894 research outputs found
Comment on " A simple model for DNA denaturation"
The replacment of mutual avoidance of polymers by a long-range interaction of
the type proposed by Garel etal (Europhys. Lett. 55, 132 (2001),
cond-mat/0101058) is inconsistent with the prevalent renormalization group
arguments.Comment: 2 pages, Comment on Garel etal. Europhys. Lett 55, 132(2001)
cond-mat/0101058. Appeared in Europhys Let
Phase diagram of a semiflexible polymer chain in a solvent: application to protein folding
We consider a lattice model of a semiflexible homopolymer chain in a bad
solvent. Beside the temperature , this model is described by (i) a curvature
energy , representing the stiffness of the chain (ii) a
nearest-neighbour attractive energy , representing the solvent
(iii) the monomer density , where and
denote respectively the number of monomers and the number of lattice sites.
This model is a simplified view of the protein folding problem, which
encompasses the geometrical competition between secondary structures (the
curvature term modelling helix formation) and the global compactness (modeled
here by the attractive energy), but contains no side chain information...Comment: 17 pages, plain tex, 2 figures available upon reques
Overlap properties and adsorption transition of two Hamiltonian paths
We consider a model of two (fully) compact polymer chains, coupled through an
attractive interaction. These compact chains are represented by Hamiltonian
paths (HP), and the coupling favors the existence of common bonds between the
chains. Using a ( component) spin representation for these paths, we show
the existence of a phase transition for strong coupling (i.e. at low
temperature) towards a ``frozen'' phase where one chain is completely adsorbed
onto the other. By performing a Legendre transform, we obtain the probability
distribution of overlaps. The fraction of common bonds between two HP, i.e.
their overlap , has both lower () and upper () bounds. This means
in particuliar that two HP with overlap greater than coincide. These
results may be of interest in (bio)polymers and in optimization problems.Comment: 13 pages, 2 figure
Directed polymer in a random medium of dimension 1+1 and 1+3: weights statistics in the low-temperature phase
We consider the low-temperature disorder-dominated phase of the
directed polymer in a random potentiel in dimension 1+1 (where )
and 1+3 (where ). To characterize the localization properties of
the polymer of length , we analyse the statistics of the weights of the last monomer as follows. We numerically compute the probability
distributions of the maximal weight , the probability distribution of the parameter as well as the average values of the higher order
moments . We find that there exists a
temperature such that (i) for , the distributions
and present the characteristic Derrida-Flyvbjerg
singularities at and for . In particular, there
exists a temperature-dependent exponent that governs the main
singularities and as well as the power-law decay of the moments . The exponent grows from the value
up to . (ii) for , the
distribution vanishes at some value , and accordingly the
moments decay exponentially as in . The
histograms of spatial correlations also display Derrida-Flyvbjerg singularities
for . Both below and above , the study of typical and
averaged correlations is in full agreement with the droplet scaling theory.Comment: 13 pages, 29 figure
A novel approach for the assessment of morphological evolution based on observed water levels in tide-dominated estuaries
Assessing the impacts of both natural (e.g., tidal forcing from the ocean) and human-induced changes (e.g., dredging for navigation, land reclamation) on estuarine morphology is particularly important for the protection and management of the estuarine environment. In this study, a novel analytical approach is proposed for the assessment of estuarine morphological evolution in terms of tidally averaged depth on the basis of the observed water levels along the estuary. The key lies in deriving a relationship between wave celerity and tidal damping or amplification. For given observed water levels at two gauging stations, it is possible to have a first estimation of both wave celerity (distance divided by tidal travelling time) and tidal damping or amplification rate (tidal range difference divided by distance), which can then be used to predict the morphological changes via an inverse analytical model for tidal hydrodynamics. The proposed method is applied to the Lingdingyang Bay of the Pearl River Estuary, located on the southern coast of China, to analyse the historical development of the tidal hydrodynamics and morphological evolution. The analytical results show surprisingly good correspondence with observed water depth and volume in this system. The merit of the proposed method is that it provides a simple approach for understanding the decadal evolution of the estuarine morphology through the use of observed water levels, which are usually available and can be easily measured.National Key R&D of China (Grant No.
2016YFC0402601), National Natural Science Foundation of China (Grant No. 51979296, 51709287,
41706088, 41476073), Fundamental Research Funds for the Central Universities (No.18lgpy29)
and from the Water Resource Science and Technology Innovation Program of Guangdong Province (Grant
No. 2016-20, 2016-21). The work of the second author was supported by FCT research contracts
IF/00661/2014/CP1234.info:eu-repo/semantics/submittedVersio
Adsorption of polymers on a fluctuating surface
We study the adsorption of polymer chains on a fluctuating surface. Physical
examples are provided by polymer adsorption at the rough interface between two
non-miscible liquids, or on a membrane. In a mean-field approach, we find that
the self--avoiding chains undergo an adsorption transition, accompanied by a
stiffening of the fluctuating surface. In particular, adsorption of polymers on
a membrane induces a surface tension and leads to a strong suppression of
roughness.Comment: REVTEX, 9 pages, no figure
Statistics of first-passage times in disordered systems using backward master equations and their exact renormalization rules
We consider the non-equilibrium dynamics of disordered systems as defined by
a master equation involving transition rates between configurations (detailed
balance is not assumed). To compute the important dynamical time scales in
finite-size systems without simulating the actual time evolution which can be
extremely slow, we propose to focus on first-passage times that satisfy
'backward master equations'. Upon the iterative elimination of configurations,
we obtain the exact renormalization rules that can be followed numerically. To
test this approach, we study the statistics of some first-passage times for two
disordered models : (i) for the random walk in a two-dimensional self-affine
random potential of Hurst exponent , we focus on the first exit time from a
square of size if one starts at the square center. (ii) for the
dynamics of the ferromagnetic Sherrington-Kirkpatrick model of spins, we
consider the first passage time to zero-magnetization when starting from
a fully magnetized configuration. Besides the expected linear growth of the
averaged barrier , we find that the rescaled
distribution of the barrier decays as for large
with a tail exponent of order . This value can be simply
interpreted in terms of rare events if the sample-to-sample fluctuation
exponent for the barrier is .Comment: 8 pages, 4 figure
THERMODYNAMICS OF A BROWNIAN BRIDGE POLYMER MODEL IN A RANDOM ENVIRONMENT
We consider a directed random walk making either 0 or moves and a
Brownian bridge, independent of the walk, conditioned to arrive at point on
time . The Hamiltonian is defined as the sum of the square of increments of
the bridge between the moments of jump of the random walk and interpreted as an
energy function over the bridge connfiguration; the random walk acts as the
random environment. This model provides a continuum version of a model with
some relevance to protein conformation. The thermodynamic limit of the specific
free energy is shown to exist and to be self-averaging, i.e. it is equal to a
trivial --- explicitly computed --- random variable. An estimate of the
asymptotic behaviour of the ground state energy is also obtained.Comment: 20 pages, uuencoded postscrip
A Solvable Model of Secondary Structure Formation in Random Hetero-Polymers
We propose and solve a simple model describing secondary structure formation
in random hetero-polymers. It describes monomers with a combination of
one-dimensional short-range interactions (representing steric forces and
hydrogen bonds) and infinite range interactions (representing polarity forces).
We solve our model using a combination of mean field and random field
techniques, leading to phase diagrams exhibiting second-order transitions
between folded, partially folded and unfolded states, including regions where
folding depends on initial conditions. Our theoretical results, which are in
excellent agreement with numerical simulations, lead to an appealing physical
picture of the folding process: the polarity forces drive the transition to a
collapsed state, the steric forces introduce monomer specificity, and the
hydrogen bonds stabilise the conformation by damping the frustration-induced
multiplicity of states.Comment: 24 pages, 14 figure
Freezing Transition of Random Heteropolymers Consisting of an Arbitrary Set of Monomers
Mean field replica theory is employed to analyze the freezing transition of
random heteropolymers comprised of an arbitrary number () of types of
monomers. Our formalism assumes that interactions are short range and
heterogeneity comes only from pairwise interactions, which are defined by an
arbitrary matrix. We show that, in general, there exists a
freezing transition from a random globule, in which the thermodynamic
equilibrium is comprised of an essentially infinite number polymer
conformations, to a frozen globule, in which equilibrium ensemble is dominated
by one or very few conformations. We also examine some special cases of
interaction matrices to analyze the relationship between the freezing
transition and the nature of interactions involved.Comment: 30 pages, 1 postscript figur
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