153 research outputs found
Switching to nonhyperbolic cycles from codimension two bifurcations of equilibria of delay differential equations
In this paper we perform the parameter-dependent center manifold reduction
near the generalized Hopf (Bautin), fold-Hopf, Hopf-Hopf and transcritical-Hopf
bifurcations in delay differential equations (DDEs). This allows us to
initialize the continuation of codimension one equilibria and cycle
bifurcations emanating from these codimension two bifurcation points. The
normal form coefficients are derived in the functional analytic perturbation
framework for dual semigroups (sun-star calculus) using a normalization
technique based on the Fredholm alternative. The obtained expressions give
explicit formulas which have been implemented in the freely available numerical
software package DDE-BifTool. While our theoretical results are proven to apply
more generally, the software implementation and examples focus on DDEs with
finitely many discrete delays. Together with the continuation capabilities of
DDE-BifTool, this provides a powerful tool to study the dynamics near
equilibria of such DDEs. The effectiveness is demonstrated on various models
Conformations of dendrimers in dilute solution
Conformations of isolated homo- dendrimers of G=1-7 generations with D=1-6
spacers have been studied in the good and poor solvents, as well as across the
coil-to-globule transition, by means of a version of the Gaussian
self-consistent (GSC) method and Monte Carlo (MC) simulation in continuous
space based on the same coarse-grained model. The latter includes harmonic
springs between connected monomers and the pair-wise Lennard-Jones potential
with a hard core repulsion. The scaling law for the dendrimer size, the degrees
of bond stretching and steric congestion, as well as the radial density, static
structure factor, and asphericity have been analysed. It is also confirmed that
while smaller dendrimers have a dense core, larger ones develop a hollow domain
at some separation from the centre.Comment: RevTeX, 14 pages, 19 PS figures, Accepted for publication in J. Chem.
Phy
On Local Bifurcations in Neural Field Models with Transmission Delays
Neural field models with transmission delay may be cast as abstract delay
differential equations (DDE). The theory of dual semigroups (also called
sun-star calculus) provides a natural framework for the analysis of a broad
class of delay equations, among which DDE. In particular, it may be used
advantageously for the investigation of stability and bifurcation of steady
states. After introducing the neural field model in its basic functional
analytic setting and discussing its spectral properties, we elaborate
extensively an example and derive a characteristic equation. Under certain
conditions the associated equilibrium may destabilise in a Hopf bifurcation.
Furthermore, two Hopf curves may intersect in a double Hopf point in a
two-dimensional parameter space. We provide general formulas for the
corresponding critical normal form coefficients, evaluate these numerically and
interpret the results
Intra-chain correlation functions and shapes of homopolymers with different architectures in dilute solution
We present results of Monte Carlo study of the monomer-monomer correlation
functions, static structure factor and asphericity characteristics of a single
homopolymer in the coil and globular states for three distinct architectures of
the chain: ring, open and star. To rationalise the results we introduce the
dimensionless correlation functions rescaled via the corresponding mean-squared
distances between monomers. For flexible chains with some architectures these
functions exhibit a large degree of universality by falling onto a single or
several distinct master curves. In the repulsive regime, where a stretched
exponential times a power law form (de Cloizeaux scaling) can be applied, the
corresponding exponents and have been obtained. The exponent
is found to be universal for flexible strongly repulsive coils
and in agreement with the theoretical prediction from improved higher-order
Borel-resummed renormalisation group calculations. The short-distance exponents
of an open flexible chain are in a good agreement with the
theoretical predictions in the strongly repulsive regime also. However,
increasing the Kuhn length in relation to the monomer size leads to their fast
cross-over towards the Gaussian behaviour. Likewise, a strong sensitivity of
various exponents on the stiffness of the chain, or on the number
of arms in star polymers, is observed. The correlation functions in the
globular state are found to have a more complicated oscillating behaviour and
their degree of universality has been reviewed. Average shapes of the polymers
in terms of the asphericity characteristics, as well as the universal behaviour
in the static structure factors, have been also investigated.Comment: RevTeX 12 pages, 10 PS figures. Accepted by J. Chem. Phy
Monte Carlo simulations of infinitely dilute solutions of amphiphilic diblock star copolymers
Single-chain Monte Carlo simulations of amphiphilic diblock star copolymers
were carried out in continuous space using implicit solvents. Two distinct
architectures were studied: stars with the hydrophobic blocks attached to the
core, and stars with the polar blocks attached to the core, with all arms being
of equal length. The ratio of the lengths of the hydrophobic block to the
length of the polar block was varied from 0 to 1. Stars with 3, 6, 9 or 12
arms, each of length 10, 15, 25, 50, 75 and 100 Kuhn segments were analysed.
Four distinct types of conformations were observed for these systems. These,
apart from studying the snapshots from the simulations, have been
quantitatively characterised in terms of the mean-squared radii of gyration,
mean-squared distances of monomers from the centre-of-mass, asphericity
indices, static scattering form factors in the Kratky representation as well as
the intra-chain monomer-monomer radial distribution functions.Comment: 12 pages, 11 ps figures. Accepted for publication in J. Chem. Phy
Prion proteins: evolution and preservation of secondary structure
AbstractPrions cause a variety of neurodegenerative disorders that seem to result from a conformational change in the prion protein (PrP). Thirty-two PrP sequences have been subjected to phylogenetic analysis followed by reconstruction of the most probable evolutionary spectrum of amino acid replacements. The replacement rates suggest that the protein does not seem to be very conservative, but in the course of evolution amino acids have only been substituted within the elements of the secondary structure by those with very similar physico-chemical properties. Analysis of the full spectrum of single-step amino acid substitutions in human PrP using secondary structure prediction algorithms shows an over-representation of substitutions that tend to destabilize Ī±-helices
On the non-equivalence of Lorenz System and Chen System
In this paper, we prove that the Chen system with a set of chaotic parameters
is not smoothly equivalent to the Lorenz system with any parameters
Biophysical and atomic force microscopy characterization of the RNA from satellite tobacco mosaic virus
Agarose gel electrophoresis, circular dichroism and differential scanning calorimetry showed that single-stranded RNA from satellite tobacco mosaic virus transforms from a conformationally āclosed stateā at 4Ā°C to a more conformationally āopen stateā at 65Ā°C. The transition is reversible and shows no hysteresis. Atomic force microscopy (AFM) allowed visualization of the two states and indicated that the conformationally āclosed stateā probably corresponds to the native encapsidated conformation, and that the āopen stateā represents a conformation, characterized as short, thick chains of domains, as a consequence of the loss of tertiary interactions. Heating from 75Ā°C to 85Ā°C in the presence of EDTA was necessary to further unravel the āopenā conformation RNA into extended chains of lengths >280ānm. Virus exposed to low concentrations of phenol at 65Ā°C, extruded RNA as distinctive āpigtailsā in a synchronous fashion, and these āpigtailsā then elongated, as the RNA was further discharged by the particles. Moderate concentrations of phenol at 65Ā°C produced complete disruption of virions and only remains of decomposed particles and disordered RNA were evident. AFM images of RNA emerging from disrupted virions appear most consistent with linear arrangements of structural domains
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