics of polymeric manifolds in the melt
The Martin-Siggia-Rose (MSR) functional integral technique is applied to the
dynamics of a D - dimensional manifold in a melt of similar manifolds. The
integration over the collective variables of the melt can be simply implemented
in the framework of the dynamical random phase approximation (RPA). The
resulting effective action functional of the test manifold is treated by making
use of the selfconsistent Hartree approximation. As an outcome the generalized
Rouse equation (GRE) of the test manifold is derived and its static and dynamic
properties are studied. It was found that the static upper critical dimension,
, discriminates between Gaussian (or screened) and
non-Gaussian regimes, whereas its dynamical counterpart, , distinguishes between the simple Rouse and the
renormalized Rouse behavior. We have argued that the Rouse mode correlation
function has a stretched exponential form. The subdiffusional exponents for
this regime are calculated explicitly. The special case of linear chains, D=1,
shows good agreement with MD- and MC-simulations.Comment: 35 pages,3 figures, accepted by J.Chem.Phy
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