1,721,002 research outputs found
THE SYNERGISTIC INTERPLAY OF AMYLOID BETA AND TAU PROTEINS IN ALZHEIMER'S DISEASE: A COMPARTMENTAL MATHEMATICAL MODEL
Full text linkThe purpose of this Note is to present and discuss some mathematical results concerning a compartmental model for the synergistic interplay of Amyloid beta and tau proteins in the onset and progression of Alzheimer's disease. We model the possible mechanisms of interaction between the two proteins by a system of Smoluchowski equations for the Amyloid beta concentration, an evolution equation for the dynamics of misfolded tau and a kinetic-type transport equation for a function taking into accout the degree of malfunctioning of neurons. We provide a well-posedness results for our system of equations. This work extends results obtained in collaboration with M.Bertsch, B.Franchi and A.Tosin
MONTE-CARLO STUDY OF 3D VESICLES
No full textA model of vesicles on a cubic lattice is studied by Monte Carlo
methods. Vesicles have spherical topology and are made of lattice
plaquettes. An osmotic pressure difference acts between interior and
exterior. Results are given for critical properties in the deflated
regime
SURFACE CRITICAL EXPONENTS FOR MODELS OF POLYMER COLLAPSE AND ADSORPTION - THE UNIVERSALITY OF THE THETA AND THETA' POINTS
No full textThe surface critical exponents are estimated both in ordinary and in
special regimes from exact series expansions of up to 28 terms for a
model of the THETA point. They are found to be in agreement with those
derived for the THETA' point, confirming the conjecture that the THETA
and THETA' points lie in the same universality class. Some essential
features of the phase diagram for a self-interacting, self-avoiding
polymer in solution are also calculated to a higher degree of accuracy
than previously obtained
Entanglement complexity of semiflexible lattice polygons
No full textWe use Monte Carlo methods to study knotting in polygons on the simple
cubic lattice with a stiffness fugacity. We investigate how the knot
probability depends on stiffness and how the relative frequency of
trefoils and figure eight knots changes as the stiffness changes. In
addition, we examine the effect of stiffness on the writhe of the
polygons
A self-avoiding walk model of random copolymer adsorption
No full textWe consider a model of random copolymer adsorption in which a
self-avoiding walk interacts with a hypersurface defining a half-space
to which the walk is confined. Each vertex of the walk is randomly
labelled with areal variable which determines the strength of the
interaction of that vertex with the hypersurface. We show that the
thermodynamic limit of the quenched average free energy exists and is
equal to the thermodynamic limit of the free energy for almost all fixed
labellings, so the system is self-averaging. In addition we show that
the system exibits a phase transition and we discuss the connection
between the annealed and quenched versions of the problem
Self-averaging in models of random copolymer collapse
No full textWe give a set of conditions under which a system is thermodynamically
self-averaging and show that several lattice models of interacting
copolymers satisfy these conditions. We prove this result for a general
potential which is linear in the numbers of various types of contacts,
and show that this includes two potentials which have previously been
used in models of random interacting linear copolymers
Collapsing animals
No full textLattice animals with fugacities conjugate to the number of independent
cycles, or to the number of nearest neighbour contacts, go through a
collapse transition at a theta-point at a critical value of the
fugacity. We examine the phase diagram of a model which includes both a
cycle and a contact fugacity with Monte Carlo methods. Using an
underlying cut-and-paste Metropolis algorithm for lattice animals, we
implement in the first instance a multiple Markov chain simulation of
collapsing animals to estimate the location of the collapse transitions
and the values of the crossover exponents associated with these.
Secondly, we use umbrella sampling to sample animals over a rectangle in
the phase diagram to examine the structure of the phase diagram of these
animals
Polymer entanglement in melts
No full textWe propose a new way of characterizing the entanglement complexity of
concentrated polymer solutions and polymer melts. This involves
considering a randomly chosen cube in the system, and investigating the
entanglements between sub-chains in this cube. We present Monte Carlo
calculations and scaling arguments for the density dependence of the
entanglement complexity, and the way in which this behaviour scales with
the size of the chosen cube
MEROMORPHIC STRUCTURE OF THE MELLIN TRANSFORMS AND SHORT-DISTANCE BEHAVIOR OF CORRELATION INTEGRALS
No full textThe short-distance behavior of the measure of a sphere and of the
correlation integral is determined, in the case of disconnected
repellers, by scaling laws whose corrections are oscillating functions,
periodic or aperiodic, depending on exact or approximate self-similarity
of the measure. The Mellin transforms prove to be the correct analytic
tool in order to investigate these corrections to scaling. It has been
previously proved that they are meromorphic for linear Cantor sets and
that the leading pole gives the correlation dimension in agreement with
the results of the thermodynamic formalism. Here we show that the
residues of these poles can also be computed to any desired accuracy
with simple algorithms and that the knowledge of the singularity
spectrum of the Mellin transforms provides the Fourier spectrum of the
scaling correction for the self-similar measure and that it reproduces
the damped oscillations in the generic case. The method applies to the
nonlinear repellers such as the disconnected Julia sets by using an
approximation theorem
CORRECTIONS TO THE SCALING LAWS OF INTEGRATED WAVELETS FROM SINGULARITIES OF MELLIN TRANSFORMS
No full textBy considering the Mellin transform of the Integrated Wavelet Transform
(IWT), we show that correction to scaling laws for the IWT can be
conveniently described in terms of the meromorphic spectrum of the
Mellin transform. Relevant singularities are the same as the ones
obtained with the energy integral formalism
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